Reasoning · Grade 2-2 The Multiplication Table
Problem
6 comes from 1×6, 2×3 and their swaps — 4 times.
Find the factor pairs 1&6 and 2&3, then count each order; that is every cell holding a 6.
3.OA.C.7Make A Systematic List15 has only 3×5 and 5×3 — twice.
Only 3 and 5 both fit inside 1-9, and each order gives one cell, so 15 shows up twice.
3.OA.C.7Make A Systematic List24 gives 3×8, 4×6 and swaps — 4 times; 2×12 is off the table.
Two factor pairs (3&8 and 4&6) each appear in both orders, so 24 fills four cells.
3.OA.C.7Make A Systematic List49 is only 7×7, and equal factors give one.
A square number like 49 = 7x7 sits on the diagonal of the table, where the two equal factors give a single cell.
3.OA.D.9Look For A Pattern49 fills only one cell, because its two factors are the same number and so the two orders collapse into one.
Factors usually come in two different partners, and each partner pair gives two cells — unless the number is its own partner.
Seven rows of seven and seven columns of seven are the same cell of the table, so swapping the order changes nothing here.
Counting how often a number shows up is just finding all its factor pairs that fit in 1-9 and remembering both orders count!