Numerical and Algebraic Expressions

Lesson 11

Math

Unit 5

6th Grade

Lesson 11 of 12

Objective


Write algebraic expressions for application situations (Part 1).

Common Core Standards


Core Standards

  • 6.EE.B.6 — Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

Foundational Standards

  • 4.OA.A.3

Criteria for Success


  1. Define variables for real-world contexts with precision (MP.2 and MP.6).
  2. Write expressions with variables to represent real-world situations involving addition, subtraction, multiplication, or division.

Tips for Teachers


Lessons 11 and 12 focus on writing expressions with variables to represent real-world contexts and situations. Lesson 11 focuses on situations with only one operation involved. 

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Anchor Problems


Problem 1

Read each story problem. Identify the unknown quantity, and write an addition or subtraction expression to represent the problem. Finally, evaluate your expression using the information given in the fourth column.

Story Problem Variable with Units Expression Evaluate if: Evaluate
Gregg has two more dollars than his brother Jeff. Write an expression for the amount of money Gregg has.     Jeff has $12.  
Gregg has two more dollars than his brother Jeff. Write an expression for the amount of money Jeff has.     Gregg has $14.  
Aaron read 6 more books than Kristen over the summer. Write an expression for the number of books Kristen read.     Aaron read 20 books over the summer.  
Ian scored 4 fewer soccer goals than Julia in the first half of the season. Write an expression for the number of goals Ian scored.      Julia scored 13 goals.  

Guiding Questions

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References

EngageNY Mathematics Grade 6 Mathematics > Module 4 > Topic F > Lesson 18Example 2

Grade 6 Mathematics > Module 4 > Topic F > Lesson 18 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Kelly and Cristina share a birthday, but Kelly is older. The table below shows some of their ages.

Cristina's age (in years)

Kelly's age (in years)
0 5
1 6
2 7
3 8

a.   If Cristina is $${16}$$ years old, how old is Kelly?

b.   If Cristina is $$C$$ years old, how old is Kelly?

c.   If Kelly is $$K$$ years old, how old is Cristina?

Guiding Questions

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References

EngageNY Mathematics Grade 6 Mathematics > Module 4 > Topic F > Lesson 19Exercise 3

Grade 6 Mathematics > Module 4 > Topic F > Lesson 19 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

In Massachusetts, there is a deposit on all carbonated beverage cans and bottles. When you return the empty can or bottle, you get the deposit back in a refund. The table below shows the amount of money refunded for different numbers of cans or bottles.

Number of Containers Returned Amount of Refund in Dollars
1 0.05
2 0.10
10 0.50
50 2.50
100 5.00

a.   If $$C$$ represents the number of containers returned, what expression represents the amount of refund in dollars?

b.   How much money would you receive in a refund if you returned 222 cans?

c.   If you received a refund of $4.50, how many containers did you return?

Guiding Questions

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References

EngageNY Mathematics Grade 6 Mathematics > Module 4 > Topic F > Lesson 20Exercise 1

Grade 6 Mathematics > Module 4 > Topic F > Lesson 20 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem Set

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Target Task


Abel runs at a constant rate. The table below shows how far Abel has run after a certain number of hours. 

Number of hours 1 2 4 5
Number of miles 5.5 11 22 27.5

a.   How many miles did Abel run after $$3$$ hours?

b.   Write an expression to represent the number of miles Abel ran after $$h$$ hours.

Student Response

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Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

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Lesson 10

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Lesson 12

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Numerical Expressions with Exponents

Topic B: Introduction to Algebraic Expressions

Topic C: Equivalent Expressions & Applications

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