Name
Chapter 1, Lesson 1
Reteach
Date
Hands On: Find Prime Numbers
CA Standard
NS 1.4
You will identify prime numbers.
Can George arrange 7 race cars in one or more rows with an equal number of race cars in
each row? To find out decide whether 7 is prime or not prime.
• A prime number is a counting number that has exactly two different factors:
1 and itself
Sieve of Eratosthenes
Step 1 Cross out 1 because it is not
1
2
3
4
5
6
7
8
prime. Circle 2, because it is prime, and
cross out all multiples of 2 because they
are not prime.
11 12 13 14 15 16 17 18
Step 2 Go to the next number that is
not crossed out. Circle it. Then cross out its
multiples.
Repeat until all the numbers are either
circled or crossed out.
7 is a prime number, so George can only
arrange the race cars in 1 row of 7 or 7
rows of 1.
9
10
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
Decide if the number is prime or not prime. You can draw arrays or
use your completed table.
1.
5
2.
12
3.
17
4.
13
5.
15
6.
42
7.
23
8.
28
9.
19
10.
31
11.
11
12.
33
Writing Math How can you use the Sieve of Eratosthenes to
find prime numbers?
Reteach
Copyright © Houghton Mifflin Company. All rights reserved.
1–34
Use with text pages 6–7.
Name
Chapter 1, Lesson 2
Reteach
Date
Find Factors of a Number
CA Standards
NS 1.1,
NS 1.4, MR 2.4
A factor is one of two or more numbers that are multiplied to give a product.
So, 5 is a factor of 30 because when 5 is multiplied by 6 the product is 30.
A prime number is a counting number greater than 1 with exactly
two different factors —1 and the number itself.
A composite number is a counting number that has more than 2 different
whole number factors.
Robert has 13 books to place on his bookcase which has 4 shelves.
Can an equal number of books go on each of the 4 shelves? To find
out, decide whether 4 is a factor of 13.
Way 1 Draw all the ways you can arrange
13 squares in an array.
Way 2 Use division.
13 ÷ 4 = 3 R1
Solution: An equal number of books can not go on the 4 shelves, so 4 is not a factor of 13.
Draw arrays to find the factors of each number. Then write if the
number is prime or composite.
1.
8
2.
10
3.
9
4.
19
8.
16
Use division to find the factors of each number. Then write if the
number is prime or composite.
5.
11
6.
15
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7.
1–40
22
Use with text pages 8–11.
Name
Chapter 1, Lesson 3
Reteach
Date
Prime Factorization
CA Standards
NS 1.4, MR 2.3
Jason needs to find all of the factors of 60 for his math homework. Follow the steps he
used to find the prime factorization of 60.
Step 1 Find two numbers
with a product of 60 (do not
use 1 and 60). Write them
as branches of a factor tree.
60
Step 2 Write each composite number as a product
of two factors. Circle prime
numbers. Continue until
the numbers at the ends of
branches are prime numbers.
Step 3 Write all the prime
number factors in order from
least to greatest.
60 = 2 × 2 × 3 × 5
60
6 × 10
6
×
10
2×3×2×5
Solution: The prime factorization of 60 is 2 × 2 × 3 × 5.
Complete each factor tree. Then write the prime factorization.
1.
2.
15
3 ×
×3
18
4.
5.
× 2
9
3×
×
9
3 ×
20
6.
54
9 × 2
3 ×
3.
21
6
× 2 ×3
5 × 4
5 ×
×
Writing Math Explain how making a factor tree can help you
find the prime factorization of a number.
Reteach
Copyright © Houghton Mifflin Company. All rights reserved.
1–46
Use with text pages 12–13.
Name
Chapter 1, Lesson 4
Reteach
Date
Exponents and Prime Factorization
CA Standards
NS 1.4, NS 1.3
Use exponents to write the prime factorization of 28.
Step 1 Write 28 as the
product of 2 factors.
Step 2 Write the factors of
each composite factor.
28
28
4
Solution: 28 = 22 × 7
4
7
2
Step 3 Use exponents to
write the prime factorization.
7
2
1
7
Write the prime factorization of each number. Use exponents if possible.
If the number is prime, write prime.
1.
32
2.
31
3.
49
4.
39
5.
40
6.
81
Write each expression using exponents.
7.
6×6×6
8.
5×5×5×5
9.
9×9×9
Writing Math Explain how a factor tree helps you identify the
base number and possible exponents in an expression.
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1–52
Use with text pages 14–15.
Name
Chapter 1, Lesson 5
Reteach
Date
Common Factors and Greatest
Common Factors
CA Standards
NS 1.4, MR 2.4
In an after school study club, there are 40 third graders and 50 fourth
graders. The teacher would like to divide the students into equal
groups with at least one third grader and fourth grader in each group.
What number of students could be in a group?
Different Ways to Find the GCF
Way 1 List all the factors of each number.
Circle the numbers that are the same in
both sets. Then identify the greatest of
these common factors.
40: 1 , 2 , 4, 5 , 8, 10 , 20, 40
Way 2 Use factor trees to find the prime
factorization of each number. Identify the
prime factors the numbers have in common.
Find the product of these common prime
factors.
40
50: 1 , 2 , 5 , 10 , 25, 50
4 × 10
The GCF of 40 and 50 is 10.
2 × 2 × 2 ×5
50
5 × 10
5 × 2 ×5
The common prime factors of 40 and 50 are
2 and 5. The GCF of 40 and 50 is 2 × 5 = 10.
List the factors of each number. Circle the common factors. Then find
the greatest common factor (GCF) of the numbers.
1.
4, 10
2.
12, 14
3.
6, 21
4.
7, 9
Writing Math Explain why 1 is the greatest common factor
(GCF) for the numbers 23 and 29.
Reteach
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1–58
Use with text pages 16–19.