Numerical and Algebraic Expressions

Lesson 1

Math

Unit 5

6th Grade

Lesson 1 of 12

Objective


Understand the meaning of exponents.

Common Core Standards


Core Standards

  • 6.EE.A.1 — Write and evaluate numerical expressions involving whole-number exponents.

Criteria for Success


  1. Understand that exponents represent repeated multiplication of the same number.
  2. Compare repeated multiplication to repeated addition. 
  3. Represent numbers with repeated multiplication and with whole-number exponents.

Tips for Teachers


In Unit 3, students worked with exponents to represent numbers using prime factorization. In this lesson, students explore the power of exponents and repeated multiplication, especially as it compares to repeated addition.

Fishtank Plus

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

Anchor Problems

25-30 minutes


Problem 1

After opening an ancient bottle you find on the beach, a genie appears. In payment for his freedom, he gives you three options as a reward:

Option A:   50,000 gold coins all at once

Option B:   5,000 gold coins every day for 28 days

Option C:   1 magical gold coin

The magic coin will turn into two gold coins on the first day. The two coins will turn into four coins total at the end of two days. By the end of the third day there will be eight gold coins total. The genie explains that the magic coins will continue this pattern of doubling each day for 28 days. 

a.   Without calculating, which prize do you choose and why?

b.   The total number of coins on the third day for Option B will be $${ 5,000 + 5,000 + 5,000}$$. Write another expression using multiplication for the total number of coins on the third day for Option B.

c.   The number of coins on the third day for Option C will be $${ 2 × 2 × 2}$$. Write another expression using exponents for the number of coins on the third day for Option C. 

d.   Write an expression for the total number of coins you will have on the 28th day for each option. Which option will give you the most number of coins? Explain or show your reasoning.

Guiding Questions

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

Student Response

Upgrade to Fishtank Plus to view Sample Response.

References

Illustrative Mathematics The Djinni's Offer

The Djinni's Offer, accessed on Dec. 18, 2017, 2:17 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 2

a.   Is $${{9\cdot 3^2}}$$ equivalent to $${3^4}$$? Justify your response.

b.    Which of the numerical expressions below are equivalent to $${{9\cdot 3^2}}$$? Select all that apply.

  1. A.   $${9^3\cdot3}$$

  2. B.   $${3^2\cdot3^2}$$

  3. C.   $${3\cdot27}$$

  4. D.   $${9^2\cdot3^2}$$

  5. E.   $${9+3^2}$$

Guiding Questions

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

Student Response

Upgrade to Fishtank Plus to view Sample Response.

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


Decide whether each equation is true or false, and explain how you know.

a.   $${2^4 = 2\cdot4}$$

b.   $${3+3+3+3+3=3^5}$$

c.   $${5^3=5\cdot5\cdot5}$$

d.   $${2^3=3^2}$$

e.   $${16^1=8^2}$$

f.   $${(1+3)^2=1^2+3^2}$$

g.   $${2\cdot2\cdot2\cdot3\cdot3\cdot3=6^3}$$

Student Response

Upgrade to Fishtank Plus to view Sample Response.

References

Illustrative Mathematics Exponent Experimentation 1

Exponent Experimentation 1, accessed on Dec. 18, 2017, 2:30 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.

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 review problems on prime factorization.

Next

Evaluate numerical expressions involving whole-number exponents.

Lesson 2
icon/arrow/right/large

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?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free