Grade 6 • Unit 2 HyperDoc

How Many Fit? Dividing Fractions at the Food Truck

You just joined the crew of the Mango Lane food truck. Every batch of sauce, every scoop of rice, every roll of dough gets split into smaller portions — and your job is to figure out how many portions fit. Tú eres parte del equipo del food truck. Tu trabajo es calcular cuántas porciones caben.

Standard: 6.NS.A.1 Topic: Dividing Fractions MCAP-aligned Work time: ~45 min

1 Engage

Hook & essential question

The truck has 3 cups of mango salsa left. Each take-out container holds ¼ cup. Before you do any math, look at the salsa bar below and make a guess: how many containers can you fill?

1 cup 1 cup 1 cup each white line cuts off ¼ cup

3 cups of salsa, each split into ¼-cup portions.

Your first estimate: how many ¼-cup containers can you fill? Type a whole number. ¿Cuántos envases puedes llenar? Escribe un número entero.

Count the white sections, or come back and fix your answer after the Explain step. (Hint: 3 ÷ ¼.)

2 Explore

Investigate before the rules

Open one resource below. Look for the big idea: dividing by a fraction asks "how many of these fit inside that?" — and the answer is often bigger than what you started with.

3D Game: Fraction Kitchen Slice batches into portions and watch the count grow. Math Hub: Unit 2 Worked examples and practice for fraction division. Graphic Novel See fraction division solve a real story problem.

While you explore, decide: when you divide a number by a fraction less than 1 (like ½ or ¼), the answer is usually…

Think: many small portions fit inside one whole.

3 Explain

Key ideas & vocabulary

Two ways to think about dividing fractions. Use the picture model to understand, and the rule to work fast.

Model: "How many fit?"

⅔ shaded each piece = ⅙

23 ÷ 16 asks: how many ⅙ pieces fit in ⅔? Count the shaded pieces → 4.

Rule: Keep–Change–Flip

Keep⅔
Change ÷ to ××
Flip⅙ → 6/1

23 × 61 = 123 = 4. Same answer as the model!

The flipped fraction is the reciprocal.

a ÷ (b/c) = a × (c/b)   — divide by a fraction by multiplying by its reciprocal.

dividend (dividendo)
The amount being split (the salsa you have).
divisor (divisor)
The size of each portion you split into.
reciprocal (recíproco)
A fraction flipped upside down. ⅖ → 5/2.
quotient (cociente)
The answer to a division problem.
Level 1 · Support Step-by-step help
  1. Keep the first fraction exactly as it is.
  2. Change the ÷ sign to a × sign.
  3. Flip the second fraction (swap top and bottom).
  4. Multiply tops together and bottoms together, then simplify.

Nivel 1: Mantén la primera fracción, cambia ÷ por ×, voltea la segunda fracción, luego multiplica y simplifica.

Tip: a whole number like 6 can be written as 6/1 before you flip.

Level 2 · Enrichment Push your thinking
  • Why does flipping and multiplying give the same answer as counting "how many fit"? Explain with the ⅔ ÷ ⅙ picture.
  • What happens when you divide a fraction by a whole number, like ¾ ÷ 2? Why does the answer get smaller?
  • Write a real food-truck word problem whose answer is exactly 2½.

4 Apply

Show what you know — auto-checked

Use the model or Keep–Change–Flip. Write fraction answers like 2/3. Then press Check my answers.

1. Back to the truck: 3 cups of salsa ÷ ¼ cup per container. How many containers? (How many ¼ fit in 3?)

2. A pitcher holds ⅔ L of horchata. Each cup is ⅙ L. How many cups? (⅔ ÷ ⅙)

3. Which expression is equal to 34 ÷ 12 ?

4. You have ½ batch of dough and a tray that holds ¾ of a batch. What fraction of the tray will the dough fill? 12 ÷ 34 = ? (Answer is a fraction. Simplify.)

5. You have ¾ cup of dressing and want to pour it into 2 equal jars. How much per jar? 34 ÷ 2 = ? (Dividing by a whole number — answer is a fraction.)

6. Stretch: ⅚ kg of beans ÷ ⅓ kg per scoop = ? scoops. 56 ÷ 13 = ? (Write 5/2, or 2 1/2, or 2.5.)

Teacher Notes & Answer Key (not printed)

Stage-by-Stage Notes (Engage → Explore → Explain → Apply → Reflect)

  • Engage: "how many ¼-cup containers fill from 3 cups?" builds the measurement meaning of division.
  • Explore: visual fraction bars show how many small pieces fit in the whole.
  • Explain: formalize Keep–Change–Flip and why ÷ a fraction = × its reciprocal.
  • Apply: answer key below.
  • Reflect: students state both meanings of division (how many fit vs fair share).

Apply — Answer Key

  • Q1: 3 ÷ ¼ = 3 × 4 = 12 containers.
  • Q2: ⅔ ÷ ⅙ = ⅔ × 6 = 4 cups.
  • Q3 (choice): answer b.
  • Q4: 2/3.
  • Q5: 3/8.
  • Q6: 5/2.

Standard

CCSS 6.NS.A.1.

5 Reflect

Make your thinking visible

Pick one prompt and answer in 2–3 sentences. Try to use the words reciprocal, quotient, and how many fit.

  • Explain Keep–Change–Flip to a friend who was absent. What do you keep, change, and flip?
  • Why is 3 ÷ ¼ bigger than 3? Use the salsa picture in your answer.

Sentence starters: "To divide by a fraction, I keep… I change… and I flip… because…" Marcos: "Para dividir entre una fracción, mantengo… cambio… y volteo… porque…"

★ Extend

Optional challenge

Design a portion plan. Pick a menu item for the Mango Lane truck. Choose how much you start with (a fraction or whole number of cups, liters, or kilograms) and the size of one portion (a fraction). Write the division problem, solve it two ways (model and Keep–Change–Flip), and explain how many servings you can sell.