Projecting and Scaling

10 min

Teacher Prep
Setup
Display one problem at a time. 1 minute of quiet think time, followed by a whole-class discussion.
Required Preparation
Make a space for students to place their sticky notes at the end of the Warm-up. For example, hang a sheet of chart paper on a wall near the door.

Narrative

This is the first Math Talk activity in the course. See the launch for extended instructions for facilitating this activity successfully.

This Math Talk focuses on reviewing fraction division. It encourages students to think about the meaning of division and to rely on what they know about the structure of mixed numbers to mentally solve problems. The strategies elicited here will be helpful later in the lesson when students perform similar calculations dividing a mixed number by a whole number. While many strategies may emerge, the focus of these problems is for students to recall and rehearse a reliable way to divide a mixed number by a whole number.

In explaining their strategy, students need to be precise in their word choice and use of language (MP6).

Launch

This is the first time students do the Math Talk instructional routine in this course, so it is important to explain how it works before starting.

Explain that a Math Talk has four problems, revealed one at a time. For each problem, students have a minute to quietly think and are to give a signal when they have an answer and a strategy. The teacher then selects students to share different strategies (likely 2–3, given limited time), and might ask questions such as “Who thought about it in a different way?” The teacher then records the responses for all to see and might ask clarifying questions about the strategies before revealing the next problem.

Consider establishing a small, discreet hand signal that students can display when they have an answer they can support with reasoning. This signal could be a thumbs-up, a certain number of fingers that tells the number of responses they have, or another subtle signal. This is a quick way to see if the students have had enough time to think about the problem. It also keeps students from being distracted or rushed by hands being raised around the class.

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 access to sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization

Student Task

Find the value of each expression mentally. 

  • 614÷26\frac14\div2

  • 1017÷510\frac17\div5

  • 413÷84\frac13\div8

  • 812÷118\frac12\div11

Sample Response

  • 3183\frac18 or 258\frac{25}{8}. Sample reasoning: 6÷2=36\div2=3 and 14÷2=18\frac14\div2=\frac18

  • 21352\frac{1}{35} or 7135\frac{71}{35}. Sample reasoning: 10÷5=210\div5=2 and 17÷5=135\frac17\div5=\frac{1}{35}

  • 1324\frac{13}{24}. Sample reasoning: 413=1334\frac13=\frac{13}{3}, and 133÷8=133⋅18=1324\frac{13}{3}\div8=\frac{13}{3}\boldcdot\frac18=\frac{13}{24} 

  • 1722\frac{17}{22}. Sample reasoning: 812=1728\frac12=\frac{17}{2}, and 172÷11=172⋅111=1722\frac{17}{2}\div11=\frac{17}{2}\boldcdot\frac{1}{11}=\frac{17}{22} 

Activity Synthesis (Teacher Notes)

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?”

Math Community
After the Warm-up, display the Math Community Chart. Remind students that norms are agreements that everyone in the class shares responsibility for, so it is important that everyone understands the intent of each norm and can agree with it. Tell students that today’s Cool-down includes a question asking for feedback on the drafted norms. This feedback will help identify which norms the class currently agrees with and which norms need revising or removing.

MLR8 Discussion Supports. Display sentence frames to support students when they explain their strategy, such as “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
Standards
Building On
  • 6.NS.A·Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
  • 6.NS.A·Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

20 min