Lesson | Loading...

Unit 6, Lesson 1

Reviewing Exponents

Extra Support Materials for Algebra 1

1.1

Warm-up

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

None

Activity Narrative

The purpose of this activity is for students to recall how to interpret expressions that use exponents. This will be useful when students have the opportunity to use exponents to represent a situation in the associated Algebra 1 lesson. As students recall how to write equivalent expressions involving exponents, they reason abstractly and quantitatively (MP2).

Launch

Before beginning the activity, pose the following question.

“Kiran thinks that is 9. Han thinks that is 6. Who do you agree with and why?”

Before students do calculations or any other work, ask the class whether they agree with Kiran or Han. Ask selected students to explain why they chose one and did not choose the other. Ask others if they agree or have something to add.

Display the table for all to see. Explain that the “expanded form” column shows the factors being multiplied, and the “exponential form” column shows how to write the repeated multiplication more succinctly with exponents. Arrange students in groups of 2. After a few minutes of quiet work time, ask students to compare their responses to their partner’s and decide if they are both correct, even if they look different. Follow with a whole-class discussion.

Activity

None

Complete the table.

expanded form	exponential form

Student Response

to access Student Response.

Building on Student Thinking

Activity Synthesis

The goal of this activity is for students to evaluate how well they understand exponential notation. Select students to share their responses. Here are some questions for discussion:

“Could any of the expanded forms be written a different way?” (Yes, the last row could be or , for example.)
“How is approaching a problem with exponents similar to approaching a problem with multiplication?” (An exponent shows how many times a base is multiplied by itself, so an exponent represents multiplication.)
“How is approaching a problem with exponents different from approaching a problem with multiplication?” (For multiplication, the two numbers we see are factors that we multiply together. For exponents, the exponent is not multiplied by the base. It shows how many times to multiply the base by itself.)

1.2

Activity

Instructional Routines

MLR6: Three Reads

Materials

None

Activity Narrative

The purpose of this activity is for students to recall how to write expressions using exponents. Students apply what they know about exponents to represent money doubling each week. They use multiplication to express a different quantity growing linearly each week. This will be useful when students represent two situations and compare them in the associated Algebra 1 lesson. When students write an expression in terms of , they express regularity in repeated reasoning (MP8).

This activity uses the Three Reads math language routine to advance reading and representing as students make sense of what is happening in the text.

1.3

Activity

Instructional Routines

Take Turns

Materials

None

Activity Narrative

In this partner activity, students take turns using exponent rules to analyze expressions and identify equivalent ones. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3). The practice will prepare students to compare growth patterns and interpret graphs to answer questions from a context in the associated Algebra 1 lesson.

Launch

If desired, demonstrate that expressions can be rewritten by substituting expressions of equal value. For example, if we were looking for an expression equivalent to , we might try replacing each 16 with the product of two 4s, like . This might help us recognize a matching expression like .

Arrange students in groups of 2. Display the task for all to see. Tell students that for each expression in List A, there is an equivalent expression in List B and List C. If time allows, choose a student to be your partner and demonstrate how to set up and do the activity. Otherwise, share these steps:

One partner picks an expression from List A.
They identify an equivalent expression in Lists B and C and explain why they think it is equivalent.
The other partner listens and makes sure they agree with the matches and the reasoning.
If they don’t agree, the partners discuss until they come to an agreement.
For the next expression in List A, the students swap roles.

To encourage reasoning about equivalent expressions, it would be best if students tackled this activity without access to a calculator.

Representation: Access for Perception. Students may benefit from watching or hearing the directions more than once.
Supports accessibility for: Language, Attention

Launch

Arrange students in groups of 2, or allow them to work individually.

Use Three Reads to support reading comprehension and sense-making about this problem. Display only the problem stem, without revealing the table and question.

For the first read, read the problem aloud, and then ask, “What is this situation about?” (It is about two people saving money from their summer jobs.) Listen for and clarify any questions about the context.
After the second read, ask students to list any quantities that can be counted or measured. (Clare saves \$5 each week. Tyler saves \$2 the first week and, for each following week, doubles the amount he saves.)
After the third read, reveal the table and task: Complete the table showing how much money each of them will have at the end of each week for the 10 weeks, and ask, “What are some ways we might get started on this?” Invite students to name some possible starting points, referencing quantities from the second read. (Clare always saves \$5, so her total adds 5 each week. Tyler doubles the amount he saves, so the amount he saved the week before is doubled and added to the amount he already saved.)

Activity

None

Clare has a summer job. She wants to save money to spend on the family vacation at the end of summer. She is going to save \$5 per week for each of the 10 weeks she is working.

Tyler also has a summer job, and he, too, would like to save money to spend on a family vacation. His aunt gives him \$1 to start saving, and Tyler decides to double the amount he saves each week.

Complete the table showing how much money each of them will have saved at the end of each week for the 10 weeks.

week	0	1	2	3	4	5	6	7	8	9	10
Clare	0	5	10	15
Tyler	1	2	4	8

Student Response

to access Student Response.

Lesson | Loading...

Settings

Audience

Assessment Access

Lesson 1

Reviewing Exponents

Warm-up

Standards Alignment

Building On

Addressing

6.EE.A.1

Building Toward

HSF-LE.A.3

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Building on Student Thinking

Activity Synthesis

Activity

Instructional Routines

Materials

Activity Narrative

Activity

Instructional Routines

Materials

Activity Narrative

Launch

Launch

Activity

Student Response

Building on Student Thinking

Activity Synthesis

Activity

Student Response

Building on Student Thinking

Activity Synthesis

Standards Alignment

Building On

Addressing

6.EE.A.1

7.EE.B.3

Building Toward

HSF-LE.A.3

HSF-LE.B.5

Standards Alignment

Building On

Addressing

6.EE.A.1

6.EE.A.4

Building Toward

HSA-SSE.A.2

HSA-SSE.B.3.c