## THE WOOLY WORM RACE [DAY 3]

### FRACTIONS & METRIC UNITS

Represent, compare, order, and add fractions involving metric unit conversions.

## Intentionality & Unit Overview

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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 denominator;
• In order to compare two or more fractional quantities, the whole must be the same;
• The numerator indicates the number of parts relative to the number of parts in the whole indicated by the denominator;
• Fractional amounts exist between whole numbers;
• Different denominators can be used to represent equivalent quantities;
• A multiplicative relationship exists between unit fractions (i.e.: one-sixth is one-half of one-third and one third is twice as big as one-sixth); and,
• The commutative and associative properties of addition (this big idea may emerge through student strategies)

## What Do You Notice? What Do You Wonder?

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.

Prompt students:

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:

What is Molly’s combined total distance?

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.

If a student says something like “3 point 8 metres”, encourage them to describe the decimal conceptually with fractional language such as “3 and 8 tenths of a metre” or “3 and 4 fifths of a metre”. Note that the language in the second example would require students to have a very strong understanding of equivalence with fractions.

Encourage students to share with their neighbours and convince them why they think their estimate is reasonable. This may be done 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.

## Reveal #1

Once students have shared and you have modelled their thinking giving students an opportunity to comment and debate the reasoning of their peers, we’re going to do a quick reveal.

This reveal will serve as an additional opportunity for students to strengthen their own understanding of partitioning a whole into fractional parts as well as slowly introducing standard notation with proper fractions and mixed numbers.

An image of the final frame of the video is included below.

## Crafting A Productive Struggle: Prompt

Share the table below which highlights the three attempts for the top 3 finishers in the race this year.

Prompt students to:

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

Use this information to rank them from first to third.

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 answer getting to help each student along their journey to develop mathematical proficiency.

## While Students Are Productively Struggling…

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## Student Approach #1: Fraction Strips

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## Student Approach #2: Number Line

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## Student Approach #3: Equivalence/Common Unit

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## Reveal #2

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

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

## Consolidation

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## Reflect and Consolidation Prompts

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

### Consolidation Prompt:

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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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