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Sample Answers
1. a) 1, 5, 25; 5
b) 1, 2, 3, 5, 6, 10, 15, 30; 2, 3, 5
c) 1, 2, 3, 4, 6, 12; 2, 3
d) 1, 2, 5, 10, 25, 50; 2, 5
e) 1, 2, 4, 7, 14, 28; 2, 7
f) 1, 2, 4, 5, 10, 20, 25, 50, 100; 2, 5
g) 1, 2, 4, 5, 10, 20; 2, 5
h) 1, 3, 7, 9, 21, 63; 3, 7
2. a) 31, 37, 41, 47
b) 32, 40, 48
3. 10, 26, 35
4. b) 3 31
d) 3 29
f) 5 3 3
a) Prime
d) Composite
b) Composite
e) Prime
c) Prime
f) Composite
5.
6.
7.
8.
9.
23 students
71, 73, 79
Read through the last 2 bullets in Connect.
Introduce the terms prime factors, prime factorization,
common factors, and greatest common factor.
Refer students back to Explore. Then ask:
• What numbers between 2 and 20 are prime?
(2, 3, 5, 7, 11, 13, 17, 19) Composite?
(4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20)
In pairs, have students write the prime numbers
and prime factorization of each composite
number. Encourage students to check the prime
factorization of each number by multiplying the
factors. Invite volunteers to share their answers
and the strategies they used with the class.
The prime numbers have only 2 factors. The composite
numbers have more than 2 factors.
a) 1, 5; 5
b) 1, 2, 4, 8; 8
c) 1, 2, 3, 6; 6
d) 1, 5; 5
a) 2 3 3
b) 5 7
c) 2 2 3 3
d) 2 5 5
I found the factors for numbers 20 to 28. The only number
that doesn’t have a factor of 2, 3, 4, or 5 is 23. 23 is also
the only prime number between 20 and 28.
Each has only 1 and itself as factors.
2, 3, 5, 7, 11, 13, 17, 19, 23, and 29 are prime numbers.
So, there are 10 days in September with prime number dates.
1 is neither prime nor composite. 4, 6, 8, 9, 10, 12, 14, 15,
16, 18, 20, 21, 22, 24, 25, 26, 27, 28, and 30 are composite
numbers. So, there are 19 days in September with composite
number dates.
Practice
Have Colour Tiles or congruent squares
available for students to use.
Assessment Focus: Question 7
Students realize that the number in question is
not divisible by 2, 3, 4, or 5. Some students may
systematically test each number from 20 to 28
for divisibility by these numbers. Other students
may use Colour Tiles to model rectangles for
each number, looking for a number that does
not have 2, 3, 4, or 5 as a factor.
To reinforce the concepts of common factors and
greatest common factor, choose a pair of factors
and have students find the common factors
and the greatest common factor. For example,
12 and 18. (Common factors: 1, 2, 3, 6; Greatest
common factor: 6)
Unit 2 • Lesson 5 • Student page 47
19
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10. All even numbers are divisible by 2. 32 is even. Any
number with 0 or 5 for a ones digit is divisible by 5.
95 is divisible by 5.
11. The spinner has 3 prime numbers (47, 13, and 59) and
3 composite numbers (55, 39, and 26). Each player has
an equal chance of winning.
12. a) There could be 1, 2, or 4 buns in one package.
b) There could be 1, 3, or 9 buns in one package.
13. No; 9 and 25 are odd numbers and each has more than
2 factors. So they are composite.
14.
Yes
Composite
Prime
Even
2
Odd
3, 5, 7, 11, 13,
17, 19, 23, 29
4, 6, 8, 10, 12, 14, 16,
18, 20, 22, 24, 26, 28, 30
9, 15, 21, 25, 27
REFLECT: You can make only a 1 by 1 rectangle with 1 tile.
So, 1 has only 1 factor. Jamie is right.
Numbers Every Day
Students should use the same strategies to round to hundred
thousands and millions as they do to round to lesser place values.
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46
10
10
52
200
000
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100
000;
000;
000;
000;
46
10
10
52
000
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000
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ASSESSMENT FOR LEARNING
What to Look For
What to Do
Reasoning; Applying concepts
✔ Students understand that a prime
number has only 1 and itself as factors.
✔ Students understand that a composite
number has more than two factors.
Extra Support: To complete question 14, suggest that students
first sort the numbers into 2 groups, prime and composite, and
then re-sort each group into even and odd.
Students can use Step-by-Step 5 (Master 2.13) to complete
question 7.
Extra Practice: Have students write the dates of their family
Accuracy of procedures
members’ birthdays, then determine whether each person’s
✔ Students can determine whether
birthday is in a prime or composite month and on a prime or
a number is prime or composite.
composite date within the month.
✔ Students can write prime numbers and
Students can complete Extra Practice 3 (Master 2.24).
the prime factorization of composite
numbers to 100.
Extension: Challenge students to research and use the Sieve of
✔ Students can find common factors and Eratosthenes method for finding the prime numbers less than 100.
the greatest common factor of a pair
Students should be able to explain why this method works.
of numbers.
Recording and Reporting
Master 2.2 Ongoing Observations:
Whole Numbers
20
Unit 2 • Lesson 5 • Student page 48