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MathematicsMathsMiddle schoolKey Stage 3

Equivalent ratios with a paint mixer that shows each student their own mistake

Every student mixes paint toward the same green. When a student adds instead of multiplying, the color comes out wrong, and Sparky asks them what they did to each color.

Jemel Fanfan

Jemel Fanfan | Founding Member at Flint

Title card reading 'Equivalent ratios with a paint mixer that shows each student their own mistake', next to a target green swatch for 2 blue to 3 yellow and a bluer swatch for a student's 6 to 7 mix, Sparky's question about what she did to each color, and her fixed answer of 9 cups of yellow.

"One student used Flint to make a unit test study guide. Another checked homework by comparing their steps to AI solutions, identifying and correcting mistakes on their own. This independence and self-awareness are key signs of deeper learning."

Chaz CleareChaz Cleare, Middle School Math Teacher at The Kinkaid School

Why this matters

A student who knows that 2 cups of blue paint go with 3 cups of yellow will often say that 6 cups of blue go with 7 cups of yellow. They added 4 to both numbers instead of multiplying both by 3. On paper, 7 looks as reasonable as 9, so the student keeps adding on every problem, and the teacher has to wait for quiz day to find out.

Maya sees her mix come out too blue, and fixes it

Maya is a 6th grader who paints in the art club. She can double a ratio, but when the numbers don't double she adds the same amount to both parts.

Every student in the class gets the same paint mixer in Sparky's first message, with the same 2:3 target and the same first problem. The rest of the chat is Maya's own: Sparky sets the problems on her mural, and each next question depends on what she just answered. Maya and her chat are an example we wrote for this page, shortened from a test run of the activity.

Sparky uses Maya's muralSparky asks a question instead of giving the answerSparky gives a harder problem after a right answer
M

Maya

Interest: Painting a muralStarting point: Can double a ratioGets stuck: Adds the same number to both parts

Sparky

Hi! This paint mixer makes green from blue and yellow paint. The target green is 2 cups of blue to 3 cups of yellow. Try a few mixes, then tell me: what would you paint if you had a big bucket of this green?
Flint's Paint Mixer interactive as it opens: a target of 2 cups of blue to 3 cups of yellow with a green swatch, an empty grey swatch for the student's mix with the status 'Add some paint', plus and minus buttons for cups of blue and cups of yellow at 0, and buttons to add the mix to a ratio table or clear the table.
InteractivePaint Mixer

Maya

A mural on the wall outside the art room

Understanding check

Your mural needs 6 cups of blue. How many cups of yellow keep the same green as the target? Try it in the mixer and tell me how you figured it out.

Maya

7 cups of yellow. I added 4 to the blue to get 6, so I added 4 to the yellow too. It says Bluer than the target.
The Paint Mixer with 6 cups of blue and 7 cups of yellow. The student's swatch is a bluer, darker green than the 2 to 3 target swatch next to it, and the status line reads 'Bluer than the target'.
InteractiveMaya's mix: 6 blue, 7 yellow

Sparky

So 6 blue and 7 yellow comes out too blue. What did you do to the blue to get from 2 to 6? And what did you do to the yellow to get from 3 to 7?

Maya

I added 4 to both. But the blue went from 2 to 6, that's times 3. So the yellow should be 3 times 3, which is 9 cups. Now it says Same green as the target.

Sparky

You found your own mistake. Now build a ratio table: three more batches that make the same green, one with 10 cups of blue, one with 12 cups of yellow, and one of your choice.

Maya

10 blue and 15 yellow. 8 blue and 12 yellow. 4 blue and 6 yellow. All three have a check mark.
The Paint Mixer at 4 cups of blue and 6 cups of yellow, matching the target, with a ratio table below listing 10 blue and 15 yellow, 8 blue and 12 yellow, and 4 blue and 6 yellow, each marked as the same green.
InteractiveMaya's ratio table

Sparky

All three are right. Change the mixer's target to 5 blue : 8 yellow. How many cups of yellow go with 20 cups of blue?

Maya

32 cups of yellow. 20 is 5 times 4, so I did 8 times 4.

Sparky

Exactly right. Back in the 2:3 green, how much blue goes with 21 cups of yellow?

Found her own mistake, then solved a 5:8 mix with no hints

What Flint did for Maya

  • The paint mixer in Sparky's first message turned Maya's 6:7 into a color next to the target, so she saw her mix was off before anyone told her.
  • Sparky asked what she did to each color instead of giving the answer, and Maya found the times 3 herself.
  • After her right answer, Sparky moved her straight to a ratio table and then a 5:8 target, without waiting for the rest of the class.
  • Sparky set the first problem on her mural, the thing she said she would paint.
  • Sparky graded her chat against the activity's rubric, which counts a mistake she fixed on her own toward Proficient.

A teacher can't stand next to 30 students at the moment each one mixes 6:7 and ask the right question. Sparky does it in every student's chat.

The activity page shows who added instead of multiplying

Activity analytics sums up what the class did across every chat. In this activity, Sparky's analysis guidelines ask it to note which students added the same number to both colors and whether they fixed it themselves.

Flint's activity page for an activity called Mix the Same Green: Equivalent Ratios with a Paint Mixer. Needs attention shows a live alert that one student wrote 'i keep getting bluer than the target' after two hints on the 6 cups of blue problem. Activity analytics lists what the class does well, including 11 students who found their own mistake after mixing it, an area of improvement where 14 students added the same number to both colors, and a follow-up with a button to create a follow-up activity. The Sessions table shows two submitted students graded Proficient and Developing and one still in progress.

Example activity page

After a 6th grade class finishes the paint mixer activity

The school and students are made up for this page. In this example, 14 students added on the first problem and most of them fixed it after seeing the color.

Set up the activity for free

The paint mixer activity is in Flint's public library, with the mixer, Sparky's guidelines, the greeting and a rubric already set up. Open it, select Try this activity to copy it into a free Flint account, and move it to a class. In the activity settings, select Try session myself to mix a few batches as a student before you assign it.

For more math activities, see Flint for math.

Start the activity for free

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