Students will determine how many pieces of Bristol board is required to cover a wall requiring the conversion of metric units of area.

As is true for any task, the intentionality or learning objective can vary depending on what mathematical thinking you are hoping to elicit. The intention for this task when we created it was to give students an opportunity to investigate and solidify their understanding of converting between metric units of area; specifically square centimetres and square metres. However, like many rich tasks, modifying the information you provide to students and/or reframing the question you ask can allow for shifting the intentionality to a different learning goal.

This task can also be a great way to help students stretch from counting and/or additive thinking to multiplicative thinking and even build flexibility with fractional amounts. This task can also help students:

• work concretely (by cutting out scale paper versions of the wall and pieces of Bristol board), visually, and/or symbolically to apply their understanding of area as how many units of Bristol board it takes to cover the wall (counting, addition, multiplication);
• thinking fractionally by referencing the wall as the whole and determining how many pieces of Bristol board “go into” the wall (quotative division);
• apply an understanding of the unit fraction by referencing the area of the wall as the “whole” and each piece of Bristol board as a partition of the whole (partitive division);
• apply an understanding of measurement with area by determining how many pieces of Bristol board will be required to cover the wall utilizing the known measures of the length and width of the wall and the Bristol board using proportional reasoning.

As you can see from the list above, this task can be used quite flexibly from primary grades through to intermediate grades to press your students for understanding.

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 work out bench.
• I notice a TV on a table.
• I notice a tripod and studio lighting.
• I notice some green Bristol board on the floor.
• I wonder if this is a workout room?
• I wonder if someone is doing a photoshoot?
• I wonder if they are making a green screen?
• And many others…

At this point, address any noticing and wondering you can to acknowledge student voice and ensure that they know that the ideas they share are important. Then, we let kids in on the context of the scenario. We are in fact creating a green screen for photography and video. So we then challenge the students with the question:

How many pieces of Bristol board will it take to cover the wall?

Make an estimate.

Challenge students to estimate how many pieces of Bristol board it will take.

Have them share out their estimate with neighbours and ensure they attempt convincing them as to why they believe their estimate is reasonable. You might want to give students a closer look by showing the second video in the Spark tab:

At this point, you must make a choice as to what information you want to share with your students.

If your intention is to have your students access this task through counting, addition, or multiplication you could simply pause the “reveal” video after 1 column of Bristol board is affixed to the wall and allow students apply their spatial reasoning skills to make a prediction for the rest. You could also consider telling the students the dimensions for the length and width of the wall in “Bristol board pieces” to see if they can either create (concretely) or draw (pictorially) the array of Bristol board pieces.

If your intention is to help students develop an understanding of dividing whole numbers by fractional amounts, you could reference the wall as the “whole” and tell students that 1 piece of Bristol board is 1 twenty-second or 1/22 of the wall. Students can often use their intuition to determine that they will require 22 pieces of Bristol board, which demonstrates the reciprocal relationship between dividing by 1 twenty-second and multiplying by 22.

While both of the intentions above are helpful for students in earlier grades, we created this task with the intent to bring in the concept of converting metric square units. 

There is a lot of fun to be had here utilizing number sense and proportional reasoning.

Watch a short video walk-through of the Sparking Curiosity portion of this task:

Watch the second part of the Spark walk-through video below:

The prompt in the Sense Making tab is:

How many sheets of Bristol board will it take to cover the wall?

Based on the intentionality we had for this lesson, we suggest that you give this information to push students to make conversions of metric units of area:

However, you might consider sharing different linear metric or imperial measures if you believe that to be a better fit for your students:

• Version #2 Information: Metric Metres and Centimetres
• Version #3 Information: Metric Centimetres
• Version #4 Information: Imperial Inches
• Version #5 Information: Imperial Feet and Inches

Here is a quick run-down video outlining the different versions you could use for this task.

Watch the walk-thru unpacking the Sense Making portion of this task if you chose to give the information included in Version #1:

If you chose to share the linear metric or imperial measures using one of the other information image versions, you might want to watch these walk through videos to support your planning for this lesson:

• Walk Through Video: Given Linear Metric Units & Using Flexible Division

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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.

Return to the questions you recorded from your list of student Noticing and Wondering and answer any questions that have not been answered.

Some extension questions you might consider using to incorporate additional purposeful practice and exploration based on the same context:

Extension #1

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Extension #2

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Extension #3

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