YEAR
6
MATHS
COPYRIGHT
The Ministry of Education owns the copyright to this Year 7 Mathematics Textbook. Schools may reproduce this in part or in full for
classroom purposes only. Acknowledgement of the CDU Section of the Ministry of Education copyright must be included on any
reproductions. Any other use of these textbook must be referred to the Permanent Secretary for Education through the Director
Curriculum Advisory Services.
Issued free to schools by the Ministry of Education.
Revised Version 2014
© Ministry of Education, Fiji, 2014
Ministry of Education
Waisomo House
Private Mail Bag
Suva
Fiji
2
YEAR
6
MATHS
ACKNOWLEDGEMENT
This Year 7 Mathematics Activity book has been produced by the Curriculum Advisory Service Unit.
The following officers as Mathematics workgroup are acknowledged for their contributions in the development
of the Activity book.
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Mr. Josefa Mebaniyaubula – St Thomas Aquinas Primary School
Mr. Johnson Rura – Lomaivuna Primary School
Ms. Arun Kaur – Arya Samaj Primary School
Mrs. Akisi Bolabola – Assemblies of God Primary School
Mr. Jope Ravolaca – SSM Primary School
Mrs. Loraini Ravoka – Dudley Intermediate Primary School
Mr. Aminisitai Dakuna – Suva Methodist Primary School
Mr. Ratu Mara Soqeta – Namalata Primary School
Mr. Maciu Kuricava – Deenbandoo Primary School
Mr. Savenaca Valesu – John Wesley Primary School
Mrs. Vika Kurisaqila – Suva Primary School
Mr. John Nute – Yat Sen Primary School
Mrs.Ulamila Moceituba – Saint Agnes Primary School
Mrs. Sereseini L. Lala – Suva Methodist Primary School
Mrs. Daxa Kapadia – MGM Primary School
Mrs. Miriama Cavu – CMF Primary School
Mr. Osea Savu – Saint Thomas Aquinas Primary School
Mr. Ilaitia Matanababa – Vatuwaqa Primary School
Mr. Anal A. Raj – Veiuto Primary School
Mrs. Anareta Bolaivuna – CDU
Mr. Esekaia Kotoisuva - CDU
3
YEAR
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MATHS
TABLE OF CONTENTS
TOPIC
PAGE
Strand 1
Number and Numeration
5
Strand 2
Algebra
42
Strand 3
Measurement
47
Strand 4
Geometry
72
Strand 5
Chance and Data
84
4
YEAR
6
MATHS
STRAND 1:
NUMBER
AND
NUMERATION
5
YEAR
6
MATHS
6
YEAR
6
MATHS
STRAND M1: NUMBER AND NUMERATIONS
SUBSTRAND M1.1 WHOLE NUMBERS AND OPERATIONS
Achievement Indicator: Identify and write numbers up to 6 digits
Read and write these numerals in
Solution - twenty-three thousand, four
words.
hundred and six.
Example: 23, 406
1. Read and write these numerals in words:
a. 23, 567________________________________________________________________
b. 652,190 ________________________________________________________________
c. 130, 911 ________________________________________________________________
d. 965, 040 ________________________________________________________________
Read and write these numbers in numerals
Solution 72,607
Example:
seventy-two thousand, six hundred and seven
2. Read and write these numbers in numerals;
a. Three hundred and six thousand and seventeen -______________________
b. Nine hundred and twenty-two thousand and four- ______________________
c. Thirty thousand, one hundred and twelve- ___________________
d. Nine hundred and sixty thousand, two hundred and twenty-two- _________________
Example: Write this number in
Solution: 796,421=700000+90000+6000+400+20+1
expanded form. 796,421
3. Write these numbers in expanded form.
a. 786,132 =_____________+ ____________ + __________ + _______ + ____ +___
b. 637,895= _____________+ ____________ + __________ + _______ + ____ +___
c. 465,312= _____________+ ____________ + __________ + _______ + ____ +___
d. 439,780= _____________+ ____________ + __________ + _______ + ____ +___
7
YEAR
6
MATHS
Achievement Indicator: To write prime factors and composite numbers up to 100
Example: Write the prime factors of 99
Solution: so the prime factors of 99 are:
Since 99 is odd number, start dividing it by 3 x 3 x 11
prime number 3.
99
3
Working: 99 ÷ 3 = 33
33
3
11
33 ÷ 3 = 11
To find the prime factors of a number, you divide the number by the smallest possible prime
number and work up the list of prime numbers until the result is itself a prime number.
Write the prime factors of each of the numbers:
a. 4
……………………………………………………………………….
b. 12
……………………………………………………………………….
c. 18
……………………………………………………………………….
d. 68
……………………………………………………………………….
e. 100
……………………………………………………………………….
A composite number is any number that has more than two factors.
Example: Write all the composite
Solution: 4,6,8,9,10,12,14,15,16,18,20
numbers up to 20.
1. Write all the composite numbers between 21 and 30:
----------------------------------------------------------------------------------------------------------------------------2. Write all the composite numbers between 32 and 40:
___________________________________________________________________________________
8
YEAR
6
MATHS
Achievement Indicator: To round off numbers to the nearest thousands and hundred thousands
Rules For Rounding Numbers
Numbers can be rounded to the nearest thousand, the nearest ten thousand, and the nearest
hundred thousand and so on. If the number you are rounding is followed by 5, 6, 7, 8, or 9,
round the number up. Example: 386,479 rounded to the nearest hundred thousand is
400,000. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number
down. Example: 74139 rounded to the nearest ten thousand is 70,000. All the numbers to the
right of the place you are rounding to become zeros.
1. Underline the number in each line which is nearest in value to the given number in bold print:
a. 5,736
700
5,000
6,000
7,000
b. 24,560
26,000
23,000
25,000
24,000
c. 384,505
38,000
380,000
400,000
84,000
d. 153,489
200,000
100,000
150,000
15,000
Achievement Indicator: Expressing numbers in ascending and descending orders
Example: Write this set of numbers in ascending order.
42,537
47,235
72,543
37,452
54,723
37,452
Example: Write this set of numbers in descending order.
42,537
47,235
72,543
37,452
Solution:
42,537
47,235
54,723
72,543
72,543, 54,723, 47,235,
42,53,
37,452
Solution:
54,723
2. Write each set of numbers in ascending order.
a.
b.
30,378
73,830
_______
_______
510,871
108,752
_______
_______
80,337
80,733
_______
_______
705,184
817,053
_______
_______
33,708
_______
758,102
_______
3. Write each set of numbers in descending order
a.
b.
683,216
642,136
651,336
673,126
_______
________
________
496,878
485,879
486,798
485,978
_______
________
________
________
________
9
653,621
________
487,689
________
YEAR
6
MATHS
Achievement Indicator: Explain properties of sets, unions, intersections, null or empty and equivalent
sets and Venn diagrams cardinal numbers, unions
SETS
Use the Venn diagrams to answer the questions
A
B
C
1
2
6
3
7
8
9
10
5
4
1. The elements of set A are …………………………………………….
2. There are ……… members in set A.
3. {3, 6, 7, 8, 9, 10} are elements of set ………….. .
4. Set B has a number property of …………. .
5. Set AUB = {……,…………………………………………………………}
6. Set A∩B = {……………..}
7. Sets A and B both have …………….members each; this means they are also called
……………………………… sets.
8. There are ……………..members in set C.
9. Set C is a …………….set or empty set.
10. We write a null set as ………………….. .
11. Write a set of Whole numbers less than 15. {…………………………………………………. }
12. Describe this set O = {1, 3, 5, 7, 9,…} A set of ………numbers than 11.
13.
E
Set E is a set of ………..numbers less than 18.
2 4 6
2
8
10
12 14 16
10
YEAR
6
MATHS
Achievement Indicator: Add and subtract six digits using place values
ADDITION AND SUBTRACTION
Example: Add these numbers.
11
298,298 + 627,489 =
Solution:
11
298, 298
When the sum is ten or more,
carry 1 to the next place value on
the left.
+ 627, 489
925, 787
1. Add these numbers to find their answers.
a. 525
b. 4,566
c. 71,432
d. 549,584
e. 4,261,345
+ 468
+ 3,236
+ 25,918
+ 657,549
+ 2,746,855
_____
______
______
_______
________
Example: Subtract this numbers.
Solution:
7,064 ─ 4,039 =
Subtracting a bigger digit from a
smaller digit, borrow 1 from next
bigger value and add 10 to the
smaller digit
7,05614
─ 4, 0 3 9
3, 0 2 5
2. Work out the differences.
a. 342
b. 5,644
c. 37,657
d. 813,782
e. 624,952
─ 126
─2,327
─13,548
─302,579
─515,798
_____
______
_______
________
________
11
YEAR
6
MATHS
Achievement Indicator: Show commutative and associative properties
COMMUTATIVE LAWS
The "Commutative Laws" we can swap numbers over and still get the same answer...
... when we add:
a+b=b+a
6+4=4+6
Or when we multiply;
(a × b) × c = a × (b × c)
(2 x 4) x 5 = 2 x (4 x 5)
1. Show commutative properties for addition and multiplication
a.
6+7=
b. 12 + 6 =
c.
8x(7x5)=
d. (12 x 4 ) x 9 =
ASSOCIATIVE LAWS
The "Associative Laws" say that it doesn't matter how we group the numbers (i.e. which we calculate first)...
... when we add:
(a + b) + c = a + (b + c)
(6 + 4) + 5 = 6 + (4 + 5)
... or when we multiply:
(a × b) × c = a × (b × c)
Examples:
This:
(2 + 4) + 5 = 6 + 5 = 11
Has the same answer as this: 2 + (4 + 5) = 2 + 9 = 11
This:
(3 × 4) × 5 = 12 × 5 = 60
Has the same answer as this: 3 × (4 × 5) = 3 × 20 = 60
12
YEAR
6
MATHS
Achievement Indicator: To multiply two to six digits by two digits
MULTIPLICATION
Example1: Find the product of 32 and 44.
Another
Solution1: (30 +2) x (40 + 4)
Solution
=(30 x 40) + (30 x 4) + (2 x 40) + (2 x 4)
=(1200 + 120 + 80 +8)
=(1408)
Example 2. Multiply 345 by 65.
Solution: 345 x 65
=(300+40+5) x (60+5)
=(300x60)+(300x5)+(40x60)+(40x5)+(5x60)+(5x5)
=(18,000+1,500+2,400+200+300+25)
=22425
Example 3. Multiply 7456 by 49.
Solution: 7,456 x 49= (6 x 9) =
54
Example 4: Multiply 378,912 by 64.
=
(6 x 40)=
240
Solution: 378,912 x 64 = 378,912
=
(50 x 9)=
450
=
(50 x 40)=
2,000
=(378,912 x 4) =
1,515,648
=
(400 x 9) =
3,600
=(378,912 x60)=
+ 22,734,720
=
(400 x 40)= 16,000
X
64
24,250,368
= (7,000 x 9)= 63,000
=(7,000 x 40)= 280,000 +
365,344
13
YEAR
6
MATHS
MULTIPLICATION
1. Multiply these numbers .
a. 34
b. 74
c. 345
d. 287
e. 62453
f. 42546
X 24
x 46
x 35
x 64
x
.........
…….
………
……..
…………
……….
………….
………….
+ ………
+…….
+……….
+……..
+………...
+……….
+ ………….
+………….
______
_____
_______
______
________
_______
________
_________
35
x
23
g. 358374
h. 413675
x
x
32
36
Examples: What is 53 x 10 = ?
Solutions: 53 x 10 = 5 3 0 shift point 1 step to the right add
What is 528 x 100 = ?
1 zero
What is 7,031 x 1,000 =?
528 x 100 = 5 2, 8 0 0 shift point 2 steps to the right add
two zeros.
7,031 x 1,000 = 7, 0 3 1 ,0 0 0 shift point 3 steps to the
right add three zeros
Achievement Indicator: Multiply any five to six digit numbers by 10 or 100 or 1000
2. Write the answers to these multiplication operations.
a. 43 x 10 =…………….
e. 76 x 100 = …………….. i. 35 x 1000 = ……………
b. 365 x 10 =…………….
f. 374 x 100 =……………… j. 54 x 1000 = ……………
c. 93,744 x 10 =……………. g. 32,81 x 100 = ……… k. 936,789 x 1000 =……………
d. 4,769 x 10 =……………
h. 791 x 100 = ……………. l. 604,456 x 1000 = …………..
14
YEAR
6
MATHS
Achievement Indicator: To write the pair of equivalent fractions
ATo write the pair of equivalentB fractions
yet to be eaten
yet to be eaten
Pizza A and B are of the same size. A is divided into 4 parts while pizza B into 8
parts. Pizza A has
yet to be eaten and B has
left. If you look carefully at the
eaten parts or left over of A and B they are of the same value or size. This means is
equal to . They are equivalent fractions because they have the same value.
Equivalent fractions are fractions with the same value.
Another way to find out: Compare the two fractions:
x
=
and .
we can see that we can multiply the top number and bottom
number of
by 2 to get .
Example 1: Find the equivalent fraction of
Solution: Multiply
So
Example 2: Find the equivalent fraction of
. Solution: Divide
15
=
by
=
÷ =
x
YEAR
6
MATHS
Achievement Indicator: To find the equivalent fraction:
Multiply the (small number) fractions top number and bottom number by any same number
Divide the (big number) fractions top number and bottom number by any same number
1. Pair up these equivalent fractions:
i.
A.
ii.
B.
iii.
C.
iv.
D.
v.
E.
vi.
F.
vii.
G.
viii.
H.
ix.
I.
x.
J.
2. Which of the fractions in the set is not equivalent to the rest :
a.
,
, ,
b.
, , ,
c.
, ,
,
,
,
,
,
,
16
YEAR
6
MATHS
3. Complete these equivalent fractions by writing three more:
a.
, ___, ___ , ___
b.
, ___ , ___, ___
c.
, ___, ___, ___
Achievement Indicator: To find the equivalent fraction
Multiply the (small number) fractions top number and bottom number by any same number
Divide the (big number) fractions top number and bottom number by any same number
There are 3 Simple Steps to add or subtract fractions:
Step 1: Make sure the bottom numbers (the denominators) are the same
Step 2: Add or subtract the top numbers (the numerators), put the answer over the
denominator.
Step 3: Simplify the fraction (if needed).
+
=
or
Think of Pizzas.
Example :
+
We need to make them the same before we can continue, because we can't add them like that.
The number "6" is twice as big as "3", so to make the bottom numbers the same we can multiply the
top and bottom of the first fraction by 2, like this:
17
YEAR
6
MATHS
×2
=
X2
Important: you multiply both top and bottom by the same amount,
to keep the value of the fraction the same.
Step 1
Now the fractions have the same bottom number ("6"), and our question looks like this: The bottom
numbers are now the same, so we can go to step 2.
+
Step 2: Add the top numbers and put them over the same denominator:
+
=
In picture form it looks like this:
+
=
Step 3: Simplify the fraction:
=
In picture form the whole answer looks like this:
+
=
18
=
YEAR
6
MATHS
Achievement Indicator; To add or subtract simple fractions with same or different denominators
ADDITION AND SUBTRACTION OF FRACTIONS
1. Add these fractions.
a.
+
b.
+
+
d.
+
e.
+
f.
+
g.
+
h.
+
i.
+
c.
2. Subtract these fractions.
a.
─
b.
-
c.
e.
─
f.
─
g.
─
─
d.
─
h.
19
─
YEAR
6
MATHS
Achievement Indicator: Convert any mixed numbers to improper fractions and vice versa
Example: Change 1
to improper
Solutions: Multiply whole number and
denominator. 1
fraction.
1
(1 x 4)= 4, add numerator
, 4 + 1= 5; place over denominator
Changing improper fractions to mixed numbers:
to mixed numbers =?
Solution: Divide numerator by denominator. 8 ÷ 6= (6 x
< 8) = 1 R 2
Answer becomes whole number and remainder the numerator 1
And simplify:
=
so the simplified answer is 1
1. Convert these mixed fractions to improper fractions:
a. 1
b. 1
c. 2
d. 2
e. 4
f. 3
g. 3
h. 9
h.
i.
2. Change these improper fractions to mixed numbers:
a.
b.
c.
d.
e.
f.
g.
20
,
simplified is =
YEAR
6
MATHS
Achievement Indicator: To add or subtract mixed fractions with the same or different denominators
A Mixed Fraction is a whole number and a fraction combined, such as 4
Adding Mixed Fractions
The best way to add mixed fractions:

convert them to Improper Fractions

then add them (using Addition of Fractions)

then convert back to Mixed Fractions:
An Improper fraction has a top number larger than or equal to the bottom number, such as
Example: What is 2
or
Solution: Convert to Improper Fractions:
+3
2
=
and
3
=
Common denominator of 4:
stays as
and
becomes
(by multiplying top and bottom by 2)
Now Add:
+
=
Convert back to Mixed Fractions:
=
Another example: what is 2
= (2 + 1) +
+1
=?
6
Regroup whole numbers and simple fractions.
+
= Add whole numbers, find common denominators for the two fractions.
+
x
Simplify.
=3 +
=
=
+
=
=3
b. 2
+ 3
=
c. 4
e. 5
+ 4
=
f.
Add these mixed numbers.
a. 1
+ 2
d.
+ 4
1
=
=
21
10
+ 3
+ 9
=
=
YEAR
6
MATHS
Subtracting Mixed Fractions
Just follow the same method, but subtract instead of add:
Example: What is 15
─ 8
?
Convert to Improper Fractions:
15
=
and
8
=
Common denominator is 12:
becomes
and
becomes
Now Subtract:
─
=
Convert back to Mixed Fractions:
Another example: What is 15
= (15 ─ 8) +
=7 +
─
─
─8
=6
=? Regroup whole numbers and fractions.
= Subtract whole number, find common denominators.
=
x
=
=
-
=
=7
Subtract these mixed fractions.
a.
e. 12
─
=
─8
=
b. 8
─ 5
f. 35
─ 27
=
c. 5
=
g. 59
22
─ 3
=
d. 20
─ 38
=
─ 15
=
YEAR
6
MATHS
Achievement Indicator: To solve multiplication of mixed fractions by whole numbers
To multiply Mixed Fractions:

convert to Improper Fractions

Multiply the Fractions

convert the result back to Mixed Fractions
1
is 1 whole pizza and 3 eighths of another pizza.
First, convert the mixed fraction (1
) to an improper fraction (
):
Cut the first whole pizza into eighths and how many eighths do you
have in total?
1 lot of 8, plus the 3 eighths = 8+3 = 11 eighths.
Now multiply that by 3:
1
x3=
x3=
.
33 eighths is 4 whole pizzas (4×8=32) and 1 eighth left over.
And this is what it looks like in one line: 1
x3=
23
x
=
= 4
= Thirty-three eights
YEAR
Another Example: What is : 1
Example: What is: 1
x 2
x3 ?
6
MATHS
=?
Think of Pizzas again.
1. Multiply these mixed fractions and whole numbers to find their answers:
a. 1
x2=
b. 2
x3=
c. 5
x3=
d. 1
x2=
e. 4
e. 7
x5=
g. 8
x 7=
h. 3
x 9=
i. 2
x 6=
j. 10 x 8 =
One More Example: What is 3
x 3
?
Convert both to improper fractions
3
x3
=
x
=
Multiply
x
=
Convert to a mixed number (and simplify):
= 10
2.
= 10
Multiply these mixed fractions:
a. 6
x1
d. 5
x2
=
=
b. 9
x2
= ____ c. 4
e. 3
x5
= _____ f. 7
x 5
x3
24
= _____
= _____
x5=
YEAR
6
MATHS
Achievement Indicator: Divisions of fractions by whole numbers
Example1: If three children equally
shared
Solution:
÷ 3 , change the operation to x
loaf bread among
x 3, write the reciprocal of 3
themselves, what fraction did each
x
get?
Multiply
loaf
x
=
loaf divide by 3 one piece is
Another example:
Example: Work out 5 ÷
Solution: change the operation to x.
=?
5x
write the reciprocal of
5x 4
Multiply 5 x 4 = 20
1. Work out these divisions of fractions by whole numbers:
a.
÷2=
b.
÷4=
c.
÷2=
d.
÷5=
e.
÷6=
f.
÷3=
g.
÷ 7=
h.
÷ 8=
i.
÷3=
j.
÷8=
2. Work out the divisions of whole numbers by fractions :
a. 2 ÷
g. 12 ÷
b. 4 ÷
i. 25 ÷
c. 3 ÷
j. 36 ÷
d. 6 ÷
e. 5 ÷
k. 54 ÷
25
l. 74 ÷
f. 8 ÷
g. 10 ÷
YEAR
6
MATHS
Achievement Indicator: Division of whole numbers by mixed fractions
Example: Three girls equally divided a
3
Solutions: 3
m dress material amongst
3
÷ 3= change to improper fraction
=
=
=
themselves. How many metres of
= change operation to x
write the reciprocal of 3
material would each girl have?
Example: How many 1
÷
x
m of ribbon can be cut
=
Solution: Change 1
=1
to improper, change to x
from a 4m long ribbon ?
4÷
and write reciprocal of , multiply.
4÷ 1
4 x
=
=?
x
=
turn to mixed number 2
1. Divide these mixed fractions by whole numbers and find their answers:
a. 1 ÷ 2 =
b. 2 ¾ ÷ 4 =
g. 5
h. 8
÷ 4=
÷ 5=
c. 3 ÷ 3= d. 2
I. 10
÷ 2= j. 8
÷6=
e. 1
÷ 3 = f. 2
÷ 3=
÷5=
k. 12 ÷ 4= l. 15
÷ 10=
2. Divide these whole numbers by mixed fractions and find their answers:
a. 3 ÷ 3
=
b. 2 ÷ 1 =
c. 5 ÷ 3
d. 4 ÷ 1
=
e. 7 ÷ 2
=
g. 8 ÷ 4
=
h. 9 ÷ 4
i. 11 ÷ 2 = j. 15 ÷ 6
=
k. 30 ÷ 13
=
=
=
26
f. 6 ÷ 5
=
m
YEAR
6
MATHS
Achievement Indicator: Division of Mixed Numbers by Mixed Numbers
Example: What is 3
÷1
Solution: change both to improper
=?
3
=
1
=
so
÷
Change the operation to: x
Write the reciprocal of
=
x
so
x
Multiply
so
x
=
turn to mixed number 2
and simplify 2
Divide these mixed numbers and find their answers.
a. 2 ÷ 1
b. 5
÷2
c. 3
÷1
d. 4
f. 6
g.
÷2
h. 10
÷4
i. 8 ÷ 4
÷3
9
27
÷1
e. 7
÷3
j.
÷6
15
YEAR
6
MATHS
Achievement Indicator: To solve simple real life problems using fractions
Try out these fraction challenges.
1. Ray bought a loaf of bread and ate
of it while his friend ate
. What fraction of the bread did
they eat altogether?
2. For breakfast one morning mum made 10 rotis. Ram ate 2 , Bimla ate 1 , Priya ate 1
(i)
How much roti did the children eat?
(ii)
How much roti was left?
3. Jone dug a rectangular garden which was
.
m long and m wide.
What was the total length of the garden?
4. Karan bought a material which was 3
m long. He used 2
m for his shirt. How much
material was left?
5. From a half watermelon Lee ate
and Suzie ate .
(i)
How much watermelon did they eat altogether?
(ii)
How much was left?
6. A whole pizza was equally divided into 16 pieces. If Jane ate one quarter
of the pizza, how:
(i)
many pieces did she eat ?
(ii)
much was left ?(answer in fraction and pieces)
7. Vili ate three pieces of pie. If each piece is 1/8 how much pie did he eat?
8. A tin of paint was litres full. Bill used
of the paint to paint his table. How much was left?
1L
0
28
YEAR
6
MATHS
More Fraction Challenges
1. Tim was selling 32 coconuts at a road side. Three eights of the coconuts were fresh bu (green
coconuts juice) and the rest matured ones. Half of the matured nuts were big while the rest
were small.
(i)
How many coconuts were fresh bu?
(ii)
What fraction of the coconuts were matured coconuts?
(iii)
How many coconuts were matured and big?
2. Sheila was selling 27 apples at the market. One third of the apples were green while the rest
were red. Two quarters of the red apples were sweet.
(i)
How many apples were green?
(ii)
What fraction of the apples was red?
(iii)
How many apples were red?
(iv)
What fraction of the red apples was not sweet?
(v)
How many apples were red and sweet?
3. How many one and a half metres of shirt material can Chan cut from a three metres long
material?
4. Priya had a five metres long ribbon and wanted to make two and a half meters
ribbon piece each from it. How many pieces of two and a half metre ribbon piece can
she make?
5. Ben made a ten metres long garden. Later he decided to group small plots of two and a half
metres in length. How many two and a half metres plot can he make?
6. A stick three and a quarter metres long need to be equally cut into a quarter metre piece long.
How many quarter metre piece stick can be cut from it?
7. A hot water urn containing ten and a half litres of tea need to be poured
out to one and half litre bottles . How many one and a half litres
bottles can be filled from the ten litres urn?
29
YEAR
6
MATHS
Achievement Indicator: To order fractions with the same or different denominator
1. Arrange these fractions in ascending order:
a. {
,
,
b. {
, ,
c. {
,
,
}
}
,
{___, ___ , ___ , ___ }
{ ___ , ___ , ___ }
,
}
{ ___ , ___ , ___ , ___ }
2. Arrange these improper fractions in ascending order:
a. {
b. {
,
,
,
c. { ,
,
,
}
{ ___, ___, ___ }
}
{ ___, ___ , ___ }
}
{ ___, ___ , ___ }
3. Arrange these mixed numbers into ascending order:
a. 2
,1
,2
,1
___ , ___ , ___, ___
b. 1 , 2
,1
,1
___ , ___ , ___ , ___
c. 4
,1
,3
___ , ___ , ___ , ___
,2
30
YEAR
6
MATHS
Achievement Indicator: To express fractions as decimal
Decimal is another way of writing mixed numbers with a decimal point. The table below shows 10
equal parts. Each part is
. We write
in decimal as 0.1 (zero point one) so
= 0.2,
= 0.3, etc.
It is easier to change any fraction to decimal that has 10, 100, 1000 as its denominator. So any
fraction that does not have 10, 100, 1000 as its denominator you should change it using the following
methods.
Method 1: Only change fractions that allow equivalent fractions whose denominators are less than 10
to 10.
Example: Write
as decimal. Solution: Use the equivalent fraction method to change
=
=
x =
since 2 x 5 =10, multiply 1 x 5 also
so =
31
and
to decimal is 0.5
to tenths.
YEAR
6
MATHS
Achievement Indicator: Fractions whose denominators are 100
This 5c a vote card contains 100 small boxes to be ticked. If one box is ticked it is
to decimal, we write it as 0.01 (zero point zero one).
= 0.02,
. To change
= 0.03 etc.
Just like it was easy to change fractions whose denominators were
10 to decimal, it is also easy to change fractions whose
denominators are 100 to decimal.
Example: Change these fractions to decimal:
a.
b.
c.
d.
e. 3
b.
c.
Solution: Remember to keep two digits after the point.
a. 0.14
b. 0.26
c. 0.75
d. 1.25
e. 3.75
Pair up these fractions with their decimals:
1.
A. 0.35
2.
B. 0.55
3.
C. 0.1
Method 2: Only change fractions that allow equivalent fractions whose denominators are more than
10 to 10 or 100.
Example 1: Change
to decimal.
Solution: Find
equivalent fraction in
Hundredths.
=
=
Since 25 x 4 = 100, multiply 4 by 4 also at the top
x
= so
32
= 0.16
YEAR
Example 2: Change
6
MATHS
to decimal.
Solution: You have two options: You use equivalent fraction either to change denominators to 10 or
hundredths.
=
or
To change to tenths:
=
=
or
=
Since 50 ÷ 5 = 10, also divide 20 by 5 at the top.
To change to hundredths:
=
=
÷
=
so = 0.4
a.
b.
c.
b. 0.25
c. 0.2
=
X
Since 50 x 2 = 100, multiply 20 and 2 at the top
Another example:
Change these fractions to decimals:

Divide the numerator by denominator

If you use calculator answers will be
a. 0.5
Long working:
a.
= 1 ÷ 2 = (2 can’t go into 1) , place a zero at the top and a point
and add a zero beside 1. Work out 2 x __=10
2 10
2
0.5
0.25
10
b. 4 10
0.5
2
2 x 5 = 10, put 5 at the top beside point.
So
= 0.5
0.2
so
─8
10
20
─ 10
─20
33
=0.25
c. 5
10 so
─10
=0.2
YEAR
6
MATHS
Match these fractions with their correct decimals:
a.
i. 0.75
b.
ii. 0.4
c.
iii. 0.8
d.
iv. 0.6
e.
v. 0.7
Change these fractions to decimals.
a.
= _____ b.
= _____
c.
= ____
d.
= ____
e.
= ____
Fill in the incomplete table below. The first one is done for you.
Fraction
Written decimal
Decimal read as
0.5
Zero point five
0.8
Zero point nine
0.25
Zero point seven five
34
YEAR
6
MATHS
Achievement Indicator: To arrange decimals in order
Example: Arrange these decimals in
Solution: Compare the values. Start with
ascending order: 0.5, 0.1, 0.7, 0.4
smallest first.
3rd
1st
last
2nd
0.5
0.1
0.7
0.4
= 0.1 , 0.4, 0.5, 0.7
1. Arrange these decimals in ascending order:
a. 0.2, 0.5, 0.1, 0.3 ____, ____, ____
b. 0.2, 0.23, 0.02
____, ____, ____
c. 0.6, 0.06, 0.16
____, ____, ____
d. 2.6, 0.62, 0.26
____, ____, ____
e. 0.7, 0.76, 0.07
____, ____, ____
Example: Arrange these decimals
Solution: Compare and start with the biggest
in descending order:
value first.
8.36, 8.06, 8.63
2nd
last
1st
8.36
8.06
8.63 = 8.63, 8.36, 8.06
2. Arrange these decimals in descending order:
a. 0.3, 0.6, 0.4, 0.1
____, ____, ____, ____
b. 4.5, 4.05, 5.4
____, ____, ____
c. 2.7, 2.74, 2.47
____, ____, ____
d. 5.07, 7.05, 0.57
____, ____, ____
e. 11.11, 11.01, 11.1____, ____, ____
35
YEAR
6
MATHS
Achievement Indicator: To add decimals with another decimal
Example: What is 0.3+0.4?
Solution: Study this number line.
0.3
+ 0.4
0.7
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
1. Add these decimals and find their answers:
a. 0.6 + 0.3 =
f.
b. 0.8 + 0.4 =
c. 0.13 + 0.32 =
d. 2.7 + 3.2 =
0.15
g. 12.9
h. 0.05
i. 3.07
j. 3.2
k. 3.43
+ 0.17
+ 0.3
+0.20
+0.31
+ 2.7
+9.24
_____
____
____
_____
____
_____
36
e. 0.07+0.09=
YEAR
6
MATHS
Achievement Indicator: To add decimals
Example:
24.27m
Solution:
17.59m
Tens
Ones
tenths
1
1
2
2
4
2
7
1 7. 5 9
1
7
5
9
+1 2. 3 6
1
2
3
6
5 4. 2 2
5
14=10+4
12=10+2
22 = 20 + 2
Put 4
Put 2
Put 2
carry 10
carry 10
carry 20
4
2
2
+ 12.36m
_________
+
Work out the answer above.
5
Group values. Add values together.
hundredths
1
1
2
2 4. 2 7
2. Work out the answers :
a. 48.39
b. 35.78
c. $343.56 d. 29.23m
+ 26.29
+36.28
+$448.67
23.73m
$30.38
364.57kg
$237.38
________
______
________
+12.36m
+$18.96
+496.87kg
+$338.70
________
_______
_________
_________
37
e. $29.37 f. 432.29 kg g. $164.73
YEAR
6
MATHS
Achievement Indicator: Subtraction of Decimals
Example: What is 82.49 ─39.42=?
Solution: Group values. Subtract.
Tens
Ones
tenths
Hundredth
7
7
─ 8
12
4
9
3
9
4
2
8 12 . 4 9
─3
Borrow
9.4 2
4 3. 0 7
1 ten
from 8
tens and
add 10 to
2
4
3
0
7
Subtract these decimals and find their answers:
1. 0.7 ─ 0.4 =
2. 0.9 ─ 0.6 =
3. 1.2 ─ 0.7 =
4. 3.3 ─ 0.9 =
5. 1.1 ─ 0.5
6. 57.28
7. 94.32
8. $732.26
9. 346.24m
10. 493.47 l
11. $ 483.27
─29.58
─29.38
─$357.77
─126.38m
─267.79 l
─$ 287.65
_____
_____
________
_________
_______
_________
12. 73.26m 13. 528.36 kg
14. 734.28km
15. 932.38m
16. 673.29 l
─27.38m
─252.48kg
─367.51km
─274.99m
─326.16 l
________
__________
________
_________
_______
38
YEAR
6
MATHS
Achievement Indicator: Multiplication of Decimals
Multiplication of decimals by whole numbers
Example: What is the product
Solution: 0.3 x 4 = If you use calculator = 1.2
of 0.3 and 4?

Ignore the zero and point , 3 x 4 = 12,

check how many numbers after the decimal
point, since it is 1,

Another example: Work out 7.8 x 7 =?
Put point between 1 and 2 = 1.2
Solution: If use calculator = 54.6
Ignore the point and think of them as 78 x 7
5
8 x 7 = 56 = 50 + 6 put down 6 carry 5
78
7 x 7 = 49 + 5 = 54
x7
7.8 has one number after the decimal point
546
so 546 = 54.6
Work out these multiplications of decimals by whole numbers:
1. 3.5 x 6 =
2. 3.2 x 4 =
3. 12.3 x 3 =
4. $3.59 x 6 =
6. $245.34
7. 424. 76km
8. 935.02m
9. 498.60
X
7
_______
x
8
________
x
3
_______
x
5
_______
39
5. 2.43m x 9 =
10. 15.07 l
x
8
______
YEAR
6
MATHS
Achievement Indicator: Multiplication of decimal numbers by 10, 100 and 1000
When you multiply whole numbers by 10, 100, 1000 and so on, you can use this shortcut:
Simply “tag” as many zeros to the product as there are in the factor 10, 100, 1000 etc.
There is a similar shortcut for multiplying decimal numbers by 10, 100, 1000 and so on: You move the
decimal point to the right as many places as there are zeros in the factors.
Multiply by 10
Multiply by 100
Example: Find 10 x 0.49 = ?
Example: Find 100 x 2.65 = ?
Solution: Move the decimal point
Solution: Move the decimal point two steps to the
one step to the right.
right.
10 x 0. 4 9 = 04.9 (remove zero) = 4.9
100 x 2. 6 5 = The number 265. would be 265.0
Another example:
or just 265
When broken down 10 x 0.49:
Another example: when broken down 100 x 2.65:
=0 . 4 0 + 0 . 0 9
= 2 . 0 0 + 0 . 6 0 + 0 . 0 5 = 200+60+5= 265
=0 . 4 0 + 0 . 0 9 = 4.0 + 0.9 = 4.9
Another example:
Multiply by 1000
1000 × 0.043 = Move the decimal point 3 steps When broken down 1000 x 0.043:
To the right. 1000 x 0 . 0 4 3
= 43
= 0. 0 4 0
+ 0 . 0 0 3 = 40 + 3 = 43
1. Multiply these decimals by 10:
a. 10 x 0.2 =
b. 10 x 1.2 =
c. 10 x 3.25 =
d. 10 x 24.34 =
e. 10 x 254.3 =
2. Multiply these decimals by 100:
a. 100 x 2.3 =
b. 100 x 3.03 =
c. 100 x 0.04 =
d. 100 x 1.726 =
3. Multiply these decimals by 1000:
a. 1000 x 0.23 = b. 1000 x 2.34 = c. 1000 x 0.003= d. 1000 x 14.02=
40
YEAR
6
MATHS
Achievement Indicator: Division of Decimals
Division of decimals by whole numbers
Example:
Solution: 95.48 ÷ 7
Divide 95.48 by 7
If you use calculator = 13.64.
13. 64
7 厂 95.48
─ 70 00
Find 7 x __
95
so 95.48 ÷ 7 = 13.64
7 x1
25 48
Find 7 x __
─ 21 00
7 x 3 = 21
4 48
Find 7 x __
─ 4 20
7 x 6 = 42
28
Find 7 x __
─ 28
7 x 4 = 28
25
44
28
Divide these decimals by whole numbers and find their answers:
1. 9.1 ÷ 7 =
2. 72.5 ÷ 5 =
6. 6
8.4m
7.
12. 9
$97.29
13. 5
17.
5 1317.90m 18.
2
3. 7.8 ÷ 2 =
4. 62.32 ÷ 4 =
5. 43.17 ÷ 3 =
33.2
8.
8 43.2
9. 6
$ 98.94
$45.45
14. 3 42.27
15.
6
9 $3612.42
19.
8 4769.92
41
20.
$87.06
4 $1316.32
YEAR
6
MATHS
STRAND 2:
ALGEBRA
42
YEAR
6
MATHS
Achievement Indicator: To identify own rule, explain, write down mathematical rule and then complete
pattern
Example:
A
3
2
5
7
4
8
B
8
5
14
20
11
23
Question: Find the rule, write down and complete the pattern.
Rule: _________________________________________.
Solution:
(i) Investigate the pattern
(ii) (ii) create own rule
(iii) (iii) use mathematical rule and
(iv) write the missing answers
A
3
2
5
7
4
8
B
8
5
14
20
11
23
1. Multiply A by 3 and subtract 1 to give B
2. (A x 3) – 1 = B, so (3 x 3) -1 = 8…
and (2 x 3) – 1 = 5…
and (5 x 3) – 1 = 14
3. Rule: 3A – 1 = B
4. When A is 7, (7 x 3) – 1 = 20
When A is 4, (4 x 3) – 1 = 11
When A is 8, (8 x 3) – 1 = 23
Find the rule and complete the pattern
X
4
3
6
y
11
8
17
8
5
9
Rule: ___________________________
43
A
3
5
4
B
7
13
10
6
YEAR
6
10
7
8
MATHS
Rule: ____________________________
44
YEAR
6
MATHS
45
YEAR
6
MATHS
Achievement Indicator: Solve for an unknown in an given equation
When writing algebraic expressions we shorten or simplify the expression as much as possible.
e.g 2 x b is written as 2b and j x k is written as jk
y ÷ 2 is written as
and c ÷ b is written as
Also there are regular equation like 3 + 4 = and algebraic equation like n + 2 = 7
Example: 4 + 4 + 4 + 4 is same as 4 lots of 4 or 4 times 4
Important to note that m x 8 is always 8m and not m8
pronumeral
numeral
1. a. Write 4 x t in a shorter way.
b. Write s ÷ 6 in another way
2. Solve for
a. 5 x (a + 3)
b. 3k – k
d. r + 5 = 12
c. 3 x c ÷ b
e.
=6
3. Lemons cost 50 cents each and banana costs 30 cents each. Write down an expression for
the cost of buying m lemons and n bananas
46
YEAR
6
MATHS
STRAND 3:
MEASUREMENTS
47
YEAR
6
MATHS
LENGTH/ AREA
Achievement Indicator: Use non-standard units and relate to standard units
Here are some non-standards units for measuring small lengths.
Activity
1. Measure the length of different objects using the non-standard of units of measuring.
2. Compare and relate your measurement to standard units of length
E.g. length of a desktop = 15 hairpins = _______mm =________cm = _________m
METRIC SYSTEMS
Millimetre(mm)
Centimetre (cm)
Meter (m)
Measure tiny
things
Measure small
things
Measure large
objects
e.g. length of
grain of rice
e.g. Length
of index
e.g. size
playground
48
Kilometre (km)
Measure long and
very large things
e.g. distance
by road from
Nadi to Ba
YEAR
6
MATHS
Achievement Indicator: To convert millimetres (mm), centimetres (cm) to metres (m) and metres to
kilometres (km) and vice versa
10 millimetres = 1 centimetre
10 mm = 1 cm
100 centimetres = 1 metre
100 cm = 1m
1000mm =1m
Use the ruler and conversion table to find answers to these:
a. How many milimetres are there in one centimetre? _______________
b. How many milimetres are there in one metre?
_______________
c. How many centimetres are there in one metre?
_______________
Achievement Indicator: To estimate and measure lengths of objects in millimetres and centimetres
Converting standard units of metric systems
mm
to
cm
÷
e.g. 20mm =………….cm
20 ÷ 10 = 2 cm
cm
to
M
÷ 100
e.g. 250cm =………….m
250 ÷ 100 = 2.5 m
m
to
km
÷
e.g. 2000m = …………km
2000÷ 1000 = 2km
km
to
m
X 1000
e.g. 3km =……………m
3 x 1000 = 3000m
m
to
cm
X 100
e.g. 4m=………..cm
4 x 100=400cm
cm
to
mm
X 10
e.g. 6cm=………..mm
6 x 10 = 60mm
1. Complete the blanks in these conversions: the first one is done for you
a. 396 mm
=
39.6 cm = 0.396 m
f. 35mm = 3cm 5mm = 3.5 cm
b. 296 mm
=
____ cm = _____ m
g. 15mm = __cm __mm=
___cm
c. 350 mm
=
____ cm = _____ m
h. __mm = __cm __mm=
7.8cm
d. ___ mm
=
12 cm = _____ m
i.
__mm = 10cm 8mm=
___cm
e. ___ mm
=
j. 111mm = __cm __mm=
___cm
____ cm =
1.5 m
49
YEAR
6
MATHS
Below shows a one metre (100cm) blackboard ruler.
0
10
20
30
40
50
60
70
80
90
100
cm
1 kilometre = 1000 metres
1 km = 1000 m
2. Complete these metric conversions to kilometres: the first one is done for you.
a. 4276 m = 4 km 276 m = 4.276 km
f. 5km 378m = 5000m + 378m = 5378 metres.
b. 2845 m = __km ___ m = _____ km g. 2km 320m =_______+_____ = ____________
c. 7250 m = __km ___ m = _____km
h. 7km 544m =_______+_____ = ____________
d. _____ m =10km 25 m = _____km
i. __km ___m = 4000m +_____= 4527 metres
e. _____ m = __km ____m =
1.5 km j. __km ___m = 10000m+276m= ____________
Achievement Indicator: To estimate and measure lengths of objects in millimetres and centimetres
Example: Without looking at the above ruler, estimate the length of the nail below. Measure and write
the answer in millimetres.
Solution: Estimate: 2cm or 20mm. Use the ruler to measure: It is about 38 mm or 3.8cm.
1. Estimate and then use your ruler to measure the lengths of these lines in mm and cm :
a.
d.
b.
c.
2. Draw straight lines of the given lengths from the marked points using your ruler.
a. 55 mm
b. 120mm
50
YEAR
6
MATHS
Achievement Indicator: To measure the perimeter of rectangles
Example: Calculate the perimeter of this shape.
4cm
Solution:
Perimeter of this shape is the distance all round
the rectangle.
2 cm
2 cm
Add all lengths and widths.
4cm + 2cm + 4cm + 2cm = 12cm
4cm
Another method: Use the perimeter rule for rectangles: Perimetre = (length + width) x 2
P =( L + W) x 2 = (4 cm + 2 cm) x 2 = 6 cm x 2 = 12cm
1. Measure the perimeter of these rectangles in centimetres:
a.
b.
c.
d.
e.
f.
g.
2. Complete the perimeter table of these rectangles: the first one is done for you.
Perimetre of rectangles = (length + width) x 2
Length
Width
Perimetre
9cm
5cm
28cm
10cm
4cm
13cm
6cm
8cm
4cm
11cm
8cm
51
YEAR
6
MATHS
To calculate the perimeter of a square
Example: Calculate the perimeter of this square:
2cm
Solution: Add all the sides: 2cm + 2cm + 2cm + 2cm = 8cm
Another short method: Since all sides are equal, just multiply one
2cm
2cm
side four times: 2cm x 4 = 8cm
2cm
1. Calculate the perimetres of these squares in cm:
a.
b.
c.
5cm
4cm
3cm
2. Complete the perimeter table of these squares: the first one is done for you.
Length of one side of the square
Perimetre
6cm
24cm
10cm
60cm
25cm
120cm
3. Complete the perimeter table of these squares in metres: the first one is done for you
Length of one side of the square
Perimetre
10m
40m
17m
116m
35m
52
YEAR
6
MATHS
To measure the perimeter of any shape
Example: Calculate the perimeter of this shape:
1cm
Solution: Add all the sides: 1cm+1cm+1cm+1cm+2cm+2cm=8cm
1cm
2cm
1cm
1. Use a ruler to measure and calculate the perimeter of each shape below in centimetres:
a.
b.
c.
e.
d.
f.
Measuring Distances using the scale for conversion
Example: Measure the length of line AB in cm. Using the scale. Convert the length to real distance.
Scale: 1cm = 10km
A
B
Solution: Measure: 6cm ; convert: 6cm x 10 = 60cm
2. Use the scale to convert the measured length in real distance: scale 1cm = 10km:
i) B
iv) H
C
ii) D
iii)
E
F
G
I
53
YEAR
6
MATHS
Achievement Indicators: To round off given length to nearest cm, m or km
Example: Round off these lengths to the nearest:
cm/m/km Solution:
13.42cm
13cm
If the number you are rounding is
2.54m
3m
followed by 5, 6, 7, 8, or 9, round the
4.5km
5km
number up. If the number you are
rounding is followed by 0, 1, 2, 3, or 4,
round the number down.
1. Round off these lengths to the nearest cm:
a. 5.2cm
b. 16. 3cm
c.
24.7cm
d. 123.6cm
e. 346.4cm
f. 102.3cm
2. Round off these lengths to the nearest m:
a. 3.7m
b. 5.8m
c. 10.3m
d. 25.6m
e. 57.3m
f. 143.4m
3. Round off these lengths to the nearest km:
a. 2.3km
b.
4.3km
c. 10.9km
d. 27.5km
e. 49.3km
f. 327.1km
Achievement Indicator: Using squared paper to find areas of shapes
Example: Calculate the area of the shapes below by counting the square centimetres.
The first one is done for you.
54
YEAR
6
MATHS
Achievement Indicator: To express a percentage of a given length or distance
Example: Express these lengths to percentages of their respective metric units:
Solutions:
i)
5mm of a cm.
50%
ii)
25cm of a m.
25%
iii)
275m of a km.
27.5%
LENGTH / VOLUME
Express these lengths or distances to percentages:
1. 6mm of a cm._____________________________ 6. 127m of a km.__________________________
2. 9mm of a cm._____________________________ 7.
584m of a km._________________________
3. 29cm of a m._____________________________
8.
978m of a km._________________________
4. 45cm of a m._____________________________
9. 20mm of a m.__________________________
5. 68cm of a m._____________________________ 10. 500cm of a km._________________________
Achievement Indicator: To construct 3D objects using cubic centimetres, and use estimation to determine
volume
VOLUMES / CAPACITY
Use sheet of vanguard/cardboard to make a net of a cube. Each square is a cm in length. This cube will have a
volume of 1 cubic centimeter (1 cm3)The space in the 1cm3 cube can hold 1ml of liquid; so 1cm3 =1ml.
1 cm
1 cm
1 cm
55
YEAR
6
MATHS
Achievement Indicator: To calculate the volume:
Multiply length, width and height (Length x width x height = 1cm x 1cm x 1cm= 1cm3 )
Estimate and calculate the volume of these prisms:
a.
3 cm
b.
2 cm
1 cm
4cm
5cm
1 cm
This jug of water holds 1 litre of water. It means. It can hold 1000ml
water. Can you see the
litre mark on the side of the jug.
How many milliliters is
a litre?
One cubic centimeter is equal to one millilitre; 1 cm3 = 1 ml
1 cm3 = 1 ml
1000 millilitres = 1 litre
Example 1: Convert this millilitre to litres:
Solution 1:
=
250ml
Example 2: Convert this litre to millilitres:
Solution 2:
1200ml
= (1.2 litre) or
1. Complete the following conversions:
a. 15 cm3 = ___ml
b. ___ cm3 = 25 ml c. 45 cm3 = ___ml
56
YEAR
6
MATHS
2. Convert these litres to millilitres:
a. 2 litres
b.
Half litre
c.
c. 5 litres
d. 10
3. Write these millilitres to litres:
a. 1 436 ml
b. 2 095 ml c. 3 005 ml d. 5 200 ml e. 750 ml
f. 4 030 ml
4. Copy and complete the table below.
cm3
4000cm
ml
1500
L
100000
900ml
2L
3L
Write <, > or = in the space below.
a. 1L………….500ml
b. 200ml……….2L
c. 50ml……….. 5L
WORD PROBLEMS.
1. Does the objects below hold more than or less than a litre?
a. Paper cup
b. wheel barrow
c. fish tank
d. baby milk bottle e. mouthful of water
2. How many containers below can be filled from a 20 litre cylinder?
a. 200ml
b.
500ml
c.
10 litre
d. 250ml
20 Litre
b. For a science project, you need 4L of water. Your container holds 500ml. How can you use it to
measure 4L?
c. Suppose you put 3 spoonful of honey on your cereal. Four small spoons hold 5ml. About how many
millitres of honey will you eat?
57
YEAR
6
MATHS
Achievement Indicator: Estimate and convert any measurement from non-standard to standard units weight
1000grams = 1 kilogram
1000g = 1 kg
Nazreen took some potatoes and weighed them on the digital scale.
The machine read ‘1000g’.
How many different ways can you represent the weight?
The standard mass units include: 1g, 5g, 10g, 20g, 50g, 100g, 500g and 1 kg.
1g 5g
10g 20g
50g
100g
500g = kg
1000g = 1 kg
1. She also used a set of balance scales in her grocery shop. She wants to have just the minimum
number of weights necessary to measure any mass up to 10 kg. How many of each weight unit will she
need ?(Use the standard masses above to help you) The first one is done for you.
a. 1g = one 1g
b. 5g =_________
c. 10g =__________
d. 15g =____________
e. 20g=___________ f. 50g =_________
g. 75g =___________
h. 100g=____________
i. 250g=___________ j. 500g=__________
k. 5kg=____________
l. 7kg=______________
58
YEAR
6
MATHS
2. Write the following as kilograms and grams: The first one is done for you.
a. 1001 g = 1000g + 1g = 1 kg 1g
f. 7294 g= 7000g +294g = 7 kg 294 g
b. 1302 g=___________________
g. _____g= 8000g +749g =__________
c. 3654 g=___________________
h. ______g= 9000g +430g =__________
d. 5932 g=___________________
i. ______g=10000g+547g=___________
e. 6542 g=___________________
j. _______g=10000g+20g=___________
Achievement Indicator:
kg,
Example 1: Write these weights in grams:
Solutions:
If 1 kg = 1000g then
÷
If 1 kg = 1000g then
If
1
1000g +(
=1500g
Example 2: Write these weights in kilograms:
Solutions:
500g
250g
750g
1500g
Complete these conversions: The first one is done for you.
1. 2
6. ___kg = 1.25kg = 1250 g
2. 3
___kg = ____g
7. ___kg = 1.75kg= _____g
3. 4
___kg = ____g
8. ___kg = ____kg= 8250 g
4. 6
___kg = ____g
9. ___kg = ____kg= 6500 g
5. 7
___kg = ____g
10.___kg = ____kg=
59
50 g
YEAR
6
MATHS
Achievement Indicator: Make your estimation and convert it to standard units.
Objects
Estimation
Converted to standard units (kg/g)
A tennis ball (1g)
1,000 tennis balls
……………………………………………………
A lollipop (1g)
500 lollipops
……………………………………………………
Bubble gum (1g)
……………………
750 grams
WORD PROBLEMS
1. Akuila was sent by his mum to buy 2
kg of potatoes. When he returned, his mum noticed that the
price tag says 2kg. How many more grams of potatoes does Akuila have to buy?
2. Sereana bought a big packet of twisties with the weight of 750g. She ate some and gave the rest to
her sister. Her sister weighs the packet and found out that it was 250g.
a. How much twisities did Sereana eat ? (answer in grams)
b. Did Sereana eat more twisties or less than her sisters ?
60
YEAR
6
MATHS
1. Time is a measure in which events can be ordered from the past through the present into
the future, and also the measure of durations of events and the intervals between
them. Time is one of four dimensions, in addition to the dimensions of space.
AM – 12 hours from midnight until noon
24 hours = 1 day
PM – 12 hours from noon until midnight
7 days = 1 week
366 days = 1 year
60 seconds = 1 minute
4 weeks = 1 month
52 weeks = 1 year
60 minutes = 1 hour
12 mon ths = 1 year
24 hour clock:
The 24-hour clock is a way of telling the time in which the day runs from midnight to midnight and is
divided into 24 hours, numbered from 0 to 24. It does not use a.m. or p.m. This system is also
referred to as military time or as continental time. In some parts of the world, it is called railway
time. Also, the international standard notation of time (ISO 8601) is based on this format.
To convert times to 24 hours:
 Written with 4 digits without decimal points
 No am or pm used but hours
 All times after 12 midday (pm) will change,
their pm times will add another 1200hours.
e.g 1.30pm =0130
+1200
1330 hours
 12.00pm(midday) =1200 hours
 12.00am(midnight)=0000hours
61
YEAR
6
MATHS
Achievement Indicator. To tell the actual time using am or pm
Draw, write each of these examples in: i) am or pm time, ii) digital 24 hour time and iii)analogue time.
Analogue
Draw
Draw
24 hour
Fourteen thirty
time
hours
a.m / p.m
Draw
8.30 a.m
11.45 p.m
___________p.m
Draw the missing hour and minute hands of the clock faces.
1. 3.37 p.m
2. 9.11 a.m
3. 11.21 a.m
62
4.
4.12 p.m
YEAR
6
MATHS
Achievement Indicator: To read a stop watch correctly
Calculating times in stop watches: Finishing time minus starting time = Finishing Time (FT)
Starting Time (ST)
Time Used (TU)
Stop watches are used to record the time of events.
2:48:84
The time shows 2 minutes 48 seconds and 84 hundredths of a second.
1. How much quicker than 3 minutes was the recorded time ?
……………………………………………. …………………………………..
2. Show these times on the digital stopwatch displays:
a. 1 minute, 48 seconds and 55 hundredths of a seconds:
:
:
b. 5 minutes, 23 seconds and 7 hundredths of a second:
:
:
TIME
Achievement Indicator: To read and interpret timetables and timelines
Refer to the FBC TV guide below to answer the questions:
6.00 a.m
6.30 a.m
7.00 a.m
Go Go Giggles(C)
Super Ninjas(C)
Sesame Street(C)
1. How long is Go Go Giggles?
……………………………………
2. What programme is the shortest?
…………………………………….
7.30 a.m
Aljazeera
10.00 a.m
Brandstar-Shop on TV
10.30 a.m
World of Bollywood
3. How long are the children’s shows
?
…………………………………….
4. Which show is the longest?
…………………………………….
11.00 a.m
Na Vakekeli-Radio
Fiji One Talkback
Show(G)
12.00 p.m
5. Work out FBC’s first half of the
day’s hours of show?
………………………………………..
Pavitra Rishta (English
Subtitles) (PG)
63
YEAR
6
MATHS
Work out the word problems below.
1. Pete went to bed at 8.45 p.m and woke up at 6.15 a.m the next day. How long did he sleep ?
………………………………………………………………………………………………………………………………
2. The Pacific Transport bus left Suva at 9.15 a.m and it reached Sigatoka at 11.30 a.m.
i) How long was the trip from Suva to
Sigatoka?....................................................................
ii) What should have been the actual arrival time if 15 minutes of delay occurred because
the bus developed mechanical problems?........................................................................
Achievement Indicator: To understand the importance of time in speed and calculate average speed
Refer to the table below to answer the questions that follow.
In a one hour test three (3) children’s finishing times were recorded.
Students
Starting Times
Finishing Times
Rita
9.00 a.m
9.50 a.m
Jane
9.00 a.m
9.30 a.m
Ben
9.00 a.m
9.55 a.m
1. Who finished first? …………………………………………………….
2. Who was last?
…………………………………………………….
3. Jane was …………………….minutes ahead of ……………………….
4. Ben was…………………….minutes behind ……………………and …………………minutes behind
Rita.
5. What is the average time of the three students?..........................................................................
64
YEAR
6
MATHS
AVERAGE SPEED
Achievement Indicator: To understand and calculate Average Speed
Average Speed = Distance(D) divide (÷ by time(T)
Average Speed = D ÷
or Average Speed =
Example: If a bus takes 4 hours to reach Lautoka from Suva covering a distance of 250 km, find its
average speed in kilometers per hour.
Solution: A.S = D ÷
A.S = 250 km ÷ 4 hours
= 250 ÷ 4
= 4 250
62.5
= 4 250
= 62.5 km / hr
AVERAGE SPEED
Answer the questions below and calculate the average speed of the following
events.
1. The Inter-City bus leaves Suva at 10.00 a.m and reaches Nadi at 1.00 p.m
covering a distance of 219 km.
i) How long did it take the bus to reach Nadi ?
ii)Find the average speed of the bus .
2. The Taunovo Bus leaves Navua at 9.15 a.m and reaches Suva after twenty-five minutes of
travelling fifty-five kilometers .
i) How long is the journey ?
ii) What is the average speed ?
3. A rental car leaves Nadi town at 10.20 a.m and reaches Sigatoka at 10.45 a.m covering a distance
of 75 kilometres.
i) How long is the drive ?
ii) Find the average of the car .
65
YEAR
6
MATHS
4. If Fiji’s fastest man Banuve Tabakaucoro completed 100 metres in 10 seconds, find his average
speed in metres per seconds ?
5. Fill in the missing data in the table below.
Average Speed
Distance
Time
20 km
10 minutes
32 km
16 minutes
71 km / hr
2.6 km / hr
2 hours
55 km
Achievement Indicator: To estimate, measure and record temperature in degrees Celsius
Temperature is how hot or cold something is. It is measured in degrees Celsius. We use the Celsius
thermometer to measure temperature. Temperatures below freezing point are written with a – sign
before the number. For example: 5 degrees below zero is written as
66
5
.
YEAR
6
MATHS
Achievement Indicator: To write temperatures in numeric forms and ascending order
Example: write the temperature ‘twenty – five degrees’ in numeric
form. Solution: twenty-five degrees = 25 C
1. Write these temperatures in numeric form:
a. twenty-four degrees Celsius
…………………………………..
b. zero degrees Celsius
………………………………….
c. forty-five degrees Celsius
…………………………………
d. thirty-two degrees Celsius
…………………………………
2. Arrange these temperatures in ascending order.
16 C
25 C
100 C
2 C
35 C
19 C
10 C
_____ _____
_____
____
_____
____
_____
Achievement Indicator: To estimate, measure and record
temperatures in degrees Celsius
Example: Read and write the temperature indicated below.
Solution: 10 C The first one is done for you.
10
……….
………
……….
……….
67
………..
YEAR
6
MATHS
Achievement Indicator: To discuss the need for and uses of money
We all need money to spend at times. Discuss these questions in groups and write the answers:
a. Do you receive spending (pocket money)? ___________________________________________________ .
b. In what ways do you get money? ____________________________________________________________.
c. Do you think children should work for their spending? Why? ____________________________________
__________________________________________________________________________________________ .
d. Do you save any money you receive? ________________________________________________________ .
e. What do you spend your money on? _________________________________________________________ .
f.
What are ‘wages’? _________________________________________________________________________ .
g. Are all people’s wages the same? Why? ______________________________________________________
__________________________________________________________________________________________ .
h. Why do you think is the most important thing about a work? _____________________________________
__________________________________________________________________________________________
Achievement Indicators: To organize simple retailing activities
Example:
Solution:
Calculate the bills, round it off to the
Add the 3 items: $11.97
nearest five cents and write the paid
$ 2.00
amount.
Lamb Chops/BBQ Chops $11.97 kg
Golden Harvest
Mixed Vegetable 500g
$2.00
Vico Malt Drink 200g
$2.30
+ $ 2.30
Total -
$16.27
Amount paid -
$16.30
(NOTE) There are no 3
cents coins.
68
YEAR
6
MATHS
Calculate the total for each of these bills. Round the total to the nearest five cents to find the actual amount to
pay.
a. 1 Skipper Albacore Tuna Flakes in
vegetable Oil 170g $1.45
1 bar Pacific Laundry Soap 400g
Oryx Assorted Cream Biscuits 82g $1.00
Bon Assorted Hair Gel 1000ml
b. 1 DelseyTwin pack Toilet Tissue 200 sheets $2.25
$1.75
1 pkt Colgate Regular/Triple Action Toothpaste 95ml
$3.52
$3.45
Total shopping
Total shopping
Exact amount paid
Exact amount paid
c. 1 Baked beans in tomato sauce 420g
d. 1 De Power Dish Washing paste Assorted 400g $1.80
$1.45
1 pkt Cocktail vegetable samosa/Spring
1 De Power Laundry Powder 900g
1 pack Camay Assorted Bathing Soap 125g
Roll 1 kg
(3 for)$3.45
$9 Chicken Nuggets Family pack 1 kg
$17.97
Total shopping
Exact amount paid
$2.54
Total shopping
Exact amount paid
69
YEAR
6
MATHS
Achievement Indicator: To describe banking systems
Most people save money in a bank, building society or credit union. Each of these service providers will keep
your money in custody and pay interest to you for the time the money is put in with them. They provide you
with a bankbook or bank statement like the one shown below to provide statistics about the account.
VANUA BANK
FIJI
Branch No. 679-178
Date
Account No.777-645-231
Particulars
Name
Withdrawal
Bean Ratu
Deposit
Balance
17. 6. 14
CASH
50.00
508.80
18. 6. 14
INTEREST
2.65
510.65
18. 6. 14
CHEQUE
28.50
539.15
22. 6. 14
PAID
23. 6. 14
CHEQUE
30. 6. 14
PAID
50.00
769.15
1. 7. 14
PAID
100.00
669.15
3. 7. 14
CHEQUE
20.00
Teller & Stamp
519.15
300.00
230.20
819.15
899.35
Discuss the bank book to find answers to these questions:
a. Whose bank account is this?
………………………………
b. What is the last balance shown in the book?
…………………………………
c. Was it a withdrawal or deposit made on 23.6.14 and for how much?...............................................
d. What date was interest paid and how much?
………………………………...
e. Was the deposit on 17.6.14 cash or cheque?
…………………………………
f.
If a cash deposit of $60.00 was made on 5.7.14, show the entry and the new balance in the book.
70
YEAR
6
MATHS
Achievement Indicator: To identify bus e-ticketing cards and understand information on the
receipts
The bus travelling public in Fiji have the privilege of using the bus e-ticketing card services.
Use the attached bus e-ticketing receipt below to answer the questions below:
CT2CT Bus Co.
TIN: 50-139 72 XXX
Bus No: FF 7X7
Card: 6792XXX000
Amount: $0.70
Balance: $1.95
Stage: 1
Time: 2014.08.22
09:53:58 AM
Driver: T.Bone
1. What is the name of the bus company ? …………………………………………………………… .
2. The bus number is …………………………………………………………………………………….. .
3. What was the fare for stage 1 ? …………………………………………………………………………
4. The passenger boarded the bus on………………………………
at
………………………….. .
5. Who was the driver on that day ?.................................................................................................. .
6. How much balance is on the card ?.............................................................................................. .
71
YEAR
6
MATHS
\
STRAND 4:
GEOMETRY
72
YEAR
6
MATHS
Shapes are either in 2D or 3D forms. 2D or 2 dimensional shapes . They are flat and
have a length (height) and width.
.STUDY THE REGULAR POLYGONS
Fill in the table below with correct information from the 2D shape above. The first one is done for you.
Names
triangle
Number of sides
Number of angles
3
3
73
YEAR
6
MATHS
circle
oval
A perfectly round
A perfectly oval (egg) shape
shape
Isosceles triangle
Right angled
Scalene
-2 sides equal
-one right angle
-none of the
-2 angles equal
sides equal
EQUILATERAL
All sides equal
All angles equal
All
2 sides equal
4 sides equal
4 right angles
All 4 right angles
equal
Has pair of parallel
sides
equal
kite
arrowhead
74
YEAR
6
MATHS
Achievement Indicators: To draw polygons
Complete this table by filling in any missing detail. Use your pencil and a ruler to draw.
Polygon’s
drawing
name
Regular or irregular
Given
side
3
scalene
4
irregular
5
6
7
8
75
YEAR
6
MATHS
Fill in the table below by drawing and colouring the polygons and show the number of triangles.
Polygon’s
Draw
Name
side
Number of
triangles
3
1
triangle
4
2
square
5
6
7
8
To study the circle
1.
Measure the radius line.
…………………….
2.
Measure the diameter line.
3.
What is the relationship between the radius and diameter ?
…………………….
…………………………………………………………………………
4.
Which is longer the circumference or the diameter ?
…………………………………………………………………………
From your observation above complete the missing details in the table below.
radius
diameter
5 cm
14 cm
8 cm
20 cm
76
YEAR
6
MATHS
Achievement Indicator:To study 3D SHAPES
3D shapes are 3 dimensional solid shapes which have lengths, widths and depths (heights).
Fill in the table below by drawing the 3D shapes and their real life like shapes.
The first one is done for you.
Name
Draw and colour
Similar shape
cone
Ice cream cone/ birthday party hat
cube
prism
cylinder
pyramid
77
YEAR
6
MATHS
Achievement Indicator: To identify lines of symmetry
From your study of the shapes above try drawing the lines of symmetry on the shapes below.
78
YEAR
6
MATHS
Study the diagram and answer the questions below.
1. Complete these sentences:
a. A line points in ……………………………….directions.
b. A line segment starts at …………………………and……………………………………………..
c. A ray begins ………………………………………and………………………………………………….
2. The difference between a ray and a line is that ……………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………..
3. The starting point of a ray is called the point of ………………………………….. .
4. Two rays starting from the same starting point form an……………………………………. .
Achievement Indicator : To investigate angles.
79
YEAR
6
MATHS
Fill the table below with missing details. The first one is done for you.
Name
Draw the angle
acute
Angles
Less than 90
right
Obtuse
straight
reflex
Complete
revolution
Achievement Indicator: To investigate interior, exterior and alternating angles.
Mark the interior angles of the polygons below. The first one is done for you.
80
YEAR
6
MATHS
Achievement Indicator: To draw exterior angles
Draw the exterior angles of the polygons below. The first one is done for you.
81
YEAR
6
MATHS
Reflections and Translations
Reflections
Show the reflection of the shape
82
YEAR
6
MATHS
Translations
A translation (notation) is a transformation of the plane that slides every point of a figure the same distance in the same
direction.
In Geometry, "Translation" simply means Moving without rotating, resizing or anything else, just moving.
83
YEAR
6
MATHS
STRAND 5:
CHANCE
AND
DATA
84
YEAR
6
MATHS
CHANCE: The likeliness of something that is going to happen or the chances of an event happening.
VOCABULARY:




Impossible (It will never happen)
Unlikely(It may happen but probably won’t)
Likely(It may happen and probably will)
Certain(It will definitely happen)
Example
DISCUSSION TIME
In a box, Jope place 8 red cubes,4 blue cubes and 1 green. If he draws the cube out of the box at random:
a)
b)
c)
d)
What is the cube that will be certainly drawn out first?
What is the cube that will likely to be drawn out first?
What is the cube that will unlikely to be drawn out first?
What is the cube that will never be drawn out of the box? Why?
85
YEAR
6
MATHS
86
YEAR
6
MATHS
Achievement Indicator:To list and count all possible outcomes of a simple experiment and to describe the
chance of these outcomes occurring.
1
2
1
1,1
1,2
2
2,1
3
4
a. How many possible outcomes are there ?
____________________________________________
b. What is the probability, written as a fraction, of
each outcome occurring ?
____________________________________________
c. By finding the sum of the two numbers thrown,
which total is most likely to appear ?
____________________________________________
d. Which total is least likely to appear ?
____________________________________________
e. What is the probability of throwing a double ?
____________________________________________
3
4
5
6
To use data to order chance events from the least likely to the most likely.
In a cloth bag, I place 7 red cubes, 2 black cubes and 1 white cube. If I draw out of the bag
at random:
a. What colour is the most likely outcome ? ______________________________
b. What colour is the least likely outcome ? _______________________________
c. What is the probability of drawing a black out of the bag ? _________________
d. What is the probability of drawing a yellow cube out of the bag ?____________
87
5
6
YEAR
6
MATHS
ACTIVITY 1
1.Take turns picking 1 cube out of the box.
2.Use the recording sheet or another piece of paper, make a tally for the colour you pick.
Put 5 red cubes and 5 blue cubes in the box.
Step 1



Pick 1 cube from the box without looking.
Mark the colour of the cube on the recording sheet.Use a tally mark.
Put the cube back in the box
Step 2


Take turns until you have chosen a cube 30 times.
Each time you pick a cube,use a tally mark to record the result.
Step 3


Now put 5 red cubes and 1 blue cube into the box.
Repeat step 2 with this box of cubes.
QUESTIONS
1.
2.
3.
4.
How often did you pick a red cube in Step2? in Step 3?
How often did you pick a blue cube in Step 2? In step 3?
Which colour cube did you pick more often in Step 3? Why?
How many cubes of each colour would you put in a bag so that you would probably pick blue cubes more than
red ones?
5. If you had 4 red cubes and 4 blue cubes, which colour would be picked more often?Why?
6. Compare your record sheet with your classmate and write your conclusion part of the activity?
88
YEAR
6
MATHS
ACTIVITY 2
Results from a deck of 10 cards
Questions
1. How can you tell which colour was picked the most even though there are no numbers on the graph?
2. Did the deck have more green cards or blue cards? Why do you think so ?
3. If you are given a set of cards to colour them red ,blue and green,how would you create your deck so you would
get results like those in the bar graph. Explain?
89
YEAR
6
MATHS
90
YEAR
6
MATHS
91