Students will solve a problem about rice involving proportions. In solving the problem, they will consider ratio, rate, and scale.

The purpose of this task is to give students an opportunity to apply their understanding of ratios and rates. Students will either scale the composed unit in tandem by revealing a scale factor, or leverage the rate that exists within this composed unit. Students will build fluency finding unknown values using ratio and/or rate reasoning. Students may or may not realize the role of division in revealing a rate or a scale factor. These are big ideas that will be explored more explicitly throughout this unit.
Some of the big ideas that may emerge in this task include:

• There are two types of ratios; composed unit and multiplicative comparison;
• A composed unit is often (not always) a ratio with two distinct units;
• A composed unit can be scaled in tandem;
• Equivalent ratios are derived from the same rate;
• When you divide a composed unit through partitive division, you reveal a rate.
• Quotative division is applied when trying to determine a scale factor between two quantities/measures of the same unit (i.e. rice and rice, water and water).

Prerequisite unit:
If your students do not currently have a solid understanding of the implications of division on ratio and rate reasoning, consider trying Planting Flowers before moving on to this unit.

Show students the following 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 it is sunny outside.
• I notice a bag of rice.
• I wonder if they are going to cook rice?
• I wonder if there is enough rice for the whole family?
• I wonder how much rice is in the bag?
• I notice 200 mL of rice.
• I wonder how many servings he plans to make?
• I wonder how much water he will need to make 200 mL of rice?
• And many others…

At this point, take their noticing and wonders and try to answer any of the wonders you can cross off the list right away. Things like whether it was close to dinner time or whether the person was going to use the remainder of the package to make the rice are all things you want to answer, if you can.

Ask students to make an estimate based on what they saw in the previous video:

How much water will be needed to make 200 mL of rice?
Make an estimate.

Have students make estimates first by thinking about a measure of water that they believe will be too low, followed by a measure that they think will be too high.

Challenge students to be risky with their low/high estimates.

Then, have them pick their best estimate and share with their neighbours before sharing and recording on the chalk/whiteboard or chart paper as a class.

Ask students what information they might need in order to figure out the answer.

Show students the following video and follow-up with the prompt verbally:

After students have shared their estimates, re-iterate the estimation prompt, ask them to update their estimates and to craft a convincing argument for why they believe that quantity of water is necessary to make this batch of rice according to instructions.

Your prompt might sound something like this:

How much water will be needed to make 200 mL of rice?
Be more precise while also crafting a convincing argument using strategies and tools that would be easy to understand.

We will have students engage in this task without the aide of a calculator and thus we will promote the use of mathematical models as tools for thinking and representing their thinking.

Encourage students to convince their peers.

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Once students have shared their answers, show them the video below.

And/or show the following screenshot:

Revisit the student answers. Have students discuss their thinking and what they would change if they did the task again. Return to the things students noticed and wondered from the SPARK section of the lesson, and answer any questions that have not been answered.

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

Consolidation Prompt #1:

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Consolidation Prompt #2:

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Consolidation Prompt #3:

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Consolidation Prompt #4:

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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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…students have difficulty figuring out how much water they need when they’re using 200 mL of uncooked rice.

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