Problem
Put the box in for a and 8 in for b, so the rule gives box times 7 plus box times 8.
Following a defined symbol is just plugging numbers into a recipe, a Grade 3 skill.
3.OA.D.8Identify SubproblemsBoth products multiply the same box, so 7 of the box plus 8 of the box is 15 of the box.
Seven groups plus eight groups of the same size is fifteen groups; this is the distributive property kids already use.
3.OA.B.5Look For A PatternThe two products both multiply the same , so they merge into the multiplied by seven-and-eight, and seven and eight make fifteen.
Because and share the as a factor, adding them is just the taken over 7 and over 8 combined into one product, .
Inside that single product the 7 and the 8 join to make 15, so is .
We need box times 15 = 135, and 9 times 15 = 135, so the box is 9.
Testing the friendly factor 9 (because 9 times 15 = 135) confirms the answer at once.
3.OA.A.3Guess And CheckA made-up symbol is just a recipe; once you see both pieces share the same number, 7 groups plus 8 groups is simply 15 groups!