Making Scaled Copies

5 min

Teacher Prep
Setup
Display problems for all to see. 2 minutes of quiet think time, followed by whole-class discussion.

Narrative

This Math Talk focuses on incomplete equations that have only an initial value and an answer. It encourages students to think about operations and to rely on what they know about relationships between numbers to make each equation true. During the whole-class discussion, students see that for any pair of values, there is both an additive and a multiplicative relationship between them. The understanding elicited here will be helpful later in the lesson when students analyze copies of figures and identify what operation relates the corresponding side lengths.

Launch

Tell students to close their books or devices (or to keep them closed). Reveal one problem at a time. For each problem:

  • Give students quiet think time and ask them to give a signal when they have an answer and a strategy.
  • Invite students to share their strategies and record and display their responses for all to see.
  • Use the questions in the activity synthesis to involve more students in the conversation before moving to the next problem. 

Keep all previous problems and work displayed throughout the talk.

Action and Expression: Internalize Executive Functions. To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization

Student Task

Complete each equation to make it true.

  • 5 =105 \space\underline{\hspace{.5in}} = 10
  • 3 =153 \space\underline{\hspace{.5in}}= 15
  • 14 =2114 \space\underline{\hspace{.5in}}= 21
  • 30 =630 \space\underline{\hspace{.5in}}= 6

Sample Response

Sample responses:

  • 5+5=105 + 5 = 10, 52=105 \boldcdot 2 = 10
  • 3+12=153 + 12 = 15, 35=153\boldcdot 5 = 15
  • 14+7=2114 + 7 = 21, 14+6+1=2114 + 6 + 1 = 21, 14÷23=2114 \div 2 \boldcdot 3 = 21, 141.5=2114 \boldcdot 1.5 = 21
  • 3024=630 - 24 = 6, 30÷5=630 \div 5 = 6, 3015=630 \boldcdot \frac15 = 6
Activity Synthesis (Teacher Notes)

Make sure that at least one strategy for each problem uses multiplication before moving to the next problem. If needed, ask “How could we use multiplication to complete this equation?”
To involve more students in the conversation, consider asking:

  • “Who can restate \underline{\hspace{.5in}}’s reasoning in a different way?”
  • “Did anyone use the same strategy but would explain it differently?”
  • “Did anyone solve the problem in a different way?”
  • “Does anyone want to add on to \underline{\hspace{.5in}}’s strategy?”
  • “Do you agree or disagree? Why?”
  • “What connections to previous problems do you see?”

The key takeaway is that for any such problem, there is a solution that uses addition (or subtraction) as well as a solution that uses multiplication (or division).

MLR8 Discussion Supports. Display sentence frames to support students when they explain their strategy. For example, “First, I _____ because . . . .” or “I noticed _____ so I . . . .” Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
Advances: Speaking, Representing

Math Community
After the Warm-up, display the class Math Community Chart for all to see and explain that the listed “Doing Math” actions come from the sticky notes students wrote in the first exercise. Give students 1 minute to review the chart. Then invite students to identify something on the chart they agree with and hope for the class or something they feel is missing from the chart and would like to add. Record any additions on the chart. Tell students that the chart will continue to grow and that they can suggest other additions that they think of throughout today’s lesson during the Cool-down.

Anticipated Misconceptions

Students may attempt to solve each problem instead of reasoning about the numbers and operations. If a student is calculating an exact solution to each problem, ask the student to look closely at the characteristics of the numbers and how an operation would affect those numbers.

Standards
Building On
  • 6.NS.3·Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
  • 6.NS.B.3·Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

10 min

10 min