## Task Teacher Guide

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### In This Purposeful Practice…

Students will divide fractions through partitive division leveraging a context.

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

- Partitive division is one of the two types of division;
- When dividing partitively, the dividend and the divisor often (not always) have two distinct units;
- The resulting quotient has a compound unit (quantity of dividend per one unit of divisor);
- The dividend and the divisor are a ratio before the division is performed;
- The quotient is a rate;
- The quotient can be revealed through scaling the ratio in tandem to one whole of the divisor;
- There are two ways to half a fraction:
- Half the numerator in order to half the number of parts while leaving the size of each part untouched (i.e.: half of \(\frac{4}{6}\) is \(\frac{2}{6}\)); or,
- Double the denominator. Double the number of parts that make up the whole by partitioning the existing parts in half, and keep the number of parts (the numerator) the same (i.e.: half of \(\frac{4}{6}\) is \(\frac{4}{12}\)).

## Math Talk

### Related String Of Problems

Present each of the following statements one at a time. In today’s string, the goal is to reinforce a key concept explored through the consolidation on Day 3, how to scale a fraction by a fraction by either reducing the numerator or increasing the denominator. In this scenario, we are using the fraction as an operator, where the fraction represents a scale factor. For each of the statements in this string, explore both ways. For example, half of \(\frac{4}{5}\) is \(\frac{2}{5}\) or \(\frac{4}{10}\).

\(\frac{1}{2}\) of \(\frac{2}{3}\)

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

\(\frac{1}{3}\) of \(\frac{3}{4}\)

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## Purposeful** Practice**

### While Students Are Practicing…

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### Questions: Dividing Fractions

**Question #1:**

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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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## 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.

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### What is…

*\(\frac{1}{2}\) of \(\frac{2}{3}\)*

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*\(\frac{1}{2}\) of \(\frac{4}{5}\)*

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*\(\frac{1}{3}\) of \(\frac{3}{4}\)*

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### 1. Marian uses…

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### 3. Consider the…

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