This document outlines a 11-day unit on number theory including lessons on prime and composite numbers, factors and prime factorization, greatest common factor, properties of operations, the distributive property, equivalent expressions, and solving expressions using related concepts. It provides learning standards, vocabulary words, and example problems for students to practice these skills in working with numbers, variables, and algebraic expressions. A unit review is also included to assess student understanding of the key concepts covered.

1. 0Unit 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 = _______ r = _______
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