Copyright 2017 - 2018 Maria Miller.
EDITION 9/2018
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If you have other needs, such as licensing for a school or tutoring centre, please contact the author at
https://www.MathMammoth.com/contact.php
2
Contents
Foreword .......................................................................................
7
Chapter 1: Some Old, Some New
Introduction ...................................................................................
9
Some Revision ................................................................................
11
The 100-Chart and More Revision ...............................................
13
Fact Families ...................................................................................
16
Ordinal Numbers ...........................................................................
18
Even and Odd Numbers ................................................................
20
Doubling .........................................................................................
22
One-Half .........................................................................................
25
Adding With Whole Tens ..............................................................
27
Subtracting Whole Tens ................................................................
30
Revision, Chapter 1 ........................................................................
32
Chapter 2: Clock
Introduction ....................................................................................
34
Revision—Whole and Half Hours .................................................
37
The Minutes .....................................................................................
38
The Minutes, Part 2 .........................................................................
41
Past and To in Five-Minute Intervals ............................................
43
How Many Hours Pass? ..................................................................
46
The Calendar: Weekdays and Months ........................................... 48
The Calendar: Dates ........................................................................
51
Revision, Chapter 2 ..........................................................................
54
Chapter 3:
Addition and Subtraction Facts Within 0-18
Introduction .................................................................................
55
Revision: Completing the Next Whole Ten ................................
59
Revision: Going Over Ten ...........................................................
61
Adding with 9 ..............................................................................
63
Adding with 8 ...............................................................................
65
Adding with 7 ...............................................................................
67
3
Adding with 6 ...............................................................................
69
Revision—Facts with 6, 7, and 8 .................................................
71
Subtract to Ten ............................................................................
73
Difference and How Many More ................................................
75
Number Rainbows—11 and 12 ...................................................
78
Fact Families with 11 ..................................................................
80
Fact Families with 12 ...................................................................
81
Number Rainbows—13 and 14 ...................................................
83
Fact Families with 13 and 14 ......................................................
84
Fact Families with 15 ..................................................................
87
Fact Families with 16 ..................................................................
89
Fact Families with 17 and 18 ......................................................
91
Mixed Revision, Chapters 1 - 3...................................................
93
Revision, Chapter 3 ....................................................................
95
Chapter 4: Regrouping in Addition
Introduction ...................................................................................
98
Going Over to the Next Ten ..........................................................
101
Add with Two-Digit Numbers Ending in 9 .................................
104
Add a Two-Digit Number and
a Single-Digit Number Mentally .................................................
106
Regrouping with Tens ..................................................................
108
Add in Columns Practice .............................................................
111
Mental Addition of Two-Digit Numbers .....................................
114
Adding Three or Four Numbers Mentally ..................................
117
Adding Three or Four Numbers in Columns ..............................
119
Mixed Revision, Chapters 1 - 4 ....................................................
123
Revision, Chapter 4 .......................................................................
125
4
Chapter 5: Geometry and Fractions
Introduction .................................................................................
127
Shapes Revision ...........................................................................
130
Surprises with Shapes ..................................................................
133
Rectangles and Squares ...............................................................
135
Making Shapes ............................................................................
138
Geometric Patterns .....................................................................
141
Solids ...........................................................................................
143
Printable Shapes ..........................................................................
145
Some Fractions ............................................................................
153
Comparing Fractions ...................................................................
156
Mixed Revision, Chapters 1 - 5 ...................................................
158
Revision, Chapter 5 .....................................................................
160
5
6
Foreword
Math Mammoth International Version Grade 2-A and Grade 2-B worktexts comprise a complete maths
curriculum for the second grade mathematics studies.
This curriculum is essentially the same as the version of Math Mammoth Grade 2 sold in the United
States (US version), only customised for international use. The US version is aligned to the “Common
Core” Standards, so it may not be properly aligned to the second grade standards in your country.
However, you can probably find material for any missing topics in neighbouring grades. For example,
let’s say multiplication tables are studied in grade or year 4 in your country. They are not found in Math
Mammoth Grade 4. Instead, you will need to use Math Mammoth Grade 3-A to study them.
The International version of Math Mammoth differs from the US version in these aspects:
z
z
z
z
The currency used in the money chapters in grades 1-3 is the Australian dollar. (The download
version of this curriculum for grades 1-3 include the chapter on money for European, South
African, Canadian, US, and British currencies.)
The curriculum teaches the metric measurement units. Imperial units, such as inches and pounds,
are not used.
The spelling conforms to British international standards.
Paper size is A4.
The four main areas of study for second grade are:
1. Understanding of the base-ten system within 1 000. This includes place value with three-digit
numbers, skip-counting in fives, tens, and multiples of hundreds, tens, and ones (within 1 000).
(chapters 6 and 8);
2. Develop fluency with addition and subtraction within 100, including solving word problems,
regrouping in addition, and regrouping in subtraction (chapters 1, 3, 4, and 8);
3. Using metric units of measure (chapter 7);
4. Describing and analyzing shapes (chapter 5).
Additional topics we study are time (chapter 2), money (chapter 9), introduction to multiplication
(chapter 10), and bar graphs and picture graphs (in various chapters).
This book, 2-A, covers reading the clock (chapter 2), the basic addition and subtraction facts within 18
(chapter 3), regrouping in addition (chapter 4), and geometry (chapter 5). The rest of the topics are
covered in the 2-B student worktext.
When you use these two books as your only or main mathematics curriculum, they are like a
“framework,” but you still have a lot of liberty in planning your child's studies. While addition and
subtraction topics are best studied in the order they are presented, feel free to go through the geometry,
clock, and money sections in a different order. This might even be advisable if your child is “stuck” on
some concept, or is getting bored. Sometimes the brain “mulls it over” in the background, and the
concept he/she was stuck on can become clear after a break. For the chapter on measuring, the child
should be familiar with three-digit numbers.
7
Math Mammoth aims to concentrate on a few major topics at a time, and study them in depth. This is
totally opposite to the continually spiralling step-by-step curricula, in which each lesson typically is about
a different topic from the previous or next lesson, and includes a lot of revision problems from past
topics.
This does not mean that your child would not need occasional revision. However, when each major topic
is presented in its own chapter, this gives you more freedom to plan the course of study and choose the
revision times yourself. In fact, I totally encourage you to plan your mathematics school year as a set of
certain topics, instead of a certain book or certain pages from a book.
For revision, the download version includes an html page called Make_extra_worksheets_grade2.htm
that you can use to make additional worksheets for computation or for number charts. You can also
simply reprint some already studied pages. Also, chapter 3, which practises addition and subtraction facts
within 18, contains a lot of pages with problems, so you can choose to “save” some of them for later
revision.
I wish you success in teaching maths!
Maria Miller, the author
8
Chapter 1: Some Old, Some New
Introduction
The first chapter of the Math Mammoth Grade 2-A contains some revision and some new topics.
In the first two lessons, we revise adding and subtracting two-digit numbers from first grade. Then
students get to revise skip-counting using the 100-chart.
Next, the lesson Fact Families revises the connection between addition and subtraction, and introduces a
new strategy for missing subtrahend problems (of the type __ − 5 = 4). In these problems, the student
can add to find the missing total. This is an early prelude to algebraic thinking.
Then we go on to the “new”, starting with ordinal numbers, which are probably familiar from everyday
language. Then, in the lesson Subtracting Whole Tens, students subtract mentally any number of whole
tens from a two-digit number, such as 72 − 40.
Even and odd numbers are presented in the context of equal sharing: if you can share that many objects
evenly (equally), then the number is even. Students may need to use manipulatives (objects you can
handle) to grasp this idea.
Then we study doubling and halving. Please do not skip the simple word problems included in these
lessons — they are very important. Children need to learn to apply the concepts they have just learned.
Also, if the student cannot solve simple word problems that involve doubling or halving, there is a good
chance the student did not actually learn those concepts.
The Lessons in Chapter 1
page
span
Some Revision ..............................................................
11
2 pages
The 100-Chart and More Revision ................................
13
3 pages
Fact Families..................................................................
16
2 pages
Ordinal Numbers ...........................................................
18
2 pages
Even and Odd Numbers .................................................
20
2 pages
Doubling ........................................................................
22
3 pages
One-Half ........................................................................
25
2 pages
Adding With Whole Tens ..............................................
27
3 pages
Subtracting Whole Tens ................................................
30
2 pages
Revision, Chapter 1 .......................................................
32
2 pages
9
Helpful Resources on the Internet
Use these free online resources to supplement the “bookwork” as you see fit.
Disclaimer: These links were valid as of the writing of this book, and to the best of our knowledge we
believe these websites to have what is described. However, we cannot guarantee that the links have not
changed. Parental supervision is recommended.
Balloon Rise - Empire State Building
Help the hot-air balloons rise to the top of the Empire State Building while counting by 5s.
http://www.free-training-tutorial.com/skip-counting/skip-counting-by-fives-empire-state.html
Number Fact Families
Practise forming fact families when given three random numbers.
https://www.topmarks.co.uk/number-facts/number-fact-families
More Fact Families
Enter the fact family for the numbers shown.
http://www.gameclassroom.com/game/43857-3175/addition-facts-20/more-fact-families
Number Cracker
Help Mr. Cracker obtain the secret code before the insidious Prof. Soup catches him by guessing what
number comes next in a series of numbers.
http://www.funbrain.com/cracker/index.html
Squigly
Squigly is hiding in one of the apples. Click on the ordinal number that tells the order of Squigly's apple.
http://www.primarygames.com/squigly/start.htm
Fruit Shoot
Shoot a fruit with an even or odd number, whichever one your aim tells you.
http://www.sheppardsoftware.com/mathgames/earlymath/Fruit_shoot_odd_even.htm
Doorway Odd and Even - Five Activities
Choose from five different activities to practise the concept of odd and even.
http://www.doorwayonline.org.uk/number/oddandeven/
Doubles Cards 1
Choose the double for each number.
http://www.ictgames.com/woodseasy.html
Fruit Splat Addition - Skill Builders
Practise adding doubles and near doubles.
http://www.sheppardsoftware.com/mathgames/fruitshoot/FS_addition.htm
Doubling and Halving Practice Zone
Practise doubling and halving with a timed quiz.
http://www.math-salamanders.com/doubling-and-halving.html
Best Maths Friends Word Problem Game
“Friend” different animals by validating or invalidating the answers to basic word problems.
http://mrnussbaum.com/bmf-word-problem-game/
Add Like Mad
Click on the squares to add the numbers so that they add up to the target number.
http://www.sheppardsoftware.com/mathgames/Add%20Like%20Mad%20Math/AddLikeMad_easy.htm
10
Some Revision
1. The box with a “T” means a TEN. The dots are ONES. Write the additions.
+
b.
+
a.
32 + 7 = 39
+
c.
_____ + ____ = _____
_____ + ____ = _____
2. Add whole tens. To help, you can draw a ten-box or ten-boxes in the picture.
+
a.
+
+
25 + 10 = _______
b.
14 + 10 = _______
c.
32 + 10 = _______
25 + 20 = _______
14 + 20 = _______
32 + 20 = _______
25 + 30 = _______
14 + 30 = _______
32 + 30 = _______
3. Subtract from 60 or from 30. One of the tens is shown with ten dots instead of a
ten-box. Cover some of the dots to subtract.
a.
b.
60 – 3 = _______
30 – 4 = _______
60 – 8 = _______
30 – 6 = _______
60 – 7 = _______
30 – 5 = _______
4. Add in columns. The two numbers to be added are shown with dots and ten-boxes.
a.
b.
+
+
11
5. Subtract. In (a) and (b) you can cross out things in the picture to help you.
c.
b.
a.
49 – 6 = ______
−
4
5
2
3
d.
−
9
8
6
5
47 – 16 = ______
6. Add and subtract.
a.
c.
b.
d.
70 + 6 = ______ 30 + 4 + 4 = ______ 90 + _____ = 94 60 + _____ = 90
50 + 9 = ______ 50 + 7 + 2 = ______ 40 + _____ = 47 40 + _____ = 80
e.
70 − 1 = ______
f.
g.
h.
5 − 5 = _____
88 − 8 = ______ 50 + _____ = 56
100 − 5 = _____ 24 − 4 = _____
57 − 7 = ______ 30 + _____ = 39
7. Solve the word problems.
a. Luke bought two colouring books for $6 each,
and a notebook for $3. What was the total cost?
b. Todd has seven marbles, and Lucy has five. Lucy gave Todd two of hers.
How many more marbles does Todd have now than Lucy?
c. Paul has twenty shirts, and ten of them are white.
How many are not white?
d. A watch costs $45. Can you buy it if you already
have $22 and your grandmother gives you another $20?
12
The 100-Chart and More Revision
1. Skip-count by fives, starting at 5.
Colour these numbers light blue.
1
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
2. Skip-count by fives, starting at 6.
Colour these numbers yellow.
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
1
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20
3. Skip-count by twos starting at 2, up to 30.
Colour these numbers pink.
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
4. Skip-count by twos backwards from 99
to 71. Colour these numbers green.
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
1
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
5. Skip-count by fours starting at 4.
Colour these numbers yellow.
It makes an interesting pattern!
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
13
6. Skip-count. First find by which number to skip-count, either by 2s, by 5s, or by 10s.
a. 40,
42, 44, _____, _____, 50, _____, _____, _____, _____, _____
b. _____,
_____, _____, _____, 48, 58, 68, _____, 88, _____
c. _____,
_____, _____, _____, 65, 63, 61, _____, _____, _____
d. _____,
_____, _____, 70, 65, 60, _____, _____, _____, _____
7. Write the addition sentences. The box with a “T” is a ten. Under each problem, there is
another, similar, addition problem for you to solve.
+
a. ____
b. 34
+
+ ____ = ____
+ 3 = ______
c. ____
d. 53
+
+ ____ = ____
+ 6 = ______
e. ____
f. 32
+ ____ = ____
+ 5 = ______
8. Subtract by crossing some out. Under each problem, there is another problem that is
similar.
a. 59
– 6 = ______
c. 47
– 5 = ______
e. 60
– 3 = ______
b. 39
– 6 = ______
d. 67
– 5 = ______
f. 50
– 3 = ______
9. Add. The problems in each box are similar.
a.
b.
c.
d.
2 + 6 = _____
4 + 4 = _____
3 + 6 = _____
8 + 2 = _____
42 + 6 = _____
74 + 4 = _____
53 + 6 = _____
48 + 2 = _____
72 + 6 = _____
94 + 4 = _____
23 + 6 = _____
98 + 2 = _____
14
10. Subtract. The problems in each box are similar.
a.
b.
c.
d.
7 – 5 = _____
9 – 4 = _____
10 – 4 = _____
8 – 5 = _____
37 – 5 = _____
29 – 4 = _____
50 – 4 = _____
38 – 5 = _____
67 – 5 = _____
99 – 4 = _____
80 – 4 = _____
88 – 5 = _____
11. Add. In some of these problems you need to make a new ten with some of the little
dots. You can also use a 100-bead abacus.
+
a.
+
17 + 8 = _____
b.
35 + 6 = _____
+
d.
+
24 + 16 = _____
c.
+
27 + 12 = _____
e.
+
19 + 24 = _____
f.
28 + 28 = _____
12. Find the number that goes into the shape.
a. 42
+3+
13. Subtract the
same number
each time.
= 50
a. –
b. 37
+
+ 1 = 40
10
b. –
c. 84
20
+
+ 4 = 90
c. –
5
50 ____
100 ____
45 ____
52 ____
20
____
95 ____
64 ____
40
____
96 ____
23 ____
21
____
11 ____
15
Fact Families
When two addition and two
subtraction facts use the same
numbers, it is called a “fact family.”
Remember that a subtraction starts
with the total. This is how it looks if
the total is missing in a subtraction:
− 8 = 20
To find the total, just add the “parts”
20 and 8. We get 20 + 8 = 28. So the
subtraction was 28 − 8 = 20.
4+5= 9
4 + 5 =9
5+4= 9
5 + 4 =9
9 −5=4
9− 5 = 4
9 −4=5
9− 4 = 5
Notice the TOTAL.
The subtraction sentences
start with the total.
Notice the PARTS.
The two parts make
up the total.
1. Write two addition and two subtraction sentences—a fact family!
a.
b.
c.
____ + ____ = _____
____ + ____ = _____
_____ + _____ = _____
____ + ____ = _____
____ + ____ = _____
_____ + _____ = _____
_____ − ____ = ____
_____ − ____ = ____
_____ − _____ = _____
_____ − ____ = ____
_____ − ____ = ____
_____ − _____ = _____
2. Fill in the missing numbers. The four problems form a fact family.
a.
2
+
=
8
8
+
2
=
8
−
2
=
8
−
=
2
b. ____ +
____ = 10
____ + ____ =
10
−
10
−
7
=
=
16
10
c. ____ +
____ + ____ = ____
9
7
____ = ____
−
=
6
____ − ____ = ____
3. Write a matching addition for the subtraction. There are two possibilities.
a. ____ + ____ = ____
8
b. ____ + ____ = ____
− 2 = 6
c. ____ + ____ = ____
20 − 7 = 13
When the first number is missing in a
subtraction, it is the TOTAL that is missing.
You can find the TOTAL by adding
the two numbers (those are the “parts”).
60 −
20 = 40
– 6 =2
The total is missing. 6 and 2 are
the “parts”. So we add them.
2 + 6 = 8. The missing number is 8!
It is like “adding backwards”:
4. The total is missing from the subtraction sentence. Solve.
– 5 = 4
a.
b.
– 7 = 2
c.
b.
– 7 = 80
c.
– 7 = 10
5. Find the missing numbers.
–2=4
a.
– 50 = 50
60 + 4 =
– 8 = 20
16 +
9–
=5
77 +
= 20
= 78
– 9 = 60
Find the missing numbers. This time
adding backwards will NOT work!
a.
50 −
= 10
33 −
= 31
b.
100 −
= 91
76 −
= 72
17
c.
10 −
−2=1
9−
−5=2
Ordinal Numbers
The numbers 1, 2, 3, 4, and so on are
called cardinal numbers.
We also often use ordinal numbers.
Ordinal numbers are used when talking
about the order of things.
List of some ordinal numbers:
Ordinal Number
1st
2nd
3rd
4th
5th
6th
7th
8th
Name
first
second
third
fourth
fifth
sixth
seventh
eighth
The fourth tree from the left is circled.
It is also the second tree from the right.
The sixth letter of the word is A.
Ordinal Number
9th
10th
11th
12th
13th
14th
15th
16th
Name
ninth
tenth
eleventh
twelfth
thirteenth
fourteenth
fifteenth
sixteenth
1. Circle.
a. The second car from the left.
b. The fifth car from the right.
c. The seventh snowflake
from the left.
d. The third snowflake
from the right.
e. The ninth letter from the left.
f. The twelfth letter from
EXTRAORDINARY
the right.
18
2. Colour.
a. The third flower from the left.
b. The first three flowers on the left.
c. The fifth flower from the right.
d. The first five flowers on the right.
3. Find the letters, and find out what Lyle's surprise gift was.
The second row from the top,
the first letter from the left.
_____
The fourth row from the top,
the third letter from the left.
_____
The first row from the top,
the fifth letter from the right.
_____
The fifth row from the bottom,
the second letter from the right.
_____
The 1st row from the bottom,
the 1st letter from the left.
_____
The sixth row from the top,
the third letter from the right.
_____
The 3rd row from the top,
the 2nd letter from the left.
_____
The 1st row from the top,
the 2nd letter from the left.
_____
4. a. Use letters from the given
word to make a new word.
S U R P R I S I N G
E
B
W
J
Y
U
O
S
H
N
D
K
D
T
L
E
K
A
Z
T
H
A
N
P
U
N
S
A
B
I
T
D
Y
O
V
G
V
L
W
I
Q
E
P
S
F
M
C
R
L
b. Put the letters in order to make a word.
The first letter of your new word is “D.”
N D
Y
R T C
I
A
I O
7th 1st 10th 9th 4th 3rd 2nd 8th 5th 6th
____
____
____
____
____
10th
5th
6th
9th
1st
D ___ ___ ___ ___ ___ ___ ___ ___ ___
19
Even and Odd Numbers
Can John and Jane share 4 marbles
evenly (so that both get as many marbles)?
John
Jane
John
Jane
Yes! Draw the marbles for John and Jane.
Can John and Jane share 6 cars evenly? Try!
Can they share 5 carrots evenly? Try it!
Can they share 9 safety-pins evenly?
Four is an EVEN number because two people can share four things evenly.
Five is an ODD number because two people cannot share five things evenly.
1. Can two people share these things evenly? If yes, circle EVEN. If not, circle ODD.
10 marbles
a. EVEN
ODD
7 marbles
b. EVEN
11 marbles
d. EVEN
ODD
6 stars
e. EVEN
9 stars
g. EVEN
ODD
h. EVEN
20
c. EVEN
ODD
4 marbles
ODD
8 marbles
ODD
3 stars
ODD
f. EVEN
ODD
5 marbles
i. EVEN
ODD
2. The chart shows how many cookies there are. Use rocks, beans, or other small items to
make these amounts. Try to share them evenly with a friend. If you can share evenly,
write “E” or “even” in the last column. If not, write “O” or “odd”.
Cookies
Share
evenly?
Even
or odd?
Cookies
11
NO
O
12
14
17
15
16
Share
evenly?
Even
or odd?
3. Colour yellow all the EVEN numbers in the chart. Notice what pattern it makes!
You can get help from your work in #1 and #2.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Now, colour all the EVEN numbers in the rest of the 100-chart in the SAME pattern.
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
The numbers you did not colour are ODD numbers.
4. Look at the chart. Fill in.
Even numbers always end in (their last digit is)
2
, ______, ______, ______, or ______.
Odd numbers always end in (their last digit is)
1
, ______, ______, ______, or ______.
21
Doubling
Doubling a number means adding it to itself. It is finding two times the number.
Examples:
Double 7 is 7 + 7 = 14.
Double 20 is 20 + 20 = 40.
1. Find the double of these numbers.
a. Double 4
b. Double 6
c. Double 8
_____ + _____ = _____
_____ + _____ = _____
_____ + _____ = _____
d. Double 10
e. Double 30
f. Double 50
_____ + _____ = _____
_____ + _____ = _____
_____ + _____ = _____
2. Find the double of these numbers by adding in the grids.
a. 22 + 22
+
b. Double 34
c. 13 + 13
+
+
d. Double 41
+
3. Make a doubles chart. Notice it has a pattern!
Double 1 = _______
6 + 6 = _______
11 + 11 = _______
Double 2 = _______
7 + 7 = _______
12 + 12 = _______
Double 3 = _______
8 + 8 = _______
13 + 13 = _______
Double 4 = _______
9 + 9 = _______
14 + 14 = _______
Double 5 = _______ 10 + 10 = _______ 15 + 15 = _______
22
When you double a number, you always get an EVEN number as a result.
Look at the answers in the doubles chart you just made. (You can colour them
yellow if you would like.) All of those numbers are EVEN numbers.
If a number is even, you can share that many things evenly.
Example. Double 13 is 13 + 13 = 26. This means that two children can share
26 toy cars evenly, and that each child gets 13 cars.
Example. Two children need to clean 18 chairs. They divide the job equally
(evenly). How many chairs does each child clean?
Use the doubles chart. Since 9 + 9 = 18, each child will clean 9 chairs.
4. Mum told two children to make 16 sandwiches.
The children shared the job equally.
How many sandwiches did each child make?
5. If you have 12 grapes and you share them evenly
with your sister, how many do you get?
6. In a board game, you throw two dice and you can move that
many spaces. Mary got double four. Amy got double six.
How many spaces did Mary move?
How many spaces did Amy move?
7. Sandra had 5 apples and Susan had 3. They put them together
and shared them evenly. How many did each girl get?
8. Circle the even numbers:
13 20 19 8 15 16
23
Each number here is an even number, so it is a DOUBLE of some number.
What number is it a double of?
6
8
10
12
14
16
18
20
22
24
The first number on the list is 6. Six is double 3. We can write 6 = 3 + 3.
The last number on the list is 24. It is double 12. We can write 24 = 12 + 12.
9. Write each number as a double of some other number.
a.
8 = ____ + ____
b.
10 = ____ + ____
c.
4 = ____ + ____
d.
12 = ____ + ____
e.
14 = ____ + ____
f.
16 = ____ + ____
10. Write above each shaded number what number it is double of. Notice the pattern!
5
6
8
10
12
14
16
18
20
22
24
11. Mum and her friend need to make 20 dolls to sell.
They share the job evenly.
How many dolls will each woman make?
12. Two teachers divide 28 worksheets evenly.
How many worksheets will each one get?
13. Mum had 7 cucumber slices in one container and 3 in another.
You and your brother shared them equally.
How many slices did you get?
14. (Challenge) A batch of brownies makes 16 brownies.
Mum makes a double batch.
How many brownies will she make?
24
26
28
30
One-Half
If you divide something into
two equal parts, you have
divided it into two halves.
Each part is half of the whole.
Write one-half this way:
or this way: 1/2.
You can also find half
of some items, if you
have an even number
of things.
1
,
2
5 + 5 = 10. So, half of
ten apples is five apples.
1. a. Colour one half of each shape.
Twelve balls are divided
into two equal parts.
That can be done
because 12 is an even
number.
6 + 6 = 12
1
of 12 is 6.
2
b. Colour two halves of each shape.
2. Draw a line through these shapes and divide them into two halves. Colour one half.
b.
a.
e.
c.
d.
3. Divide the things into two EQUAL groups. Write an addition. Find half of the total.
a. 10
b. 40
c. 24
____ + ____ = _____
____ + ____ = _____
____ + ____ = _____
1
of 10 is ____.
2
1
of 40 is _____.
2
1
of 24 is _____.
2
25
Doubling and halving are opposite operations.
7 + 7 = 14, so
1
2
of 14 is 7.
4. Fill in the doubles chart. Then use it to find one-half of the given numbers.
11 + 11 = ______
1
2
of 16 is _______.
7 + 7 = ______
12 + 12 = ______
1
2
of 28 is _______.
8 + 8 = ______
13 + 13 = ______
1
2
of 26 is _______.
9 + 9 = ______
14 + 14 = ______
1
2
of 30 is _______.
10 + 10 = ______ 15 + 15 = ______
1
2
of 22 is _______.
6 + 6 = ______
5. Divide the dots into two EQUAL groups. Find half of the total.
a.
c.
b.
1
of 30 is ______.
2
1
of _____ is ______.
2
1
of _____ is _____.
2
6. Solve the problems. Then fill in another chart of doubles. It has a pattern! Find it!
a. Jack and Jared split $60 evenly.
How many dollars did each one get?
10 + 10 = ______
15 + 15 = ______
b. Half of 100 students were sick.
How many were not sick?
20 + 20 = ______
c. Aunt Karen gave Marsha half of
25 + 25 = ______
$40. Marsha spent $10 on a toy.
How many dollars does Marsha
have now?
30 + 30 = ______
d. The recipe called for 10 apples. That was exactly
35 + 35 = ______
half of the apples Mum had. How many apples
did Mum have to begin with?
40 + 40 = ______
26
Adding with Whole Tens
1. The numbers are shown with ten-sticks and one-dots. Write the sums.
+
+
a.
54 + 10 = ______
b.
______ + 20 = ______
+
c.
+
d.
______ + ______ = ______
______ + ______ = ______
+
e.
+
f.
______ + ______ = ______
______ + ______ = ______
Adding whole tens and
another 2-digit number
Break down the other
number into tens and ones.
Add the tens. Then, add the ones.
2. Add. Break the second number into tens and ones first. Then add the tens.
a.
10 + 34 = _______
b.
(10 + 30 + 4)
10 + 28 = _______
c.
(10 + _____ + _____ )
20 + 24 = _______
(20 + _____ + _____ )
d.
30 + 21 = _______
e.
50 + 17 = _______
f.
40 + 33 = _______
g.
60 + 23 = _______
h.
30 + 37 = _______
i.
70 + 25 = _______
27
3. Add. Break the first number into tens and ones first. Then add the tens.
a.
45 + 20 = _______
(40 + 5 + 20)
b.
27 + 20 = _______
( _____ + _____ + 20 )
45 + 40 = _______
c.
( _____ + _____ + 40)
d.
46 + 30 = _______
e.
16 + 50 = _______
f.
38 + 60 = _______
g.
20 + 77 = _______
h.
58 + 40 = _______
i.
40 + 39 = _______
4. Explain in your own words how you can add 21 + 60 in your head.
5. Fill in the chart of doubles
again, and notice its
PATTERN.
5 + 5 = _______
30 + 30 = _______
10 + 10 = _______
35 + 35 = _______
15 + 15 = _______
40 + 40 = _______
20 + 20 = _______
45 + 45 = _______
25 + 25 = _______
50 + 50 = _______
6. Erika got 30 books out of the library, and read half of them in two
days. How many books does she have left to read?
7. Betty and Mum went shopping. They bought shoes for $40, a blouse for $20,
and a skirt for $30. Mum paid half of the cost and Betty paid the rest.
How much did Betty pay?
8. Trevor had $61. Then he bought a toy for $30. How much money does he have left?
28
9. Fill in the missing numbers and find how many tens were added.
a. 12
+ _____ = 22
b. 45
+ _____ = 65
c. 23
+ _____ = 63
12 + _____ = 52
45 + _____ = 55
23 + _____ = 53
12 + _____ = 42
45 + _____ = 75
23 + _____ = 93
10. Add 10, 20, 30, or 40. In the box below the number, write “E” if the number is even,
and “O”, if the number is odd. What do you notice?
+ 20
+ 10
12
22
19
E
E
O
+ 40
+ 30
32
+ 30
23
+ 40
37
+ 20
+ 10
7
58
85
How many different solutions can you find for this puzzle?
Find at least two. All numbers are whole tens.
+
+
+
+
+
+
+
+
= 100
+
+
+
+
+
=
100
+
+
+
+
=
80
= 70
+
= 70
=
80
29
+
+
+
+
=
60
= 70
= 100
+
+
=
100
= 70
=
60
Subtracting Whole Tens
Cross out two tens.
In the problem 47 – 20, think of the tens.
The first number (47) has four tens. We take
away two tens. So, there are TWO tens left.
The first number also has 7. That does not change.
47 – 20 = ______
1. Cross out as many ten-pillars as the problem indicates. What is left?
a. 70
– 50 = ______
b. 65
– 30 = ______
c. 46
– 20 = ______
Notice: The amount of ONES does not change in these subtractions.
You can just think of the TENS.
2. Count by tens backwards.
a.
76, 66, ________ , ________ , ________ , ________ , ________
b.
_______ , ________ , 52, 42, ________ , ________ , ________
3. Subtract.
a.
b.
c.
23 – 10 = ________
48 – 20 = ________
56 – 10 = ________
23 – 20 = ________
48 – 30 = ________
56 – 30 = ________
d.
e.
f.
75 – 10 = ________
31 – 10 = ________
81 – 40 = ________
75 – 20 = ________
31 – 20 = ________
81 – 50 = ________
30
4. Find the pattern and continue it.
a.
88 – 10 = ______
b.
100 – 60 = ______
c.
34 – 10 = ______
88 – 20 = ______
90 – 50 = ______
44 – 20 = ______
88 – 30 = ______
80 – 40 = ______
54 – 30 = ______
88 – ______ = ______
_____ – _____ = _____ _____ – _____ = _____
88 – ______ = ______
_____ – _____ = _____ _____ – _____ = _____
88 – ______ = ______
_____ – _____ = _____ _____ – _____ = _____
88 – ______ = ______
_____ – _____ = _____ _____ – _____ = _____
5. Use rounded numbers to solve these problems.
a. Three suitcases weigh 29 kg, 18 kg, and 31 kg.
About how much is their total weight?
b. Chairs cost $29 each. Can Darlene
buy three of them with $80?
c. Tyrone received $50 for his birthday.
If he buys three books that cost $9
each, about how much will he have left?
Find
numbers
for the
puzzles.
+
–
= 90
–
+
=
30
–
+
= 30
=
30
+
–
=
80
31
= 40
= 30
=
10
Revision, Chapter 1
1. Add. The problems in each box are similar.
a.
b.
c.
d.
51 + 7 = _____
46 + 3 = _____
72 + 5 = _____
35 + 5 = _____
81 + 7 = _____
96 + 3 = _____
32 + 5 = _____
95 + 5 = _____
2. Subtract. The problems in each box are similar.
a.
b.
c.
d.
49 – 5 = _____
29 – 3 = _____
60 – 7 = _____
38 – 4 = _____
89 – 5 = _____
69 – 3 = _____
80 – 7 = _____
78 – 4 = _____
3. a. How much would three shirts for $20 each cost in total?
b. Marlene went to the toy store and bought a board game for $30,
a toy car for $5, crayons for $2, and a colouring book for $5.
What was the total cost?
4. Add and subtract whole tens.
a.
b.
c.
d.
21 + 40 = _____
40 + 23 = _____
72 – 50 = _____
89 – 30 = _____
56 + 30 = _____
20 + 78= _____
66 – 40 = _____
45 – 20 = _____
5. Use letters from the word W O N D E R F U L to make two new words.
____
____
____
____
____
____
____
____
1st
5th
9th
9th
4th
2nd
3rd
5th
32
6. Fill in the missing numbers. The four problems form a fact family.
2 +
a.
+
= 10
2
b.
= 10
____ + ____ =
9
____ + ____ =
9
c.
____ + ____ = ____
10 − ____ =
9
−
10 −
9
− ____ = ____
= ____
7
____ + ____ = ____
= ____
8
− ____ =
5
____ − ____ = ____
7. The total is missing from the subtraction sentence. Solve.
– 8 = 8
a.
b.
– 5 = 4
8. Circle the even numbers.
– 30 = 30
c.
72
31
59
60
8
9. Divide the dots into two EQUAL groups. Find half of the total.
a.
1
of 50 is ______.
2
b.
c.
1
of 88 is ______.
2
1
of 46 is _______.
2
10. Two boys divided equally 18 toy cars.
How many did each boy get?
11. Mrs. Taylor used half of her potatoes to make mashed potatoes.
Now she has 13 potatoes left. How many did she have at first?
12. Mary has 13 coloured pencils and Theresa has twice as many.
How many coloured pencils do the girls have together?
33
Chapter 2: Clock
Introduction
The second chapter of Math Mammoth Grade 2-A deals with reading the clock to the five-minute
intervals, and finding simple time intervals.
It is helpful to have a non-digital practice clock, where the student can turn the hands of the clock.
First, we practise telling time in the hours:minutes form (such as 10:20), and then using the colloquial
phrases “to” and “past.”
Also studied are simple time intervals, or how many whole hours pass. When practising these, tell the
student to imagine moving the hour hand on a clock. He/she can initially use a practice clock for this.
The section also has one lesson about the calendar. Of course, the calendar and the months are best
learned just in the context of everyday life, as the months pass. Hang a wall calendar on the wall and
instruct your child to look at it every day, and to cross out days as they pass.
The Lessons in Chapter 2
page
span
Revision—Whole and Half Hours .......................... 37
1 page
The Minutes ...........................................................
38
3 pages
The Minutes, Part 2 ................................................
41
2 pages
Past and To in Five-Minute Intervals .....................
43
3 pages
How Many Hours Pass? .........................................
46
2 pages
The Calendar: Weekdays and Months ...................
48
3 pages
The Calendar: Dates ..............................................
51
3 pages
Revision, Chapter 2 ...............................................
54
1 page
Helpful Resources on the Internet
Use these free online resources to supplement the “bookwork” as you see fit.
Disclaimer: These links were valid as of the writing of this book, and to the best of our knowledge we
believe these websites to have what is described. However, we cannot guarantee that the links have not
changed. Parental supervision is recommended.
Flashcard Clock
Read the analogue and type in the time in digital form.
http://www.teachingtreasures.com.au/maths/FlashcardClock/flashcard_clock.htm
Clockwise
Plug in a time, and the clock runs till it, or the clock runs to a time and you type it in.
http://www.shodor.org/interactivate/activities/ClockWise/
34
What Time Is It?
Look at the analogue clock and pick the digital clock that shows the same time.
http://www.primarygames.com/time/start.htm
That Quiz: Time
Online quizzes for all time-related topics: reading the clock, time passed,
adding/subtracting with time, conversion of time units, and time zones practice. The
quizzes have many levels, can be timed or not, and include lots of options for
customisation. Easy to use and set up.
http://www.thatquiz.org/tq-g/math/time
Time Matching Game
Match each analogue clock with the corresponding digital time.
http://www.math-play.com/Time-Matching-Game/Time-Matching-Game.html
Under the Sea
Practise time and calendar topics. Finish all the topics to unlock a treasure!
http://www.learnalberta.ca/content/me3usa/flash/index.html?goLesson=13
On Time
Set the clock's hands to the given time. Four different levels.
http://www.sheppardsoftware.com/mathgames/earlymath/on_time_game1.htm
Clock Shoot
A game where you need to click on the clock with the matching time (analogue/digital). Three different
levels: whole hours, half hours, or quarter hours.
http://www.sheppardsoftware.com/mathgames/earlymath/clock_shoot.htm
Crazy Clock
A matching game for two players where you match the analogue time given by the clock to a digital time
given by cards, but as in a normal matching game, you need to click on a card to flip it and see the digital
time.
http://www.counton.org/games/crazy-clock/index.html
Parking Time
Steer the car into the parking place that shows the correct time.
http://www.mathnook.com/math/parking-time.html
Matching Pairs Time
Match analogue to analogue, analogue to digital, analogue to words, or digital to words. Choose “5
minute intervals” for this game.
http://www.topmarks.co.uk/Flash.aspx?f=matchingpairstimev3
Telling the Time in Words
This page contains several activities to practise telling time, including word problems, worksheets, and a
timetable.
http://mathsframe.co.uk/en/resources/resource/117/telling_the_time_in_words
35
Teaching Time
Analogue/digital clock games and worksheets. Also an interactive “class clock” to demonstrate time.
http://www.teachingtime.co.uk/
Time-for-time
Resource site to learn about time: worksheets, games, quizzes, time zones.
http://www.time-for-time.com/default.htm
ELAPSED TIME
Elapsed Time Line
This interactive tool shows 2 clocks that have fingers you drag to set a “from” and “to” time, and a
number line. You can demonstrate how to use a number line to calculate elapsed time.
http://www.teacherled.com/2008/10/05/elapsed-time-line/
Elapsed Time Worksheets
Generate printable worksheets for elapsed time. You can practise the elapsed time, finding the starting
time, or finding the ending time. The time interval can be to the accuracy of 1 minute, 5 minutes, 10
minutes, 15 minutes, 30 minutes, or whole hours.
http://www.mathnook.com/elapsedtimegen.html
CALENDAR
Days of the Week
This interactive activity has various levels which practice the order of the days of the week.
https://www.helpfulgames.com/subjects/english/days-of-the-week.html
Months of the Year
Practise the order of the months of the year, plus how many days each month has.
http://www.transum.org/Maths/Activity/Time/Months.asp
Calendar Clowns
Answer questions about the calendar by clicking on the correct date.
http://mrnussbaum.com/calendarclowns/
36
Revision—Whole and Half Hours
1. Write or say the time using the expressions o'clock or half past.
a. ________________
b. ________________
c. ________________
d. ________________
________________
________________
________________
________________
2. Write the time in two ways: using the expressions o'clock or half past, and with
numbers.
a. _____ o'clock
b. half past _____
______ : ______
c. half past _____
______ : ______
d. _____ o'clock
______ : ______
______ : ______
3. Write the time an hour later. Use numbers.
Now it is:
a. 6:00
b. 11:30
c. 3:00
d. 2:30
e. 9:30
c. 12:30
d. 10:00
e. 1:30
An hour
later, it is:
4. Write the time a half-hour later. Use numbers.
Now it is:
a. 5:00
b. 7:30
A half-hour
later, it is:
37
The Minutes
When the hour hand moves from one number to the next
(from 1 to 2, or from 6 to 7, etc.), it takes one hour to do
so.
In that same one hour of time, the minute hand travels
from 0 to 60 minutes. So one hour is 60 minutes.
A half-hour is 30 minutes.
When you read the minute hand, you use the green numbers
(marked outside the clock face of the clock on the right).
They go by fives, and are not normally marked on clocks.
You need to know them. Just skip-count in fives!
The hour hand is past 8.
The minute hand is at 15.
The time is 8:15.
The hour hand is past 2.
The minute hand is at 25.
The time is 2:25.
1 hour = 60 minutes.
1/2 hour = 30 minutes.
The hour hand is past 11.
The minute hand is at 10.
The time is 11:10.
1. The arrow shows how much the minute hand travels. How many minutes pass?
a. ______ minutes
c. ______ minutes
b. ______ minutes
38
d. ______ minutes
2. Write the time using the special clock that shows the numbers for hours and for
minutes.
a. _____ : ______
b. _____ : ______
c. _____ : ______
d. _____ : ______
e. _____ : ______
f. _____ : ______
g. _____ : ______
h. _____ : ______
3. Write the time using the normal clock. Remember, the numbers for the minute hand are
not shown, and they go by fives!
a. ______ : ______
b. ______ : ______
c. ______ : ______
d. ______ : ______
e. ______ : ______
f. ______ : ______
g. ______ : ______
h. ______ : ______
39
4. Find the clock that shows 11:25 and the clock that shows 11:05.
a.
b.
c.
d.
5. Write the time.
a. _____ : ______
b. _____ : ______
c. _____ : ______
d. _____ : ______
6. Write the time that the clock shows, and the time 5 minutes later. Imagine the minute
hand moving one “step” further. You can use your practice clock.
5 min.
later →
5 min.
later →
a.
b.
c.
d.
_____ : ______
_____ : ______
_____ : ______
_____ : ______
_____ : ______
_____ : ______
_____ : ______
_____ : ______
e.
f.
g.
h.
_____ : ______
_____ : ______
_____ : ______
_____ : ______
_____ : ______
_____ : ______
_____ : ______
_____ : ______
40
The Minutes, Part 2
Notice! The hour
hand looks like it is
pointing to 2. But the
minute hand has
not yet reached
60 minutes, so it is
not yet 2 o'clock!
Another example.
The hour hand looks
like it is pointing to 10.
But the minute hand
has not yet reached
60 minutes, so it is
not yet 10 o'clock.
We still say it is 1 hour (and some minutes).
We still say it is 9 hours (and some minutes).
The minute hand is at 45. The time is 1:45. The minute hand is at 55. The time is 9:55.
1. Choose the correct time.
a.
Is it 1:50 or 2:50?
b.
c.
Is it 2:45 or 3:45?
Is it 6:55 or 7:55?
2. Draw the minute hand to match the given time. The hour hand is already drawn.
a. 1:35
b. 2:45
c. 3:15
d. 6:55
e. 5:30
f. 7:40
g. 7:35
h. 12:20
41
3. Write the time. Note: the hour hand is close to a number, but it has not reached it yet.
a. _____ : ______
b. _____ : ______
c. _____ : ______
d. _____ : ______
e. _____ : ______
f. _____ : ______
g. _____ : ______
h. _____ : ______
4. Write the time that the clock shows, and the time 5 minutes later.
5 min.
later →
a.
b.
c.
d.
_____ : ______
_____ : ______
_____ : ______
_____ : ______
_____ : ______
_____ : ______
_____ : ______
_____ : ______
The children played 5-minute hide-and-seek, where they
always took exactly 2 minutes for hiding and 3 for seeking.
They used a watch to time it right.
After playing five rounds, Mum called them in to have an
evening snack at 8:05. At what time did they start the game?
42
Past and To in Five-Minute Intervals
We can also tell the time by
saying how many minutes it
is past the whole hour.
Use the expression “so-many
8:05 OR 5 past 8
1:20 OR 20 past 1
minutes past” only if the
minutes are 30 or less.
“20 minutes past 1 o'clock”. “5 minutes past 8 o'clock”.
1. How many minutes is it past the whole hour?
a.
b.
c.
d.
It is _____ minutes
It is _____ minutes
It is _____ minutes
It is _____ minutes
past 2 o'clock.
past 3 o'clock.
past ____ o'clock.
past ____ o'clock.
e.
f.
______ past _____
g.
______ past _____
______ past _____
h.
______ past _____
2. Write the time the clock shows and the time 5 minutes later. Use “past” or “half past.”
a.
5 min.
later →
b.
c.
______ past _____
______ past _____
______ past _____
_________________
_________________
_________________
_________________
_________________
_________________
43
We can also say how many minutes it is to the next whole hour. Use this when the
time is between half past some hour and the next whole hour (for example, between
half past 6 and 7 o'clock).
To find how many minutes it is
to the next whole hour, count
by fives again—either from the
next whole hour to the minute
hand, or from the minute hand
to the next whole hour.
20 to 1
10 to 2
“20 minutes to 1 o'clock.” “10 minutes to 2 o'clock.”
Notice that in this wording we use the next whole hour — the hour still yet to come.
The times 6:35 and 25 to 7 look
different, but they mean the same.
The time 6:35 shows the hour that
the hour hand has passed (six),
whereas 25 to 7 shows the hour that
the hour hand is coming to (seven),
6:35 OR 25 to 7
3:55 OR 5 to 4
or the next hour.
3. Show how many minutes it is to the next whole hour.
a.
b.
c.
d.
It is ____ minutes
It is ____ minutes
It is ____ minutes
It is ____ minutes
to 7 o'clock.
to ____ o'clock.
to ____ o'clock.
to ____ o'clock.
e.
f.
g.
h.
____ to ____
____ to ____
____ to ____
____ to ____
i.
j.
k.
l.
____ to ____
____ to ____
____ to ____
____ to ____
44
4. Write the time using the wordings “past” or “to”, and using numbers.
a.
b.
c.
______________________
______________________
______________________
______ : ______
______ : ______
______ : ______
d.
e.
f.
______________________
______________________
______________________
______ : ______
______ : ______
______ : ______
5. Write the time using the hours:minutes way. Use your practice clock to help.
a. 10 past 8
b. 15 to 7
c. 25 past 12
d. half-past 7
______ : ______
______ : ______
______ : ______
______ : ______
e. 9 o'clock
f. 20 to 6
g. 5 to 11
h. 25 to 4
______ : ______
______ : ______
______ : ______
______ : ______
6. Write the time using the expressions “past”, “to”, or “half past”.
a. 6:45 ____________________________________________________________
b. 9:30 ____________________________________________________________
c. 12:10 ____________________________________________________________
d. 4:55 ____________________________________________________________
e. 8:35 ____________________________________________________________
f. 1:40 ____________________________________________________________
45
How Many Hours Pass?
The chart below shows the whole hours in one 24-hour period = one night + one day.
From midnight to noon we call the hours “AM”. This comes from Ante Meridiem
(Latin), and means before noon. From noon to midnight we call the hours “PM”,
which comes from Post Meridiem (Latin), and means after noon.
How many hours is it from 6 AM to 12 AM?
You could use the chart, and count. Since both hours are AM, you can use
subtraction to find the difference: 12 − 6 = 6 hours.
How many hours is it from 3 AM to 3 PM?
Now you cannot use subtraction because the answer clearly is not zero hours. Since
the number is the same (3), it means the hour hand travels through the entire clock face,
starting at 3 and ending at 3. The difference is 12 hours.
How many hours is it from 8 AM to 3 PM?
One of the times is AM, and the other is PM, so you cannot subtract them.
Instead, do it in two parts:
1) How many hours from 8 AM to noon? It is four hours.
2) How many hours from noon to 3 PM? It is three hours.
All totalled, there are 7 hours from 8 AM to 3 PM.
1. How many hours is it?
from
to
5 AM
7 AM
9 AM
11 AM
10 AM
12 noon
1 PM
4 PM
11 PM
7 PM
hours
2. How long is the school day, if it starts and ends at given times?
Start:
8 AM
8 AM
9 AM
10 AM
8 AM
End:
12 noon
1 PM
3 PM
3 PM
2 PM
hours:
46
3. How many hours is it to midnight?
from
to
4 PM
7 PM
12 noon
9 AM
7 AM
12 midnight
12 midnight
12 midnight
12 midnight
12 midnight
hours
4. How many hours does Mark sleep if he goes to bed and gets up at these times?
Go to bed
9 PM
8 PM
9 PM
11 PM
midnight
Get up
6 AM
7 AM
5 AM
9 AM
9 AM
Sleep hours
5. a. How many hours do you usually spend in school each day?
b. How many hours do you usually sleep?
6. a. Dad's workday starts at 8:00 in the morning, and ends at 5 PM.
How many hours is Dad at work?
b. Marian's school day starts at 9 AM and ends at 2 PM. How long is it?
c. The aeroplane took off at 10 AM and landed at 1 PM. Then it took off again
at 2 PM and landed at 6 PM. How many hours was the aeroplane in the air?
7. a. How many hours are there in one day-night period?
b. How many hours are there in two day-night periods?
8. a. The turkey needs to cook three hours in the oven to be ready at 7 PM.
When should it be put into the oven?
b. Two teams want to play soccer for two hours, and be done by 1 PM.
When should they start playing?
c. Mum needs seven hours of sleep tonight. She wants to wake up at 6 AM.
When should she go to bed?
47
The Calendar: Weekdays and Months
Calendar
January
Su Mo Tu We Th
1
4 5 6 7 8
11 12 13 14 15
18 19 20 21 22
25 26 27 28 29
February
Fr
2
9
16
23
30
Sa
3
10
17
24
31
Su Mo Tu We Th
1 2 3 4 5
8 9 10 12 12
15 16 17 18 19
22 23 24 25 26
April
Su Mo Tu We
1
5 6 7 8
12 13 14 15
19 20 21 22
26 27 28 29
Th
2
9
16
23
30
Th
2
9
16
23
30
Fr
3
10
17
24
Sa
4
11
18
25
Sa
7
14
21
28
Su
1
8
15
22
29
Mo
2
9
16
23
30
Tu
3
10
17
24
31
Sa
2
9
16
23
30
August
Fr
3
10
17
24
31
Sa
4
11
18
25
Sa
3
10
17
24
31
Su Mo Tu We Th Fr Sa
1
2 3 4 5 6 7 8
9 10 11 12 13 14 15
16 17 18 19 20 21 22
23 24 25 26 27 28 29
30 31
Su
1
8
15
22
29
Mo
2
9
16
23
30
Tu
3
10
17
24
We
4
11
18
25
Th
5
12
19
26
48
Th
5
12
19
26
Fr
6
13
20
27
Sa
7
14
21
28
Su Mo
1
7 8
14 15
21 22
28 29
Tu
2
9
16
23
30
We
3
10
17
24
Th
4
11
18
25
Fr
5
12
19
26
Sa
6
13
20
27
September
November
Fr
2
9
16
23
30
We
4
11
18
25
June
Su Mo Tu We Th Fr
1
3 4 5 6 7 8
10 11 12 13 14 15
17 18 19 20 21 22
24 25 26 27 28 29
31
October
Su Mo Tu We Th
1
4 5 6 7 8
11 12 13 14 15
18 19 20 21 22
25 26 27 28 29
Fr
6
13
20
27
May
July
Su Mo Tu We
1
5 6 7 8
12 13 14 15
19 20 21 22
26 27 28 29
March
Su Mo Tu
1
6 7 8
13 14 15
20 21 22
27 28 29
We
2
9
16
23
30
Th
3
10
17
24
Fr
4
11
18
25
Sa
5
12
19
26
Fr
4
11
18
25
Sa
5
12
19
26
December
Fr
6
13
20
27
Sa
7
14
21
28
Su Mo Tu
1
6 7 8
13 14 15
20 21 22
27 28 29
We
2
9
16
23
30
Th
3
10
17
24
31
1. You see “Su Mo Tu We Th Fr Sa” in the calendar. What does it mean?
Ask your teacher if you don’t know!
___________________________________________________________________________
They are called the “days of the week.” Learn to say them from memory.
2. Fill in the weekday before and after the given day. Try NOT to look at the calendar!
Tuesday
Friday
Sunday
3. What day of the week is it today? _____________________________________
4. Let’s say it is Friday. What day of the week will it be...
a. in 1 day? ____________________________ b. in 7 days? _____________________________
c. in 5 days? ___________________________ d. in 3 days? _____________________________
5. Tell what day of the week is...
your birthday in 20_ _
__________________________________________
1 January, 20_ _ (New Year’s Day) __________________________________________
10 May, 20_ _ (Mother’s Day)
__________________________________________
26 December, 20_ _ (Boxing Day) __________________________________________
____________________________ __________________________________________
____________________________ __________________________________________
____________________________ __________________________________________
(Fill in some other dates of your choosing for the last three lines.)
49
6. a. Circle all the months in this list that have 31 days.
January February March April May June July August September October November December
b. Circle all the months in this list that have 30 days.
January February March April May June July August September October November December
c. Which month didn’t get circled either time? _____________________
It normally has 28 days, but every four years (each LEAP year) it has 29 days.
7. Fill in the month before and after the given month. Try NOT to look at the calendar!
March
August
November
In April, Mrs. Warwick sent a parcel to her friend in China. It took a long
time to arrive, and it got there in August. How many months did the parcel
take to arrive?
Count up the months until August, but don’t start at April; start at the month just
after April (which is May). May, June, July, August. You counted up four months.
The parcel took four months to arrive.
8. Let’s say it is JUNE now. Children figure out how long it is until their birthday.
Count up the months, and fill in the blanks.
a. Anna’s birthday is in September. It is still ______ months until Anna’s birthday.
b. Kyle’s birthday is in August. It is only ______ months until Kyle’s birthday.
c. May’s birthday is in December. It is ______ months until May’s birthday.
9. How about you? In what month is your birthday? __________________________
How many months is it until your birthday this year? _______ months
Or, if you already had it, how many months ago was it? _______ months ago
50
The Calendar: Dates
Calendar
January
Su Mo Tu We Th Fr
1
3 4 5 6 7 8
10 11 12 13 14 15
17 18 19 20 21 22
24 25 26 27 28 29
31
Su
3
10
17
24
April
Mo Tu We Th Fr
1
4 5 6 7 8
11 12 13 14 15
18 19 20 21 22
25 26 27 28 29
February
Sa
2
9
16
23
30
Sa
2
9
16
23
30
Su Mo Tu We Th Fr
1 2 3 4 5
7 8 9 10 11 12
14 15 16 17 18 19
21 22 23 24 25 26
28 29
Su
1
8
15
22
29
Mo
2
9
16
23
30
May
Tu We Th
3 4 5
10 11 12
17 18 19
24 25 26
31
July
Su Mo Tu We Th Fr
1
3 4 5 6 7 8
10 11 12 13 14 15
17 18 19 20 21 22
24 25 26 27 28 29
31
March
Fr
6
13
20
27
Sa
6
13
20
27
Sa
7
14
21
28
Su Mo Tu
1
6 7 8
13 14 15
20 21 22
27 28 29
Fr
4
11
18
25
Sa
5
12
19
26
Fr
3
10
17
24
Sa
4
11
18
25
Su Mo Tu We Th
1
4 5 6 7 8
11 12 13 14 15
18 19 20 21 22
25 26 27 28 29
Fr
2
9
16
23
30
Sa
3
10
17
24
December
Tu We Th
1
6 7 8
13 14 15
20 21 22
27 28 29
Fr
2
9
16
23
30
Sa
3
10
17
24
31
Su Mo
5 6
12 13
19 20
26 27
August
Sa
2
9
16
23
30
October
Su Mo Tu We Th Fr Sa
1
2 3 4 5 6 7 8
9 10 11 12 13 14 15
16 17 18 19 20 21 22
23 24 25 26 27 28 29
30 31
Su Mo
1
7 8
14 15
21 22
28 29
Su Mo
6 7
13 14
20 21
27 28
Tu
2
9
16
23
30
We
3
10
17
24
31
Th
4
11
18
25
November
Tu We Th
1 2 3
8 9 10
15 16 17
22 23 24
29 30
We
2
9
16
23
30
Th
3
10
17
24
31
June
Tu We Th
1 2
7 8 9
14 15 16
21 22 23
28 29 30
September
Fr
5
12
19
26
Fr
4
11
18
25
Sa
6
13
20
27
Sa
5
12
19
26
Su Mo
4 5
11 12
18 19
25 26
1. Mary goes swimming every Thursday. Look at the calendar, and write the May
dates when Mary goes swimming. Use the form (day) (month), such as 5 May.
_________________ _______ ___________
_________________ _______ _____________
_________________ _______ ____________
_________________ _______ _____________
51
2. Circle these public holidays on the calendar on the previous page. Circle also some
other important holidays for your country.
1 January
New Year’s Day
8 May
Mother's Day
14 February Valentine’s Day
21 June
Summer Solstice
11 April
25 December Christmas Day
Easter Monday
3. For this exercise, you need a current calendar. Look at this year’s calendar
and write the dates in the form (day) (month) (year), such as 15 June, 2016.
month
a. today’s date
b. tomorrow’s date
c. your birthday this year
d. Christmas day of this year
e. the first Monday of June
f. the last Friday of August
day
year
___________________________ ______ _________
___________________________ ______ _________
___________________________ ______ _________
___________________________ ______ _________
___________________________ ______ _________
___________________________ ______ _________
4. Cindy sent a letter to her friend on 25 October. The letter took
two days to reach her friend. What date did her friend get it?
5. Julie got glasses in June. The eye doctor told her to come back
in four months. Count four months, starting your count at the
month after June. In what month will Julie go back to the eye doctor?
6. The soccer team played their last game in late November, and then they
took a 2-month break. In what month did they start playing again?
52
On the calendar, 14 October is highlighted. The date one
week before is just above that: it is 7 October (underlined).
October
Su Mo Tu We Th Fr Sa
1
2 3 4 5 6 7 8
9 10 11 12 13 14 15
16 17 18 19 20 21 22
23 24 25 26 27 28 29
30 31
The date one week later than 14 October is just below that:
it is 21 October (underlined).
What would the date be two weeks later than 14 October?
What date is 1 week later than
29 October?
29 October is a Saturday, so
the date one week later is also a
Saturday. It will be the first
Saturday of November.
That is 5 November.
What would be the date two
weeks later than 29 October?
October
Su Mo Tu We Th Fr Sa
1
2 3 4 5 6 7 8
9 10 11 12 13 14 15
16 17 18 19 20 21 22
23 24 25 26 27 28 29
30 31
November
Su Mo Tu
1
6 7 8
13 14 15
20 21 22
27 28 29
We
2
9
16
23
30
Th
3
10
17
24
Fr
4
11
18
25
7. Fill in the missing dates in the table. Use the calendar to help!
Date 1 week ago
Date now
Date 1 week later
14 July
8 December
26 January
Date 2 weeks ago
Date now
Date 2 weeks later
8 August
18 October
23 February
8. The painting class meets every two weeks. Their first meeting of the year is
12 January. What are the dates for the next two meetings?
53
Sa
5
12
19
26
Revision, Chapter 2
1. Write the time with hours:minutes, and using “past,” “to,” “half past,” or “o'clock.”
b.
a.
c.
d.
______ : ______
______ : ______
______ : ______
______ : ______
_____ to ____
_____ past ____
________________
________________
e.
f.
______ : ______
_____ to ____
g.
h.
______ : ______
______ : ______
______ : ______
________________
________________
________________
2. Write the later time.
Time now
2:30
6:55
Time now
5 minutes
____ : _____ ____ : _____
later
9:05
5:40
10 minutes
____ : _____ ____ : _____
later
3. Father starts his work at 9 AM, and leaves to go back home at 5 PM.
How many hours is his work day?
4. Jane goes to kindergarten at 8 AM and stays there four hours.
At what time does she leave kindergarten?
5. Bill goes to the chess club every Thursday. He went today, 17 March.
What is the date he will go the next time?
6. Ken got the August issue of a magazine in the mail. The next
magazine comes in three months. What month will that be?
54
Chapter 3: Addition and Subtraction Facts
Within 0-18
Introduction
The third chapter of Math Mammoth Grade 2-A provides lots of practice for learning and memorising the
basic addition facts of single-digit numbers where the answer is between 10 and 18.
This chapter includes lots of repetition, drill, and practice. Therefore, you are welcome to mix the lessons
from this chapter with some geometry, place value, clock, or measuring, in order to prevent boredom.
The goal is to memorise these facts, or at least become so fluent with them that an outsider cannot tell if
the student remembers the answer or uses some mental maths strategy to get the answer.
Some students will accomplish this quicker, needing less practice. Some will need more practice. You
can also add in some internet-based games (a list of online games is provided on the next page).
Learning addition and subtraction facts is very important for later study. For example, we will soon study
regrouping (carrying/borrowing) in addition and in subtraction, which requires that the student be able to
recall all the sums of single-digit numbers and corresponding subtraction facts efficiently and fluently.
We will start the chapter by reviewing how to complete the next whole ten. This concept is very
important. For example, what number do you add to 23 to get 30? As an equation, we write:
23 + __ = 30.
In the next lesson, we study sums that go over ten, doing these sums in two parts. For example, in the
sum 9 + 7, the student first completes 10 by adding 9 + 1. Then, the student adds the rest, or 6, to 10.
Learning this prepares the student for addition facts where the sum is more than 10.
The next lessons, Adding with 9, Adding with 8, Adding with 7, and Adding with 6, provide lots of
practice for learning and memorising the basic addition facts. There are 20 such facts:
9 + 2 to 9 + 9:
8 + 3 to 8 + 8:
7 + 4 to 7 + 7:
6 + 5 to 6 + 6:
8 facts
6 facts
4 facts
2 facts
After those lessons, we study subtraction. First, the student subtracts to ten. This means subtracting from
14, 15, 16, etc. so that the answer is 10, for example 16 − __ = 10. In the next step, we study subtractions
with an answer less than 10, such as 16 − 7. The student practises these by subtracting in two parts: first
subtracting to ten, then the rest. For example, 16 − 7 becomes 16 − 6 − 1, or 14 − 6 becomes 14 − 4 − 2.
The last part of this chapter includes various lessons titled Number Rainbows and Fact Families with ...,
which give lots of practice and reinforcement for the basic addition and subtraction facts. These lessons
also include many word problems. They emphasize the connection between addition and subtraction to
solve basic subtraction facts such as 13 − 8 or 15 − 6. Alongside them, you can also use games or
flashcards to reinforce the learning of the facts.
Please see also my videos at http://www.youtube.com/watch?v=XSVlrkBf_Ns and
http://www.youtube.com/watch?v=jdIzuGPRhRQ (Or go to www.youtube.com/mathmammoth and
find the videos about addition and subtraction facts). These two videos explain several strategies for
learning addition and subtraction facts, many of which are studied in this chapter.
55
The Lessons in Chapter 3
page
span
Revision: Completing the Next Whole Ten ...........
59
2 pages
Revision: Going Over Ten .....................................
61
2 pages
Adding with 9 ........................................................
63
2 pages
Adding with 8 ........................................................
65
2 pages
Adding with 7 ........................................................
67
2 pages
Adding with 6 ........................................................
69
2 pages
Revision—Facts with 6, 7, and 8 ...........................
71
2 pages
Subtract to Ten ......................................................
73
2 pages
Difference and How Many More ............................ 75
3 pages
Number Rainbows—11 and 12 ..............................
78
2 pages
Fact Families with 11 ............................................
80
1 page
Fact Families with 12 ............................................
81
2 pages
Number Rainbows—13 and 14 .............................
83
1 page
Fact Families with 13 and 14 .................................
84
3 pages
Fact Families with 15 .............................................
87
2 pages
Fact Families with 16 .............................................
89
2 pages
Fact Families with 17 and 18 .................................
91
3 pages
Mixed Revision, Chapters 1-3 ...............................
93
2 pages
Revision, Chapter 3 ................................................
95
3 pages
Helpful Resources on the Internet
Use these free online resources to supplement the “bookwork” as you see fit.
Disclaimer: These links were valid as of the writing of this book, and to the best of our knowledge we
believe these websites to have what is described. However, we cannot guarantee that the links have not
changed. Parental supervision is recommended.
Video: Strategies for Subtraction Facts
Maria's own video that shows how to use fact families in order to facilitate the learning and memorisation
of the basic subtraction facts.
http://www.youtube.com/watch?v=XSVlrkBf_Ns
Video: Strategies for Addition Facts
Maria's own video which lists several strategies to learn the basic addition facts, including
the 9-trick, the 8-trick, the doubles, and doubles plus one more.
http://www.youtube.com/watch?v=jdIzuGPRhRQ
56
Bridging Shuttle
Bridging Through Ten means the same as adding to ten first, then the rest. Get a “flight plan”, then first
add to ten by typing the number needed in the oval, and press the red button. Then type the rest that the
shuttle needs to go in the other oval, and press the red button.
http://www.ictgames.com/bridging.html
Power Lines Puzzle
Arrange the numbers into the pattern so that the numbers on the “lines” add up to the given sum.
http://www.primarygames.co.uk/pg2/powerlines/powerlines1.html
Online Addition Flashcards
http://www.thegreatmartinicompany.com/additionfill.html
Catch the Stars
Catch the stars that add up to the number on the bucket. Click on the bucket to change the number. Don't
let any of the stars fall away! You have all of the answers in your bucket.
http://www.sheppardsoftware.com/mathgames/catchthestars/addition/catchthestarsAdd9.htm
Penguin Party Addition
Feed a fish to the penguin that has the correct answer to the addition problem. Choose level four.
http://www.sheppardsoftware.com/mathgames/popup/popup_addition.htm
Car Wash Addition
Wash cars while practising addition facts. Then, participate in a race!
http://www.multiplication.com/games/play/car-wash-addition
Bugabaloo Shoes
How many shoes do the bugs have? This game practises basic addition facts.
http://www.sheppardsoftware.com/mathgames/earlymath/bugabalooShoes.htm
Math Downhill Slalom
Win a gold medal by skiing through and around the correct flags.
http://mrnussbaum.com/slalom/
Number-Line Jump Maker
Illustrate jumps on the number line with this interactive tool.
http://www.ictgames.com/numberlineJumpMaker/
57
Digit Drop
Drop the blocks into the empty slots to complete the subtraction sentences. Choose “Subtraction” and the
level “Hard”.
http://www.mathnook.com/math/digitdrop.html
Math Lines
Practise adding in this fun game. First, choose which number you want to practise. Then, shoot the
numbered marble from the cannon into a numbered marble such that the numbers total the target number.
http://www.mathnook.com/math/math-lines-6.html
Number Twins
First, click on the number that you want to practise. Then, match pairs of balls that add up to that number.
http://www.sheppardsoftware.com/mathgames/numbertwins/numbertwins_add_10.htm
Addition Games
Practise addition facts with these fun games!
http://www.multiplication.com/games/addition-games
Subtraction Games
Practise subtraction facts with these fun games!
http://www.multiplication.com/games/subtraction-games
Left Turn Otto Even and Odd
Help Otto get the even or odd numbers as required on the top of the screen.
http://www.mathnook.com/math/left-turn-otto-even-odd.html
Aplus Maths Games
Matho (maths and bingo combined), concentration, hidden picture, and Planet Blaster games for the basic
operations.
http://www.aplusmath.com/games/
Tux Maths
A versatile free software for maths facts with many options. Includes all operations. You need to shoot
falling comets that can damage penguins' igloos.
http://sourceforge.net/projects/tuxmath
58
Revision: Completing the Next Whole Ten
1. Write the previous and next whole ten. Then, circle the ten that is nearer the given
number.
a. ______,
56, ______
b. ______,
72, ______
c. ______,
94, ______
d. ______,
37, ______
e. ______,
25, ______
f. ______,
31, ______
52 and how many more makes the next ten (60)? We can write 52 + _____ = 60.
You can solve it using a helping problem: 2 and how many more makes ten?
The answer to both problems is the same. It is 8.
2. Complete to the next ten. Below, write a helping problem using numbers within 0-10.
a.
17 + _____ = 20
b.
62 + ____ = ______
7 + _____ = 10
c.
2 + ____ = ______
94 + ____ = ______
4 + ____ = ______
3. Complete to the next ten. Think of the helping problem that uses numbers within 0-10.
a.
42 + _____ = 50
b.
34 + ____ = _______
c.
66 + ____ = _______
d.
61 + ____ = _______
e.
97 + ____ = _______
f.
83 + ____ = _______
4. Circle the even numbers. 8
9 12 15 10 19 11 6 17
5. Now pick the even numbers from the previous exercise, and write each of them as a
double of the number.
a. ______
= ______ + ______
b. ______
= ______ + ______
c. ______
= ______ + ______
d. ______
= ______ + ______
59
6. Complete the next ten... and then add one more! Compare the two problems in each box.
a.
73 + _____ = 80
b.
73 + _____ = 81
35 + _____ = 40
c.
35 + _____ = 41
14 + _____ = 20
14 + _____ = 21
7. Find your way through the maze! Start at the top. You can only colour a square if the
sum is a whole ten (10, 20, 30, 40, 50, 60, 70, 80, 90, or 100).
13 + 6
54 + 6
73 + 8
45 + 7
99 + 4
15 + 9
14 + 8
15 + 5
13 + 6
32 + 7
45 + 7
73 + 7
64 + 5
82 + 9
16 + 7
30 + 12
39 + 1
74 + 6
73 + 9
52 + 7
46 + 7
32 + 7
31 + 9
86 + 4
65 + 4
92 + 4
21 + 8
24 + 7
22 + 8
32 + 6
83 + 6
11 + 7
98 + 2
57 + 3
17 + 9
44 + 9
12 + 8
95 + 6
38 + 5
53 + 9
71 + 9
34 + 4
36 + 7
19 + 4
28 + 11
53 + 7
29 + 2
26 + 6
78 + 6
32 + 5
8. Complete the next whole ten.
a.
17 + _____ + 1 = 20
b.
35 + _____ + 2 = 40
c.
41 + _____ + 6 = 50
12 + _____ + 4 = 20
32 + _____ + 3 = 40
44 + _____ + 3 = 50
13 + _____ + 4 = 20
36 + _____ + 3 = 40
42 + _____ + 5 = 50
9. Find as many different sums as you can to make one hundred!
90 + ___ + ___ = 100
90 + ___ + ___ = 100
90 + ___ + ___ = 100
90 + ___ + ___ = 100
90 + ___ + ___ = 100
90 + ___ + ___ = 100
90 + ___ + ___ = 100
90 + ___ + ___ = 100
90 + ___ + ___ = 100
60
Revision: Going Over Ten
Sums that go over 10
Imagine that 8 wants to get some from 6 Imagine that 9 wants to get some from 7
in order to make a ten. Six gives two
in order to make a ten. Seven gives one
to 8, and has only four left for itself!
to 9, and has only six left for itself!
8+ 6
| \
8+2+4
9+ 7
| \
9+1+6
In the end, we
have 10 and 4.
We get 14.
10 + 4 = 14
In the end, we
have 10 and 6.
We get 16.
10 + 6 = 16
1. Circle all the blue balls and some of the red so that they make a ten. Then add
the rest.
a.
8 +
4
8
9
+
6
d.
9
10 + _____ = ______
e.
7
+
+
5
10 + _____ = ______
2 = ______
10 +
c.
b.
+
3
10 + _____ = ______
5
f.
10 + _____ = ______
9
+
8
10 + _____ = ______
2. Write a number on the empty line inside the balloon so that the numbers in the balloon
make a ten. Then add the last number to 10.
a.
b.
+ 2 = _____
d.
c.
+ 3 = _____
e.
+ 4 = _____
+ 4 = _____
f.
+ 7 = _____
61
+ 5 = _____
3. Fill in. Imagine that the first number wants to become a ten.
a.
8 + 7
/
+
10 +
d.
9 + 4
/
b.
\
8 + 9
/
8 + 5
/
c.
\
+ ______
5
+ ______
10 + _____ = _____
5 = 15
9 + 6
/
e.
\
+ ______
10 + _____ = _____
\
10 + _____ = _____
9 + 9
/
f.
\
+ ______
10 + _____ = _____
\
+ ______
10 + _____ = _____
4. Add so you get 10, 11, 12 and notice the patterns!
a.
b.
c.
d.
8 + ______ = 10
7 + ______ = 10
9 + ______ = 10
6 + ______ = 10
8 + ______ = 11
7 + ______ = 11
9 + ______ = 11
6 + ______ = 11
8 + ______ = 12
7 + ______ = 12
9 + ______ = 12
6 + ______ = 12
15
5. Circle the even numbers.
24
40
58
51
67
89
100
99
2
6. Solve the word problems. ALSO, write an addition and subtraction sentence for them!
a. You have $8 and you buy a toy for $5 and candy for $2.
How much money do you have now?
b. Lucy had $8. Then she found $5 in her piggy bank, and her
mum gave her $2. How much money does she have now?
c. Matt had $8. He spent $3 on a litre of juice
Later he found $2 in the street. How much
money does he have now?
62
Adding with 9
9 wants to be a 10! So, it takes one
from the other number (from 3).
So, 9 becomes 10, and two dots
are left over.
Imagine that 9 really wants to be a 10!
It takes one from the other number
(from 5). So, 9 becomes 10, and
four dots are left over.
+
9
+
=
5
=
=
10 + 4
=
+
14
=
=
9 + 3 = 10 + 2 =
Use the list on the right to practise. Don't write the answers there.
Just point to different problems and say the answer aloud.
1. Circle the ten, then add.
12
9+1=
9+2=
9+3=
a.
9+5
10 + 4 = ____
b.
9+4
c.
9+7
10 + ____ = _____ 10 + ____ = _____
9+4=
9+5=
9+6=
9+7=
d.
9 + ____
e.
9 + ____
f.
9 + ____
10 + ____ = _____ 10 + ____ = _____ 10 + ____ = _____
9+8=
9+9=
2. It is good to memorise the doubles, also. Fill in.
a.
2 + 2 = _____
b.
5 + 5 = _____
c.
8 + 8 = _____
3 + 3 = _____
6 + 6 = _____
9 + 9 = _____
4 + 4 = _____
7 + 7 = _____
10 + 10 = _____
63
3. Add to nine. Think how 9 wants to be a ten, and takes 1 from the other number.
a.
9 + 6
b.
10 + 5 = _____
d.
9 + 8
c.
10 + _____ = _____
9 + 7
e.
10 + 6 = _____
9 + 5
10 + _____ = _____
9 + 9
9 + 3
f.
10 + _____ = _____
10 + _____ = _____
4. Addition facts with nine. Do not write the answers down. Just practise the sums.
9+0=
9+5=
9+9=
9+3=
9+6=
9+1=
9+7=
9+8=
9+2=
9 + 4=
9 + 10 =
5. Add. Remember, you can add both ways. For example, 7 + 9 is the same as 9 + 7.
a.
9 + 4 = _____
b.
9 + 7 = _____
c.
3 + 9 = _____
d.
5 + 9 = _____
8 + 9 = _____
4 + 9 = _____
9 + 2 = _____
8 + 9 = _____
9 + 5 = _____
9 + 4 = _____
9 + 9 = _____
9 + 6 = _____
6. What is missing?
a.
9+
= 13
9+
= 15
b.
9+
= 16
9+
= 14
c.
+ 9 = 11
You can use this same “trick” with 19, 29, 39, 49, and
so on. Imagine that 49 really wants to be 50, and so it
“takes” 1 from the number you add. Solve.
a. 49 + 7 = _____
b. 59 + 5 = _____
c. 69 + 3 = _____
19 + 6 = _____
89 + 9 = _____
29 + 6 = _____
64
+ 9 = 17
Adding with 8
Imagine that 8 wants to be a 10! It takes
two from the other number (from 3).
So, 8 becomes 10, and only 1 is left over.
+
8
+
=
3
=
8 wants to be a 10! So, it takes two
from the other number (from 5).
So, 8 becomes 10, and 3 are left over.
=
10 + 1
=
+
11
8
+
=
5
=
=
10 + 3
=
13
Use the list on the right to practise. Do not write the answers there.
Just point to the different problems and say the answer aloud.
8+1=
1. Add. First, circle the ten.
8+2=
8+3=
8+4=
a.
8+5
10 + 3 = ____
b.
8+4
c.
10 + ____ = ____
8 + ____
10 + ____ = ____
8+5=
8+6=
8+7=
d.
8 + ____ =
10 + ____ = ____
e.
8 + ____ =
f.
10 + ____ = ____
8 + ____ =
10 + ____ = ____
8+8=
8+9=
2. It is good to memorise the doubles, also. Fill in.
a.
2 + 2 = _____
b.
5 + 5 = _____
c.
8 + 8 = _____
3 + 3 = _____
6 + 6 = _____
9 + 9 = _____
4 + 4 = _____
7 + 7 = _____
10 + 10 = _____
65
Addition facts with eight. Do not write the answers down, but just practise the sums.
8+0=
8+5=
8+8=
8+9=
8+3=
8+7=
8+1=
8+4=
8 + 10 =
8+1=
8+6=
8+2=
3. Add and fill in what is missing.
a.
8 + 4 = _____
b.
8 + 6 = _____
d.
8 + ____ = 13
7 + 8 = _____
3 + 8 = _____
c.
8 + 5 = _____
e.
8 + ____ = 12
8 + ____ = 15
8 + 9 = _____
____ + 8 = 11
f.
8 + ____ = 16
____ + 8 = 14
4. a. Jane ate 8 strawberries, and John ate 5 more than what Jane did.
How many strawberries did John eat?
b. Angie is 13 years old, and Mike is 5.
How many years older is Angie than Mike?
5. Find the patterns and continue them.
a.
b.
8 + 2 = _____
18 + 2 = _____
1
2
of 0 is ______.
8 + 4 = _____
18 + 4 = _____
1
2
of 2 is ______.
8 + 6 = _____
18 + 6 = _____
1
2
of 4 is ______.
8 + ____ = _____
18 + ____ = _____
1
2
of _____ is ______.
_____ + ____ = _____
_____ + ____ = _____
1
2
of _____ is ______.
_____ + ____ = _____
1
2
of _____ is ______.
_____ + ____ = _____
1
2
of _____ is ______.
_____ + ____ = _____
_____ + ____ = _____
66
c.
Adding with 7
We have already studied these facts:
These are the new facts with 7:
7 + 8 = _____
8 + 7 = _____
7 + 4 = _____
7 + 6 = _____
7 + 9 = _____
9 + 7 = _____
7 + 5 = _____
7 + 7 = _____
7 + 10 = _____
10 + 7 = _____
Tricks for remembering addition facts with 7
z
z
z
z
7+1=
7 + 7 = 14 is one of the doubles. Memorise all the doubles!
If you forget, you can do 5 + 5 = 10, then 6 + 6 = 12, and
then 7 + 7 = 14.
7 + 6 is just one more than the doubles fact 6 + 6 = 12. So, it is 13.
Or, 7 + 6 is just one less than the doubles fact 7 + 7 = 14.
7 + 4 is just one more than the ten-fact 7 + 3 = 10. So, 7 + 4 is 11.
7 + 5 is just one more than 7 + 4, or just one less than 7 + 6,
so if you remember those, you can figure out 7 + 5, too.
Or maybe you have your own trick for it!
7+2=
7+3=
7+4=
7+5=
7+6=
7+7=
Use the list on the right to practise. Do not write the answers there.
Just point to the different problems and say the answer aloud.
1. Let’s practise doubles—and doubles plus one more.
Notice: the answer is also just one more!
a.
6 + 6 = _____
b.
6 + 7 = _____
d.
9 + 9 = _____
9 + 10 = _____
7 + 7 = _____
c.
7 + 8 = _____
e.
5 + 5 = _____
6 + 5 = _____
67
8 + 8 = _____
8 + 9 = _____
f.
4 + 4 = _____
4 + 5 = _____
7+8=
7+9=
Addition facts with seven. Do not write the answers down; just practise the sums.
7+0=
7+5=
7+6=
7+9=
7+3=
7+9=
7+7=
7+4=
7 + 10 =
7+8=
7+1=
7+2=
2. Fill in the missing numbers.
a.
e.
7 + 4 = _____
b.
8 + 7 = _____
c.
7 + _____ = 14
d.
7 + _____ = 12
6 + 7 = _____
7 + 10 = _____
7 + _____ = 13
7 + _____ = 16
7 + 5 = _____
3 + 7 = _____
7 + _____ = 15
7 + _____ = 11
7 + 7 = _____
f.
4 + 7 = _____
g.
8 + _____ = 13
h.
_____ + 7 = 17
9 + 7 = _____
7 + 9 = _____
8 + _____ = 16
_____ + 7 = 10
7 + 8 = _____
3 + 7 = _____
8 + _____ = 17
_____ + 7 = 12
+7
+8
+9
3. Try these boxes!
Add 7 each time.
Add 8 each time.
Add 9 each time.
4
11
3
11
2
____
7
____
6
____
4
____
8
____
5
____
7
____
10
____
7
____
8
____
5
____
2
____
3
____
9
____
4
____
5
____
68
Adding with 6
+
=
+
=
6 + 5 = ____
6 + 6 = ____
This is just one more
than 5 + 5 = 10.
This is one of
the doubles!
Here are addition facts where we add to six. Do not write the answers down. Just go over
the problems until you remember them easily.
6+0=
6+5=
6+9=
6+3=
6+7=
6+4=
6 + 10 =
6+1=
6+2=
6+6=
6+8=
1. Fill in the missing numbers.
a.
b.
c.
d.
6 + 4 = _____
6 + 8 = _____
6 + _____ = 14
_____ + 6 = 12
6 + 6 = _____
6 + 9 = _____
6 + _____ = 16
_____ + 6 = 15
6 + 5 = _____
6 + 7 = _____
6 + _____ = 12
_____ + 6 = 11
e.
f.
g.
h.
5 + 6 = _____
9 + 6 = _____
7 + _____ = 14
_____ + 6 = 13
6 + 7 = _____
8 + 6 = _____
8 + _____ = 14
_____ + 6 = 14
4 + 6 = _____
6 + 6 = _____
9 + _____ = 14
_____ + 6 = 15
69
Trick! When you add three or four numbers, first add
the numbers that make ten. It makes adding easier!
8 + 6 + 4
5 + 3 + 2 + 5
= 8 + 10 = 18
= 10 + 5 = 15
2. Add. First find the numbers that make 10. You can circle or colour them. Then add the
rest. This is like hide-and-seek! Where are those numbers hiding that make ten?
a.
b.
c.
1 + 6 + 9 = ______
3 + 6 + 7 + 2 = ______
6 + 5 + 1 + 4 = ______
6 + 8 + 2 = ______
1 + 5 + 5 + 7 = ______
8 + 3 + 2 + 6 = ______
5 + 7 + 5 = ______
2 + 7 + 8 + 2 = ______
9 + 6 + 1 + 4 = ______
3. Solve the word problems.
a. There were some apples on the table. The children came in
and ate 5 apples. Later, there were still 7 apples on the table.
How many apples were there at first?
b. Jason had $12. He bought a toy truck, and then he had $6 left.
How much did the toy truck cost?
c. Mum bought some bananas. She ate one, Dad ate two, and the
children ate two. Then there were four bananas left.
How many bananas did Mum buy?
d. Mitch solved 9 maths problems. Shane solved 5 more than Mitch.
How many did Shane solve?
e. Barry picked 14 coconuts and Dylan picked 7 coconuts.
How many more did Barry pick than Dylan?
70
Revision—Facts with 6, 7, and 8
1. Here are the 20 addition facts with single-digit numbers where the sum is between 10
and 20. Connect the problems to the right answer.
6+6
5+8
9+5
8+6
5+7
11
9+2
12
5+6
3+9
7+7
9+9
15
16
8+7
17
9+8
4+7
13
9+4
6+7
14
8+3
4+8
7+9
18
8+8
6+9
2. Figure out the pattern and continue it.
a.
b.
c.
9 + ____ = 19
____ + 16 = 17
6 + ____ = 6
8 + ____ = 18
____ + 14 = 17
6 + ____ = 8
7 + ____ = 17
____ + 12 = 17
6 + ____ = 10
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
____ + ____ = ____
71
3. Fill in the addition table.
+
6
8
4
5
7
3
9
7
9
5
4. Solve.
a. A herd of elephants was feeding on the grass. Four of them left, but fourteen
stayed and continued to feed. How many elephants were there to begin with?
b. Susan has five more dolls than Alba. Susan has 10 dolls. How many does Alba have?
Hint 1: Draw Susan's dolls. Hint 2: Think which girl has more dolls.
Should you draw more or fewer dolls for Alba?
c. Ryan and Lucas emptied wastebaskets. Ryan emptied four more wastebaskets
than Lucas. Lucas emptied five baskets. How many did Ryan empty?
Hint 1: Draw Lucas' baskets. Hint 2: Think which boy emptied more of them.
Should you draw more or fewer baskets for Ryan?
d. Stella ate 10 peanuts. Mary ate 7 more than Stella.
How many peanuts did Mary eat?
5. Add. In some problems, you can find numbers that make a ten.
a.
b.
c.
6 + 6 + 2 = ______
8 + 6 + 3 = ______
6 + 2 + 3 + 7 = ______
1 + 4 + 9 = ______
2 + 2 + 8 = ______
3 + 6 + 7 + 2 = ______
72
Subtract to Ten
1. Subtract the “ones” that are not in the ten-group. You should only have ten left!
a. 14
− _____ = 10
b. 16
− ____ = _____
c. 15
− ____ = _____
d. 13
− _____ = 10
e. 17
− ____ = _____
f. 19
− ____ = _____
Subtracting in parts
Let's subtract 13 − 5. First we subtract
enough dots that we have only 10 left.
So, first we take away 3 dots. 13 − 3 = 10.
We still need to subtract 2 more. We
subtract those from 10. There are 8 left.
13 − 5
/ \
13 − 3 − 2
= 8
2. First subtract enough that you have only 10 left. Then subtract the rest.
You can cover some dots to help.
a. 15
− 7
/ \
15 − 5 − 2
= ______
d. 14
− 9
/ \
14 − ____ − ____
= ______
b. 13
− 8
/ \
13 − ____ − ____
= ______
e. 12
− 5
/ \
12 − ____ − ____
= ______
73
c. 13
− 4
/ \
13 − ____ − ____
= ______
f. 16
− 8
/ \
16 − ____ − ____
= ______
3. First subtract enough so that you have only 10 left. Then subtract the rest.
a.
16 − 7
b.
/
12 − 4
\
c.
/
13 − 6
\
/
\
16 − ____ − ____
12 − ____ − ____
13 − ____ − ____
= _____
= _____
= _____
d.
11 − 3
e.
/
12 − 7
\
f.
/
15 − 8
\
/
\
11 − ____ − ____
12 − ____ − ____
15 − ____ − ____
= _____
= _____
= _____
4. Subtract. You can cover dots to help.
a.
12 − 4 = _____
b.
15 − 6 = _____
c.
14 − 5 = _____
12 − 5 = _____
15 − 9 = _____
14 − 8 = _____
12 − 3 = _____
15 − 7 = _____
14 − 7 = _____
12 − 6 = _____
15 − 8 = _____
14 − 6 = _____
5. First subtract those that are not in the ten-group. Compare the top and bottom problems.
a.
b.
c.
15 − 7 = _____
13 − 6 = _____
16 − 9 = _____
25 − 7 = _____
23 − 6 = _____
26 − 9 = _____
Can you apply the idea of this lesson to larger numbers? First,
subtract to the previous whole ten. Then, subtract some more.
a. 22 − 7
/
b. 34 − 5
\
22 − ____ − ____ = _____
/
c. 72 − 6
\
/
34 −____ − ____ = _____
74
\
72 − ____ − ____ = _____
Difference and How Many More
The difference or distance between two numbers means how far apart they are from
each other on the number line. The difference between 3 and 12 is 9, because they are
NINE steps apart.
1. Find the differences between these numbers using the number line above.
a. difference between 10 and 6: ________
b. difference between 12 and 8: ________
c. difference between 14 and 2: ________
d. difference between 17 and 6: ________
We can solve the difference between two numbers by subtracting.
What is the difference between 10 and 4? Subtract 10 – 4 = 6. The difference is 6.
2. Write a subtraction to find the difference between the numbers.
a. The difference between
b. The difference between
c. The difference between
10 and 4
2 and 9
8 and 3
______ – _____ = ______
______ – _____ = ______
_____ – _____ = ______
d. The difference between
e. The difference between
f. The difference between
20 and 50
10 and 90
19 and 8
______ – ______ = ______
______ – ______ = ______
_____ – ____ = ______
3. Solve the subtractions by thinking of the distance between the numbers—how far
apart they are from each other.
a.
b.
c.
d.
20 – 16 = _____
40 – 38 = ______
65 – 61 = ______
36 – 31 = ______
e.
f.
g.
h.
100 – 99 = ______
87 – 84 = ______
55 – 50 = ______
75
79 – 78 = ______
You can also solve the difference between two numbers by thinking of addition:
how many more do you need to add to the one number to get the other?
For example, to find the difference between 12 and 7, think: 7 + ____ = 12.
(“7 and how many more makes 12?”) The answer is 5.
4. Write a “how many more” addition to find the difference between the numbers.
a. The difference between 10 and 6
b. The difference between 6 and 12
6 + ______ = 10
6 + ______ = 12
c. The difference between 15 and 8
d. The difference between 4 and 11
______ + ______ = ______
______ + ______ = ______
5. Subtract. Think how far apart the two numbers are from each other.
+3
a. 15
– 12 = ____
12 and how many more makes 15?
+____
b. 11
+____
– 9 = ____
9 and how many more makes 11?
c. 16
– 11 = ____
11 and how many more makes 16?
There are two ways to find a difference between two numbers:
(1) Subtraction
(2) A “how many more” addition
Find the difference between 100 and 2.
It is easier to subtract 100 – 2 = 98.
The difference is 98.
Find the difference between 100 and 95.
It is easier to think: 95 + ____ = 100.
The difference is 5.
6. Find the differences.
a. The difference between 60 and 56
b. The difference between 22 and 20
c. The difference between 35 and 1
d. The difference between 67 and 3
e. The difference between 50 and 30
f. The difference between 40 and 100
76
Whenever a word problem asks “how many more,” you can solve it in two ways.
You can either subtract, or you can write a “how many more” addition.
Either way, you are finding the difference between the two numbers.
7. Solve the word problems.
a. Jane is on page 20 and Toby is on page 17 of the same book.
How many more pages has Jane read?
b. Mum has one dozen eggs plus five in another carton. A dozen means 12.
How many eggs does Mum have?
c. Becky is reading a 50-page book. She is on page 42.
How many more pages does she have left to read?
d. Heidi worked in the garden for 2 hours in the morning and 3 hours
in the afternoon. Andrew worked for 8 hours in the shop.
Who worked more hours?
How many more?
e. Tanya has a house full of flies! She killed 28 flies. Her husband killed 5 flies.
How many more did she kill than him?
f. The next day, Tanya had a house full of flies again. She killed 5 flies
in the living room, 12 in the kitchen, and 2 in her room.
How many flies did she kill in total?
g. Mal had $12 and Brett had $6. Then both brothers worked helping Dad
in the garden. Mal earned $5 and Brett earned $9.
Now, who has more money?
How much more?
77
Number Rainbows—11 and 12
This is a number rainbow for 11. If two numbers are connected with an arc, they add up to
11. Use the number rainbow to help you with addition and subtraction facts!
1. Practise subtraction from 11. Do not write the answers; just do them mentally.
11 – 6 =
11 – 7 =
11 – 8 =
11 – 2 =
11 – 3 =
11 – 9 =
11 – 4 =
11 – 5 =
2. Similarly, practise subtraction from 12.
12 – 5 =
12 – 7 =
12 – 10 =
12 – 6 =
12 – 9 =
12 – 4 =
12 – 3 =
12 – 8 =
78
3. Fill and colour the number rainbows. Do not look at the previous page!
Then practise the subtraction problems.
11 – 4 =
11 – 2 =
11 – 3 =
11 – 9 =
11 – 8 =
11 – 5 =
11 – 6 =
11 – 7 =
12 – 8 =
12 – 3 =
12 – 4 =
12 – 9 =
12 – 6 =
12 – 10 =
12 – 7 =
12 – 5 =
For more practice, make your own number rainbows and subtractions on blank paper!
79
Fact Families with 11
1. Fill in. In each fact family, colour enough marbles to equal the first number. Then use
another colour to colour the rest.
Fact families with 11
10, 1, and 11
9, _____, and 11
8, ____, and 11
7, ____, and 11
6, ____, and 11
10 +
1 = _____
11 – 10 = ____
1 + 10 = _____
11 – 1 = ____
9 + ____ = 11
_____ – ____ = ____
____ + ____ = _____
_____ – ____ = ____
8 + ____ = 11
_____ – ____ = ____
____ + ____ = _____
_____ – ____ = ____
7 + ____ = 11
_____ – ____ = ____
____ + ____ = _____
_____ – ____ = ____
6 + ____ = 11
_____ – ____ = ____
____ + ____ = _____
_____ – ____ = ____
2. Check yourself! Can you subtract quickly without looking above?
a.
11 – 10 = _____
b.
11 – 2 = _____
c.
11 – 3 = _____
11 – 9 = _____
11 – 4 = _____
11 – 6 = _____
11 – 6 = _____
11 – 5 = _____
11 – 9 = _____
11 – 8 = _____
11 – 7 = _____
11 – 4 = _____
80
Fact Families with 12
1. Fill in. In each fact family, colour enough marbles to equal the first number. Then use
another colour to colour the rest.
Fact families with 12
10, 2, and 12
9, _____, and 12
10 + 2 = _____
12 – 10 = ____
2 + 10 = _____
12 – 2 = ____
9 + ____ = 12
_____ – ____ = ____
____ + ____ = _____
8, ____, and 12
7, ____, and 12
_____ – ____ = ____
8 + ____ = 12
_____ – ____ = ____
____ + ____ = _____
_____ – ____ = ____
____ + ____ = _____
_____ – ____ = ____
____ + ____ = _____
_____ – ____ = ____
____ + ____ = _____
_____ – ____ = ____
6, ____, and 12
2. Check yourself! Can you subtract quickly from 12 and from 11 without looking above?
a.
b.
c.
d.
12 – 4 = _____
11 – 8 = _____
12 – 6 = _____
12 – 3 = _____
11 – 9 = _____
12 – 7 = _____
11 – 4 = _____
12 – 10 = _____
12 – 8 = _____
11 – 3 = _____
12 – 9 = _____
11 – 5 = _____
11 – 6 = _____
12 – 5 = _____
12 – 4 = _____
11 – 7 = _____
81
3. Let's practise “how many more” additions! Remember the fact families with 11 and 12.
a. 6
+ ____ = 11
b. 7
8 + ____ = 11
+ ____ = 12
c. ____
8 + ____ = 12
+ 9 = 11
____ + 7 = 11
d. ____
+ 6 = 12
____ + 9 = 12
4. Explain how you can use addition to solve a subtraction problem, such as 11 – 8.
5. Find the pattern and continue it.
16 – 1
= _____
16 – 3
= _____
2 + 15 = ____
15 – 3
= _____
16 – 5
= _____
4 + 13 = ____
15 – 5
= _____
_____ – ____ = _____
____ + ____ = ____
_____ – ____ = _____
_____ – ____ = _____
____ + ____ = ____
_____ – ____ = _____
_____ – ____ = _____
____ + ____ = ____
_____ – ____ = _____
_____ – ____ = _____
____ + ____ = ____
_____ – ____ = _____
_____ – ____ = _____
____ + ____ = ____
_____ – ____ = _____
a.
b.
0 + 17 = ____
c.
15 – 1 = _____
A child stacked 14 blocks in three stacks. One stack has 6 and
the third stack has 4. How many are in the middle stack?
We can write an addition where one number is missing: 6 + ____ + 4 = 14.
Figure out a way to solve this problem! Then solve the rest of the problems below.
a.
6 + ____ + 4 = 14
8 + ____ + 3 = 13
b.
2 + ____ + 2 = 8
3 + ____ + 3 = 9
c.
10 + ____ + 4 = 17
10 + ____ + 2 = 15
See also the game http://www.carstensstudios.com/mathdoodles/sumsstacker.html
82
Number Rainbows—13 and 14
1. Fill and colour the number rainbows. Then practise the subtractions.
13 – 7 =
13 – 4 =
13 – 9 =
13 – 10 =
13 – 5 =
13 – 6 =
13 – 11 =
13 – 8 =
14 – 8 =
14 – 3 =
14 – 7 =
14 – 6 =
14 – 5 =
14 – 9 =
14 – 11 =
14 – 4 =
For more practice, make your own number rainbows and subtractions on blank paper!
83
Fact Families with 13 and 14
1. Fill in. In each fact family, colour the marbles so they match the numbers in it.
Fact families with 13
10, 3, and 13
9, _____, and 13
8, ____, and 13
7, ____, and 13
10 + 3 = _____
13 – 10 = ____
3 + 10 = _____
13 – 3 = ____
9 + ____ = 13
_____ – ____ = ____
____ + ____ = _____
_____ – ____ = ____
8 + ____ = 13
_____ – ____ = ____
____ + ____ = _____
_____ – ____ = ____
7 + ____ = 13
_____ – ____ = ____
____ + ____ = _____
_____ – ____ = ____
2. Draw a line to connect the problems that are from the same fact family. You do not
need to write the answers.
13 – 7 =
11 – 4 =
12 – 7 =
5+
11 – 8 =
13 – 6 =
11 – 3 =
5+
3+
8+
12 – 5 =
13 – 5 =
12 – 3 =
6+
= 13
3+
= 11
7+
9+
= 12
4+
= 11
= 12
= 13
= 11
= 13
84
= 12
3. Fill in. In each fact family, colour the marbles so they match the numbers in it.
Fact families with 14
10, 4, and 14
9, _____, and 14
8, ____, and 14
7, ____, and 14
10 + 4 = _____
14 – 10 = ____
4 + 10 = _____
14 – 4 = ____
9 + ____ = 14
_____ – ____ = ____
____ + ____ = _____
_____ – ____ = ____
8 + ____ = 14
_____ – ____ = ____
____ + ____ = _____
_____ – ____ = ____
7 + ____ = 14
_____ – ____ = ____
____ + ____ = _____
_____ – ____ = ____
4. Subtract.
a.
13 – 8 = ____
13 – 6 = ____
b.
13 – 5 = ____
c.
13 – 4 = ____
12 – 7 = ____
13 – 7 = ____
d.
12 – 9 = ____
13 – 9 = ____
5. Find the missing numbers (addends).
a.
9+
–9=4
d.
g.
= 14
14 –
=8
b.
6+
–7=7
e.
h.
= 14
12 –
=7
85
c.
6+
–9=3
f.
i.
= 12
13 –
=8
6. Solve the word problems.
a. Tim arranged his toy cars in rows. The first row had seven
cars, the second had seven, and the third row had four.
How many cars does Tim have?
b. If you have 14 strawberries and I have eight,
how many more do you have?
c. Dad has six cherries and Mum has five more than him.
How many cherries does Mum have?
d. At first Mum had 20 apples to make some pies,
but she gave each of the four children one apple
before she made the pies. How many apples did
she have left to use in the pies?
7. Figure out the patterns and continue them!
a.
+
40
b.
+
17
+
48
+
21
+
56
+
25
+
64
+
72
+
29
+
_____
86
+
+
_____
_____
+
+
_____
_____
+
_____ _____
+
_____ _____
Fact Families with 15
1. Fill in. In each fact family, colour the marbles so they match the numbers in it.
Fact families with 15
10, 5, and 15
9, _____, and 15
8, ____, and 15
10 + 5 = _____
15 – 10 = ____
5 + 10 = _____
15 – 5 = ____
9 + ____ = 15
_____ – ____ = ____
____ + ____ = _____
_____ – ____ = ____
8 + ____ = 15
_____ – ____ = ____
____ + ____ = _____
_____ – ____ = ____
2. Subtract.
a. 15
– 5 = ______
b. 15
– 8 = ______
c. 15
– 4 = ______
d. 15
– 9 = ______
e. 15
– 6 = ______
f. 15
– 7 = ______
3. Audrey does not remember the answer to 15 – 9.
Explain how she can solve it using addition.
4. Count by threes.
+ 3
+ 3
+ 3
+ 3
+ 3
9
+ 3
+ 3
+ 3
33
87
5. These word problems all have to do with “more.” Draw a picture of how many things
the one person has in the problem. Then think carefully who has more. Will you need
to draw more or fewer things for the other person in the problem?
a. Martina has 7 peaches and Jeff has three more than her.
How many does Jeff have?
b. William has three more books than Lars. William has 11 books.
How many does Lars have?
c. Marty picked 15 pine cones and David picked 9.
How many more did Marty pick than David?
d. Erika picked 5 more pine cones than Susan.
If Erika picked 15, how many did Susan pick?
6. Write each number as a double of some other number.
a.
6 = ____ + ____
b.
12 = ____ + ____
c.
10 = ____ + ____
d.
18 = ____ + ____
e.
20 = ____ + ____
f.
8 = ____ + ____
7. Drew picked 7 tomatoes from the garden, and John picked 9.
Then they gave half of their tomatoes to a neighbour.
How many tomatoes did they keep?
8. Write or say all the even numbers from 0 to 20.
9. Find the total cost of all the items.
a. A toy truck, $28, and a game, $30
b. A watch, $47, a book, $30, and a toy, $10
Total $ _________
Total $ _________
88
Fact Families with 16
1. Fill in. Colour the marbles, using two colours, so that the colouring matches the
numbers.
Fact families with 16
10, 6, and 16
9, _____, and 16
10 + 6 = _____
16 – 10 = ____
6 + 10 = _____
16 – 6 = ____
9 + ____ = 16
_____ – ____ = ____
____ + ____ = _____
_____ – ____ = ____
8 + ____ = 16
_____ – ____ = ____
____ + ____ = _____
_____ – ____ = ____
8, ____, and 16
2. Subtract.
a.
b.
c.
d.
15 – 10 = _____
13 – 9 = _____
14 – 8 = _____
15 – 7 = _____
13 – 10 = _____
16 – 9 = _____
13 – 8 = _____
16 – 7 = _____
16 – 10 = _____
14 – 9 = _____
16 – 8 = _____
13 – 7 = _____
3. Connect the problems to the correct answer with a line.
15 – 9
3
17 – 9
7
17 – 9
14 – 9
4
16 – 9
8
16 – 9
14 – 10
5
16 – 10
9
18 – 9
13 – 9
6
18 – 9
10
19 – 9
89
4. Figure out the patterns and continue them!
+
a.
+
9
6
+
b.
+
12
+
15
+
16
12
+
+
+
+
+
____
____
____
____
+
+
+
+
____
____
____
____
+
20
24
____
____
5. Solve the word problems.
a. A class has 24 children. One day, two of them were
sick and two had to leave to go to the dentist.
How many children were in class that day?
b. If you have $10, and Mum gives you $4 more,
can you buy a book that costs $13?
c. You had $20 and you bought sandals for
$17. How many dollars do you have left?
d. Ellie has saved $12. She wants to buy a gift that
costs $16. How much more money does she need?
e. Five boys came to play soccer. Then, seven girls came. Then, one girl
had to go home. Are there now more boys or girls playing soccer?
How many more?
6. Compare and write < , > or = .
a.
35
20 + 5
b.
23 + 5
23 + 6
c.
16 – 8
15 – 8
d.
15
6+7
e.
31 + 4
31 + 3
f.
15 – 9
16 – 9
90
Fact Families with 17 and 18
1. Fill in. Colour the marbles, using two colours, so that the colouring matches the
numbers.
Fact families with 17
10, 7, and 17
9, _____, and 17
10 + 7 = _____
17 – 10 = ____
____ + ____ = _____
_____ – ____ = ____
9 + ____ = 17
_____ – ____ = ____
____ + ____ = _____
_____ – ____ = ____
Fact families with 18
10, 8, and 18
9, _____, and 18
10 + 8 = _____
18 – 10 = ____
____ + ____ = _____
_____ – ____ = ____
9 + ____ = 18
_____ – ____ = ____
____ + ____ = _____
_____ – ____ = ____
2. Subtract, practising the basic facts. Remember to think of fact families.
a.
b.
c.
d.
17 – 10 = _____
15 – 9 = _____
14 – 6 = _____
12 – 9 = _____
17 – 9 = _____
15 – 8 = _____
14 – 7 = _____
12 – 8 = _____
18 – 10 = _____
16 – 9 = _____
13 – 6 = _____
11 – 9 = _____
18 – 9 = _____
16 – 8 = _____
13 – 7 = _____
11 – 8 = _____
91
3. Write < , > or = . Can you compare these without calculating?
a. 45 + 8
d.
1
2
45 + 5
1
2
of 16
of 14
b. 50 – 6
50 – 8
c.
1
2
of 12
12
e. 27 – 6
27 – 3
f.
1
2
of 20
10
4. Fill in the missing numbers.
a.
14 – 8 =
d.
g.
17 –
b.
– 9 =6
e.
=9
h.
16 – 8 =
c.
– 8 =7
f.
=9
i.
18 –
17 – 8 =
– 4 =8
15 –
=6
5. Solve the word problems.
a. A baby slept four hours and woke up to eat. Then she slept another
two hours and woke up to eat. Then she slept three hours more and
ate again. Then she slept three hours until the morning.
How many hours did the baby sleep?
b. Mum needs 16 eggs to make cakes. The store sells eggs in cartons of 12.
How many cartons does she need to buy?
How many eggs will she have left over?
6. Find the missing numbers. You can also work backwards, starting from 70!
–10
100
–1
______
–5
______
–4
______
92
–2
______
–8
______
70
Mixed Revision, Chapters 1 - 3
1. Write the time.
a. _____ : ______
b. _____ : ______
c. _____ : ______
d. _____ : ______
2. Write the time that the clock shows, and the time 5 minutes later.
a.
b.
c.
d.
______ : ______
______ : ______
______ : ______
______ : ______
5 min.
later → ______ : ______
______ : ______
______ : ______
______ : ______
3. How many minutes pass? Subtract (or figure out the difference).
from
2:25
2:20
7:00
11:30
6:05
to
2:35
2:40
7:15
11:50
6:15
minutes
10 minutes
4. Amy shared 18 raisins and 12 almonds equally with her brother.
How many raisins did each child get?
How many almonds?
5. Write each number as a double of some other number.
a.
10 = ____ + ____
b.
16 = ____ + ____
93
c.
40 = ____ + ____
6. Fill in the missing numbers for this subtraction “journey”.
–2
–2
−5
−1
–5
−3
–2
−7
–3
80
7. Solve the problems.
a. Mary ate 20 strawberries and Nora ate half that many.
How many did Nora eat?
How many did the girls eat together?
b. Frank used half of his money to buy a toy car. Now he has $10 left.
How much money did he have at first?
c. Jane ate 10 strawberries more than what John ate.
John ate 12 strawberries. How many did Jane eat?
d. Beth is 30 years old, and Tara is 4 years old.
How many years older is Beth than Tara?
e. Amanda had 12 toy cars, and Jill had 10. Then Amanda got two more cars.
Now who has more cars?
How many more?
f. Jordan has $6 and Jacob has $7 more than Jordan.
How much money does Jacob have?
94
−10
Revision, Chapter 3
1. Here are the 20 addition facts with single-digit numbers where the sum is between 10
and 20. Connect the problems to the right answer.
5+6
4+8
6+8
11
6+6
12
4+7
6+7
9+4
6+9
15
8+8
16
7+8
17
9+8
7+7
13
3+9
3+8
14
8+5
2+9
5+7
7+9
18
9+9
5+9
2. Draw a line to connect the problems that are from the same fact family. You do not
need to write the answers.
13 – 7 =
12 – 5 =
15 – 7 =
7+
11 – 8 =
13 – 6 =
11 – 3 =
9+
5+
8+
15 – 8 =
17 – 8 =
14 – 5 =
6+
= 13
3+
7+
9+
= 14
= 15
= 17
= 12
= 17
= 14
= 11
+ 5 = 12
3. Find the difference...
a. ...between 80 and 87 ________
b. ...between 45 and 2 ________
c. ...between 15 and 8 ________
d. ...between 13 and 4 ________
95
4. Find the missing numbers.
a.
8+
= 15
b.
7+
= 14
d.
13 −
=5
e.
14 −
=8
g.
11 − 6 =
h.
12 − 7 =
c.
6+
= 13
f.
15 −
=9
i.
12 − 4 =
5. Find the missing steps.
–5
75
–5
______
–2
______
–3
______
–6
______
–3
______
51
6. a. You have an odd number of cookies and so does your friend. You put your cookies
together and share them. Can you share them evenly or not?
Cookies Cookies your Together
Can you
even/odd
you have friend has
we have
share evenly?
3
5
5
9
9
3
9
7
b. You have an odd number of cookies and your friend has an even number of cookies.
You put your cookies together and share them. Can you share them evenly or not?
Cookies Cookies your Together
Can you
even/odd
you have friend has
we have
share evenly?
5
6
7
8
9
4
1
12
96
7. Solve the puzzle. What happened to the teddy bear in the desert?
Key:
5+9 7+8
13 – 8 2 + 9 10 + 5
9+7
4+7
9+6
____ ____
____
____
____
____
7 + 7 13 – 6
19 – 4 11 + 5 13 – 7
3 + 13 11 – 5 13 – 4
6+9
____ ____
____
____
____
A
9
____
____
____
____
____
____
E I O G H T W N
6 14 11 5 16 15 8 7
8. Solve the word problems.
a. Josh has 13 tennis balls and Judy has 20.
How many more does Judy have than Josh?
b. Emily has three more flowers than Sheila. Emily
has 14 flowers. How many does Sheila have?
c. In a chess game, Paul has 2 more pawns than Oliver.
Oliver has five pawns. How many does Paul have?
d. You have $20, and you want to buy a doll that costs $28.
How many dollars do you still need to save?
Later, a neighbour pays you $2 for helping rake leaves.
How much more money do you need after that?
e. In a board game, you need to move 18 more spaces to get to the end
of the game. You roll 6 and 5 on two dice and move that many spaces.
Now how many more spaces are there to the end?
What kind of numbers on the two dice would get you to the end?
97
Chapter 4: Regrouping in Addition
Introduction
The fourth chapter of Math Mammoth Grade 2-A deals with addition within 0-100, both mentally and in
columns, especially concentrating on regrouping in addition (carrying).
Mental maths
Mental maths is important because it builds number sense. We study adding mentally a two-digit number
and a single-digit number where the answer goes to the next ten (problems such as 36 + 8 or 45 + 9).
These additions use the helping problem composed of the single-digit numbers (6 + 8 or 5 + 9). The
student knows that 6 + 8 fills the first ten and is four more than the ten. He/she will learn to use that fact
when adding 36 + 8. The sum 36 + 8 fills the next whole ten (40), and is four more than that, or 44.
Regrouping in tens
We also study adding two-digit numbers in columns, and regrouping with tens, or “carrying,” which is
illustrated and explained in detail with the help of visual models. These visual models take the place of
base-ten blocks or other manipulatives. You are welcome to use actual manipulatives if you prefer. The
main concept to understand is that 10 ones make a new ten, and this new ten is regrouped with the other
tens, written using a little “1” in the tens column.
In order to prepare for adding three or four two-digit numbers in columns, we practise explicitly how to
add 3 or 4 single-digit numbers, such as 7 + 8 + 6 + 4, and the principle of adding in parts (such as
13 + 16 is the same as 10 + 10 and 3 + 6).
The lessons also include lots of word problems, and occasional revision problems about doubling and
even and odd numbers.
The Lessons
page
span
Going Over to the Next Ten ................................................................ 101
3 pages
Add with Two-Digit Numbers Ending in 9 ........................................ 104
2 pages
Add a Two-Digit Number and a Single-Digit Number Mentally........ 106
2 pages
Regrouping with Tens ........................................................................
108
3 pages
Add in Columns Practice .................................................................... 111
3 pages
Mental Addition of Two-Digit Numbers ............................................ 114
3 pages
Adding Three or Four Numbers Mentally .......................................... 117
2 pages
Adding Three or Four Numbers in Columns....................................... 119
4 pages
Mixed Revision, Chapters 1 - 4 .......................................................... 123
2 pages
Revision, Chapter 4 ............................................................................
2 pages
98
125
Helpful Resources on the Internet
Use these free online resources to supplement the “bookwork” as you see fit.
Disclaimer: These links were valid as of the writing of this book, and to the best of our knowledge we
believe these websites to have what is described. However, we cannot guarantee that the links have not
changed. Parental supervision is recommended.
Number Pieces Manipulative
Drag ones, tens, and hundreds into the practise area to illustrate numbers.
http://www.mathlearningcenter.org/web-apps/number-pieces/
Hundred Hunt - Add 9
Practise adding 9 to the target number.
http://www.ictgames.com/100huntadd9.html
Addition Level 2
A matching game where you add a one-digit number and a two-digit number.
http://www.quia.com/mc/65798.html
Callum's Addition Pyramid
Add the pairs of numbers to get a number on the next level and finally the top number. Three difficulty
levels.
http://www.amblesideprimary.com/ambleweb/mentalmaths/pyramid.html
Techno Tortoise
Practise adding 2 two-digit numbers part-by-part by using a number line.
http://www.ictgames.com/technowithflock.html
Mr. Martini's Classroom: Addition and Subtraction Inequalities
Compare expressions that involve addition and subtraction of one and two-digit numbers.
http://www.thegreatmartinicompany.com/inequalities/number-comparison.html
and
http://www.thegreatmartinicompany.com/inequalities/add-subtract-comparison.html
Mathionare Addition Quiz
Answer increasingly more difficult addition questions (one and two-digit numbers), and win a million!
http://www.mathsisfun.com/games/mathionaire-addition-quiz.html
Speed Grid Addition
Find numbers on the grid that add up to the given number. This uses both single-digit and two-digit
numbers.
http://coolsciencelab.com/speed_grid_addition.html
Fruit Splat Addition
Add a two-digit number to a one-digit number with regrouping. Choose Level 5.
http://www.sheppardsoftware.com/mathgames/fruitshoot/fruitshoot_addition.htm
Adding Two Digits Concentration Game
Match each addition problem with the correct answer.
http://www.math-play.com/two-digit-addition-game/adding-two-digits-concentration.html
99
Canoe Puppies Addition
Answer the addition problems correctly to help your canoe win the race.
http://www.mathplayground.com/ASB_Canoe_Puppies.html
Addition Blocks
Combine blocks to make the target sum. How many numbers will it take?
http://www.mathplayground.com/addition_blocks.html
Drag-and-Drop Maths
Practise basic addition or subtraction. Choose 2 numbers, each with 2 digits.
http://mrnussbaum.com/drag-and-drop-math/
Rock Hopper
Help the frog get across the pond by clicking on the rocks that add up to or subtract to the target number.
http://www.eduplace.com/kids/mw/swfs/rockhopper_grade2.html
Mr. Martini's Classroom: Long Addition
Practise adding two-digit numbers in columns online.
http://www.thegreatmartinicompany.com/longarithmetic/longaddition.html
Teaching Treasures - Year 2 Maths Worksheets
Simple online addition and subtraction worksheets where the student types in the answer and can check
it. http://www.teachingtreasures.com.au/maths/maths_level2.html
100
Going Over to the Next Ten
Sums that go over to the next ten
Let's add 59 + 5 so that we first complete 60.
59 + 5
|
\
59 + 1 + 4
60 + 4 = 64
The 5 is broken into two parts: 1 and 4.
That is because 59 and 1 makes sixty.
Then, we have 60 and 4. We get 64.
9 and 1 make a ten.
We get 6 tens.
59 + 5 = 64
1. Circle ten little cubes to make a ten. Count the tens and ones. Write the answer.
a. 13 + 9 = ______
b. 15 + 8 = ______
c. 17 + 7 = ______
d. 24 + 7 = ______
e. 25 + 6 = ______
f. 37 + 9 = ______
g. 36 + 6 = ______
h. 48 + 4 = ______
i. 58 + 5 = ______
101
2. Complete. Break the second number into two parts so that you complete the next ten.
a.
28 + 8
b.
/
47 + 5
\
28 + 2 + ____
/
39 + 3
/
/
27 + 5
\
/
80 + ____ = ______
f.
38 + 7
\
/
39 + ____ + ____
27 + ____ + ____
40 + ____ = ______
______ + ____ = _____
\
79 + ____ + ____
50 + ____ = ______
e.
79 + 9
\
47 + 3 + ____
30 + ____ = ______
d.
c.
\
38 + ____ + ____
______ + ____ = _____
3. Write the additions that the number line pictures illustrate. Think how long each line is.
a.
____ + ____ = ________
b.
____ + ____ = ________
4. Show these additions on the number line by drawing two lines.
a. 19
+ 7 = _____
b. 14
+ 18 = _____
102
5. Solve the problems. Write a number sentence for each problem, not just the answer.
a. Benjamin wants to buy a kite that costs $30.
He has saved $22. How much more money
will he need?
b. Hope had already saved $20. She earned $5 by
selling eggs, and earned $5 more by selling fruit.
How much money does she have now?
c. Mum bought 28 fruit trees and has planted
eight of them. How many still need planted?
d. Thirty-seven people attended Uncle Sam's
50th birthday party. Thirty-two of them came
before noon. How many came after noon?
e. Dad bought a bunch of 40 grapes and ate half of them.
Then, little sister ate seven grapes. How many are left now?
6. Continue the patterns. COMPARE the columns, and NOTICE what is the same.
a.
b.
c.
9 + 1 = _______
39 +
1
= _______
59 + 1 = _______
9 + 2 = _______
39 +
2
= _______
59 + 2 = _______
9 + 3 = _______
39 +
3
= _______
59 + 3 = _______
9 + 4 = _______
39 +
4
= _______
59 + 4 = _______
9 + ____ = _______
39 + ____ = _______
59 + ____ = _______
9 + ____ = _______
39 + ____ = _______
59 + ____ = _______
103
Add with Two-Digit Numbers Ending in 9
Imagine that 29 wants to be 30...
so it “grabs” one from 5.
Then, 29 becomes 30, and 5 becomes 4.
The addition problem is changed to 30 + 4 = 34.
1. Circle the nine dots and one more dot to form a complete ten. Add.
a.
19 + 5 = ______
b.
29 + 7 = ______
c.
49 + 5 = ______
d.
29 + 8 = ______
e.
39 + 6 = ______
f.
49 + 9 = ______
2. Add. For each problem, write a helping problem using the “ones” from the first
problem.
a.
19 + 7 = _______
b.
49 + 3 = _______
9 + 7 = ______
____ + _____ = ______
c.
39 + 4 = _______
____ + _____ = ______
3. Add. Compare the problems.
a.
9 + 3 = ________
b.
19 + 3 = ________
d.
9 + 7 = ________
9 + 6 = ________
c.
39 + 6 = ________
e.
9 + 9 = ________
9 + 4 = ________
49 + 4 = ________
f.
9 + 5 = ________
39 + 7 = ________
69 + 9 = ________
19 + 5 = ________
29 + 7 = ________
79 + 9 = ________
59 + 5 = ________
104
4. These problems revise the basic facts with 9 and 8. By this time you should already
remember these addition facts. Try to remember what number will fit without counting.
c.
a.
b.
d.
9 + _____ = 14
4 + 9 = _____
8 + _____ = 15
7 + 8 = _____
9 + _____ = 15
8 + 9 = _____
8 + _____ = 17
8 + 8 = _____
9 + _____ = 13
2 + 9 = _____
8 + _____ = 12
5 + 8 = _____
9 + _____ = 18
5 + 9 = _____
8 + _____ = 14
6 + 8 = _____
9 + _____ = 12
6 + 9 = _____
8 + _____ = 13
3 + 8 = _____
9 + _____ = 17
9 + 9 = _____
8 + _____ = 18
9 + 8 = _____
9 + _____ = 16
7 + 9 = _____
8 + _____ = 16
4 + 8 = _____
5. Find the difference between numbers. The number line can help.
c. Difference between 59 and 48:
a. Difference between 41 and 53: _______
_______
b. Difference between 60 and 46: _______
6. Find the patterns and continue them!
0
b.
+
+
a.
1
+
_____
+
+
3
+
____
+
6
+
____
10
+
+
_____
_____
105
+
+
_____
_____
+
44
+
_____ _____
+
48
+
52
56
Add a Two-Digit and a Single-Digit Number Mentally
Imagine that 38 wants to be 40, so it “grabs” two from 7.
Then, 38 becomes 40, and 7 becomes 5.
The addition problem is changed to 40 + 5 = 45.
1. Circle the eight dots and two more dots to form a complete ten. Add.
a.
18 + 6 = ______
b.
28 + 7 = ______
c.
48 + 8 = ______
d.
38 + 4 = ______
e.
38 + 6 = ______
f.
48 + 5 = ______
2. Add. Think of the trick explained above.
a.
18 + 7 = _______
b.
38 + 6 = _______
c.
58 + 5 = _______
3. Add. Compare the problems. What is similar about the problems in each box?
a.
8 + 3 = _______
18 + 3 = _______
d.
8 + 2 = _______
b.
8 + 6 = _______
c.
38 + 6 = _______
e.
8 + 9 = _______
8 + 4 = _______
78 + 4 = _______
f.
8 + 5 = _______
38 + 2 = _______
68 + 9 = _______
18 + 5 = _______
28 + 2 = _______
78 + 9 = _______
58 + 5 = _______
106
When you add a two-digit number and a single-digit number, such as 45 + 6 or 77 + 4,
think of the “helping” problem: the addition with just the ones digits.
Example. 45 + 6
Example. 67 + 8
Think of the helping problem 5 + 6 = 11.
(Drop the 40 from 45, and you have 5 + 6.)
Think of the helping problem 7 + 8 = 15.
(Drop the 60 from 67, and you have 7 + 8.)
5 + 6 is ONE more than the next ten (11),
and 45 + 6 is also ONE more than the next
ten (51).
7 + 8 is FIVE more than the next ten (15),
and 67 + 8 is also FIVE more than the next
ten (75).
4. Add. Compare the problems! The top problem is a helping problem for the bottom one.
a.
7 + 6 = ________
b.
6 + 8 = ________
c.
7 + 7 = ________
27 + 6 = ________
76 + 8 = ________
87 + 7 = ________
(three more than the next ten)
(four more than the next ten)
(four more than the next ten)
d.
5 + 8 = ________
35 + 8 = ________
e.
6 + 9 = ________
26 + 9 = ________
f.
8 + 7 = ________
48 + 7 = ________
5. Fill in: To add 73 + 8, I can use the helping problem ___ + ___ = ______. Then since
the answer to that is ___ more than 10, the answer to 73 + 8 is ____ more than ______.
6. Add.
a.
34 + 8 = _______
b.
47 + 7 = _______
c. 59
+ 5 = _______
7. Solve the word problems.
a. Jenny needed 24 eggs to make omelettes for her family.
She already had 10 eggs. How many more does she need?
b. Jenny's large family eats a lot of potatoes. Dad bought a 25-kilogram
bag of potatoes. Now, only 5 kg are left. How many kilograms
of potatoes have they eaten?
107
Regrouping with Tens
tens
When adding 3 + 9, we can circle ten
little ones to form a ten. We write “1”
in the tens column.
ones
3
+
There are two little ones left over, so
we write “2” in the ones column.
With 35 + 8, we circle ten little ones
to make a ten. There already are three
tens, so in total we now have four tens.
So, we write “4” in the tens column.
9
1
2
tens
ones
3
5
+
8
There are three little cubes left over, so
we write “3” in the ones column.
4
3
1. Circle ten cubes to make a new ten. Count the tens, including the new one. Count the
ones. Write the tens and ones in their own columns. You can also use manipulatives.
a.
c.
e.
tens
ones
tens
ones
3
3
2
5
+
b.
9
+
8
tens
ones
tens
ones
3
8
2
7
+
d.
9
+
7
tens
ones
tens
ones
3
6
2
5
+ 1
8
+ 2
7
f.
108
When we make a new ten from the ones, we
are regrouping. The ten ones get grouped
as a ten, and are counted with the other tens.
tens ones
1
This is also called carrying to tens.
Imagine someone “gathering” ten little
cubes in his lap and “carrying” them over into the tens column as 1 ten.
3
+ 2
6
5
7
2
To show this new ten, write a little “1” in the tens column above the other numbers.
Then add in the tens-column as usual, adding the little “1” also.
2. Circle ten ones to make a new ten. Add the tens and ones in columns.
a.
tens
1
ones
tens
1
ones
1
3
2
4
+ 2
9
+ 3
8
b.
2
c.
tens
1
ones
tens
1
ones
3
5
2
4
+ 1
9
+ 4
7
d.
e.
f.
g.
h.
109
3. Add. If you can make a new ten from the ones, regroup.
a.
4 2
+ 1 5
b.
2 7
+ 4 5
c.
6 5
+ 2 6
d.
8 3
+ 1 5
e.
3 4
+ 1 9
f.
5 2
+ 4 1
g.
1 3
+ 4 4
h.
6 3
+ 2 7
i.
3 6
+ 5 1
j.
6 6
+ 2 9
1
We can add three numbers by writing them under each other.
This is not any more difficult than adding two numbers.
3
2
On the right, first add the ones. 2 + 7 + 5 = 14. You get a new
ten. So, regroup and write that new ten with the other tens.
2
7
+ 1
5
7
4
In the tens, add 1 + 3 + 2 + 1 = 7.
4. Add. Regroup the ones to make a new ten.
a.
3 4
1 9
+ 2 6
b.
1 5
2 7
+ 4 5
c.
1 3
2 7
+ 2 6
d.
2 6
4 2
+ 1 9
5. Show the additions on the number line by drawing lines that are that long.
a.
13 + 9 + 11 = _____
b.
27 + 16 = _____
110
e.
3 4
2 1
+ 1 9
Add in Columns Practice
1. Add in columns.
a.
9
+ 71
b.
24
+ 67
c.
55
+ 36
d.
45
+ 25
e.
38
+ 14
f.
34
9
+ 35
g.
25
42
+ 49
h.
58
30
+ 6
i.
29
44
+ 12
j.
16
14
+ 19
2. Write the numbers so that the ones and tens are in their own columns. Add.
a. 45 + 27
b. 8 + 56
c. 40 + 32
d. 25 + 45
e. 47 + 9
f. 6 + 31 + 25
g. 40 + 7 + 9
h. 46 + 8 + 20
i. 5 + 8 + 13
j. 5 + 4 + 57
111
Here we have more
than 10 tens.
Ten tens make
a hundred (100)!
Add the tens: 8 + 7 = 14 tens. The “1” of the 14 goes in the hundreds column,
and the “4” stays in the tens column. The answer 149 is read “one hundred forty-nine.”
Another example. Add the tens normally: 1 + 5 + 6 = 12 tens.
Then write the 12 so that the “1” is in the hundreds column,
and the “2” is in the tens column. The 12 tens make 1 hundred
and 2 tens.
The answer 123 is read “one hundred twenty-three.”
You will study more about hundreds later.
3. Add. You will have more than 10 tens.
a. 27 + 80
b. 95 + 47
c. Double 56
d. 62 + 84
4. Add.
b.
+
67
61
g.
+
65
18
26
a.
f.
c.
+
90
65
h.
+
74
7
45
d.
+
39
81
i.
+
68
47
32
112
e.
+
85
62
j.
+
12
88
49
+
29
94
+
8
50
79
5. Solve the word problems. You may need to add or subtract in columns.
a. Jerry worked for 27 hours this week.
Philip worked for 16 hours more than Jerry.
How many hours did Philip work?
b. Natalie read 29 books and Matthew read 16.
How many more books did Natalie read than
Matthew?
c. Mum put 13 red flowers and 11 blue flowers in one
vase. Then she put 22 flowers in another vase.
Which vase has more flowers? How many more?
d. Stan had saved $24 and his brother Tyrone had saved $41.
Then Stan earned $20. Now, who has more money?
How much more?
e. Ted bought a pencil case for $13, three
markers for $9, and a book for $21.
What was the total cost?
113
Mental Addition of Two-Digit Numbers
Example 1. Add in parts 40 + 55.
First break 55 into its tens and ones. 55 is 50 + 5.
So, 40 + 55 becomes 40 + 50 + 5.
Now add 40 and 50. You get 90. Then add the 5. You get 90 + 5 = ______.
Example 2. Add in parts 36 + 30.
First break 36 into tens and ones. 36 is 30 + 6.
So, 36 + 30 becomes 30 + 6 + 30.
Now add 30 and 30. That is 60. Then add the 6. You get 60 + 6 = _______.
1. Add in parts, breaking the second number into its tens and ones.
a.
20 + 34 = _______
70 + 18 = _______
b.
20 + ______ + ____
c.
70 + ______ + ____
50 + 27 = _______
50 + ______ + ____
2. Add in parts. Mentally break the number that is not whole tens into its tens and ones.
a.
17 + 10 = _______
b.
16 + 20 = _______
c.
50 + 14 = _______
26 + 10 = _______
34 + 30 = _______
60 + 23 = _______
42 + 10 = _______
67 + 20 = _______
30 + 45 = _______
3. Add mentally. We already studied these. The first one is the helping problem.
a.
b.
c.
d.
7 + 8 = ______
4 + 9 = ______
8 + 4 = ______
7 + 9 = ______
17 + 8 = ______
14 + 9 = ______
48 + 4 = ______
57 + 9 = ______
37 + 8 = ______
44 + 9 = ______
78 + 4 = ______
37 + 9 = ______
114
16 + 19
How can you easily add 16 + 19?
Think about it before you go on!
= 6 + 9 + 10 + 10
Here is the answer: again, add in parts.
= 15 + 10 + 10 = _____
Look at the example on the right.
4. Add in parts.
13 + 18
a.
b.
15 + 15
= ____ + ____ + 10 + 10
= ____ + ____ + 10 + 10
=
=
17 + 18
c.
d.
19 + 15
= ____ + ____ + 10 + 10
= ____ + ____ + 10 + 10
=
=
e.
18 + 12 = ______
f.
13 + 16 = ______
g.
16 + 17 = ______
h.
17 + 15 = ______
5. a. Lucy owns 13 cats. Five of her cats live in the house.
How many of her cats live outside?
b. Lucy’s cats eat 10 kg of cat food in a week. Lucy has two 2-kg
bags at home. How many more kilograms of cat food does she
need to have enough for one week?
6. Count by threes.
42, 45, _______, _______, _______, _______,_______, _______, _______
7. Find the pattern and continue it. This pattern “grows” at each step.
+
1
+
3
+
7
+
13
+
21
115
+
31
+
_____
+
_____ _____
Add two-digit numbers: Add the tens and ones separately
45 + 27
40 + 20 + 5 + 7
60 + 12 = 72
Add tens on their own.
Add ones on their own.
Lastly, add the two sums.
8. Add by adding tens and ones separately.
a.
36 + 22
30 + 20 + 6 + 2
b.
______ + ______ = _______
______ + ______ = _______
54 + 37
c.
50 + 30
72 + 18
70 + 10 + 2 + 8
24 + 55
d.
___ + ___ + __ + __
+ 4+7
_______ + _______ = _______
_______ + _______ = _______
f.
36 + 36
e.
42 + 68
___ + ___ + __ + __
_______ + _______ = _______
g. 45 + 18
h. 37 + 58
Figure out the missing numbers for these addition problems.
a.
b.
+ 1
4
4
1
c.
+
7
d.
e.
3
+ 2
5
+ 7
8
+ 2
6
1
5
1
9
1
6
1
116
Adding Three or Four Numbers Mentally
Perhaps add 8 and 8 first: Or perhaps add 8 and 6 first:
When you add three
numbers, you can add
8 + 8 +6
8+ 8 + 6
them in any order you
wish.
= 16 + 6 = ______
= 8 + 14 = ______
1. Add three numbers.
a.
8 + 8 + 8 = ______
b.
7 + 9 + 6 = ______
c.
5 + 8 + 9 = ______
d.
7 + 9 + 5 = ______
e.
8 + 6 + 4 = ______
f.
2 + 9 + 5 = ______
When you add four numbers, often it is easier
to add them in pairs: two numbers at a time.
Occasionally, some other
way of adding is easier.
Add 7 and 3.
Add 5 and 6:
Add the first two,
and the last two:
Double 8 makes 16,
then to that add 4:
7 +5+ 3 +6
6 + 9 +8+5
9+ 8 + 8 +4
= 10 + 11 = ______
= 15 + 13 = ______
= 16 + 4 + 9 = ______
2. Add four numbers. Look at the example.
a.
d.
8 + 8 +2+8
b.
7+5+5+6
c.
4+7+2+5
= 16 + 10
= ______ + ______
= ______ + ______
= 26
= ______
= ______
6+7+9+8
e.
8+5+2+6
f.
4+5+3+9
= ______ + ______
= ______ + ______
= ______ + ______
= ______
= ______
= ______
117
3. Practise adding three or four numbers.
a.
4 + 8 + 6 = ______
b.
4 + 9 + 5 + 6 = ______
c.
7 + 8 + 7 + 9 = ______
d.
9 + 9 + 5 = ______
e.
8 + 3 + 5 + 4 = ______
f.
2 + 6 + 6 + 5 = ______
g.
8 + 4 + 4 = ______
h.
9 + 2 + 4 + 6 = ______
i.
2 + 3 + 8 + 9 = ______
4. Mary took photos of her friends. She took eight photos
of Millie, nine photos of Charlotte, and eight of Erika.
How many photos did Mary take in total?
5. Greg has seven toy cars and Larry has nine. They put
their cars together. Can they share the cars evenly?
If yes, how many would each boy get?
6. Logan made 8 sand towers and Brad made 11. Can
the boys share the towers in a game they are playing?
If yes, how many would each boy get?
7. Add mentally. What would be the easiest order to add the numbers!
a.
30 + 2 + 40 + 8 = ________
c.
9 + 40 + 1 + 4 = ________
b.
50 + 4 + 10 + 7 = ________
d.
20 + 10 + 8 + 9 = ________
8. Compare the expressions and write < , > or = .
a.
c.
8+5+6
8+8+7+7
5+6+9
9+9+6+6
118
b.
54 + 8
53 + 9
d.
48 − 6
38 + 5
Adding Three or Four Numbers in Columns
Sometimes we get two or three new tens from the ones. We need to regroup.
In the ones, we add
8 + 7 + 8 = 23.
In the ones we add 9 + 9 + 7 + 6
= 18 + 13 = 31. We write three
new tens in the tens column.
2
4 8
2 7
+ 1 8
We write the two new
tens in the tens column.
Complete the problem.
3
3
1
2
+2
In the tens, we add
3 + 3 + 1 + 2 + 2 = 11. The
answer is more than one hundred.
It is 111 (one hundred and eleven).
3
9
9
7
6
111
1. Add mentally. Remember to first try to find if any of the numbers make 10.
a.
8 + 4 + 5 = ______
b.
3 + 8 + 7 = _______
c.
8 + 5 + 6 + 4 = _______
2. Add. The answers are “hidden” in the list of numbers below the problems.
a.
5 2
3 0
+ 1 1
b.
1 3
2 5
+ 5 4
c.
3 3
3 8
+ 2 7
d.
3 6
2 7
+ 1 9
e.
3
2
1
+ 1
6
7
8
6
f.
4
1
1
+ 2
0
8
6
2
g.
1
1
1
+ 3
5
7
8
9
h.
1
2
2
+ 1
1 9
6 9
+ 1 9
j.
5 6
3 2
+ 2 9
k.
4 5
5 5
+ 1 9
l.
i.
74
80
82
89
91
92
93
96
119
97
98
117
107
120
119
2
9
5
4
5 9
1 9
+ 4 2
122
3. Find the total cost.
a. Two dolls for $17 each;
b. Three action figures
roller-skates for $49.
d. A purse for $89, a
each; two pillows
for $19 each.
for $17 each.
e. Two pairs of shoes for
diary for $12, and
chocolate for $7.
a.
4. Find the errors
in these additions,
and correct them.
c. Two lamps for $24
$36 each, two sweaters
for $23 each.
f. A toy car for $19
and three watches
for $29 each.
b.
33
+ 48
711
55
+ 39
814
120
5. Solve the problems. You need to add or subtract.
a. One bus has 35 people on it, and another has 22.
How many more people does the first one have
than the second?
b. A bus had some people on it. Then, 13 more people
got on. Now there are 19 people on the bus.
How many were on the bus originally?
c. One bus can seat 40 people. There were already 33 people.
Is there room for nine more people?
Yes/No, because
d. One bus can seat 40 people.
How many buses do you need for 76 people?
How many buses do you need for 99 people?
e. A bus was full with 40 people, but then six people got off.
How many people are on the bus now?
f. A bus was full with 40 people. First it dropped off 3 people.
Then it dropped off seven more people. How many people
were left on the bus?
121
6. Add.
3
1
1
+ 2
a.
9
5
8
8
b.
3
4
1
+ 1
3
8
6
3
c.
1
3
2
+ 3
7
7
5
4
d.
5
1
1
+ 2
5
8
5
7
7. Are these numbers even or odd? Mark an “X”. If the number is even, write it as a double
of some number.
Number Even? Odd? As a double:
8
X
Number Even? Odd? As a double:
4+4
18
16
24
100
15
19
21
Skip-count from 25 (in the
middle) to the outer edge.
Each sector has a different
skip-counting pattern—
either by 2s, by 3s, by 4s,
by 5s, or by 10s.
122
Mixed Revision, Chapters 1 - 4
1. Find one-half and double of the given numbers.
a.
1
2
of 6 is ______.
b.
d. Double 6 is _______
1
2
of 10 is ______.
c.
e. Double 10 is _______
1
2
of 8 is ______.
f. Double 8 is _______
2. Find the number that goes into the shape.
a.
73 +
= 80
b. 78
+ 92 = 100
d.
+
= 98
– 20 = 5
e.
c. 96
–
= 56
– 50 = 41
f.
3. Draw a line to connect the problems that are from the same fact family.
(You do not need to solve them.)
13 – 8 =
13 – 6 =
15 – 6 =
6+
11 – 2 =
13 – 5 =
11 – 9 =
7+
5+
8+
15 – 9 =
15 – 8 =
11 – 5 =
5+
= 13
9+
7+
6+
= 11
= 15
= 15
= 13
= 15
= 11
= 11
+ 6 = 13
4. Subtract.
a.
b.
c.
d.
15 – 9 = _____
13 – 9 = _____
14 – 8 = _____
15 – 7 = _____
13 – 6 = _____
14 – 7 = _____
16 – 8 = _____
13 – 5 = _____
123
5. Write the time.
a. _____ : ______
b. _____ : ______
c. _____ : ______
d. _____ : ______
6. Write the time 10 minutes later than what the clocks show in the previous exercise.
a. _____ : ______
b. _____ : ______
c. _____ : ______
7. Solve the problems.
a. In a game, Karen got 14 points, Sam got double that many points,
and Adriana got 10 more points than Karen.
Who got the most points?
How many points was that?
b. You are 8 years old and your brother is double your age.
How many years older is your brother than you?
c. Susan got 7 points more in a game than Matthew.
Matthew got 31 points. How many points did Susan get?
d. One toy costs $26 and another costs $6 more than that.
How much does the other toy cost?
e. There were 7 more birds in the oak tree than in the elm tree.
The oak tree had 15 birds. How many birds were in the elm tree?
f. Erika has 12 markers and Tamara has 6. Together they share their
markers evenly. How many does each girl get?
124
d. _____ : ______
Revision, Chapter 4
1. Add in your head.
a.
17 + 10 = _______
b.
42 + 10 = _______
16 + 20 = _______
c.
67 + 20 = _______
50 + 14 = _______
30 + 45 = _______
2. Add.
a.
27 + 8 = _______
54 + 7 = _______
b.
18 + 9 = _______
c.
73 + 8 = _______
5 + 87 = _______
7 + 88 = _______
3. Add by adding tens and ones separately.
a.
36 + 22
30 + 20 + 6 + 2
b.
72 + 18
70 + 10 + 2 + 8
______ + ______ = _______
c.
54 + 37
______ + ______ = _______
24 + 55
d.
___ + ___ + __ + __
50 + 30 + 4 + 7
_______ + _______ = _______
_______ + _______ = _______
4. Solve the problems.
a. Dean and Sabrina picked fruit for Mr. Morris. Dean earned $25 and
Sabrina earned double that. How much did Sabrina earn?
How much did the two earn together?
b. Brenda has 24 flowering plants in her yard. Alana has half that many.
How many flowering plants does Alana have?
125
5. Add.
a.
4 3
+ 2 8
f.
b.
3 3
+ 3 9
g.
3 8
1 3
+ 4 2
c.
2 4
+ 4 7
h.
3 9
1 0
+ 4 6
d.
2 3
+ 3 8
i.
4 1
4 4
+ 3 6
3 8
7
4 9
+ 2 3
e.
5 5
+ 1 7
j.
2
3
1
+ 3
6. Solve.
a. Kendra bought some
potatoes for $18, onions
for $15, and meat for $40.
What was the total cost?
b. If you buy three
shirts for $34 each,
what is the total cost?
d. Andrew had $47 in his wallet. He earned $15 by selling
lemonade. Can he buy a remote-controlled toy car for $65?
If yes, how many dollars would he have left after buying it?
If no, how many more dollars would he need to buy it?
126
c. Dorothy has 29 stickers.
So does Jane. Polly has
22 and Jenny has 26.
How many stickers are
there in total?
7
6
9
5
Chapter 5: Geometry and Fractions
Introduction
The fifth chapter of Math Mammoth Grade 2-A covers geometry topics and an introduction to fractions.
In geometry, the emphasis is on exploring shapes. Students are supposed to recognize and draw basic
shapes, and identify triangles, rectangles, squares, quadrilaterals, pentagons, hexagons, and cubes.
Drawing is done by first drawing dots on paper, then connecting those with a ruler.
We also study some geometric patterns, have surprises with pentagons and hexagons, and make shapes in
a tangram-like game. These topics are to provide some fun while also letting students explore geometry
and helping them to memorise the terminology for basic shapes.
In the section on fractions, the student divides some basic shapes into halves, thirds, and fourths
(quarters). They also learn the common notation for fractions (such as 1/3) and colour parts to show a
given fraction. We also study comparing fractions using visual models.
The Lessons
page
span
Shapes Revision ..............................................
130
3 pages
Surprises with Shapes .....................................
133
2 pages
Rectangles and Squares ..................................
135
3 pages
Making Shapes ...............................................
138
1 page
Geometric Patterns .........................................
141
2 pages
Solids ..............................................................
143
2 pages
Printable Shapes .............................................
145
4 pages
Some Fractions...............................................
153
3 pages
Comparing Fractions ......................................
156
2 pages
Mixed Revision, Chapters 1 - 5 ......................
158
2 pages
Revision, Chapter 5 ........................................
160
2 pages
127
Helpful Resources on the Internet
Use these free online resources to supplement the “bookwork” as you see fit.
Disclaimer: These links were valid as of the writing of this book, and to the best of our knowledge we
believe these websites to have what is described. However, we cannot guarantee that the links have not
changed. Parental supervision is recommended.
SHAPES
Shifting Shapes
Figure out what shape it is when viewing through a small opening! Click on the “eye” button to see it in
its entirety.
http://www.ictgames.com/YRshape.html
Polygon Matching Game
http://www.mathplayground.com/matching_shapes.html
Polygon Playground
Drag various colourful polygons to the work area to make your own creations!
http://mathcats.com/explore/polygons.html
Shapes Splat
Click on the correct shapes to earn points. This game can be played with basic shapes or 3-D shapes.
http://www.sheppardsoftware.com/mathgames/earlymath/shapes_shoot.htm
Shapes Identification Quiz from ThatQuiz.org
An online quiz in a multiple-choice format, asking to identify common two-dimensional shapes. You can
modify the quiz parameters to your liking.
http://www.thatquiz.org/tq-f/math/shapes/
Patch Tool
An online activity where the student designs a pattern using geometric shapes.
http://illuminations.nctm.org/ActivityDetail.aspx?ID=27
Shape Cutter
Draw any shape (polygon), cut it, and manipulate the cut pieces. You can have the computer mix them
up, and then try to recreate the original shape.
http://illuminations.nctm.org/ActivityDetail.aspx?ID=72
Construct It
Transform the grey background into a colourful mosaic.
http://www.mathplayground.com/logic_construct_it.html
Pattern Blocks
Have fun making patterns with colourful shapes!
http://www.mathplayground.com/patternblocks.html
Building Blocks
Drag the shapes to complete the figure in the middle.
http://www.mathplayground.com/buildingblocks.html
128
3-D Shapes Ice Cream Attack
Help keep Officer Ice Cream from melting by correctly identifying the 3-D shapes.
https://www.education.com/game/3d-shapes-ice-cream-attack/
Tangram Puzzles for Kids
Use the seven pieces of the Tangram to form the given puzzle. Complete the puzzle by moving and
rotating the seven shapes.
http://www.abcya.com/tangrams.htm
Logic Tangram game
Note: this uses four pieces only. Use logic and spatial reasoning skills to assemble the four pieces into the
given shape.
http://www.mathplayground.com/tangrams.html
FRACTIONS
Who Wants Pizza?
Lessons and interactive exercises about fractions, based on the pizza model.
http://math.rice.edu/~lanius/fractions/frac.html
Matching Fractions Level 1
Match each fraction to its visual model.
http://www.sheppardsoftware.com/mathgames/fractions/memory_fractions1.htm
Fractions Splat
Four levels: (1) Identify equal or unequal parts; (2) Identify shapes that are divided into halves, thirds,
and fourths; (3) and (4) Find the visual model that matches the given fraction.
http://www.sheppardsoftware.com/mathgames/earlymath/fractions_shoot.htm
Concentration from Illuminations
A matching game you can play by yourself or against a friend, matching fractions to equivalent visual
representations. (The game also allows you to play a matching game with whole numbers, shapes, or
multiplication facts.) Also available for your phone or tablet.
http://illuminations.nctm.org/Activity.aspx?id=3563
Fraction Frenzy 4
Choose the pizza picture that matches the fraction shown using the four arrow keys.
http://www.mathwarehouse.com/games/our-games/fraction-games/fraction-frenzy-4/
Fractions Side by Side
Compare two fractions to see if one is larger or if they are the same. Try the different graphics to see
them in different ways.
http://www.bbc.co.uk/skillswise/game/ma17frac-game-fractions-side-by-side
Compare Fractions
Visualise and compare the fraction of the filled circles. Determine if they are less than, greater than, or
equal.
http://www.mathgames.com/skill/1.12-compare-fractions-same-numerator-or-denominator
129
Shapes Revision
1. Draw three dots on the right.
Connect the dots with straight
lines. You have drawn a triangle
(tri means three).
It has _____ vertices (corners)
and three sides.
Draw yet two more triangles in the
same space. They can overlap.
2. Draw FOUR dots on the right.
Connect the dots with straight lines.
You have drawn a quadrilateral
(quadri means four; lateral has to do with sides).
It has ______ vertices (corners)
and four sides.
Draw two more quadrilaterals in
the same space.
3. The figures on the right are a square and
a rectangle. Can you tell which is which?
Squares and rectangles are
quadrilaterals because they have
four sides.
Draw at least one more square and one
more rectangle into the picture, the best
you can.
130
4. Draw FIVE dots on the right.
Connect the dots with straight lines.
You have drawn a pentagon
(penta means five).
It has _____ vertices and _____ sides.
Draw yet one more pentagon in the space.
5. Draw SIX dots on the right. Connect
the dots with straight lines.
You have drawn a hexagon (hex means six).
It has _______ vertices and _____ sides.
Draw yet one more hexagon in the space.
6. How is a circle different from all of the shapes above?
7. Continue the pattern, and colour it with pretty colours!
8. Colour all triangles yellow.
Colour all quadrilaterals green.
Colour all pentagons blue.
Colour all hexagons purple.
Or choose your own colours
for each kind of shape.
131
9. Now, this is a challenge to check if you remember the words for different shapes.
Do not look at the previous pages! You can use the “dot” method: first draw dots
for the corners, then use a ruler to draw the lines connecting the dots.
a. Draw a big and a small four-sided shape. What are four-sided shapes called?
b. Draw a skinny and a fat three-sided shape. What are three-sided shapes called?
c. Draw a blue five-sided shape and a green six-sided shape. What are five and six-
sided shapes called?
132
Surprises with Shapes
1. Connect the dots using a ruler.
Be neat! What shape do you get?
_______________________________
2. Draw a line from one corner to
some other corner. This divides
your shape into two new shapes.
What shapes are they?
_______________________________
3. Draw more lines from a corner
to some corner so that the whole
shape gets divided into triangles.
4. Connect the dots using a ruler.
Be neat! What shape do you get?
_______________________________
5. Draw a line from one corner to the
opposite corner. Then repeat so that
each corner gets connected to the
opposite corner. You need to draw
three lines to do that.
6. Decorate your shape now so that
it becomes a SNOWFLAKE!
ALL snowflakes have this basic
shape.
133
7. Connect the dots in the numbered
order using straight lines.
Be neat! What do you get?
_______________________________
8. In the middle of that shape,
another shape is formed.
What is it?
_______________________________
9. Also connect the dots in the order
1 - 4 - 2 - 5 - 3 - 1. What shape is
formed now?
_______________________________
10. Connect the dots 1-2-3 using a
ruler. Then connect the dots
a-b-c also. Be neat!
What shape do you get?
_______________________________
11. In the middle of that shape,
another shape is formed.
What is it?
_______________________________
12. Also connect the dots in the
order 1 - a - 2 - b - 3 - c - 1.
What shape is formed now?
_______________________________
134
Rectangles and Squares
1. Continue these patterns that use rectangles and squares.
a.
b.
c.
d.
Make your own patterns here!
135
Jack counted how many little squares were inside of this
rectangle. There were 12 little squares.
2. Now you do the same. Count how many little squares are inside of each rectangle.
a.
b.
c.
______ little squares
______ little squares
______ little squares
3. Draw rectangles so they have a certain number of little squares inside. Guess and check!
a.
b.
10 little squares
15 little squares
c.
d.
8 little squares
Can you make two different ones?
12 little squares
Can you make two different ones?
136
4. Here is a pattern where several squares are inside of each other. Continue the pattern.
Use pretty colours.
5. Design your own pattern, where you start with a small rectangle in the middle, then
draw bigger ones around it as in the pattern above.
137
Making Shapes
We can make new shapes by putting several shapes together.
For example, these two triangles together form a square:
1. Cut out the shapes on the next page. What shapes can you use to make the given
shapes? There may be several possible
solutions. The figures below are smaller
than the ones you will cut out.
a.
b.
c.
d.
e.
f.
2. Now, you do the same. Put some shapes together. Trace the outline of your combined
shape on paper, and give that to a friend to solve.
3. The game you just played is very similar to the ancient Chinese puzzle called Tangram.
Play an interactive tangram game online at
http://nlvm.usu.edu/en/nav/frames_asid_112_g_2_t_1.html or
http://www.abcya.com/tangrams.htm
138
139
(This page left intentionally blank.)
140
Geometric Patterns
1. The design below is often seen on Greek vases. Continue it.
2. This is a pattern from an apron used by Kirdi people in Cameroon, Africa. Notice it
uses PARALLELOGRAMS that are inside each other. Continue the colouring in the
pattern. (G = green, R = red, B = blue, W = white, Or = orange, Y = yellow)
141
3. This is a geometric design found on a Greek vase.
a. What two shapes are used in this design?
_______________________________ and _________________________________
b. Copy the design at least once in the empty shapes.
142
Solids
This is a box. It is
also called a
“rectangular prism.”
A cube is a box, too,
but all of its sides
are equal in length.
A pyramid has a pointed top. Its bottom
shape can be any many-sided figure, such as
a triangle, a rectangle, a square, or a pentagon.
A cylinder has a
circle at the top
and the bottom.
This is a
sphere, or
just a ball.
A cone has a pointed top,
as well, but it has a rounded
shape on the bottom.
1. Make a cube, a cylinder, a cone, and a pyramid using the cut-outs on the following
pages. Your teacher will help you.
2. A face is any of the flat sides of a solid.
a. Count how many faces a cube has.
_________ faces
What shapes are they?
b. Count how many faces a box has.
_________ faces
What shapes are they?
c. Count how many faces this pyramid has.
What shapes are they?
143
_________ faces
3. You might have seen safety cones on the street. They are used to
mark off areas where people are not supposed to go. Can you think
of other things in real life that are in the shape of a cone, or a part
of them is a cone?
_____________________________________________________
_____________________________________________________
(Hint: One thing that is cone-shaped tastes really yummy!)
(Hint: Another thing you might see at birthday parties.)
4. Label the pictures with box, cube, cylinder, pyramid, or cone.
a.
_________________________
b.
_________________________
d.
_________________________
e.
j.
_________________________
_________________________
f.
_________________________
g.
_________________________
c.
_________________________
h.
i.
_________________________
k.
_________________________
l.
_________________________
144
_________________________
Cube Cut-out
145
[This page is intentionally left blank.]
146
Cone Cut-out
147
[This page is intentionally left blank.]
148
Cylinder Cut-out
It might be easier to use a toilet paper roll as a model for a cylinder than to cut and glue/tape this cut-out
together. However, putting this together will help the student to understand that the “body” of the
cylinder is in the shape of a rectangle.
149
[This page is intentionally left blank.]
150
Square Pyramid Cut-out
151
[This page is intentionally left blank.]
152
Some Fractions
We will now divide shapes into EQUAL parts = parts that are the same size.
When we divide something into TWO equal parts, the parts are called halves.
When we divide something into THREE equal parts, the parts are called thirds.
When we divide something into FOUR equal parts, the parts are fourths or quarters.
Here, two halves of the square
Here, one-half of the square
2
are coloured. We write 2 or 2/2.
1
is coloured. We write 2 or 1/2.
This is the same as 1 (one whole).
Now, four quarters of the circle
Here, one-third of the square
4
or 4/4.
4
This is the same as 1 (one whole).
are coloured. We write
1
is coloured. We write 3 or 1/3.
In a fraction, we use two numbers, one on the top and one on the bottom.
Two-thirds of the square is coloured.
One-fourth of the pie is coloured.
how many parts coloured
how many equal parts
→ 1
→ 4
how many parts coloured
how many equal parts
→ 2
→ 3
1. Divide these shapes. Then colour as you are asked to.
a.
Divide this into
halves. Colour
b.
1
2
Divide this into
.
thirds. Colour
e.
Divide this into
quarters. Colour
c.
1
3
Divide this into
.
f.
4
4
thirds. Colour
2
2
Divide this into
.
g.
Divide this into
.
halves. Colour
d.
2
3
Divide this into
.
153
fourths. Colour
fourths. Colour
2
4
.
h.
1
4
Divide this into
.
halves. Colour
2
2
.
1
Jack divided the square into fourths, and then coloured 4 of it.
Notice: the whole rectangle has 16 little squares inside of it.
The fourth that Jack coloured has 4 little squares inside of it.
2. Complete.
a.
b.
1
Divide this into halves. Colour
2
Divide this into halves. Colour
______ little squares in one-half
______ little squares in one-half
_____ little squares in the whole rectangle
_____ little squares in the whole rectangle
c.
1
2
d.
1
Divide this into fourths. Colour 4
Divide this into fourths. Colour 4
1
______ little squares in one-fourth
______ little squares in one-fourth
_____ little squares in the whole rectangle
_____ little squares in the whole rectangle
e.
f.
3
2
Divide this into fourths. Colour 4
Divide this into thirds. Colour 3
______ little squares in three-fourths
______ little squares in one-third
_____ little squares in the whole rectangle
_____ little squares in the whole rectangle
154
Mary divided a rectangle into
Judy divided a rectangle into quarters
1
quarters one way, and then coloured 4 .
another way, and then coloured 4 .
1
Which one is MORE? Well, they are both one-fourth! So, they are equal.
THINK: If you had a chocolate bar cut into quarters Mary's way or Judy's
way, and you got 1/4, either way you would get to eat the same amount.
3. The dots show you how to divide the shape. Divide it, then colour.
a. Colour
1
2
b. Colour
1
2
c. Colour
Which is more?
c. Colour
3
4
1
2
d. Colour
Which is more?
d. Colour
3
4
a. Colour
Which is more?
1
3
b. Colour
Which is more?
4. Tell what fraction is coloured.
a.
1
2
b.
c.
155
d.
1
3
Comparing Fractions
1. Colour the whole shape. Write 1 whole as a fraction. Then, read what you wrote
with numbers.
1=
1=
a.
b.
“One whole is 3 thirds.”
1=
1=
c.
d.
2. Colour. Then compare and write < , > or = . Which is more “pie” to eat?
a.
b.
1
3
1
2
2
4
1
2
2
3
3
4
1 whole
2
2
c.
e.
d.
1 whole
3
4
1
2
2
3
f.
3. Divide the shapes into two, three, or four equal parts so that you can colour the fraction.
Then compare and write < , > or = .
a.
b.
1
4
1
2
2
2
156
3
3
More fractions
When we divide something into FIVE equal parts, the parts are called fifths.
When we divide something into SIX equal parts, the parts are called sixths.
Here, five-sixths of the square
Here, two fifths of the circle
is coloured. We write 6 or 5/6.
are coloured. We write 5 or 2/5.
5
2
4. Colour the given fraction.
a. Colour
4
5
b. Colour
2
5
5
6
c. Colour
d. Colour
1
6
5. Colour. Then compare and write < , > or = . Which is more “pie” to eat?
a.
b.
1
5
1
6
d.
c.
3
4
3
5
e.
2
5
1
2
4
6
2
3
1
5
1
4
f.
3
6
1
2
6. Divide the shapes into two, three, or four equal parts so that you can colour the fraction.
Then compare and write < , > or = .
b.
a.
1
2
2
3
1
4
157
3
4
Mixed Revision, Chapters 1 - 5
1. Find the differences...
a. ...between100 and 95 ________
b. ...between 40 and 20 ________
c. ...between 16 and 8
d. ...between 56 and 4 ________
________
2. Subtract. Think of the difference.
a.
25 − 22 = ______
b.
76 − 71 = ______
c.
51 − 49 = ______
3. Find the missing numbers.
a.
14 −
d.
=5
b.
−6=6
e.
13 −
=8
c.
−7=4
f.
16 −
=9
−4=9
4. Add. Compare the problems.
a.
8 + 3 = ________
b.
18 + 3 = ________
d.
46 + 7 = ________
6 + 6 = ________
c.
86 + 6 = ________
e.
8 + 7 = ________
48 + 7 = ________
47 + 9 = ________
f.
88 + 5 = ________
5. Add. Regroup the ones to make a new ten.
a.
b.
6 4
1 5
+2 5
c.
4 7
2 7
+2 3
d.
1 3
5 6
+2 6
158
1
2
4
+1
5
6
7
9
e.
2 7
9
3 5
+2 5
6. Find the total cost of the items.
a.
b.
Perfume, $38
Lotion, $9
Shampoo, $8
A pair of pants, $79
A shirt, $22
A tie, $11
c.
Three puzzles,
$29 each
7. Add four numbers. Look at the example.
a.
8+ 8+2+8
b. 9
+5+5+8
c. 6
+7+3+5
= 16 + 10
= ______ + ______
= ______ + ______
= 26
= ______
= ______
d. 7
+7+8+8
= ______
e.
9+4+4+7
= ______
f.
6+4+4+9
= ______
8. Solve the problems. You need to add or subtract.
a. One book costs $78,
and another costs
$23 more than the
first. Find the price
of the second book.
b. One necklace costs $29
and another costs $15.
How much more does
the first necklace cost
than the other?
159
c. You bought both
necklaces in
problem (b).
How much did
they cost together?
Revision, Chapter 5
1. Connect the dots. Use a ruler!
What shape do you get?
______________________________
2. Choose one corner of your shape.
Now draw a line (with a ruler)
from that corner to some other
corner so that you will divide the
shape into a triangle and a pentagon.
3. Draw a square in the grid that
has 4 little squares inside.
4. Draw a rectangle in the grid that
has 18 little squares inside.
5. What is this shape called? ______________________________
How many faces does it have? _______
What shape are the faces? ______________________________
160
6. Sarah put together these two triangles. What new shape did she get?
→←
7. Label the pictures as box, cylinder, pyramid, or cone.
a.
b.
_________________________
c.
_________________________
_________________________
8. Colour the whole shape. Then write 1 whole as a fraction. Lastly, read what you wrote
with numbers.
1=
1=
a.
b.
9. Divide the shapes into two, three, or four equal parts so that you can colour the fraction.
c.
a.
d.
b.
2
4
1
3
2
3
2
2
10. Colour. Then compare and write < , > or = . Which is more “pie” to eat?
a.
c.
b.
1
3
1
2
2
3
3
4
161
1 whole
3
4