Multiplication and Division Facts to 100
Warm-up
Flash a 60-second "facts sprint" of twelve mixed multiplication and division facts, then ask the honest question: "Which two facts made you pause?" Collect the class's stubborn facts on the board — typically 7×8, 6×7, 48÷6, 9×6.
Today isn't about learning facts from scratch; it's about closing the last gaps and making retrieval automatic enough to support fractions, ratios, and algebra, where a slow fact stalls a whole solution.
Explore
Run a derived-facts workshop on the class's stubborn list: each pair takes one stubborn fact and builds two derivation ropes for it (7×8 = 7×4 doubled = 56; or 5×8 + 2×8 = 40 + 16). Pairs post their ropes and teach them.
Then invert everything: for each multiplication fact posted, students write its two division siblings and one "missing factor" form (7 × ▢ = 56). The wall becomes a map showing every fact family the class once feared, each with a rescue rope attached.
Formalize
Formalize the derivation strategies by name — doubling, halving, adding a group, subtracting a group, splitting through 5 or 10 — and the family structure that makes division free:
The distributive idea underneath every rope, shown once with an array: . Students don't need the property's name today — they need to see that splitting a factor splits the rectangle, so the strategy is guaranteed, not lucky.
Practice
Practice in three rounds: a facts ladder (each answer feeds the next problem), missing-factor forms, and five "extend the fact" items (7×8 → 70×8, 7×80, 56÷7, 560÷8).
Exit ticket: your two personal stubborn facts, each written with its full family and your chosen rescue rope.
Exit ticket
Practice in three rounds: a facts ladder (each answer feeds the next problem), missing-factor forms, and five "extend the fact" items (7×8 → 70×8, 7×80, 56÷7, 560÷8).
Exit ticket: your two personal stubborn facts, each written with its full family and your chosen rescue rope.
Rope 1 — through 5: .
Rope 2 — doubling: doubled .
Rope 3 — through the square: , one more six → .
Check the family rides along: , , .
The standard: within a week, 42 should arrive in under two seconds — but if it ever slips, three ropes are waiting.
Step 1: Anchor: .
Step 2: Scale one factor: (ten times as many nines). .
Step 3: Scale both: — one ten from each factor, two tens total.
Step 4: Divisions come free: , .
Step 5: The trap case, handled by thinking in tens: . Fact: , which already ends in zero; attach the two tens → (not 300). Count factors of ten; never just "add the zeros."
Step 1: Hunt the nearest seven-fact below 58: .
Step 2: Quotient 8, remainder . So r .
Step 3: The fluency point: this took one retrieval and one subtraction. A student who scans the whole seven-times column () spends ten times longer — remainder problems are where slow facts become visible.
Step 4: Write the check equation that certifies the answer: ✓. Quotient-times-divisor-plus-remainder equals the original: the certificate every division carries.