## Task Teacher Guide

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### In This Purposeful Practice…

Students will continue adding, subtraction and multiplying fractions and decimals by whole numbers. Students will explore the need for a standard order of operating.

### Intentionality…

The purpose of the Day 4 activities is to reinforce key concepts from previous days. 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 practice questions should be done **without the use of a calculator**.

Today’s learning serves to develop a deeper understanding of the following **big ideas**:

- Fractions can be represented in a variety of ways;
- Fractions (and their decimal representation) represents values relative to a whole (for example, one whole dollar);
- Quantities represented as a decimal are fractions limited to base ten denominators (i.e.: tenths, hundredths, thousandths, etc.);
- Standard representation of coin values are expressed as decimal hundredths;
- When the order of operations is not considered, the solution can vary;
- The order of operations can be revealed through the context;
- Multiple expressions can be used to represent the same value;
- Removal subtraction of a positive value or adding the negative of that same value has the same result, i.e., 6 – 2 = 6 + (-2).

## Math Talk

### Related String of Problems

($0.25 + $1.00 – $0.25 + (4 x $0.10) + $2.00 – $0.10)

\(\frac{1}{4} + 1 – \frac{1}{4} + (4 \times \frac{1}{10} ) + 2 – \frac{1}{10}\)

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### Visual Number Talk Prompt #1

Play the following visual number talk prompt video and prepare to pause where indicated.

Students will see dollar amounts including negative quantities (or debts) and then asked:

What is the total amount of money?How could you convince your neighbour?

After students are given time to think and strategize with their neighbours, take time to facilitate a discussion and model student thinking using the mathematical model that matches their approach best.

While the models you have used to represent student thinking from the room might be enough for the entire group to be convinced of what the total sum of money will be, you might consider also sharing this silent solution animation or a portion thereof if it helps push thinking forward.

One model that can be helpful here is a tape diagram showing both positive and negative quantities based on the expression given in the original visual number talk prompt.

Be sure to highlight the partitions that were used to represent the different quantities (fourths/quarters of a dollar for quarters, tenths for dimes, etc.).

It might also be helpful to highlight the use of brackets surrounding the 4 groups of $0.10 in the expression as a means to explicitly “group” those quantities together despite not necessarily requiring the use of brackets.

In the animation, you can also see the use of the zero principle as we cancel positive sums of money with negative sums of money.

When some students choose to add different quantities (or coins) first, it can be helpful to highlight the use of the * commutative property of addition* and subtraction being helpful here.

After cancelling out quantities by leveraging the * zero principle*, we can then begin adding other quantities to determine our sum.

**Purposeful Practice**

### While Students Are Practicing…

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### Questions: Operating With Fractions & Decimals

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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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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## Videos & Images

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## Keynote Slides

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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.

### Visual Math Talk Prompt #1

### Math Talk Prompt #2

*\(\frac{1}{4} + 1 – \frac{1}{4} + (4 \times \frac{1}{10} ) + 2 – \frac{1}{10}\)*

### Math Talk Prompt #3

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### Math Talk Prompt #4

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### Math Talk Prompt #5

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### 1. Consider the…

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### 2. Consider the following…

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### 3. Gracie went to…

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### 4. Consider the…

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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