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One Array, Two Division Facts
Lesson
Children often believe division is a separate, harder operation rather than the reverse of multiplication; grounding each division sentence in the coconut-array image (N=D×Q) helps correct this. Watch for children who write only one division fact per multiplication — pause and ask whether swapping divisor and quotient still checks out. The web activity works well in pairs so children can talk through each circle and square placement aloud.
0–10Draw a 5-by-7 dot array on the board; ask children how many dots in all, then invite them to write the multiplication fact. Record 5×7=35 and 7×5=35, then ask: if you know the total and one side, how do you find the other? Collect two or three verbal answers and write the pair 35÷5=7 and 35÷7=5 beside the array. Establish that N=D×Q means the dividend equals the divisor times the quotient.
10–20Think and answer, p.119 ("Given 35÷1=___, write the corresponding multiplication fact...."). Children work individually; one or two share, and the class checks each answer against the array idea: multiply divisor by quotient to recover 35.
20–32Let Us Play, p.120 ("Identify numbers to fill circles so that square values are the products...."). Pairs complete the multiplication-division web; bring the class together to compare choices and notice each correct placement satisfies both a multiplication and a division fact simultaneously.
32–40Let Us Do Q1, p.120 ("Solve four multiplication problems (30×30, 400×8, 15×60, 200×16)...."). Children work the four products then write the two division facts each yields; teacher circulates and listens for children who reverse divisor and dividend, prompting them to re-read the array idea.
Let Us Do Q1, p.120 — Solve four multiplication problems (30×30, 400×8, 15×60, 200×16) and write two division statements for each.
Which pair of division facts follows directly from 8 × 9 = 72?
- A 72 ÷ 8 = 9 and 72 ÷ 9 = 8
- B 72 ÷ 8 = 9 and 80 ÷ 9 = 8
- C 72 ÷ 8 = 8 and 72 ÷ 9 = 9
- D 72 ÷ 7 = 9 and 72 ÷ 9 = 7
A. 72 ÷ 8 = 9 and 72 ÷ 9 = 8
What each wrong option reveals
- B The student kept one fact correct but replaced 72 with 80 in the second, showing the dividend is not fixed in their understanding.
- C The student swapped quotients, assigning each divisor its own value rather than the other's.
- D The student replaced one factor (8) with a nearby number (7), showing a recall slip rather than a conceptual error.
Also saved as 8 periods or 11 periods.
- 2Scaling Up: What Happens to Quotients?
Lesson - 3Scaling Division — Story Problems and Puzzles
Lesson - 4Split It or Halve It: Mental Division Strategies
Lesson - 5Susie's Method: Building Quotients Step by Step
Lesson - 6Coconut Farm Word Problems and Scaffold Frames
Lesson - 7Multi-Step Word Problems on the Coconut Farm
Lesson - 8Distributing by Place: Hundreds, Then Tens, Then Ones
Lesson - 9Finding What's Missing: Divisors, Dividends and Riddles
Lesson - 10Word Problems, Patterns and Missing Information
Lesson - 11Fluency with the Place-Value Algorithm: 12 Problems
Lesson - 12Always, Sometimes, Never: Reasoning About Arithmetic
Lesson - 13Coconut Farm: Connecting Every Strand of Division
Lesson
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