Curriculum / Math / 6th Grade / Unit 5: Numerical and Algebraic Expressions / Lesson 1
Math
Unit 5
6th Grade
Lesson 1 of 12
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Understand the meaning of exponents.
The core standards covered in this lesson
6.EE.A.1 — Write and evaluate numerical expressions involving whole-number exponents.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
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.
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.
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.
A. $${9^3\cdot3}$$
B. $${3^2\cdot3^2}$$
C. $${3\cdot27}$$
D. $${9^2\cdot3^2}$$
E. $${9+3^2}$$
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
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. $${2\cdot2\cdot2\cdot3\cdot3\cdot3=6^3}$$
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.
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.
Lesson 2
Topic A: Numerical Expressions with Exponents
6.EE.A.1
Evaluate numerical expressions involving whole-number exponents.
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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).
Topic C: Equivalent Expressions & Applications
Identify equivalent expressions (Part 1).
6.EE.A.3 6.EE.A.4
Identify equivalent expressions (Part 2).
Write equivalent expressions using the distributive property (Part 1).
Write equivalent expressions using the distributive property (Part 2).
Write algebraic expressions for application situations (Part 1).
6.EE.B.6
Write algebraic expressions for application situations (Part 2).
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