Expressions and Equations Expanding, Factoring, and Distributing Expressions Common Core: Engage New York 6.EE.1, 6.EE.2, 6.EE.3 and 6.EE.4 Lessons 9-14: 6.EE.2a, 6.EE.2b, 6.EE.3, 6.EE.4
Lessons 11 & 12: Factoring & Distributing Expressions
What does 6.EE.A.1 cover? Write and evaluate numeric expressions involving whole-number exponents.
What does 6.EE.A.2 cover? Write, read, and evaluate expressions in which letters stand for numbers a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract 𝑦 from 5” as 5−𝑦. b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2(8+7) as a product of two factors; view (8+7) as both a single entity and a sum of two terms. c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas 𝑉=𝑠3 and 𝐴=6𝑠2 to find the volume and surface area of a cube with sides of length 𝑠=1/2.
What does 6.EE.A.3 cover? Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2+𝑥) to produce the equivalent expression 6+3𝑥; apply the distributive property to the expression 24𝑥+18𝑦 to produce the equivalent expression 6(4𝑥+3𝑦); apply properties of operations to 𝑦+𝑦+𝑦 to produce the equivalent expression 3𝑦.
What does 6.EE.A.4 cover? Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions 𝑦+𝑦+𝑦 and 3𝑦 are equivalent because they name the same number regardless of which number 𝑦 stands for.
Table of Contents Date Title Page 3/17/14 2/6/14 NEW Focus 8- Algebraic Expression Scale and Chart Fresh Left F8 Engage NY Lesson 1 –Add and subtract Relationship 2/7/14 F8 Engage NY Lesson 2 – Multiplication and Division Relationship 2/10/14 F8 Engage NY Lesson 3-Multiplication and Addition Relationship 2/11/14 F8 Engage NY Lesson 4-Division and Subtraction Relationship 2/19/14 F8 ENY L5- Exponents 2/20/14 F8 ENY L6- Order of Operations 2/25/14 F8 ENY L7- Replacing Letters with Numbers 2/28/14 F8 ENY L8- Replacing Numbers with Letters 3/3/14 F8 ENY L9- Writing + & - Expressions 3/4/14 F8 ENY L10- Writing & Expanding X Expressions 3/17/14 F8 ENY L11&12- Factoring & Distributing Marzano: Pre- ???/??? Post- ???/???
MARZANO SCALE RATING Before we start the Learning Target Lesson, think about the Learning Target for today…. How much prior knowledge do you have regarding that goal? Chart your prior knowledge using your pre-target score icon.
Today, I work towards achieving the Learning Goal by focusing on the Learning Target for this lesson. I will model and write equivalent expressions using the distributive property. I will move from an expanded form to a factored form of an expression. Take a moment to ANALYZE today’s Learning Target, using Marzano’s scale (0-4) evaluate and rate your prior knowledge, understanding and application.
Focus 8 Algebraic Expression Learning Goal I am able to work with numerical expressions and use letters to represent unknowns in problem solving situations I am able to investigate and apply properties of operation in numerical contexts, such as the associative, distributive, and commutative properties. I can build on my understanding of inverse operations to solve algebraic expressions.
Lesson 11: Factoring Expressions- Ex. 1
Lesson 11: Factoring Expressions- Ex. 1
Lesson 11: Factoring Expressions- Ex. 2
Lesson 11: Factoring Expressions- Ex. 2
Lesson 11: Factoring Expressions- Ex. 3
Lesson 11: Factoring Expressions- Ex. 3
Lesson 11: Factoring Expressions- Ex. 3
Lesson 11 Closing
Lesson 11 Summary An Expression in Factored Form: An expression that is a product of two or more expressions is said to be in factored form.
Lesson 12: Distributing Expressions
Lesson 12: Distributing Expressions- Ex. 1
Lesson 12: Distributing Expressions- Ex. 1
Lesson 12: Distributing Expressions- Ex. 2
Lesson 12: Distributing Expressions- Ex. 2
Lesson 12: Distributing Expressions- Ex. 3
Lesson 12: Distributing Expressions- Ex. 4
Lesson 12 Closing State what the expression 𝑎(𝑏+𝑐) represents. 𝑎 groups of the quantity 𝑏 plus 𝑐. Explain in your own words how to write an equivalent expression in expanded form when given an expression in the form of 𝑎(𝑏+𝑐). Then create your own example to show off what you know. To write an equivalent expression, I would multiply 𝑎 times 𝑏 and 𝑎 times 𝑐. Then, I would add the two products together. Examples will vary. State what the equivalent expression in expanded form represents. 𝑎𝑏+𝑎𝑐 means 𝑎 groups of size 𝑏 plus 𝑎 groups of size 𝑐.
Today, I worked towards achieving the Learning Goal by mastering the Learning Target for this lesson. I CAN model and write equivalent expressions using the distributive property. I CAN move from an expanded form to a factored form of an expression. Take a moment to REFLECT on today’s Learning Target, using Marzano’s scale (0-4) evaluate and rate how you built upon your prior knowledge, demonstrated understanding and application.
Lesson 11 Exit Ticket & Lesson 12 Exit Ticket 6th Grade Math HOMEWORK Lesson 11 Exit Ticket & Lesson 12 Exit Ticket