Students will demonstrate the concepts and skills that they have developed through this context and learning experience related to multiplication and division, multiplication with decimals, and solving linear equations.

The purpose of this assessment is for students to demonstrate their understanding of the following big ideas:

• 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).

The independent assessment will allow students to demonstrate concepts and skills related to the following learning goals:

• I will solve quotative division problems using an appropriate model to communicate my thinking.
• I will demonstrate an understanding of the relationship between quotative division and multiplication.
• I will multiply decimals by a whole number using partial products.
• I will demonstrate an understanding of when a variable is used.
• I will represent scenarios as an equation that includes one variable.
• I will solve for an unknown quantity.

Students might write and/or model their answers independently. Students can also be interviewed by their teacher.

An alternative assessment opportunity should be offered if this tool will not successfully capture what the student knows, understands or can do.

In today’s math talk, students will use an appropriate model to solve for an unknown quantity in each of the equations. Consider leveraging a context similar to the scenarios explored in previous days. For example, if the cost of admission is $8.25/person, how many tickets were purchased for a total cost of $99? If the cost for admission was $8.25 for admission, plus a $4 processing fee, how many tickets were purchased for $103? Today’s string lends itself to scenarios that could be solved through quotative division.

Encourage students to model their thinking and accurately represent the context. The different sentences below lend themselves to a variety of strategies, particularly the use of partial products. Highlight student strategies as they share their thinking using an open array and/or on a number line. Look for opportunities to reinforce the relationship between multiplication and division.

8n = 80
0.25n = 2.50
8.25n = 82.50

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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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Question #4:

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Based on the student thinking demonstrated on this assessment, provide students with descriptive feedback – written, verbal, or both – which includes next steps students should take in order to promote extending what they know, understand and can do.

Since assessment should be an opportunity for students to learn and for the teacher to understand where a student is in their learning journey, this should not close the door on these big ideas, models, and strategies.

What opportunities can you provide students with to demonstrate any further learning they engage in after this assessment day?

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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