Task Teacher Guide
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In This Task…
Students will explore the idea of scaling in tandem with a ratio as a composed unit.
Intentionality…
In this task, students will have an opportunity to reason through an activity involving the ratio between two quantities; scoops of hot chocolate and glasses of hot chocolate. Through this task, students will have the opportunity to apply models including the double number line and the ratio table. They will also explore big ideas including the following:
- Unitizing;
- Ratio reasoning through scaling in tandem;
- The relationship between repeated addition and multiplication;
- The relationship between multiplication and division, particularly quotative division; and,
- A composed unit is one way of defining the relationship that exists in a ratio.
Spark
What Do You Notice? What Do You Wonder?
Show students the video below showing a can of hot chocolate mix being placed on the counter.
Ask students to engage in a notice and wonder protocol. ANYTHING and EVERYTHING that comes to mind is fair game.
Write down all of the student noticing and wondering. For example:
- I notice hot chocolate.
- I notice a glass.
- I wonder if the hot chocolate is already made in the container?
- I wonder if someone is making hot chocolate?
- I wonder if that is YOU in the video.
- And many others…
Then, ask students to continue adding to their list as they view the next spark video showing students how many scoops are placed in a single glass of hot chocolate.
More noticing and wondering can be shared out such as:
- I saw him place 9 scoops in the glass.
- Why is he putting hot chocolate mix in a glass and not a mug?
- How many scoops in total are in the container?
- And many others…
Take time to acknowledge the noticing and wondering your students have engaged in and try to answer any that you can address right away.
Sense Making
Crafting A Productive Struggle: Prompt
Then, pose the following question:
How many scoops will he need to make 8 glasses of hot chocolate?
Follow up that question with:
How might we convince someone that the quantity you come up with is correct without the use of a calculator?
Let them loose to make some estimates based on what they saw.
During Moves
While Students Are Productively Struggling…
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Student Approach #1: One-to-One Counting
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Student Approach #2: Skip Counting
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Student Approach #3: Scaling, Then Additive
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Student Approach #4: Multiplication Using Known Facts
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Next Moves
Consolidation
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Reveal
After consolidating learning using student generated solution strategies and by extending their thinking intentionally, we can share what really happened by showing the video revealing how many scoops for 3 glasses, followed by an image showing how many scoops for 8 glasses:
Alternatively or in addition to the video, you can show the still image below.
Answer: 24 scoops of hot chocolate mix.
Revisit the student answers.
Reflect
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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.
Extend
Crafting A Productive Struggle: Extension Prompt
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Intentionality…
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Student Approach #1: Multiplication With Known Facts, Then Repeated Addition
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Student Approach #2: Doubling, Then Partitioning
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Student Approach #3: Flexible Division Using Repeated Subtraction
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Consolidation
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Reveal
After using student generated solutions to make connections, you can reveal this image.
ANSWER: 18 â…“ glasses
Reflect
Provide students an opportunity to reflect on their learning by offering this consolidation prompt 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.
Download Editable/Printable Handout
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Resources and Downloads
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Lesson Tip Sheet
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Videos & Images
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Keynote Slides
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PowerPoint Slides
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Printable Handout
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Explore The Entire Unit of Study
This Make Math Moments Task was designed to spark curiosity for a multi-day unit of study with built in purposeful practice, and extensions to elicit and emerge mathematical models and strategies.
Click the links at the top of this task to head to the other related lessons created for this unit of study.
Consolidation Prompt
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Prompt
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Extend: Image
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Extend: Reveal
Extend: Consolidation Prompt
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Download Editable/Printable Handout
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