DATE
NAME
Patterns in the 2 Times Table
The numbers you say when counting by a number from 0 are called the multiples of that number.
The numbers 0, 2, 4, 6, 8, 10, … are multiples of 2.
1.a)
Shade the multiples of 2 on the
hundreds chart.
1
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20
b)Where are the multiples of 2? Use the
words “row” or “column” in your answer.
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
c)Look at the ones digits of the multiples of
2 in the third row of the hundreds chart:
91 92 93 94 95 96 97 98 99 100
21 22 23 24 25 26 27 28 29 30
Underline the ones digits of the multiples of 2 in any other row.
What do you notice?
d)How can you tell whether a number between 1 and 100 is a multiple of 2 without
counting up?
COPYRIGHT © 2013 JUMP MATH: TO BE COPIED. CC EDITION
Multiples of 2 are called even numbers.
Numbers that are not multiples of 2 are called odd numbers.
2. a) Circle the even numbers.
7
18
32
21
76
30
44
68
83
89
94
67
15
82
b) Circle the odd numbers.
5
3
75
60
37
92
100
c)Pick an even number. Add 2 to your number. Do you get an even or an odd number?
Will the answer be the same for any even number? Explain.
Blackline Master — Operations and Algebraic Thinking — Teacher’s Guide for AP Book 4.2
L-7
DATE
NAME
Patterns in the 5 Times Table
The numbers 0, 5, 10, 15, 20, 25, … are multiples of 5.
1.a)
On a hundreds chart, shade the multiples of 5.
1
b)Where are the multiples of 5? Use the words
“row” or “column” in your answer.
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
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
2
71 72 73 74 75 76 77 78 79 80
c)Look at the ones digits of the multiples of 5
in the fourth row of the hundreds chart:
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
31 32 33 34 35 36 37 38 39 40
Now look at the ones digits of the multiples of 5 in any other row.
What do you notice?
d)How can you tell whether a number between 1 and 100 is a multiple of 5 without
counting up?
2. Circle the multiples of 5.
45
27
b)
203
205
217
62
385
90
426
85
755
11
931
25
5,123
50
4,145
37
89,430
3. a) Write the first ten multiples of 5 in order.
0
,
5
,
,
,
,
,
,
,
,
b) Circle the multiples of 5 that are even. What pattern do you notice?
L-8
c) Explain why the pattern in part b) holds.
Blackline Master — Operations and Algebraic Thinking — Teacher’s Guide for AP Book 4.2
COPYRIGHT © 2013 JUMP MATH: TO BE COPIED. CC EDITION
a)
8
DATE
NAME
Patterns in the Times Tables (Advanced)
1. a) Sort the numbers below into the Venn diagram. Cross out the numbers as you go.
10 25 15 37 86 49
50
6
5
17 61 40 36 65
79 24
8
96
Multiples of 2
Multiples of 5
10
b) Find two more numbers from 50 to 100 that would go in the central part of the
diagram:
,
c) Find two more numbers from 50 to 100 that would be placed outside the circles:
,
BONUS
Add one four-digit number to each part of the Venn diagram.
2. Sort the numbers below into the Venn diagram.
32 40 57 24 25 80 62 17 16
56 60 35 48
8
75 72 30
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Multiples of 2
BONUS
5
Multiples of 8
dd one three-digit number to each part of the Venn diagram that already
A
has a number in it.
Blackline Master — Operations and Algebraic Thinking — Teacher’s Guide for AP Book 4.2
L-9
DATE
NAME
Patterns in the 11 Times Table
The numbers 0, 11, 22, 33, … are multiples of 11.
1.a)
Shade the multiples of 11 on the special
hundreds chart.
b)Where are the multiples of 11? Use the words
“row,” or “column,” or “diagonal” in your answer.
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 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
c)Serena knows that 11 × 7 = 77, so she thinks
that 11 × 10 = 1,010. Explain her mistake.
11 × 27 = 2 9 7
2.
Minar notices a pattern:
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
and
11 × 53 = 5 8 3
2+7
a) Multiply. Does Minar’s pattern work for these numbers?
5+3
i)ii)iii)iv)
4 2
2 3
5 4
×
+
1
1
2
3
2
3
2
5
×
1
1
×
1
1
×
1
1
1
3
2+3
b) Multiply. Does Minar’s pattern work for these numbers?
i)ii)iii)iv)
5 8
4 7
3 9
×
7
1
1
×
1
1
×
1
1
×
8
6
1
1
c)When does Minar’s pattern work? Explain.
L-10
Blackline Master — Operations and Algebraic Thinking — Teacher’s Guide for AP Book 4.2
COPYRIGHT © 2013 JUMP MATH: TO BE COPIED. CC EDITION
0
DATE
NAME
Number Pyramids
1.Examine the number pyramids and describe the rule by which the patterns in the
pyramids were made below.
5
2
2
3
1
6
9
1
6
9
5
3
3
1
2
2. Use your rule from Question 1 to find the missing numbers.
b) c) d) e)
4
a)
2
4
f) 1
9
2
5
6
g) h) i)
10
12
7
4
k)
7
6
l)
25
12
7
7
10
3
j)
16
5
11
m) n) o)
60
81
20
30 40
52
75
BONUS
p)
q)
r)
15
COPYRIGHT © 2013 JUMP MATH: TO BE COPIED. CC EDITION
10
2
3
5
s)
7
6
3
2
t)
u)
19
11
3
15
17
10
49
32
57
Blackline Master — Operations and Algebraic Thinking — Teacher’s Guide for AP Book 4.2
L-11
DATE
NAME
Problems and Puzzles
1.Use multiplication or a calculator to find the first few products. Look for a pattern.
Use the pattern to fill in the rest of the blanks.
a)999 × 2 =
b)6 × 9 =
999 × 3 =
6 × 99 =
999 × 4 =
6 × 999 =
=
=
=
=
BONUS
Using a calculator, can you discover any more patterns like the ones in Question 1?
2. How many triangles will be needed for the 6th figure?
Figure 1
Figure 2
Figure 3
3. Sue makes ornaments using squares and triangles. She has 12 squares.
a)How many triangles will she need to use to make
ornaments with all 12 squares?
b)How did you solve the problem? Did you use a T-table?
A picture? A model?
4. What strategy would you use to find the 23rd shape in this pattern? What is the shape?
a) I am greater than 21 and less than 26. I am a multiple of 3. What am I?
b) I am greater than 29 and less than 33. I am a multiple of 4. What am I?
c) I am less than 15. I am a multiple of 3 and a multiple of 4. What am I?
6. Emma makes a stairway using stone blocks.
How many blocks will she need to build a
stairway 6 steps high?
1 step
L-12
2 steps
3 steps
Blackline Master — Operations and Algebraic Thinking — Teacher’s Guide for AP Book 4.2
COPYRIGHT © 2013 JUMP MATH: TO BE COPIED. CC EDITION
5. Find the mystery number.