Task Teacher Guide
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In This Purposeful Practice…
Students will solve equations involving whole numbers and decimals.
Intentionality…
The purpose of the Day 4 activities is to reinforce key concepts from Days 1, 2 and 3. Students will engage in a string of related problems through a math talk and will have an opportunity to complete independent purposeful practice. They will solve problems involving whole numbers and decimal numbers.
The math talk and purposeful practice serve to develop a deeper understanding of the following big ideas and should be completed without the help of a calculator.
- Multiplication and division are related.
- There are two types of division.
- Quotative (or measured) division reveals the numbers of parts when the rate is known.
- The dividend from any division sentence can be decomposed into smaller parts to allow for friendlier division by the divisor. This strategy is known as partial quotients. (i.e.: 85 ÷ 5 = 45 ÷ 5 + 40 ÷ 5 = 9 + 8 = 17).
- Partial products, made possible by the distributive property, allows one or both of the factors to be decomposed in order to simplify a multiplication sentence.
- Variables are used to represent changing or unknown quantities.
- When solving an equation where the coefficient of the unknown variable is not equal to 1, division is required to determine the value of the unknown variable and the context of the problem determines which type of division is required (i.e.: the Aero Car context requires quotative division).
Math Talk
Related String of Problems
Present the equations below one at a time. Encourage students to identify and solve for the unknown quantity using a model. When the context is not provided for you, ask students to share a context that could be represented by each equation.
$15 per ticket multiplied by the number of participants plus a $20 tip is equal to $200. How many participants were there?
12 eggs per carton multiplied by the number of cartons purchased minus 3 broken eggs is equal to 129 eggs. How many cartons were purchased?
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Purposeful Practice
While Students Are Practicing…
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Questions: Using Variables and Solving Equations With One Variable
Allow students the opportunity to engage in purposeful practice without the use of a calculator to promote their fluency and flexibility with these concepts and to model their thinking:
Question #1:
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Question #2:
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Question #3:
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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.
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Resources and Downloads
Lesson Tip Sheet
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Printable Handout
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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.
How many participants?
$15 per ticket multiplied by the number of participants plus a $20 tip is equal to $200.
How many cartons?
12 eggs per carton multiplied by the number of cartons purchased minus 3 broken eggs is equal to 129 eggs.
What is the value of c?
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What is the value of b?
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1. Write an equation…
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2. Write an equation…
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3. Write a context…
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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