Numerical and Algebraic Expressions

Lesson 4

Math

Unit 5

6th Grade

Lesson 4 of 12

Objective


Evaluate 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.

Foundational Standards

  • 5.MD.C.5.B

Criteria for Success


  1. Replace variables in algebraic expressions and formulas with numbers to create numerical expressions.
  2. Evaluate numerical expressions using the order of operations.
  3. Use parentheses to indicate multiplication or to indicate an exponent being applied to a value.

Tips for Teachers


In regard to pacing, this lesson may be extended over two days to ensure students have adequate time to practice. 

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems


Problem 1

A square prism is shown below.

The formula $${ V=s^2 h}$$ can be used to find the volume of the square prism. What is the volume of the prism when the side length of the base measures $${1.5}$$ inches and the height measures $$8$$ inches? 

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 2

Kia is wrapping a box in the shape of a rectangular prism. Each side of the box will be covered with wrapping paper. The total area of all of the sides of the box is called the surface area and can be found using the formula $${ S=2(lw+wh+lh)}$$, where $$l$$ refers to length, $$w$$ refers to width, and $$h$$ refers to height of the box. 

The box that Kia is wrapping is shown below. What is the surface area of the box?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 3

Evaluate the algebraic expressions for the given values of the variables. 

a.   $${ x^3+18y^2}$$, where $$x$$ is $${{1\over2}}$$ and $$y$$ is $${{1\over3}}$$

b.   $$2(x^2-1)+4y$$, where $$x$$ is $$6$$ and $$y$$ is $$3$$

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem Set

Fishtank Plus Content

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

Target Task


A cube has $$6$$ equal sides, each with an area of $${s^2}$$ square units. The surface area of a cube is the total area of all six sides, and is represented by the formula $$S=6{s^2}$$.

Find the surface area of a cube with the side lengths below.

a.   $${s=3}$$ inches

b.   $${s=1.2}$$ cm

c.   $${s={2\over3}}$$ ft

Student Response

Create a free account or sign in to view Student Response

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.

  • Include problems using the formulas for temperature to convert between degrees Fahrenheit and Celsius: $${F={9\over5}C+32}$$ and $${ C={5\over9}(F-32)}$$
  • Include problems where students evaluate geometric formulas for volume, surface area, area, and perimeter; students can draw or write their own problems and swap with peers; include decimals and fractions for spiraled review of rational number computation.
  • Challenge: Explore the Pythagorean Theorem and Fermat's Last Theorem. Can you find values for $$a$$$$b$$, and $$c$$, such that $$a^2 +b^2 =c^2 $$? What about $$a^3 + b^3 = c^3$$?
icon/arrow/right/large copy

Lesson 3

icon/arrow/right/large

Lesson 5

Lesson Map

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

Topic A: Numerical Expressions with Exponents

Topic B: Introduction to Algebraic Expressions

Topic C: Equivalent Expressions & Applications

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

Effective Instruction Made Easy

Effective Instruction Made Easy

Access rigorous, relevant, and adaptable math lesson plans for free