Task Teacher Guide
Be sure to read the teacher guide prior to running the task. When you’re ready to run the task, use the tabs at the top of the page to navigate through the lesson.
In This Purposeful Practice…
Students will explore contexts that involve ratio and the ratio’s related rates. Students will continue to use models to reveal the rate through partitive division.
Intentionality…
In today’s math talk and purposeful practice, students will solve problems involving partitive division. Students will examine sample solutions in an effort to name the strategy and/or model, and offer an alternative strategy.
Some of the big ideas that may emerge through this task include:
- Partitive division is one of the two structures of division;
- In partitive division, the dividend is the quota and the divisor is the number of parts or groups;
- When dividing partitively, the quotient reveals a rate, how many per part (or the quota per group);
- The quotient can be expressed as any fraction equivalent to the dividend over the divisor;
- The number of partitions determines the fraction unit and gives the quantity its name (i.e.: partitioning a whole into 5 parts creates “5 fifth” parts);
- Different denominators can be used to represent equivalent quantities;
- Rate reasoning involves dividing one part of a ratio by the other through partitive division in order to reveal a rate.
Math Talk
Related String of Problems
Write each of the following ratios on the board, one at a time. Ask students to develop a context for the following quantities and reveal both of the related rates through partitive division. Ask students to model how the rate can be revealed.
16 : 4
12 : 3
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
Purposeful Practice
While Students Are Practicing…
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
Practice: Dividing Whole Numbers Through Partitive Division to Reveal a Rate
Question #1:
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
Question #2:
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
Question #3:
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
We suggest collecting this reflection as an additional opportunity to engage in the formative assessment process to inform next steps for individual students as well as how the whole class will proceed.
Download Editable/Printable Handout
Become a member to access purposeful practice to display via your projector/TV, download the PDF to upload to your LMS and/or print for students to have a physical copy
Resources and Downloads
Lesson Tip Sheet
Download the lesson plan in PDF format so you can keep it handy and share with colleagues.
Videos & Images
Download the videos, images, and related media files to your computer to avoid streaming.
Keynote Slides
Download in Apple Keynote format to avoid streaming video and run the lesson smoothly.
PowerPoint Slides
Download in Microsoft PowerPoint format to avoid streaming video and run the lesson smoothly.
Printable Handout
Download/edit the handout so you can keep it handy and share with colleagues.
Explore The Entire Unit of Study
This Make Math Moments Task was designed to spark curiosity for a multi-day unit of study with built in purposeful practice, and extensions to elicit and emerge mathematical models and strategies.
Click the links at the top of this task to head to the other related lessons created for this unit of study.
Create a…
Create a context for the following ratio and reveal both related rates.
16:4
…
12:3
…
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
1. Sam used…
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
2. Consider the…
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
3. Write your own…
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
Download Editable/Printable Handout
Become a member to access purposeful practice to display via your projector/TV, download the PDF to upload to your LMS and/or print for students to have a physical copy