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Grade 6 Math WebQuest · Unit 3 · 6.RP

Pixel Forge: The Color Lab

The indie game studio Pixel Forge just hired you as a junior color technician. Every sprite in their new game gets its color from a paint recipe — a ratio of cyan drops to magenta drops. Your job: scale recipes up without changing the color, prove your batches are consistent on a graph, and judge which artist mixed the truer shade. Get the ratios right, or the whole game looks wrong.

⏱ 1–2 class periods 📊 Ratio tables 📈 Graphing ratios ⚖️ Comparing recipes

Welcome to the Color Lab

At Pixel Forge, a color is never just "pink." It is a ratio: for every 2 drops of cyan, add 3 drops of magenta to make the studio's signature "Sunset Pink" (a 2 : 3 recipe). The hard part is staying exact when you mix a tiny test batch or a giant tank — the ratio has to stay the same, or the color shifts.

The Driving Question

How can a ratio table and a graph prove that two different-sized batches are really the same color — and help you compare two recipes fairly?

Level 1 · Support A ratio compares two amounts. "2 : 3" means 2 of one thing for every 3 of another. Equivalent ratios are the same comparison written with bigger or smaller numbers, like 2 : 3 and 4 : 6. You make them by multiplying (or dividing) both numbers by the same number. En español: Una razón compara dos cantidades. "2 : 3" significa 2 de una cosa por cada 3 de otra. Las razones equivalentes son la misma comparación con números más grandes o más pequeños (2 : 3 y 4 : 6). Multiplica o divide ambos números por el mismo número.
Level 2 · Enrichment Here is the deep idea you will prove today: if you plot equivalent ratios as points (cyan, magenta), they all land on one straight line that passes through the origin (0, 0). That line is the color. A point that falls off the line is a different recipe — a different shade. Watch for it in Step 3.

The Task

By the end of this WebQuest you will submit a Color Lab Report for Pixel Forge. A complete report must:

  • Finish a ratio table that scales the Sunset Pink recipe (cyan : magenta = 2 : 3) up to a full batch.
  • Plot three of your batches as points (cyan, magenta) and show they sit on one straight line.
  • Compare two artists' recipes and decide which one makes the more magenta-heavy (pinker) color — with a reason.
  • Pass the Check Your Understanding self-check at the bottom.
Sunset Pink — cyan : magenta = 2 : 3. The magenta block is wider because the recipe uses more magenta.

Deliverable:

One Color Lab Report (completed ratio table + a sketched or described graph + your recipe comparison with a reason) AND this page saved as a PDF or DOC with your name from the bar at the top.

The Process

Work through the steps in order. Each step builds one part of your Color Lab Report.

Step 1 — Build the ratio table

The Sunset Pink recipe is 2 drops cyan : 3 drops magenta. To mix a bigger batch, multiply both numbers by the same amount. Copy this table and fill in the magenta-colored blanks.

Sunset Pink ratio table (cyan : magenta = 2 : 3)
× Cyan (drops) Magenta (drops)
×1 2 3
×2 4 6
×3 6 ?
×5 ? 15
×8 16 ?

Worked example — the ×3 row:

Cyan: 2 × 3 = 6. Magenta: 3 × 3 = 9. So the ×3 batch is 6 : 9 — still Sunset Pink, just bigger.

Level 1 · Support Stuck on the ×5 row? You already know magenta is 15. Ask: "3 times what equals 15?" That is 5, so multiply cyan by 5 too: 2 × 5 = 10. En español: La magenta es 15. Pregunta: "¿3 por cuánto es 15?" Es 5. Entonces multiplica el cian por 5 también: 2 × 5 = 10.

Step 2 — Read the table sideways

A ratio table hides a useful pattern: in every Sunset Pink row, magenta is bigger than cyan by the same comparison. Look down both columns. Cyan goes 2, 4, 6, 10, 16 and magenta goes 3, 6, 9, 15, 24. Every pair simplifies back to 2 : 3.

Level 2 · Enrichment Find the unit ratio: how much magenta for exactly 1 drop of cyan? Divide 3 ÷ 2 = 1.5. So Sunset Pink uses 1.5 drops of magenta per drop of cyan. This single number is the fastest way to compare any two recipes — keep it in mind for Step 4.

Step 3 — Plot the batches on a graph

Now prove your batches are the same color. Plot each pair as a point (cyan across, magenta up). The grid below already shows the ×1 and ×2 batches. Find where the ×3 batch (6, 9) belongs and notice how all the points line up.

Graph of Sunset Pink batches: points (2,3) and (4,6) on a straight line through the origin, heading toward (6,9). (2, 3) (4, 6) (6, 9)? Cyan drops → Magenta drops → 0
Level 1 · Support To plot (6, 9): start at 0, move right to 6 on the cyan axis, then go up to 9 on the magenta axis. Put a dot. It should land right on the dashed purple line with the others. En español: Para marcar (6, 9): empieza en 0, ve a la derecha hasta 6 (cian), luego sube hasta 9 (magenta). Cae sobre la línea morada.

Step 4 — Compare two artists' recipes

Two artists send you their "pink" recipes for the same boss-monster sprite. You must pick the one that is more magenta-heavy (the pinker shade). Compare them fairly using equivalent ratios.

Worked example — compare 2 : 3 vs 3 : 4 fairly:

Make the cyan parts match. Maya 2 : 3 ×3 = 6 : 9. Devon 3 : 4 ×2 = 6 : 8. Same cyan (6). Maya has 9 magenta, Devon has 8. Maya's recipe is pinker.

Level 2 · Enrichment Check it the unit-ratio way: Maya = 3 ÷ 2 = 1.5 magenta per cyan; Devon = 4 ÷ 3 ≈ 1.33 magenta per cyan. 1.5 > 1.33, so Maya is pinker — both methods agree. Which method felt faster to you, and why?

Step 5 — Write your Color Lab Report

Put it together: your completed ratio table, your three plotted points (and the fact that they form a straight line through the origin), and your recipe comparison with a clear reason. Then take the self-check below.

Resources

Use these Neft Teacher tools as you work. They open in the same window — use your back button to return.

Unit 3 · 3D Ratio GameMix and scale ratios, then see them snap onto the line. Ratio LabBuild ratio tables and plot equivalent ratios live. Unit 3 Graphic NovelThe ratios story with pictures and bilingual support. Math Writing Help · EN/ESSentence frames and bilingual vocabulary support.

Key vocabulary · Vocabulario clave

Evaluation

Your Color Lab Report will be scored on this rubric.

Criteria 4 · Lead Artist 3 · Color Tech 2 · Apprentice 1 · Getting started
Ratio table All blanks correct; multiplying both columns shown. One blank wrong, method clear. Some equivalent ratios attempted with errors. Table mostly blank or incorrect.
Graphing ratios All points correct and clearly on one line through origin. Points correct; line idea partly explained. Points plotted with errors. No points or no graph.
Comparing recipes Correct choice with equivalent-ratio reasoning shown. Correct choice; reasoning thin. Attempts comparison; reasoning unclear. No comparison made.
Math language Uses ratio, equivalent, origin correctly throughout. Uses most terms correctly. Few math terms used. No math vocabulary.
Self-check 6 of 6 correct. 5 of 6 correct. 3–4 of 6 correct. 0–2 of 6 correct.
Teacher Notes & Answer Key (not printed)

Pixel Forge · Color Lab Report — pairs with the Evaluation rubric above.

Sample Answers — Color Lab Report

  • Ratio table (cyan : magenta = 2 : 3): cyan 2, 4, 6, 10, 16 / magenta 3, 6, 9, 15, 24. Every pair simplifies to 2 : 3.
  • Graph: plotting (cyan, magenta) pairs (2,3), (6,9), (10,15)… all fall on one straight line through the origin.
  • Compare recipes: Maya 2 : 3 vs Devon 3 : 4 — match cyan: Maya 6 : 9, Devon 6 : 8. Maya has more magenta (9 > 8), so Maya is pinker. Unit-ratio check: Maya 3÷2 = 1.5 vs Devon 4÷3 ≈ 1.33 magenta per cyan.

Facilitation

  • Connect the table, the straight-line graph, and the unit ratio (1.5 magenta per cyan) as three views of the same relationship.
  • For the compare, make a common term (same cyan) so the comparison is fair.

Standard

CCSS 6.RP.A.3a.

Check Your Understanding

Answer all six. Click Check My Answers when you are done. These match the steps in your report.

1.In the Sunset Pink table (2 : 3), the ×3 row has 6 cyan. How many magenta drops?
Hint / Pista: 3 × 3, or scale 2 : 3 by 3.
2.A batch uses 15 magenta drops and stays Sunset Pink (2 : 3). How many cyan drops does it need?
Hint / Pista: 3 × 5 = 15, so multiply cyan by 5 too.
3.Which ratio is equivalent to Sunset Pink (2 : 3)?
Hint / Pista: multiply both numbers of 2 : 3 by the same value.
4.You plot Sunset Pink batches as points (cyan, magenta). Which point lies on the same line as (2, 3) and (4, 6)?
(2,3) (4,6)
Hint / Pista: it must be an equivalent ratio of 2 : 3.
5.Maya mixes 2 : 3 (cyan : magenta). Devon mixes 3 : 4. Whose color is more magenta-heavy (pinker)?
Hint / Pista: make the cyan parts equal, then compare magenta.
6.A giant tank batch of Sunset Pink uses 24 drops of cyan. Keeping the 2 : 3 ratio, how many magenta drops are needed?
Hint / Pista: 2 × 12 = 24, so multiply 3 by 12 too.

Your score also saves to the panel at the top. Use Save as PDF or Save as DOC there to turn in your Color Lab Report with your name.

Conclusion

You did exactly what real game artists and color scientists do: you kept a color exact across any batch size, proved it on a graph, and judged two recipes fairly. A ratio table, a straight line through the origin, and a fair comparison are the same tools used to color every sprite in a game — and to mix paint, dye fabric, and tune photos. Pixel Forge's boss monster is going to look perfect.

Take it further · Level 2

Invent a third recipe that is between Maya's and Devon's in pinkness. Prove it with equivalent ratios.

Reflect · Reflexiona

How does the graph show that two batches are the same color? ¿Cómo muestra la gráfica que dos mezclas son el mismo color? Explain in 2–3 sentences.

Real careers · Carreras reales

Game artists, paint chemists, and photo editors all use ratio tables and graphs to keep colors consistent — exactly the skill you just used.

Neft Teacher · Grade 6 Math · Unit 3 · Ratio Reasoning · 6.RP