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.

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)

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.

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 Abby’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.

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.

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 Abby’s combined total distance compared to the length of the climbing track? Update your estimate.

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The following reveal video will “silently” model the results: A screenshot of the last frame in the video is as follows:

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Provide students an opportunity to reflect on their learning by offering this consolidation prompt to be completed independently. Consolidation Prompt: Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units. 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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