Students will explore modelling and solving proportional reasoning problems that relate to percent using a variety of strategies along a double number line. Students will engage in a math talk that poses a dilemma of which coupon to use: a 30% off coupon or a $30 off coupon. 

The purpose of the Day 4 activities is to reinforce key concepts from Day 3. Students will engage in a string of related problems through a math talk and will have an opportunity to complete independent purposeful practice. The math talk and purposeful practice serve to develop a deeper understanding of the following big ideas:

• Percent is a comparison measured out of 100;
• decreasing by a percentage will lower the original value.
• increasing by a percentage will increase the original value.
• A percentage decrease, followed by a percentage increase of the same value will result in a change of value.
• Reducing a value by 20% is the same as retaining 80% of the value.
• Increasing a value by 20% is the same as 120% of the original value..
• To solve percent related problems we can use the following strategies:
  • Analyze Between and Within Ratios (Scaling Up or Down);
  • Find a Unit Rate

Present the following percent problems one at a time (use the visual prompts). Encourage students to first predict which coupon will create the better deal and then have them determine which coupon is the better deal.

As you and your class work through these problems some students will start to make predictions on which price is the “it doesn’t matter price”. Hold back on confirming these predictions with your students. Encourage your students to prove any hypothesis they might have.

Would you rather use:
a $30 off coupon or a 30% off coupon.

Bear #1: $40
Bear #2: $80
Bear #3: $140
Bear #4: $96
Bear #5: $250

Consider watching this silent solution animation to help you prepare to facilitate this math talk utilizing a double number line to model possible solutions.

Show students the following visual math talk prompt and be prepared to pause the video where indicated:

Then ask students:

Which coupon would you rather use?

Similar to Day 1,2, and 3 of the Bear Builder problem-based unit, students may use a benchmark strategy to find 10%.

Since we are aiming to build fluency and flexibility working with percent by using multiplication and division we are going to ensure students are not leveraging the calculator as a tool.

As the facilitator, we are going to do our best to work from a double number line to highlight the strategies students use to determine the percent value.

While students are determining the discounted price using the 30% off coupon some students will choose to place benchmarks along their number line like 50% by using a halving strategy. They may then break the bottom half of the number line up into five 10% sections, revealing that each 10% is $4 units and each 5% is $2. . Reducing by 30% is reducing by 3 groups of 10% so 3×4 = $12. So the final price of the bear is $40-$12 = $28

Some students may also use the indirect method of determining 70% of 40 as the final price after using the 30% off coupon.

Show students the following visual math talk prompt and be prepared to pause the video where indicated:

Then ask students:

Which coupon would you rather use?

Again, facilitating this based on student thinking and modelling on the board for all to see is helpful here rather than simply playing the silent solution animation.

As you progress through each of the prompts you may want to consider highlighting and alternating different strategies.

Show students the following visual math talk prompt and be prepared to pause the video where indicated:

Then ask students:

Which coupon would you rather use?

Again, facilitating this based on student thinking and modelling on the board for all to see is helpful here rather than simply playing the silent solution animation.

As you progress through each of the prompts you may want to consider highlighting and alternating different strategies.

Login/Join to access one (1) additional Math Talk Prompt as well as the Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem-based units.

Login/Join to access one (1) additional Math Talk Prompt as well as the Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem-based units.

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

Login/Join to access one (1) additional Math Talk Prompt as well as the 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.

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