expressions and equations expanding, factoring, and distributing expressions

Expressions and Equations

Expanding, Factoring, and Distributing Expressions

Common Core: Engage New York6.EE.1, 6.EE.2, 6.EE.3 and 6.EE.4Lessons 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.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 𝑦from 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 = 3 𝑉 𝑠 and =6 2 𝐴 𝑠to find the volume and surface area of a cube with sides of length =1/2𝑠 .

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 24 +18 𝑥 𝑦to produce the equivalent expression 6(4 +3 )𝑥 𝑦 ; apply properties of operations to + + 𝑦 𝑦 𝑦 to produce the equivalent expression 3𝑦.

Table of ContentsDate Title Page

2/6/14 NEW Focus 8- Algebraic Expression Scale and Chart Fresh Left

2/6/14 F8 Engage NY Lesson 1 –Add and subtract Relationship Fresh Left

2/7/14 F8 Engage NY Lesson 2 – Multiplication and Division Relationship Fresh Left

2/10/14 F8 Engage NY Lesson 3-Multiplication and Addition Relationship Fresh Left

2/11/14 F8 Engage NY Lesson 4-Division and Subtraction Relationship Fresh Left

2/19/14 F8 ENY L5- Exponents Fresh Left

2/20/14 F8 ENY L6- Order of Operations Fresh Left

2/25/14 F8 ENY L7- Replacing Letters with Numbers Fresh Left

2/28/14 F8 ENY L8- Replacing Numbers with Letters Fresh Left

3/3/14 F8 ENY L9- Writing + & - Expressions Fresh Left

3/4/14 F8 ENY L10- Writing & Expanding X Expressions Fresh Left

3/17/14 F8 ENY L11&12- Factoring & DistributingMarzano:

Fresh LeftPre- ???/??? Post- ???/???

MA

RZANO 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 ( + ) represents. 𝑎 𝑏 𝑐• 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 ( + ). Then create your own example to show 𝑎 𝑏 𝑐off 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.

6th Grade Math HOMEWORK

Lesson 11 Exit Ticket&

Lesson 12 Exit Ticket