Reasoning · Grade 2-1 Cryptarithms and Magic Squares
Problem
Column 2 is four circles summing to 40, so sharing it in four gives circle = 10.
When a whole line is the same shape, its total split into equal parts hands you that shape at once.
2.NBT.B.6Work BackwardsA line built from one repeated shape hands you that shape's value the moment you share the line total equally.
Four identical circles in a line is four equal groups of the circle's value, which is exactly what multiplying by four means.
Knowing four of something totals a given amount, dividing that amount by four gives back the one thing, because dividing undoes multiplying.
Row 1 is two triangles and two circles making 34; take off 20 and halve to get triangle = 7.
Take away the part you already know (the circles) and what's left must be the triangles.
2.NBT.B.5Identify SubproblemsColumn 1 is three triangles and a square making 26; take off 21 to get square = 5.
Knowing the total and all but one part, the missing part is found by taking the parts away from the total.
1.OA.B.4Work BackwardsColumn 4 is circle, star, square, star making 33; take off 15 and halve to get star = 9.
Subtract the shapes you already know, then split the rest between the two equal stars.
2.NBT.B.5Identify SubproblemsSubstituting the values and adding the remaining lines gives 35, 25, 36, 31.
Once every shape has a number, each blank is just adding up that line's four numbers.
2.NBT.B.6Guess And CheckStart with the line made of just one shape -- that one gives a number for free, and the rest fall into place with Grade 2 add-and-subtract!