## Task Teacher Guide

Be sure to read the teacher guide prior to running the task. When you’re ready to run the task, use the tabs at the top of the page to navigate through the lesson.

### In This Task…

Students will:

- solve a problem involving the multiplication of a fraction by a whole number; and/or,
- solve a problem involving the multiplication of a fraction by a fraction.

The question(s) students will solve with this task are:

- How many scoops of mix do you need for 3 protein shakes?
- How many scoops of mix do you need for 1 and 1 half protein shakes?

### Intentionality…

This task is a great way to give students an opportunity to make connections between fractional thinking and proportional reasoning by determining how many fractional scoops of protein mix will be required to make a variety of protein shake servings.

This task provides an opportunity for students to approach a problem involving fractional thinking in different ways depending on their level of readiness: through counting, addition, or multiplication.

As is true for **any task**, the intentionality or learning objective can vary depending on what mathematical thinking you are hoping to elicit.

### Spark

Show students this video:

Ask students to engage in a **notice and wonder** protocol. ANYTHING and EVERYTHING that comes to mind is fair game. Here’s some of the “everything and anything” students noticed and wondered on chart paper:

- I notice a big container.
- I notice nice counters.
- I notice protein mix.
- I wonder if someone is going to make a smoothie?
- How much mix will be needed to make a smoothie?
- How much does that big container of protein mix cost?
- And many others…

Take some time to acknowledge the noticing and wondering your students have engaged in and try to answer any that you might be able to address right away.

### Information: Video #2

Show this video and ask students if they have any more noticings and wonderings:

After watching this clip, students had more noticings and wonderings:

- I notice that less than a whole scoop of mix was used.
- I wonder if that was 3 fourths of a scoop?
- I wonder if they lost the “real” scoop and that’s why they can’t use a whole scoop?
- I how many scoops you’ll need for the 3 glasses?
- And many others…

### Sense Making

Then, pose the following question:

I wonder how many scoops you’ll need for those 3 glasses?

Follow up that question with:

How might we convince someone that the quantity you come up with is correct?

Let them loose to make some **estimates** based on what they saw – even though they don’t yet know EXACTLY how many scoops was used on the single glass.

Ask students to estimate a number of scoops that they think is too high and a number of scoops that they think is too low before making their “best estimate”. After sharing out their estimates, **without the aide of a calculator**, have students improve the precision of their estimates by using the following information and they must convince their mathematical community of peers as well as the teacher.

**Monitor** student thinking by circulating around the room and listening to the mathematical discourse. **Select** and **sequence** some of the student solution strategies and ask a student from the selected groups to share with the class from:

- most accessible to least accessible solution strategies and representations;
- most common/frequent to least common/frequent strategies and representations; or,
- choose another approach to selecting and sequencing student work.

The tools and representations you might see students using to convince their peers and/or the teacher include:

- Connecting cubes, square tiles, and/or relational rods used to model fractional amounts concretely.
- Area models and/or number lines drawn to make counting, adding, and/or multiplying unit fractions easier.
- As well as others…

Have students share their strategies for determining the number of full scoops of powder needed to make three protein shakes. Ask them to convince you and their peers that their answer is correct by sharing mathematical models.

Discuss their strategies and elicit student thinking during your consolidation to build off of their current prior knowledge and understanding rather than “fixing” or “funnelling” student thinking to a strategy and/or model that does not connect to their strategy and/or approach.

**Student Response #1:**

I used an area model to represent 3 groups of 3 fourths.

I drew rectangles to represent the scoops.

So, I think that 9 fourths of a scoop of powder is needed to make three protein shakes.

9 fourths is the same as 2 full scoops and 1 fourth of a scoop.

**Student Response #2**

I used a number line to represent the 3 fourth jumps needed to make three glasses of protein shake.

I can think of it as a double number line.

Or I could think of it as a ratio table.

So, I think that the quantity of mix needed to make three protein shakes is 9 fourth scoops. That is the same as 2 and 1 fourth scoops.

**Student Response #3:**

I used repeated addition to multiply a whole number by a fraction.

3 fourths + 3 fourths + 3 fourths = 9 fourths of a scoop

9 fourths of a scoop is the same as 2 full scoops and 1 fourth of a scoop.

I could write this as:

3/4 + 3/4 + 3/4 = 9/4 scoops, or 2 1/4 scoops.

Or I could write it as:

3 x 3/4 = 9/4 scoops, or 2 1/4 scoops.

Discuss and consolidate the learning to ensure that the mathematical thinking you intended to elicit is clear to all students. For example, students may recognize that they can think of multiplication of a fraction by a whole number in terms of proportional reasoning.

**Anticipate:**

What do you think YOUR students might do with this task?

How might you modify this task to work in your classroom with your diverse learners?

If you want to be bold, test what you’ve anticipated by doing the task in your classroom and come back to report your thinking in the comments. As mentioned in many of our tasks, the learning goal **you** have selected for a task may be different than what I have in mind. This is especially true when we consider that this task could be used in a variety of classrooms with varying levels of student readiness.

### Reveal

### Reveal #1: How Many Whole Scoops Were Used?

After consolidating learning using student generated solution strategies and by extending their thinking intentionally, we can share what really happened with this video.

Revisit the student answers. Have students discuss their thinking and what they would change if they did the task again.

Ask students why it makes sense that the three partial scoops turned into a little more than two full scoops.

### Reveal #2: Re-unitizing From Improper Fraction to Mixed Numbers

In this video, students can watch as we **re-unitize** the protein mix powder from 9 fourth scoops (improper fraction) to 2 whole and 1 fourth scoops (mixed number).

Return to the questions you recorded earlier in the Notice and Wonder protocol during the **SPARK **section of the task and answer any questions that have not been answered.

### Extend #1

**Extend #1: Spark**

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**Extend #1: Prompt**

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### Extend #2, #3, #4

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### Next Moves

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### What do you notice? What do you wonder?

### Information

### Reveal #1

### Reveal #2

### Extend #1: Spark

### Extend #1: Prompt

### Extend #2

*How many scoops of protein shake mix will be required to make 8 protein shakes?*

### Extend #3

*How many protein shakes were made if 12 1/2 scoops were used?*

### Extend #4

*How might your thinking have changed if only 1 fourth of the full scoop had been used each time? What if 2 thirds of a scoop had been used each time?*