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

Lesson 9: Writing Addition and Subtraction Expressions Focus Standard: 6.EE.A.2a 6.EE.A.2b 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.

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 3/3/2014 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 2/19/2014 F8 ENY L5- Exponents 2/20/2014 F8 ENY L6- Order of Operations 2/25/2014 F8 ENY L7- Replacing Letters with Numbers 2/28/2014 F8 ENY L8- Replacing Numbers with Letters 3/3/2014 F8 ENY L9- Writing + & - Expressions

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.

Today, I work towards achieving the Learning Goal by focusing on the Learning Target for this lesson. I will write expressions that record addition and subtraction operations with numbers. Take a moment to ANALYSIS today’s Learning Target, using Marzano’s scale (0-4) evaluate and rate your prior knowledge, understanding and application.

How much prior knowledge do you have regarding that goal? MY PROGRESS CHART 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.

Example 1 (3 minutes)- This lesson requires the use of a white board for each student. Create a bar diagram to show 3 plus 5. How would this look if you were asked to show 5 plus 3? Are these two expressions equivalent?

Example 2 (3 minutes)- This lesson requires the use of a white board for each student. How can we show a number increased by 2? Can you prove this using a model?

Example 3 (3 minutes)- This lesson requires the use of a white board for each student. Write an expression to show the sum of 𝑚 and 𝑘. Which property can be used in Examples 1-3 to show that both expressions given are equivalent?

Example 4 (3 minutes)- This lesson requires the use of a white board for each student. How can we show 10 minus 6? Draw a bar diagram to model this expression. What expression would represent this model? Could we also use 6−10?

Example 5 (3 minutes)- This lesson requires the use of a white board for each student. How can we write an expression to show 3 less than a number? Start by drawing a diagram to model the subtraction. Are we taking away from the 3 or the unknown number? We are starting with some number and then subtracting away 3. What expression would represent this model?

Example 6 (3 minutes)- This lesson requires the use of a white board for each student. How would we write an expression to show the number 𝑐 being subtracted from the sum of 𝑎 and 𝑏? Start by writing an expression for the sum 𝑎 and 𝑏. Now show 𝑐 being subtracted from the sum.

Example 7 (3 minutes)- This lesson requires the use of a white board for each student. Write an expression to show 𝑐 minus the sum of 𝑎 and 𝑏. Why are parentheses necessary in this example and not the others? Replace the variables with numbers to see if 𝑐−(𝑎+𝑏) is the same as 𝑐−𝑎+𝑏.

Worksheet Exercises (12 minutes) Independently, you are going to complete a worksheet demonstrating your understanding and application of today’s Learning Target. Read each problem carefully and I encourage you to refer to your class notes, if you have any questions. You have up to 12 minutes so your focus is required.

Start Tuesday- period 1, 2

Closing (7 min) 𝑚+𝑘 𝑘+𝑚 𝑚−𝑘 𝑘−𝑚 Write the following in words. Is 𝑚+𝑘 equivalent to 𝑘+𝑚? Is 𝑚−𝑘 equivalent to 𝑘−𝑚? Discuss with your partner. 𝑚+𝑘 is equivalent to 𝑘+𝑚. Both of these expressions have the same result. However, 𝑚−𝑘 and 𝑘−𝑚 will NOT have the same result. It would be starting a new total amount and taking away a different amount as well. This will give different solutions. Example, 4+6=10 and 6+4=10. However, 6−4=2, but 4−6 ≠2!

Exit Learning Target Assessment (5 mins) Writing Addition & Subtraction Expressions On the back of the Lesson 9 Worksheet, you are going to complete the following directions to assess your understanding and application of today’s Learning Target. Read each direction carefully and refer your class notes, to clarify any questions. Write an expression showing: the sum of 8 and a number 𝑓. Write an expression showing: 5 less than the number 𝑘. Write an expression showing: the sum of a number ℎ and a number 𝑤 minus 11.

Today, I worked towards achieving the Learning Goal by mastering the Learning Target for this lesson. I CAN write expressions that record addition and subtraction operations with numbers. 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.

How much prior knowledge do you have regarding that goal? MY PROGRESS CHART 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.

The End of Lesson 9 Writing Addition and Subtraction Expressions 