Students will multiply fractions leveraging context and an area model and scale ratios in tandem.

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 continue investigating scaling a ratio in tandem through ration reasoning.

The math talk and purposeful practice serve to develop a deeper understanding of the following big ideas.

Number:

• Multiplication can be interpreted as “groups of” or “parts of”, where the first factor is the number of groups, and the second factor is the quota;
• Multiplication can be represented using an array or area model;
• A part of a whole unit can be expressed as a fraction;
• A fraction described the number of parts relative to a whole;
• The fractional unit (the denominator) communicates how the whole is partitioned (number of parts);
• Equivalent values can be represented by different fractional notation (for example, \(\frac{1}{4} \) is equal to \(\frac{3}{12} \));
• The product when multiplying fractions is relative to the whole unit.
• Ratio reasoning is when the units represented by a ratio are scaled in tandem.

Write each expression on the board, one at a time. Read the expression using the word “of”. For example, for the first problem, we would say that “one-fourth times 2-fifths” is “one-fourth of two-fifths”. Note that we can make a connection here by mentioning that we typically use multiplication language involving how many groups of a quantity. For example, 4 x 3 would sound like “4 groups of 3 items”.

Encourage students to develop a context and a model that could be represented by the expression below, then solve.

\(\frac{1}{4} \times \frac{2}{5}\)

\(\frac{1}{2} \times \frac{5}{6}\)

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Question #1:

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Question #2:

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Question #3:

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Question #4:

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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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