6th Grade Math HOMEWORK ANSWERS

Lesson 13 Exit Ticket

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Lesson 14 Exit Ticket

Expressions and Equations

Expressing Operations in Algebraic Form

Common Core: Engage New York

6.EE.1, 6.EE.2, 6.EE.3 and 6.EE.4

Lessons 15-17: 6.EE.2b

Lessons 15 & 16: Read and Write Expressions in Which Letters Stand for Numbers

6.EE. A.2b

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.

Table of Contents

Date Title Page

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

Fresh Left

3/18/14 F8 ENY L13&14- Writing Division Expressions Marzano:

Fresh Left

3/19/14 F8 ENY L15&16- Read & Write Expressions with Variables

Marzano: Fresh Left

Pre- ??? Post- ???

Pre- ???/??? Post- ???/???

Pre- ??? Post- ???

MA

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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 read expressions in which letters stand for numbers. I will assign operation terms to operations when reading.

• I will identify parts of an algebraic expression using mathematical terms for all operations.

• I will write algebraic expressions that record all operations with numbers and letters standing for the numbers.

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.

Mathematical Words & Operations

Lesson 15: Read Expressions in Which Letters Stand for Numbers- Ex. 1 Write an expression using words.

• 𝑎 − 𝑏

• 𝑥𝑦

• 4𝑓 + 𝑢

• 𝑑 − 𝑏3

• 5 𝑢 − 10 + ℎ

•3

𝑑+𝑓

Lesson 15: Read Expressions in Which Letters Stand for Numbers- Ex. 1

Exercises- Write ALL the vocabulary words that could be used to describe the given expression.

6ℎ − 10 Addition Subtraction Multiplication Division

5𝑑

6 Sum Difference Product Quotient

5 2 + 𝑑 − 8 Add Subtract Multiply Divide

𝑎𝑏𝑐 More than Less than Times Each

Lesson 15: Read Expressions in Which Letters Stand for Numbers- Ex. 1

Write an expression using vocabulary to represent each given expression.

• 8 − 2𝑔

• 15(𝑎 + 𝑐)

•𝑚+𝑛

5

• 𝑏3 − 18

• 𝑓 −𝑑

2

•𝑢

𝑥

Lesson 15 Closing

Peter says the expression 11 − 3𝑐 is three times 𝑐 decreased by 11.

Is he correct? Why or why not?

Lesson 16: Write Expressions in Which Letters Stand for Numbers

Lesson 16: Write Expressions in Which Letters Stand for Numbers- Ex. 1

Identify the key words in each statement.

• The sum of twice 𝑏 and 5.

• The quotient of 𝑐 and 𝑑.

• 𝑎 raised to the fifth power then increased by the product of 5 and 𝑐.

• The quantity of 𝑎 plus 𝑏 divided by 4.

• 10 less than the product of 15 and 𝑐.

• 5 times 𝑑 increased by 8.

Lesson 16: Write Expressions in Which Letters Stand for Numbers- Ex. 1

Change the expressions given in the opening exercise from words to variables and numbers.

• The sum of twice 𝑏 and 5.

• The quotient of 𝑐 and 𝑑.

• 𝑎 raised to the fifth power then increased by the product of 5 and 𝑐.

• The quantity of 𝑎 plus 𝑏 divided by 4.

• 10 less than the product of 15 and 𝑐.

• 5 times 𝑑 increased by 8.

Lesson 16: Write Expressions in Which Letters Stand for Numbers- Ex. 2

Change each real world scenario to an expression using variables and numbers. Underline the text to show the key words before writing the expression.

• Marcus has 4 more dollars than Yaseen. If 𝑦 is the amount of money Yaseen has, write an expression to show how much money Marcus has.

• Mario is missing half of his assignments. If 𝑎 represents the number of assignments, write an expression to show how many assignments Mario is missing.

• Kamilah’s weight has tripled since her first birthday. If 𝑤 represents the amount Kamilah weighed on her first birthday, write an expression to show how much Kamilah weighs now.

Lesson 16: Write Expressions in Which Letters Stand for Numbers- Ex. 2

Exercises- Mark the text by underlining key words, and then write an expression using variables and numbers for each statement below.

• 𝑏 decreased by 𝑐 squared.

• 24 divided by the product of 2 and 𝑎.

• 150 decreased by the quantity of 6 plus 𝑏.

• The sum of twice 𝑐 and 10.

• Marlo had $35 but then spent $𝑚.

Lesson 16: Write Expressions in Which Letters Stand for Numbers- Ex. 2

Exercises- Mark the text by underlining key words, and then write an expression using variables and numbers for each statement below.

• Samantha saved her money and was able to quadruple the original amount, 𝑚.

• Veronica increased her grade, 𝑔, by 4 points, and then doubled it.

• Adbell had 𝑚 pieces of candy and ate 5 of them. Then he split the remaining candy equally among 4 friends.

• To find out how much paint is needed, Mr. Jones must square the side length of the gate, and then subtract 15.

• Luis brought 𝑥 cans of cola to the party, Faith brought 𝑑 cans of cola, and De’Shawn brought ℎ cans of cola. How many cans of cola did they bring all together?

Lesson 16 Closing • How is writing expressions with variables and numbers

similar to writing expressions using words?

• Possible answers: The same vocabulary words can be used; identifying parts of the expression before writing the expression is helpful.

• How is writing expressions with variables and numbers different than writing expressions using words?

• Possible answers: When an expression with words is provided, it is possible that it might be represented mathematically in more than one way. However, when an algebraic expression is written, there can only be one correct answer.

Today, I worked towards achieving the Learning Goal by mastering the Learning Target for this lesson.

• I CAN read expressions in which letters stand for numbers. I CAN assign operation terms to operations when reading.

• I CAN identify parts of an algebraic expression using mathematical terms for all operations.

• I CAN write algebraic expressions that record all operations with numbers and letters standing for the 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.

6th Grade Math HOMEWORK

Lesson 15 Exit Ticket

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Lesson 16 Exit Ticket