A pattern-hunting worksheet for 3rd grade math built around a 6-by-6 multiplication chart. Students locate 3 × 5 and 5 × 3 to meet the commutative property, compare the 2s and 4s rows to find the doubling pattern, decide why the 4s row holds only even numbers, and break 6 × 7 into 6 × 5 plus 6 × 2. It covers Common Core 3.OA.5 and 3.OA.9 with written-explanation lines throughout, and every explanation has a model answer in the key.
3.OA.5
“Apply properties of operations as strategies to multiply and divide.² Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30. (Associative property of multiplication.) Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 × (5 + 2) = (8×5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)”
The turnaround facts in Part 1 (3 × 5 and 5 × 3) and the break-apart work in Part 4, where 6 × 7 becomes 6 × 5 plus 6 × 2.
3.OA.9
“Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.”
Parts 2 and 3: the doubling relationship between the 2s and 4s rows, and question 7 on why every product of 4 is even.
Using the printed chart from 1 × 1 to 6 × 6, students find 3 × 5 and 5 × 3, explain what happens when factors swap, and write their own turnaround pair with a shared product.
A two-row table lines up 2 × n against 4 × n from ×1 to ×5. Students describe what happens down each column, then explain how Maya can double 2 × 8 = 16 to solve 4 × 8.
The 4s row products 4, 8, 12, 16, 20, 24 sit above a three-option multiple choice, followed by a written prompt on why 4 times any whole number lands on an even answer.
Students split 6 × 7 into 6 × 5 and 6 × 2, add 30 and 12, then repeat the strategy alone on 8 × 6 broken into 5 + 1.
Discovery lesson
Let pairs work Part 1 before you name the commutative property. The chart makes the symmetry visible, and question 3 asks them to find their own pair.
Math talk
Put question 7 on the board and collect explanations before showing the key's version about splitting into two equal teams. The wrong answers are the interesting ones.
Strategy bridge
Use Part 4 the week before you push facts beyond the printed chart. A student who can break 8 × 6 into 8 × 5 + 8 × 1 no longer needs the chart at all.
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