Unit 2 · Bakery · 6.NS.A.1

Order Architect: Dividing Fractions

What to do: You run the bakery. For each order, divide the fractions to find how many servings you can make. Use the tools, type your answers, then press Check My Work.

Orders done: 0 of 6

Learning Target

Standard CCSS 6.NS.A.1
Estimated time 45–55 minutes
Materials Pencil, scratch paper, this page
Product Completed activity saved as PDF or DOC
Teacher Notes (click to expand — not for student assessment)

Pacing

One 45–55 minute period. Suggested flow: activate prior knowledge — "what does division mean?" (3 min) → Orders 1–2 together as a class, modeling keep–change–flip on the board (15 min) → Orders 3–5 independently or in pairs (15 min) → Order 6 (reasoning backwards) as a class challenge (7 min) → Check My Work, discuss, save deliverable (10 min). Two-day option: Day 1 = Orders 1–4 with visual bar and KCF; Day 2 = Orders 5–6, reflection, and save.

Grouping Suggestions

Order 1 (visual bar) and Order 4 (drag-and-drop match) work especially well as pair activities. Orders 2, 3, and 5 are best done individually to check each student's procedural fluency. Order 6 (working backwards) can spark good small-group discussion: "What do we need to divide 1/2 by to get 4?"

Differentiation

  • Support: Provide fraction strips or a printed number line. Encourage students to draw a picture of each division problem before computing. For Order 6, prompt: "If 1/2 ÷ x = 4, then x = 1/2 ÷ 4. Can you compute that?" Allow mixed-number answers expressed as improper fractions (accept equivalents).
  • Challenge / Extension: Have students create their own bakery order that requires dividing a mixed number by a fraction (extend to 6.NS.A.1 mixed numbers). Ask: "Why does dividing a fraction by a fraction sometimes give an answer bigger than 1? Always? When?" Have students prove Order 4 answers using a diagram as well as the algorithm.

ESOL / Language Supports

  • Pre-teach: fraction, numerator, denominator, reciprocal, dividend, divisor, quotient, equal groups, "how many fit?". Post a word wall with fraction notation and visual examples.
  • Sentence frames: "I found the reciprocal by ___." / "I kept ___, changed ÷ to ×, and flipped ___ to get ___." / "The answer means ___ servings fit into ___."
  • The visual tray bar in Order 1 is intentionally concrete — let students tap and explain in their home language before writing. Pair strategically for the drag-and-drop task.
  • For word problems (Orders 3 and 6), have students underline the total amount and circle the size of each group before computing.

Order 1 — Cut the dough

You have 1 whole tray. Each cookie needs 1/4 of the tray.

Tap the tray to cut it into fourths. How many cookies can you make? That is 1 ÷ 1/4.

Order 2 — Keep, Change, Flip

Solve 3/4 ÷ 1/8.

Keep 3/4. Change ÷ to ×. Flip 1/8 to its reciprocal. Then type the whole-number answer.

Order 3 — Bagging flour

You have 6 cups of flour. Each bag holds 3/4 cup.

How many bags can you fill? Solve 6 ÷ 3/4.

Order 4 — Match the recipe cards

Drag each answer tile to the matching problem. Keyboard: press a tile, then press a slot. (Answers are whole numbers.)

1/2 ÷ 1/4 =
drop here
3/4 ÷ 1/8 =
drop here
5/6 ÷ 1/12 =
drop here

Order 5 — Half a recipe

Solve 2/3 ÷ 4.

Dividing by a whole number makes a smaller piece. Write the answer as a fraction in lowest terms.

Order 6 — Build the order

A chef has 1/2 pan of brownies and wants to make exactly 4 servings.

Pick the serving size so that 1/2 ÷ (serving) = 4.

Scoring Rubric — Dividing Fractions (6.NS.A.1)

Skill Expert (4) Proficient (3) Developing (2) Beginning (1)
Whole ÷ Unit Fraction
Order 1 · 6.NS.A.1		 Correctly solves 1 ÷ 1/4 = 4; explains using a visual model (tray cut into fourths). Correctly solves 1 ÷ 1/4 = 4. Sets up the problem correctly but makes a calculation error (e.g., answers 1/4 instead of 4). Cannot set up or solve a whole number divided by a unit fraction.
Reciprocal / Keep–Change–Flip
Order 2 · 6.NS.A.1		 Correctly identifies reciprocal as 8/1 and computes 3/4 ÷ 1/8 = 6; explains each KCF step. Correctly identifies reciprocal and computes the correct answer. Finds the reciprocal correctly but makes a multiplication error, or vice versa. Cannot identify reciprocal or apply KCF without significant help.
Whole Number ÷ Fraction (Word Problem)
Order 3 · 6.NS.A.1		 Correctly solves 6 ÷ 3/4 = 8 and connects the answer to context ("8 bags can be filled"). Correctly solves 6 ÷ 3/4 = 8. Sets up 6 ÷ 3/4 but makes an error (e.g., 6 × 3/4 = 4.5 instead of using KCF). Does not recognize this as a division problem.
Fraction ÷ Fraction (Matching)
Order 4 · 6.NS.A.1		 Correctly matches all three problems to their answers (2, 6, 10) and can verify each by multiplying back. Correctly matches all three problems. Matches at least two of the three correctly. Cannot match correctly; fewer than two correct.
Fraction ÷ Whole Number
Order 5 · 6.NS.A.1		 Correctly solves 2/3 ÷ 4 = 1/6 in lowest terms; explains that dividing a fraction by a whole number makes it smaller. Correctly solves 2/3 ÷ 4 = 1/6 in lowest terms. Sets up correctly but does not reduce to lowest terms (e.g., writes 2/12). Cannot set up or solve fraction divided by a whole number.
Reasoning Backwards
Order 6 · 6.NS.A.1		 Correctly identifies 1/8 pan as the serving size; explains the reasoning (1/2 ÷ 4 = 1/8). Correctly selects 1/8 pan. Shows understanding that the serving size should be small but selects incorrect answer. Cannot reason backwards from the quotient to the divisor.
Teacher Answer Key (click to expand)
  1. Order 1 — 1 ÷ 1/4: 1 whole tray cut into 1/4-sized pieces = 4 cookies. Keep–change–flip: 1 × 4/1 = 4.
  2. Order 2 — Reciprocal of 1/8: Flip numerator and denominator → 8/1 (also written as 8). 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6.
  3. Order 3 — 6 ÷ 3/4: Keep 6, change ÷ to ×, flip 3/4 to 4/3: 6 × 4/3 = 24/3 = 8 bags.
  4. Order 4 — Matching: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2. 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6. 5/6 ÷ 1/12 = 5/6 × 12/1 = 60/6 = 10.
  5. Order 5 — 2/3 ÷ 4: Keep 2/3, change ÷ to ×, flip 4 to 1/4: 2/3 × 1/4 = 2/12. Simplify: GCF(2,12) = 2, so 2/12 = 1/6.
  6. Order 6 — Serving size for 1/2 ÷ x = 4: Solving: x = 1/2 ÷ 4 = 1/2 × 1/4 = 1/8. Each serving = 1/8 pan. Check: 1/2 ÷ 1/8 = 1/2 × 8 = 8/2 = 4. ✓

Sample reflection: "Dividing fractions means finding how many equal groups of the second fraction fit inside the first. Keep–change–flip works because multiplying by the reciprocal is the same as dividing. This is like asking 'how many 1/4-cup scoops fit in 3/4 cup?' — the answer is 3."

Reflection

Answer in 2–3 sentences:

Explain in your own words: why does dividing a fraction by a fraction sometimes give an answer bigger than the original fraction? Use an example from the bakery orders to support your explanation.

Deliverable: Complete all 6 orders above, then click Check My Work. After your results appear, click Save as PDF or Save as DOC to download a copy with your name and score. Turn in that file.