Depth · one concept from first principles · step 2 of 4
Chowon = 6 large (100 each) + 3 small (10 each): 6 x 100 + 3 x 10 = 630.
Turning the scaled house symbols into a count is the core skill of a scaled pictograph.
3.MD.B.3Identify SubproblemsDalbit = Chowon - 140 = 630 - 140 = 490, a multiple of 7 (7 x 70) so the 5/7 step divides evenly.
Subtracting 140 from Chowon gives Dalbit, and that value (490) happens to be a multiple of 7, so the next 5/7 step divides evenly.
3.NF.A.1Work BackwardsTaeyang = 5/7 of Dalbit: split 490 into 7 parts (70 each), take 5 → 5 x 70 = 350.
Understanding 5/7 as 5 of the 7 equal parts of a whole is the Grade 3 meaning of a fraction.
3.NF.A.1Identify SubproblemsFive sevenths of Dalbit's 490 households is Taeyang's 350 households.
Splitting Dalbit's 490 into 7 equal parts puts 70 households in each part.
Since 7 equal parts multiply back up to 490, finding one part means undoing that multiplication by dividing 490 by 7, which gives 70.
The 7 parts are cut with nothing left over and nothing overlapping, so they add back up to the whole 490.
Taking 5 of those equal 70-parts gives 5 times 70, which is 350.
Five equal groups of 70 is 70 added over and over, and that repeated adding is exactly what 5 times 70 counts.
Mugunghwa = Taeyang + 120 = 350 + 120 = 470.
Adding 120 to 350 is a clean within-1000 addition.
3.NBT.A.2Work BackwardsSolve the clues one after another - read the graph, then 5 of the 7 equal parts, then add 120!
A parent dashboard for the family lives at sensimlab.com.
The same shape shows up later on the AMC, as Branching State Enumeration, Lattice / Grid Pattern from Small Cases, Small-Domain Constrained Search. Why the shapes repeat →