Mix a batch. Keep the taste.

SparkClass

Change the amounts. Watch the relationship.

CCSS 6.RP.A.2 · 6.RP.A.3a–b
Live Taste Test
Same taste
Original Recipe1 recipe · 5 cups
2:3
concentrate : water
New Mixture2 batches · 10 cups
4:6
concentrate : water
Double Number Lines
OriginalNew
Double number lines for concentrate and water The original and new concentrate marks align with their matching water marks.
01

Both parts are multiplied by 2. The batch grows, but the concentrate share stays at 40%—same color, same taste.

New Ratio · Simplest Form2 : 3
New Mixture · Total10 cups

Teacher notes · Ratio Mixer

Start with the default 2:3 recipe and factor 2. The key question is not “How many cups?” but “What relationship stays the same?”

1

Scale the recipe

In Multiply mode, move from 2:3 to 4:6. Ask students to identify the unchanged concentrate share (40%) and both unit rates: 2/3 cup concentrate per cup of water, and 3/2 cups water per cup of concentrate.

2

Read the aligned marks

Each line has its own cup scale. Matching original marks align vertically, and matching new marks align vertically when the ratio is equivalent. Test factors 0.5 and 4 to check the boundary cases.

3

Confront the additive misconception

Keep 2:3 and 2 selected, then switch to Add the same. Compare 2:3 → 4:6 with 2:3 → 4:5. The marks separate, the concentrate share rises from 40% to about 44.4%, and the color changes. Adding the same amount does not generally preserve a ratio; equal starting parts are the exception.

4

Reverse the unit rate

Ask: “How much concentrate for 1 cup of water?” Then reverse it: “How much water for 1 cup of concentrate?” Have students explain why the two rates are reciprocals.

CCSS alignment: 6.RP.A.2 — understand ratio relationships and unit rate. 6.RP.A.3a — represent equivalent ratios with double number lines and relate them to ratio tables. 6.RP.A.3b — solve unit-rate problems. The color is a visual concentration model, not a simulation of real pigment mixing.