Numerical and Algebraic Expressions

Lesson 3

Math

Unit 5

6th Grade

Lesson 3 of 12

Objective


Use variables to write algebraic expressions.

Common Core Standards


Core Standards

  • 6.EE.A.2 — Write, read, and evaluate expressions in which letters stand for numbers.
  • 6.EE.A.2.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 = 6 s² to find the volume and surface area of a cube with sides of length s = 1/2.
  • 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.2
  • 4.OA.A.3

Criteria for Success


  1. Compare and contrast numerical and algebraic expressions
  2. Understand a variable is a letter that represents a number; a variable can represent an unknown quantity or a quantity that varies. 
  3. Write an algebraic expression using a variable for a quantity that is unknown.
  4. Write an algebraic expression using a variable for a quantity that changes or varies.

Tips for Teachers


Using variables in expressions is a concept and skill that students will return to and build on in 7th and 8th grades. In using variables to represent unknown or changing values, students are decontextualizing the situation to represent the values as symbols which they can manipulate (MP.2).

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Anchor Problems

25-30 minutes


Problem 1

Sarita has a fish tank in the shape of a rectangular prism. The bottom of the fish tank measures $${10}$$ inches by $$8$$ inches. Sarita wants to add some sand to cover the bottom of the tank, and she uses the formula $${ V=l × w × h}$$ to determine the volume of sand she needs.

a.   If the height of the sand measures $$2$$ inches, what is the volume of sand needed? 

b.   If the height of the sand measures $${3.5}$$ inches, what is the volume of sand needed?

c.   Sarita cannot decide how high she wants the sand to be in the tank. What expression can she use to represent the volume of sand needed for any height of sand? 

Guiding Questions

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Student Response

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Problem 2

In each example, write an expression to represent the quantity.

a.   Thomas is $$x$$ years old. 

  1. His sister is $$5$$ years older. How old is his sister?
  2. His dog is $$3$$ years younger. How old is his dog? 
  3. His cousin is $${3\over4}$$ his age. How old is his cousin? 
  4. His friend is $$y$$ years younger. How old is his friend?

b.   Reina has $$5$$ more quarters than dimes. 

  1. She has $$8$$ dimes. How many quarters does she have?
  2. She has $$15$$ quarters. How many dimes does she have?
  3. She has $$d$$ dimes. How many quarters does she have?
  4. She has $$q$$ quarters. How many dimes does she have? 

Guiding Questions

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Student Response

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Problem 3

a.   A numeric expression like $${5+(8+2)^2}$$ has one and only one value. What is it?

b.   Consider the expression $${ {5+(x+2)^2}}$$. What are some values it can have? Make sure you organize your work so anyone can tell which value for the expression goes with which $$x$$ value.

c.   How many different values can an algebraic expression like $${5+(x+2)^2}$$ have?

Guiding Questions

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Student Response

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References

Illustrative Mathematics Introducing Equivalent Expressions 2

Introducing Equivalent Expressions 2, accessed on Dec. 18, 2017, 3:07 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem Set

15-20 minutes


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes


A frame shop creates custom frames for different sized pictures. A customer has several rectangular-shaped photographs that he wants framed. All of the photographs measure $${10 {1\over2}}$$ inches for the width but vary in the length.

The manager at the frame shop knows she can use the formula for perimeter to determine the amount of wood that she’ll need for each photograph: $${P=2l+2w}$$.

a.   One of the photos is $${15}$$ inches long. How much wood is needed for the frame?

b.   Another photo is $${20 {3\over4}}$$ inches long. How much wood is needed for the frame?

c.   What expression can the manager use to determine the amount of wood needed for any  photograph the customer has? 

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.

Next

Evaluate algebraic expressions.

Lesson 4
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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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