Author:
Angela Vanderbloom
Subject:
Mathematics
Material Type:
Lesson Plan
Level:
Middle School
Grade:
6
Tags:
  • 6.EE.A.1 Exponential Expressions
    License:
    Creative Commons Attribution Non-Commercial
    Language:
    English

    Education Standards

    6.EE.A.1 Lesson 2

    6.EE.A.1 Lesson 2

    Overview

    Students will evaluate numerical expressions with whole-number exponents.

    Warm Up - Which One Doesn't Belong: Twos

    This warm-up prompts students to compare expressions. It encourages students to explain their reasoning, hold mathematical conversations, and gives you the opportunity to hear how they use terminology and talk about characteristics of the expressions in comparison to one another. 

    Launch

    Arrange students in groups of 2–4. Display the questions for all to see. Ask students to indicate when they have noticed one expression that doesn’t belong and can explain why. Give students 1 minute of quiet think time and then time to share their thinking with their small group. In their small groups, tell each student to share their reasoning why a particular question doesn’t belong and together find at least one reason each question doesn't belong.

    Expressive Language: Eliminate Barriers. Provide sentence frames for students to explain their reasoning (i.e., ____________ doesn't belong because _____________.).

    Student Response

    Answers vary. Sample responses:

    Problem 1 doesn’t belong because it is the only expression that shows 4 repeated factors being multiplied.

    Problem 2 doesn’t belong because it is the only one that is just a number.

    Problem 3 doesn’t belong because it is the only expression that uses exponents.

    Problem 4 doesn’t belong because it is the only expression that is not equal to 16.

    Activity Synthesis

    Ask each group to share one reason why a particular expression does not belong. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which one does not belong, attend to students’ explanations and ensure the reasons given are correct.

    During the discussion, ask students to explain the meaning of any terminology they use, such as “exponents.” Also, press students on unsubstantiated claims.

    Which one doesn’t belong?

    2⋅2⋅2⋅2

    16

    24

    4⋅2

    Evaluate the Expression

    Lesson Guide

    Review use of the multiplication dot instead of the multiplication sign to indicate multiplication.

    Have students evaluate the expression 4 ⋅ 6 ÷ 1 + 1 − 1 + 5 ⋅ 2. Write the values students find on the board.

    Ask students: Why do you think we got so many different answers?

    Let students know that in this lesson, they are going to come up with ways to avoid getting more than one value when evaluating a numerical expression.

    If students do not come up with more than one answer, show them the following variations:

    Calculating from left to right (ignoring order of operations):

    4 · 6 = 24       24 ÷ 1 = 24       24 + 1 = 25       25 – 1 = 24       24 + 5 = 29       29 · 2 = 58

    Following the order of operations:

    24 + 1 − 1 + 10 = 34

    Tell students that in algebra, parentheses specify the order in which to evaluate parts of an expression. Explain that when they use parentheses in expressions, there will be no question about the order of the operations. The operations inside parentheses are done first. If an expression has nested parentheses, the operations in the innermost parentheses are evaluated first.

    Tell students that if they see an expression that does not have parentheses, they can use the following conventions that mathematicians have agreed on. Outside of parentheses, multiplication and division operations should be done (working from left to right) before addition and subtraction operations.

    Thus, the order of operations is as follows:

    1. Operations inside parentheses first
    2. Exponents
    3. Then multiplication and division, working from left to right
    4. Then addition and subtraction, working from left to right

    Avoid acronyms such as PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) because they are misleading. PEMDAS leads to errors such as 8 − 3 + 4 = 8 − 7 = 1, because it suggests that the addition should be done before the subtraction.

    Opening

    Sometimes a dot is used to indicate multiplication rather than the times sign (“×”).

    For example, you can write 4 × 3 as 4 · 3. Both of these expressions say to multiply 4 by 3.

    • Evaluate the following expression: 4 · 6 ÷ 1 + 1 − 1 + 5 · 2

    Expression Explosion

    In this activity, students use the order of operations to evaluate expressions with exponents. They engage in MP3 as they listen and critique their partner’s reasoning when they do not agree on the answers.

    Launch

    Arrange students in groups of 2. Partners work individually on their expression in each row, then check their answers and discuss. Follow with a whole-class discussion.

    Social-Emotional Functioning: Peer Tutors. Pair students with their previously identified peer tutors.

    Student Response

    • 29
    • 80
    • 48
    • 28
    • 18

    Work Time

    Evaluate Expressions

    Lesson Guide

    Ask questions such as the following as students are working:

    • How did you get that answer?
    • Which operation will you perform first in this expression? Why?
    • What do the parentheses mean?

    Answers

    1.   49

    2.   516

    3.   8

    4.   36

    Work Time

    When you evaluate numerical expressions, perform operations in this order:

    • Operations inside parentheses
    • Exponents
    • Multiplication and division, working from left to right
    • Addition and subtraction, working from left to right

    When you write numerical expressions, use parentheses to show which operation(s) should be performed first.

    Evaluate these expressions:

    1.   (4 + 3)2

    2.   616 – 4 • 52

    3.   5 + 52 ÷ 5 – 2

    4.   3• 2 – (15 + 3)

    Cool - Down: Calculating Volumes

    Student Response

    Noah's solution is correct. Reasoning varies. Sample reasoning: The cube has a volume of 1,000 cubic units and the additional 20 cubic units from the prism makes the total volume 1,020 cubic units. The exponent calculation comes before addition.

    Jada and Noah wanted to find the total volume of a cube and a rectangular prism. They know the prism's volume is 20 cubic units, and they know the cube has side lengths of 10 units. Jada says the total volume is 27,000 cubic units. Noah says it is 1,020 cubic units. Here is how each of them reasoned:

    Jada's Method:                      Noah's Method:

    20 + 103                                20 + 103
    303                                        20 + 1,000
    27,000                                  1,020

    Do you agree with either of them? Explain your reasoning.