Multiplication and Division Facts to 100
Warm-up
Annex-zeros chain: 7x4=28. So 7x40=? (280.) 7x400=? (2,800.) 70x40=? (2,800.) 70x400=? (28,000.) Patterns: the product core (28) stays the same; zeros are added from both factors. This is mental multiplication of multi-digit numbers using a single-digit fact.
Explore
Strategy showcase: each student receives 3 hard facts (from the 6s, 7s, 8s, 9s). They must solve each using TWO different strategies and present both to a partner. The presentation deepens understanding and builds a community strategy bank.
Formalize
Fact family extension: 7x8=56 gives 8x7=56, 56/7=8, 56/8=7. Now annex zeros: 7x80=560, 70x8=560, 560/7=80, 560/80=7. One fact generates eight related computations. This economy of knowledge is powerful.
Multiplication and Division Facts to 100
Connect to Grade 5 computation: 6x47 = 6x40 + 6x7 = 240 + 42 = 282. Here 6x4=24 (annex zero: 6x40=240) and 6x7=42 come from known facts. Multi-digit multiplication is facts + distributive property.
Practice
Students play a multiplication fact game for 10 minutes, then complete 12 annex-zeros exercises (e.g., given 7x8=56, find 7x800, 70x80, 700x8). Exit ticket: use any strategy to find 8x7, and then 8x70.
Exit ticket
Students play a multiplication fact game for 10 minutes, then complete 12 annex-zeros exercises (e.g., given 7x8=56, find 7x800, 70x80, 700x8). Exit ticket: use any strategy to find 8x7, and then 8x70.
Step 1: Collect every multiplication pair that makes 36: 1×36, 2×18, 3×12, 4×9, 6×6. (Order-partners count as the same pair.)
Step 2: Show each as an array sketch — five rectangles, same area, different shapes. 6×6 is the square of the family.
Step 3: Read off the division facts for free: 36 ÷ 4 = 9, 36 ÷ 12 = 3 … every pair donates two.
Step 4: The vocabulary upgrade: the pair-members are FACTORS of 36; 36 is a MULTIPLE of each. Factor-hunting is fact fluency pointed backwards.
Step 5: The puzzle that tests it: "I'm thinking of a number under 40 with exactly three factors." Three factors means a×b and a square (factors pair up UNLESS the number is a square — one factor partners itself): candidates 4 (1,2,4), 9 (1,3,9), 25, 49… under 40 with exactly three: 4, 9, 25. Squares are the only numbers with an odd factor count — discovered, not announced.
Step 1: Anchor: 7 × 8 = 56. One retrieval.
Step 2: Scale one factor by ten: 70 × 8 = (7 × 10) × 8 = 56 × 10 = 560. Say WHY, not just "add a zero": seventy is ten sevens, so the product is ten times bigger.
Step 3: Scale further: 700 × 8 = 5,600. And 70 × 80 = 56 × 100 = 5,600 — count the tens: one from 70, one from 80.
Step 4: The zero-trap that exposes rule-followers: 50 × 40. The fact is 5 × 4 = 20 (which already ends in 0), then two more tens → 2,000. Students chanting "attach the zeros" write 200 — one zero got swallowed by the 20. Students who THINK "tens times tens are hundreds" don't lose it.
Step 5: Fluency sweep: 6 × 30, 400 × 5, 90 × 70, 800 × 60 — answer each in under five seconds WITH the tens-reasoning said aloud once.
Step 1: The slow way, to have a baseline: 234 ÷ 3 → 3 into 23 goes 7 (21), remainder 2; bring down 4 → 24 ÷ 3 = 8. Quotient 78, remainder 0. Yes, 3 divides 234.
Step 2: The detective's shortcut: add the digits — 2 + 3 + 4 = 9. If the digit-sum is divisible by 3, so is the number. 9 is → 234 is. (Test it on a NO case: 235 → digits sum 10 → not divisible ✓ matches the leftover.)
Step 3: Stack the quick tests: ends in even digit → divisible by 2; ends in 0 or 5 → by 5; ends in 0 → by 10; digit-sum divisible by 9 → by 9.
Step 4: Deploy on a real task: "can 234 students split into 6 equal teams?" Six = 2 × 3: is 234 even ✓ AND divisible by 3 ✓ → yes, 39 per team.
Step 5: Why it works (Grade-5 version, optional but golden): 100 and 10 each leave remainder 1 when divided by 3 — so 234 = 2 hundreds + 3 tens + 4 leaves the same remainder as 2 + 3 + 4. The digits ARE the remainders' bookkeeping.