Name: ________________________________________________ Date:________________________
LESSON 61: PRIME NUMBERS
Saxon 7/6 page 294
*Numbers that only have _____________ factors are called _______________ numbers.
*The only factors of a prime number are _____ and ___________.
Example:
Number
Factors
Prime?
1
2
3
4
5
6
7
8
1
1, 2
1, 3
1, 2, 4
1, 5
1, 2, 3, 6
1, 7
1, 2, 4, 8
No
*All prime numbers (except for 2) are ________.
*Are all odd numbers prime? _________
Odd Numbers That Are NOT Prime: _____, _____, _____, _____, _____, _____
Example: The first four prime numbers are 2, 3, 5, and 7. What are the next four prime numbers?
8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
Prime Numbers Activity:
1
2
11
12
21
22
31
32
41
42
3
13
23
33
43
4
14
24
34
44
5
15
25
35
45
6
16
26
36
46
7
17
27
37
47
8
18
28
38
48
9
19
29
39
49
10
20
30
40
50
a. Draw a line through the number 1. The number 1 is not a prime number.
b. Circle the prime number 2. Draw a line through all the other multiples of 2 (4, 6, etc.).
c. Circle the prime number 3. Draw a line through all the other multiples of 3.
d. Circle the prime number 5. Draw a line through all the other multiples of 5.
e. Circle the prime number 7. Draw a line through all the other multiples of 7.
f. All the numbers in the chart that are not crossed off are prime numbers. Circle all the prime numbers.
Practice:
Which number in each group is a prime number?
a. 21, 23, 25
b. 31, 32, 33
c. 43, 44, 45
Which number in each group is not a prime number?
d. 41, 42, 43
e. 31, 41, 51
f. 23, 33, 43
Prime numbers can be multiplied to equal numbers that are not prime (2x2x3= 12). Show which prime
numbers we multiply to make these products:
g. 16
h. 18
Name: ________________________________________________ Date:________________________
LESSON 62: SUBTRACTING MIXED NUMBERS WITH REGROUPONG, PART 2
Saxon 7/6 page 299
Step 1: set up your problem by writing the fractions up and down
Step 2: make sure fractions have common denominators
Step 3: regroup if needed
Step 4: subtract
Step 5: reduce if needed
2
Example: 3
3
1
−1 =
2
2
2
4
3 x =3
3
2
6
1
3
2
3
−1 x
=1
3
6
2
1
Example: 5
2
6
2
−1 =
3
1 3
5 x
2 3
−
1
=5
3
6
2 2
4
1 x =1
3 2
6
Practice:
1
1
2
3
2
5
3
6
5
1
6
3
a. 5 – 3
d. 7 – 3
g. 4 – 1
1
1
4
3
1
1
6
2
1
5
2
6
b. 4 – 2
e. 6 – 1
h. 6 – 3
1
3
2
4
1
1
3
2
2
3
3
4
c. 6 – 1
f. 4 – 1
i. 8 – 5
Name: ________________________________________________ Date:________________________
LESSON 63: POLYGONS
Saxon 7/6 page 303
**Polygons are _________________ shapes with __________________ sides.
*Polygons are named by the number of sides they have.
SHAPE
POLYGONS
NUMBER OF SIDES
3
NAME OF POLYGON
Triangle
4
Quadrilateral
5
Pentagon
6
Hexagon
8
octagon
When two sides of a polygon meet, we say they __________________.
The place where they intersect is called a ________________. More than one is called _______________.
*A polygon has the same number of vertices as it has sides. (Check this out in the chart above)
Example: What is the name of a polygon that has four sides?
Correct Answer: ___________________________ Incorrect Answer: ______________ or _____________
*If all the sides of a polygon are the same length and all the angles are the same measure, then the
polygon is called a ___________________________________. An example would be a ______________.
Example: The area of a square is 25 square centimeters.
a.) What is the length of each side of the square?
b.) What is the perimeter of the square?
Example: A regular octagon has a perimeter of 96 inches. How long is each side?
Practice:
a. What is the name of this six-sided shape?
b. How many sides does a pentagon have?
c. Can a polygon have 19 sides?
d. The area of a square is 16 square inches. What is its perimeter?
Name: ________________________________________________ Date:________________________
LESSON 64: PRIME FACTORIZATION ● DIVISION BY PRIMES ● FACTOR TREE
Saxon 7/6 page 308
If a whole number is not prime, it is ___________________________. This means that it has more than
two factors. (see chart from lesson 61)
Prime Factorization: When we write a composite number as a product of its prime factors.
Example:
4=2∙2
6=2∙3
8=2∙2∙3
9=3∙3
*There are two methods for finding prime factorization. Division by Primes and Factor Trees.
Division by Primes:
5
3)15
2)30
2)60
Prime Factorization for 60 = 2 ∙ 2 ∙ 3 ∙ 5
Factor Trees:
60
6
2
10
3 2
Prime Factorization for 60 = 2 ∙ 2 ∙ 3 ∙ 5
5
Practice:
a. Which of these numbers are composite numbers? 19, 20, 21, 22, 23
b. Write the prime factorization of each composite number in problem (a).
c. Use a factor tree to find the prime factorization of 36.
d. Use division by primes to find the prime factorization of 48.
e. Write 125 as a product of prime factors.
f. Write the prime factorization of 10 and of 100. What similarities do you notice? Can you guess what the
prime factorization of 1000 is?
Name: ________________________________________________ Date:________________________
LESSON 65: MULTIPLYING MIXED NUMBERS
Saxon 7/6 page 314
STEPS:
1. Put whole numbers over one and
change mixed numbers into improper
fractions.
2. Multiply
3. Reduce and change improper
fractions to mixed numbers
Example: 2
Example: 2
2
3
1
2
x4
x1
Example: 5 x 2
8
3
1
5
3
2
4
x
1
4
x
3
=
32
3) 32
3
20
=
6
=
10
3
2
3
Practice:
a. 1
1
2
d. 1
2
3
1
g. 3
3
x
2
b. 1
3
e. 2
x3
x1
2
3
2
3
1
2
h. 2
3
4
x
3
4
x2
x2
2
3
1
c. 1
2
x1
f. 3 x 1
i. 2 x 3
3
4
1
2
2
3
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