## 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…

The Wooly Worm caterpillars can attempt the climb three times. The winner of the competition will be awarded to the caterpillar who climbs to the greatest height when all three attempts are combined.

### Intentionality…

In this task, students will represent the distances travelled by each caterpillar in all three rounds. Students will then add the heights from each of the three rounds to determine the total distance travelled. The caterpillar with the greatest combined height will win the competition.

Some of the * big ideas* that may emerge through this task include:

- Fractions can be represented in a variety of ways;
- How you partition the whole determines the fractional unit (i.e.: partitioning a whole into 6 parts will result in 6 sixth parts);
- As you partition a whole into more parts, the smaller the size of each part;
- As you partition a whole into more parts, the larger the unit fraction (called the denominator in later grades);
- In order to compare two or more fractional quantities, the whole must be the same;
- The count (called the numerator in later grades) indicates the number of parts relative to the number of parts in the whole indicated by the unit fraction (the denominator);
- Fractional amounts exist between whole numbers;
- Different unit fractions can be used to represent equivalent quantities; and,
- The commutative and associative properties of addition (
*this big idea may emerge through student strategies*)

## Spark

### Consider This...

Remind students of the Wooly Worm competition that you explored on Day 1. You could even consider re-sharing the reveal video from Day 1, if you’d like.

Then, share the following video with students to extend the context from Day 1.

Pausing the video at the end or leaving this screenshot from the final frame of the video can also be left up on the screen.

What do you think is going on here?

Allow students to discuss with their groups and then share out to the whole group.

If students describe the situation reasonably well, then affirm what they’ve shared and/or describe the scenario that:

On Day 1, the winner of The Wooly Worm Race was decided after a single attempt by each caterpillar, the officials have decided to change the rules this year.

During this particular competition, each caterpillar was allowed to attempt the climb a total of three times.

The caterpillar with the greatest combined height from its three attempts was declared the winner.

### Estimation: Prompt

After we have heard students and demonstrated that we value their voice, we can land on the first question we will challenge them with:

About how far is Molly’s combined total distance compared to the length of the climbing track?

Make an estimate.

Ask them to make an estimate and we want them to try to be as * precise *as possible despite the fact that they only have their spatial reasoning to work with. Encourage students to be strategic so they are not simply making a random guess.

### While Students Are Estimating...

* Monitor *student thinking by circulating around the room and listening to the mathematical discourse.

Encourage students to use * fractional language *as you may find that many students tend to resort to decimal notation. This is a result of students being exposed to decimal notation before they are conceptually ready either by an overemphasis of calculator use (most calculators reveal a result in decimal notation) or by moving there too quickly in the math classroom.

Encourage students to share with their neighbours and convince them why they think their estimate is reasonable. This may be done by using strips of paper to create fraction strips or by drawing a model.

As students share with the whole group, do your best to model what students are describing to you to give your students an opportunity to study and explore different mathematical models that can be used to partition for this low floor estimation task.

Models you might use could include the bar model as it is less abstract than partitioning a number line. Of course, if students are experienced enough with the number line, it could be worth exploring as well.

## Sense Making

### Crafting A Productive Struggle: Prompt

Share the following video that will partition each “bar” representing the length of the climbing track into equal partitions to push students to reason as they attempt to come up with a more precise combined distance for the 3 climb attempts:

Consider pausing the video near the end or leaving this screenshot up for students to reference.

Ask students:

About how far is Molly’s combined total distance compared to the length of the climbing track?

Update your estimate.

## During Moves

### While Students Are Productively Struggling....

**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:

- Concrete materials such as fractions strips or relational rods
- A pictorial representation such as a bar model
- A number line

Have students share their strategies and reasoning for how to represent the total combined distance relative to the length of the climbing track after 3 attempts. 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 Approach #1: Paper Folding

I cut strips of paper to create fraction strips. I made two fraction strips that were partitioned into thirds to represent rounds 1 and 3 and one fraction strip partitioned into sixths. Then, I coloured 1 third on each of the fraction strips representing round 1 and round 3. I coloured 1 sixth on the fraction strip representing the 2nd round. Then, I cut them out and lined them up on a new fraction strip. It looked like I could fold that fourth paper strip into sixths and the cut out parts filled 5 sixths of that strip.

## Next Moves

### Consolidation

During today’s consolidation, the goal is to continue leveraging the concrete and pictorial linear model as a tool to add fractions. The concrete and pictorial representations will lead students intuitively toward the idea of common denominator and equivalence.

Students may not recognize the multiplicative relationship between the unit fractions depending on their developmental readiness. Be sure to highlight how unit fractions can be partitioned further (i.e.; halving thirds into sixths and doubling the number of parts) or unitized into larger parts (i.e.: doubling the size of a sixth will half the number of parts) and can be very helpful when it comes to comparing and adding fractions.

You might see students leveraging both the * commutative *and

*property of addition. For example, students might immediately add the 1 third from round 1 and 1 third from round 3 to know that the sum is 2 thirds, then addressing the 1 sixth afterwards.*

**associative**

### Reveal

The following reveal video will “silently” model the results:

A screenshot of the last frame in the video is as follows:

### Extend

Prompt students with the following:

The distance travelled in each round by the top 3 finishers are shown below:

Determine the total distance climbed by each caterpillar after three rounds.

Use this information to rank them from first to third.

Justify your ranking using a model of your choice.

As always, remind students that we will not be relying on the use of a calculator and that the most important work we will do here is creating a case to convince others of our thinking. There should be no yelling out of a final answer nor should you even share your final answer until you have described your reasoning to your peers.

It is critical that we continue to build a culture of * thinking* rather than a culture of

*to help each student along their journey to develop mathematical proficiency.*

**answer****getting**Consolidating this extension with the group similar to how you did with the Sense Making prompt should be considered.

### Reflect

Provide students an opportunity to reflect on their learning by offering this consolidation prompt to be completed independently.

**Consolidation Prompt:**

Show the following clip and verbally explain what is happening in the video to set them up for your consolidation prompt.

In another competition, The King and Snowflake were the top two finishers. Their three attempts are recorded in the table below.

Determine the total distance travelled by each caterpillar to help you determine who won this competition.

Justify your reasoning using a model of your choice.

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.

Click the links at the top of this task to head to the other related lessons created for this unit of study.

### Consolidation Prompt #1: Video

*In another competition, The King and Snowflake were the top two finishers. Their three attempts are recorded in the table below.*

*Determine the total distance travelled by each caterpillar to help you determine who won this competition.*

*Justify your reasoning using a model of your choice.*