Task Teacher Guide
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In This Task…
Students will estimate a quantity greater than 100 by visually decomposing the prompt into smaller arrays.
Intentionality…
In this task, students will have an opportunity to reason through an estimation activity. Students are encouraged to consider decomposing the large quantity into smaller arrays in order to make a reasonable estimate. This task will allow students to apply the array model and develop a deeper understanding of big ideas, including the following:
- Numbers can be decomposed
- The relationship between repeated addition and multiplication
- The relationships between rows and columns in an array
- The distributive property of multiplication over addition and over subtraction
Spark
What Do You Notice? What Do You Wonder?
Show students the video below displaying ErikTheElectric preparing to eat a large quantity of Reese’s Peanut Butter Cups for his YouTube subscribers.
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 students’ noticing and wondering. For example:
- Why does he want to eat so much?
- Is he swearing?
- His shirt magically changed.
- How did he do that?
- He went to Target.
- He bought all of the Peanut Butter Cups.
- How much did it cost to buy all of those Peanut Butter Cups?
- How many calories is that?
- 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.
Prompt and Estimate
Then, pose the following question:
How many Reese’s Peanut Butter Cups are there?
Follow up that question with:
How might we convince someone that the quantity you come up with is correct?
Let them loose to make some estimates based on what they saw.
Ask students to estimate a number of Peanut Butter Cups that they think is too high and a number of cups that they think is too low before making their “best estimate”.
Sense Making
Crafting A Productive Struggle
After sharing out their estimates, have students improve the precision of their estimates by using the following video and/or image and they must convince their mathematical community of peers as well as the teacher.
After students update their estimates, you may choose to provide the following image giving more detail as to the stacks of peanut butter cups from the above video and image.
It should be noted that the dimensions shared above are approximations as some rows and columns are not consistent.
During Moves
While Students Are Productively Struggling…
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Student Approach #1: One-to-One & Doubling
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Student Approach #2: Partial Products
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Student Approach #3: Partial Products and Standard Algorithm
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Next Moves
Consolidate
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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 below.
Here is a short clip that just reveals the total number of Reese’s Peanut Butter Cups Erik ate:
Answer: 250 Reese’s Peanut Butter Cups
Revisit the student answers. Ask students why their answers may or may not have been exact.
Reflect
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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Resources and Downloads
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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.
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Consolidation Prompt #1
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Consolidation Prompt #2
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Download Editable/Printable Handout
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