Students will determine which store is offering the best sale price for potatoes. 

The purpose of this task is to give students an opportunity to apply their understanding of ratios and rates. Students will be asked to determine rates to compare potato sales taking place at three competing grocery stores. In today’s task, students will use either ratio or rate reasoning to reveal the cost per kilogram of potatoes. Some of the following big ideas may emerge in this task: 

• 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; 
• 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. dollars and dollars, pounds and pounds);
• Composed units can be scaled to the same quantity of one variable in order to identify the “better buy”;
• Revealing a rate can be helpful to make direct comparisons in order to identify the “better buy” when comparing the cost of goods at the store.

Show students this video:

Then, ask students:

What do you notice?

What do you wonder?

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 three flyers.
• I notice it says sale. 
• I notice the same three stores. 
• I notice they are selling potatoes.
• I notice different prices and different amounts. 
• I wonder which store is offering the best deal.
• I wonder which country these stores are located in.
• I wonder what currency this is.
• I wonder if we have to add tax. 
• I wonder if these are good prices. 

At this point, take their noticing and wonders and try to answer any of the wonders you can cross off the list right away without giving too much away.

Share the following prompt with student and display the screenshot on the screen:

Which store is offering the best price per kilogram of potatoes?

Make a prediction and share why with a neighbour.

This is an opportunity for students to share their thinking based on the limited information that has been shared.

Some student responses you might anticipate include:

• Bargain Bin because it is the most expensive and looks like it has the most potatoes. Usually the larger the quantity (i.e.: bulk), the cheaper it costs per item.
• I don’t know there isn’t enough information.
• Deal City, because it is always the best prices.
• And so on.

Show students the following animation:

Share the following prompt verbally and leave the screenshot up on the screen:

Which store is offering the best price per kilogram of potatoes?

Use a model of your choice to convince your math community.

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

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Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

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Today, students were asked to find a rate for each sale price.
Some students may have gone about this by scaling the composed unit back to a ratio that involves 1 kilogram of potatoes. Students revealed a ratio with a quantity of 1. This strategy involves ratio reasoning. This solution can be represented using ratio notation. For example, 2.25 : 1 or 2.25 to 1.

However, to truly reveal a rate, with a compound unit (dollars/kg), students will use partitive division to divide the quantity of dollars by the quantity of kilograms. This is called rate reasoning.

In today’s consolidation, we will highlight rate reasoning to reveal a rate with a compound unit.

Scenario 1

Scenario 2:

This solution can be represented using rate notation, for example, $2.25/kg.

If students are ready, you might consider making a connection between this concrete approach and the use of partial quotients in the flexible algorithm.

Scenario 3:

Discuss how rates are useful when deciding where to make a purchase. Considering the best value for a good allows you to make wise decisions about spending. 

Share the following reveal video:

Here is a screenshot of the final frame of reveal video:

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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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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