Task Teacher Guide
Be sure to read the teacher guide prior to running the task. When you’re ready to run the task, use the tabs at the top of the page to navigate through the lesson.
In This Task…
Students will determine which store is offering the best value for jellybeans.
Intentionality…
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 for the purpose of comparison. Today’s task promotes consumer awareness as students determine the best value for their money when deciding between two stores to buy jelly beans. 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;
- Composed units can be scaled to the same quantity of one variable in order to identify the “better buy”;
- Unit rates can be used to make direct comparisons in order to identify the “better buy”.
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.
Spark
What Do You Notice? What Do You Wonder?
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 a scale.
- I wonder if this is at a grocery store.
- I notice some kind of colourful candy.
- I wonder if they are jelly beans.
- I notice 3 on the scale.
- I notice $13.50.
Estimation: Prompt
Student prompt:
Which store is offering a better deal on jelly beans?
Make an estimate.
Have students make predictions by reasoning through their comparison of the two stores through conversation alone.
Give students an opportunity to discuss their reasoning with a partner for about 2 minutes.
Take a vote from students on which store will offer the best value for jelly beans. Do not have students share their justification at this point, this may rob the thinking from fellow classmates.
Sense Making
Crafting A Productive Struggle: Prompt
Show students the following screenshot and follow-up with the prompt verbally:
You have been asked to purchase 6 pounds of jelly beans for a large event with a limited budget. Which store, Bargain Bin or Deal City is offering the best value for jelly beans? Where will you be shopping for jelly beans and why?
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.
During Moves
While Students Are Productively Struggling…
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
Student Approach #1: Scaling up in the ratio table
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
Student Approach #2: Scaling down in the ratio table
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
Student Approach #3: Using partitive division to reveal a rate
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
Next Moves
Consolidation: Making Connections
The comparison of the quantities of pounds to dollars in this scenario is a specific type of ratio called a composed unit where one can consider the two quantities in the ratio as a single unit. For example, when we consider the 3 pounds and $13.50, we can view these two quantities together as one unit (composed of two unique units) that can increase and decrease in tandem (together).
Some students likely used the composed unit to scale the ratio up to 6 pounds or down to 1 pound in order to compare. Some students may have also scaled up to a common multiple of 3 and 4 such as 12, and then possibly divided by two.
We are going to call this strategy ratio reasoning.
Scenario 1:
Scenario 2:
Scenario 3:
A second strategy that may have been used is revealing a rate through partitive division. When we take the two quantities within a composed unit and divide through partitive division, a rate is revealed. A single quantity with a compound unit (dollar/pound or pound/dollar).
We are going to call this strategy rate reasoning.
Reveal
Show students different variations of the reveal videos below.
Here is a screenshot of the final frame of reveal video:
Reflect
Provide students an opportunity to reflect on their learning by offering these consolidation prompts to be completed independently.
Consolidation Prompt #1:
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
Consolidation Prompt #2:
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
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
Become a member to access purposeful practice to display via your projector/TV, download the PDF to upload to your LMS and/or print for students to have a physical copy
Resources and Downloads
Oh No! You Must Be Logged In!
Download a printable lesson plan, video/images, and presentation slides in Keynote and PowerPoint format to make the experience as smooth as possible by becoming a member of the Make Math Moments Academy.
Lesson Tip Sheet
Download the lesson plan in PDF format so you can keep it handy and share with colleagues.
Videos & Images
Download the videos, images, and related media files to your computer to avoid streaming.
Keynote Slides
Download in Apple Keynote format to avoid streaming video and run the lesson smoothly.
PowerPoint Slides
Download in Microsoft PowerPoint format to avoid streaming video and run the lesson smoothly.
Printable Handout
Download/Edit the handout so you can keep it handy and share with colleagues.
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 #1
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
Consolidation Prompt #2
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
Download Editable/Printable Handout
Become a member to access purposeful practice to display via your projector/TV, download the PDF to upload to your LMS and/or print for students to have a physical copy
Task Teacher Guide
Be sure to read the teacher guide prior to running the task. When you’re ready to run the task, use the tabs at the top of the page to navigate through the lesson.
In This Task…
Students will determine which store is offering the best value for jellybeans.
Intentionality…
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 for the purpose of comparison. Today’s task promotes consumer awareness as students determine the best value for their money when deciding between two stores to buy jelly beans. 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;
- Composed units can be scaled to the same quantity of one variable in order to identify the “better buy”;
- Unit rates can be used to make direct comparisons in order to identify the “better buy”.
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.
Spark
What Do You Notice? What Do You Wonder?
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 a scale.
- I wonder if this is at a grocery store.
- I notice some kind of colourful candy.
- I wonder if they are jelly beans.
- I notice 3 on the scale.
- I notice $13.50.
Estimation: Prompt
Student prompt:
Which store is offering a better deal on jelly beans?
Make an estimate.
Have students make predictions by reasoning through their comparison of the two stores through conversation alone.
Give students an opportunity to discuss their reasoning with a partner for about 2 minutes.
Take a vote from students on which store will offer the best value for jelly beans. Do not have students share their justification at this point, this may rob the thinking from fellow classmates.
Sense Making
A Productive Struggle: Prompt
Show students the following screenshot and follow-up with the prompt verbally:
You have been asked to purchase 6 pounds of jelly beans for a large event with a limited budget. Which store, Bargain Bin or Deal City is offering the best value for jelly beans? Where will you be shopping for jelly beans and why?
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.
During Moves
While Students Are Productively Struggling…
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
Student Approach #1: Scaling up in the ratio table
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
Student Approach #2: Scaling down in the ratio table
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
Student Approach #3: Using partitive division to reveal a rate
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
Next Moves
Consolidation: Making Connections
The comparison of the quantities of pounds to dollars in this scenario is a specific type of ratio called a composed unit where one can consider the two quantities in the ratio as a single unit. For example, when we consider the 3 pounds and $13.50, we can view these two quantities together as one unit (composed of two unique units) that can increase and decrease in tandem (together).
Some students likely used the composed unit to scale the ratio up to 6 pounds or down to 1 pound in order to compare. Some students may have also scaled up to a common multiple of 3 and 4 such as 12, and then possibly divided by two.
We are going to call this strategy ratio reasoning.
Scenario 1:
Scenario 2:
Scenario 3:
A second strategy that may have been used is revealing a rate through partitive division. When we take the two quantities within a composed unit and divide through partitive division, a rate is revealed. A single quantity with a compound unit (dollar/pound or pound/dollar).
We are going to call this strategy rate reasoning.
Reveal
Show students different variations of the reveal videos below.
Here is a screenshot of the final frame of reveal video:
Reflect
Provide students an opportunity to reflect on their learning by offering these consolidation prompts to be completed independently.
Consolidation Prompt #1:
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
Consolidation Prompt #2:
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
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
Become a member to access purposeful practice to display via your projector/TV, download the PDF to upload to your LMS and/or print for students to have a physical copy
Resources and Downloads
Oh No! You Must Be Logged In!
Download a printable lesson plan, video/images, and presentation slides in Keynote and PowerPoint format to make the experience as smooth as possible by becoming a member of the Make Math Moments Academy.
Lesson Tip Sheet
Download the lesson plan in PDF format so you can keep it handy and share with colleagues.
Videos & Images
Download the videos, images, and related media files to your computer to avoid streaming.
Keynote Slides
Download in Apple Keynote format to avoid streaming video and run the lesson smoothly.
PowerPoint Slides
Download in Microsoft PowerPoint format to avoid streaming video and run the lesson smoothly.
Printable Handout
Download/Edit the handout so you can keep it handy and share with colleagues.
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.