Reasoning · Grade 3-2 Multiplication Patterns
Problem
Left runs 1, 2, 4, 8 and right 37, 74, 148, 296.
Doubling is just adding a number to itself, a Grade 3 skill, and listing the rows keeps the partners lined up.
3.OA.B.5Make A Systematic List14 = 8 + 4 + 2, so the partners add to 518.
Splitting 14 into 8+4+2 and adding the matching doubles is the distributive property: 14×37=(8+4+2)×37.
3.OA.B.5Look For A PatternSplitting 14 into 8 plus 4 plus 2 and adding the matching doubled rows gives 14 times 37 exactly.
Multiplying a split-up number is the same as multiplying each piece and adding the results, so the group may be broken apart.
The chosen rows rebuild 14 with no piece missing and no piece used twice, so their partners rebuild the product just as exactly.
The second table doubles 42: 42, 84, 168, 336, 672.
Each right-column entry is just the one above it doubled, so the table grows with simple repeated addition.
3.OA.B.5Make A Systematic List25 = 16 + 8 + 1, so the partners add to 1050.
Picking exactly the rows that rebuild 25 means I am computing (16+8+1)×42, which equals 25×42.
3.OA.B.5Look For A PatternAny number is just some doubles added together, so doubling and picking the right rows lets you multiply with only adding!