Reasoning · Grade 2-2 Multiplication Facts
Problem
Slide a four-cell window along the rows and the columns.
A multiplication fact is just 'so many equal groups'; reading four cells as a x b = (number) turns each window into one fact to check.
3.OA.A.1Make A Systematic ListColumn 1's 8, 8, 6, 4 gives 8 × 8 = 64.
Eight eights is sixty-four, a basic times-table fact.
3.OA.C.7Guess And CheckRow 3's 7, 7, 4, 9 gives 7 × 7 = 49.
7 x 7 is a basic times-table fact, so a young solver can verify it instantly.
3.OA.C.7Guess And CheckColumn 4's 5, 8, 4, 0 gives 5 × 8 = 40.
Five eights is forty, an easy fact from the times tables.
3.OA.C.7Guess And CheckThe bottom row's 4, 8, 3, 2 gives 4 × 8 = 32.
Four eights is thirty-two, a quick times-table recall.
3.OA.C.7Guess And CheckNo other window works, so four is all of them.
Each equation describes a rectangular array (rows of equal groups), the picture behind every times-table fact.
2.OA.C.4Make A Systematic ListEvery one of the four equations is a rectangle of dots, rows of equal groups, which is what a times-table fact draws.
Multiplying a by b means taking a equal groups with b in each, and stacking those groups as rows draws exactly a rectangle.
Reading the same rectangle down its columns instead of across its rows gives the same count, so the fact can be found scanning either way.
If you know your times tables, you can hunt down hidden multiplication facts just by sliding a four-box window across the grid!