1. Unit 4: Number Theory Approximate Pacing: 11 days
NYS Common Core Textbook
Topic On Core Vocabulary
Learning Standard Resource
4.OA.4 Prime & Composite / Divisibility Rules 4-1 - divisible, prime,
composite
4.OA.4 Factors & Prime Factorization 4-2 - factor, prime factorization
6.NS.4 Greatest Common Factor 4-3 1-6 greatest common factor
6.NS.4 Properties p. 669 & 1-5 - Commutative Property
~Commutative Property (addition & multiplication) Associative Property
~Associative Property (addition & multiplication) Identity Property of Zero
~Identity Property of Zero (addition) Identity Property of One
~Identity Property of One (multiplication) Property of Zero
~Property of Zero (multiplication)
6.NS.4 Distributive Property p. 669 3-5 Distributive Property
6.NS.4 Distributive Property with GCF - 3-5
6.EE.3 Two Equivalent Expressions / - 3-5 like terms, equivalent
6.EE.4 Distributive Property with Variables expression
Common task:
Secret Number
Unit 4 Lesson 1 Prime & Composite / Divisibility Rules
Unit 4 Lesson 2 Factors & Prime Factorization
Unit 4 Lesson 3 Greatest Common Factor
Unit 4 Lesson 4 Properties
Unit 4 Lesson 5 Distributive Property
Unit 4 Lesson 6 Distributive Property with GCF
Unit 4 Lesson 7 Two Equivalent Expressions (Combining Like Terms)
Unit 4 Lesson 8 Distributive Property with Variables (Combining Like Terms)
Unit 4 Lesson 8 Day 2 Solving Distributive Property with Variables (Combining Like Terms)

2. Name ____________________________________ Date _________________________
Mrs. Labuski / Mrs. Portsmore Period _________ Unit 4 Review
Unit 4 Lesson 1 Prime & Composite / Divisibility Rules
Directions: Tell whether each number is divisible by 2, 3, 4, 5, 6, 9 or 10.
1) 118 _______________________________________________
2) 342 _______________________________________________
3) 170 ______________________________________________
4) 90 _______________________________________________
5) Which numbers is 284 NOT divisible by: 2, 3, 4, 5, 6, 9, and 10
Directions: Tell whether each number is PRIME or COMPOSITE.
6) 121 _______ 7) 61 _______
8) 97 _______ 9) 77 _______
10) 118 _______ 11) Identify the only EVEN number that is PRIME _______
Unit 4 Lesson 2 Factors & Prime Factorization
Directions: List all of the factors of each number. Use “List Method”
12) 60 13) 72
14) 85 15) 56
Directions: Write the Prime Factorization of each number in exponential form.
16) 65 17) 99
18) 76 19) 46

3. Unit 4 Lesson 3 Greatest Common Factor
Directions – Use Factor Trees to find the GCF.
20) 36 and 60
21) 50, 75 and 125
Unit 4 Lesson 4 Properties
Directions – Identify the PROPERTY shown and the missing variable.
Menu of Properties
- Commutative Property of Addition/Multiplication
- Associative Property of Addition/Multiplication
- Identity Property of ZERO With Addition
- Identity Property of ONE With Multiplication
- Property of Zero With Multiplication
22) 3 x (2 x 6) = (3 x 2) x n 23) 64 + 18 = x + 64
n = _______ x = ______
Property = _________________ Property = _________________
24) 99 x n = 99 25) 34 x (32 X 64) = (y x 32) x 64
n = _______ y = _______
Property = _________________ Property = _________________
26) n + 79 = 79 27) 10098 x 0 = r
n = _______ n = _______
Property = _________________ Property = _________________

4. Unit 4 Lesson 5 Distributive Property
Directions – Solve using the Distributive Property.
28) 12(x + 1) 29) 7(a + 13)
30) 23x(x + y) 31) 12x(8x – 5y)
Unit 4 Lesson 6 Distributive Property with GCF
Write each of the following sums as two factors of their GCF and a sum.
32) 24 + 16 33) 30 + 60 34) 49 + 63
______________ _______________ ________________
35) 35a + 40a 36) 9cd + 12c 37) 27x + 72x
______________ _______________ ________________
38) 49x2 + 63x 39) 6a + 15a2 40) 12x2y + 16xy
______________ _______________ ________________
Unit 4 Lesson 7 Two Equivalent Expressions (Combining Like Terms)
Simplify.
41) 8k2 + 4k - 3k2 + 32 - k + 5 42) 10x3 + 5y2 + 2xy - 4y2 + 4xy - x3
__________________________ __________________________
43) 3a + 2b2 + 6c + a - 2c + b2 + c 44) 12x4 + 6x2 + 5x3 - x2 + 2xy - 8x4
__________________________ __________________________
45) 9p6 + q2 + 6p + 5q2 + 5p - 5q2 46) h2 + 4h + 4h2 - h + 4 + h2 + 7h

5. __________________________ __________________________
47. Find the perimeter of the rectangle. 48. Find the perimeter of the triangle.
Unit 4 Lesson 8 Distributive Property with Variables (Combining Like Terms)
Distribute. Simplify.
49. 6(7 + 2m) + 3(5m – 4) 50. 6x(4x + 7) + x
Unit 4 Lesson 8 Day 2 Solving Distributive Property with Variables
Distribute. Simplify. Plug. Solve. (In that order!)
51) 6(4 + m) + 3(6m – 5); x = 2 52) 2m(4 + m) + 3(2m + 8); x = 3
Simplify. Solve.
53) 5y + 2y = 21 54) 9x – 3x = 42
Write as an algebraic expression.
55) 6 plus m multiplied by 6 ___________
56) 54 divided by the sum of 9 and a number_______
Write as an equivalent expression.

6. 57) x + x = _____________________ 58) x • x = __________________________