Lesson 5 | Numerical and Algebraic Expressions | 6th Grade Mathematics

Objective

Write expressions for verbal statements and vice versa (Part 1).

Common Core Standards

Core Standards

The core standards covered in this lesson

6.EE.A.2.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.

Expressions and Equations

6.EE.A.2.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.
6.EE.A.2.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.

Expressions and Equations

6.EE.A.2.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.

Foundational Standards

The foundational standards covered in this lesson

5.OA.A.2

Operations and Algebraic Thinking

5.OA.A.2 — Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Describe expressions with one operation in multiple ways, paying attention to the order of the terms where the operation is not commutative.
Distinguish between $${x-y}$$ and $${y-x}$$ and the different ways to describe each expression.
Represent expressions with sums, differences, and products in written and algebraic forms.
Define a term as a part of an expression that is separated from other terms by addition and subtraction. A term can be a single numerical value or a product of numbers and variables.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Lessons 5 and 6 engage students in representing expressions verbally and algebraically, extending on their work with 5.OA.2 where they wrote numerical expressions to record calculations. In Lesson 5, students start with expressions with only one operation. They build towards expressions with combined operations using sums, differences, and products, paying close attention to the order of the terms and where parentheses are needed. In Lesson 6, students will look at more complex expressions, including those involving quotients and exponents.
The commutative property of addition comes into play as students discover they can represent $$x+2$$ as both "the sum of $$x$$ and 2" and "the sum of 2 and $$x$$", but yet the same does not hold true for subtraction. Students are familiar with the concept of the the commutative property from elementary grades, however, they have not necessarily used the formal term. This is an opportunity to introduce the term and connect it to the concept at hand. There will be additional opportunities to use this language throughout the unit.

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

Four expressions are shown in the chart below. For each one, write all the ways to read the expressions that you can think of.

$${x+2}$$	$${x-2}$$

$${2x}$$	$${x\div2}$$

Guiding Questions

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Problem 2

Two tape diagrams are shown below. The shading indicates subtraction.

Statements a–h below can be used to describe either Diagram 1 or Diagram 2. Match each statement to one of the diagrams.

a. The difference of $$4$$ and $$m$$

b. The difference of $$m$$ and $$4$$

c. $$4$$ less than $$m$$

d. $$m$$ less than $$4$$

e. $$4$$ less $$m$$

f. $$m$$ less $$4$$

g. Subtract $$4$$ from $$m$$

h. Subtract $$m$$ from $$4$$

Guiding Questions

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Problem 3

For each verbal statement, write the algebraic expression it describes.

a. The sum of $$e$$ and $$f$$ subtracted from $$g$$

b. $$g$$ less than the sum of $$e$$ and $$f$$

c. $$g$$ more than twice $$f$$

Guiding Questions

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Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

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Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Problem 1

Which verbal statement describes the algebraic expression $${2m-n}$$?

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Problem 2

Which algebraic expression represents the statement “the difference of $$8$$ and the sum of $$3$$ and $$x$$”?

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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.

An activity idea is to play the game memory in pairs by matching expressions written as verbal statements to expressions written in algebraic form. Teachers can create the cards or give students notecards and have them write their own examples to use.

EngageNY Mathematics Grade 6 Mathematics > Module 4 > Topic E > Lesson 16 — Problem Set (Split problems over Lesson 5 and Lesson 6 based on concepts covered)
Kuta Software Free Pre-Algebra Worksheets Variable and Verbal Expressions — Add in or edit problems to be like Anchor Problem #3 or the Target Task
Kuta Software Free Algebra 1 Worksheets Writing Variable Expressions — Add in or edit problems to be like Anchor Problem #3 or the Target Task
Illustrative Mathematics Rectangle Perimeter 1
EngageNY Mathematics Grade 6 Mathematics > Module 4 > Topic E > Lesson 17 — Problem Set (Split problems over Lesson 5 and Lesson 6 based on concepts covered)
EngageNY Mathematics Grade 6 Mathematics > Module 4 > Topic E > Lesson 15 — Problem Set (Split problems over Lesson 5 and Lesson 6 based on concepts covered)
EngageNY Mathematics Grade 6 Mathematics > Module 4 > Topic D > Lesson 9 — Exercises and Problem Set

Lesson 4

Lesson 6

Lesson Map

Topic A: Numerical Expressions with Exponents

Understand the meaning of exponents.

6.EE.A.1

Evaluate numerical expressions involving whole-number exponents.

6.EE.A.1

Topic B: Introduction to Algebraic Expressions

Use variables to write algebraic expressions.

6.EE.A.2 6.EE.A.2.C 6.EE.B.6

Evaluate algebraic expressions.

6.EE.A.2 6.EE.A.2.C

Write expressions for verbal statements and vice versa (Part 1).

6.EE.A.2.A 6.EE.A.2.B

Write expressions for verbal statements and vice versa (Part 2).

6.EE.A.2.A 6.EE.A.2.B

Topic C: Equivalent Expressions & Applications

Identify equivalent expressions (Part 1).

6.EE.A.3 6.EE.A.4

Identify equivalent expressions (Part 2).

6.EE.A.3 6.EE.A.4

Write equivalent expressions using the distributive property (Part 1).

6.EE.A.3 6.EE.A.4

Write equivalent expressions using the distributive property (Part 2).

6.EE.A.3 6.EE.A.4

Write algebraic expressions for application situations (Part 1).

6.EE.B.6

Write algebraic expressions for application situations (Part 2).

6.EE.B.6

Numerical and Algebraic Expressions

Objective

Common Core Standards

Core Standards

Expressions and Equations

Expressions and Equations

Foundational Standards

Operations and Algebraic Thinking

Criteria for Success

Tips for Teachers

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Target Task

Problem 1

Problem 2

Additional Practice

Lesson Map

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