### The other day a teacher asked me to create a lesson that had elements of a Number Talk involving percents. Her students had recently been discussing proportional reasoning and the constant of proportionality. Knowing this, I decided to combine percents and proportional reasoning with **Desmos**. Here’s the resulting lesson.

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**Part A: Percents and the Double Number Line**

- Draw the line (Steps 2 – 7 are designed to be the low entry piece)
- Fill in the symbols (% and $)
**Me**: “Whisper to your elbow partner what I added to the number line”- Write in 100% and $50
**Me**: “Discuss with your elbow partner the meaning of the 100 and 50.- Write in 0% and $0
**Me**: ” Discuss with your elbow partner the meaning of the 0 and 0.”**Me**: “What percent do you think I’m going to add to the double number line next?”- Typically, students will say 50% – which is the percent I’m looking for. If a student offers a different percent, I say, “Thanks, I’m going to come back to that one.” (see step 13)

**Me**: Write the dollar value that 50% of $50 represents.- Call on student to give answer and strategy.
- Repeat for steps 9 and 10 for 25%
- Repeat step 9 for 75%. Make sure to give ample “think time”
**Strategies**: Students came up with 4 different strategies for getting $37.50. The process of discussing the different strategies was my number talk element.

- Depending on time, ask students to find 10%, 5%, 1% 16% etc… This is when you can address the guess from step 8

**Part B: Desmos & The Constant of Proportionality**

- Go to link: bit.ly/PercentDesmos
- Ask students to finish filling in the x/y chart.
- Discuss the fact the information forms a diagonal line.
- Ask students to add more information to the chart. i.e. Enter in the dollar amount for a percent greater than 100.
- If the student information is correct, then the point will fall “in line”. If not, then the point will distort the line. (see pic)
- Ask the students to move the red line so it completely covers the purple line and then acknowledge the constant of proportionality (k value)
**Group question**: Why is the constant of proportionality 2?**This questioned garnered a range of responses!****Testing the equations**- At this point, I asked students to enter 2x = y into Desmos and asked them to describe what happened.
**Student Responses**:- The line changed color,
- The line got longer
- The line now goes into infinity.

- This led students to understand that the equation represents the pattern in the x/y chart and that all 3 equations shared are equivalent.
- When entering y/x = 2, the line changed color again. This time green.

The lesson met the teachers expectations!! She intends to revisit this process using a different dollar amount, such as $40 in place of $50.

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- My blog post on Number Talks: A Touch of Number Sense
- For other activities and posts involving Desmos, click here