Reasoning · Grade 4-1 Joining and Cutting Figures
Problem
By side length a triangle fits only the trapezoid's short sides.
Comparing side lengths before trying anything removes a whole family of impossible arrangements straight away.
2.G.A.1Draw A DiagramThe trapezoid is mirror-symmetric, so left and right are the same spot.
Spotting the mirror symmetry of the base piece halves the amount of listing to do, because left and right versions never need to be counted separately.
8.G.A.2Draw A DiagramBecause the trapezoid is its own mirror image, a left-hand arrangement and its right-hand twin are the same shape.
Flipping the whole figure keeps every length and angle, so a flipped arrangement is the same shape standing the other way round.
Grouping the arrangements into mirror pairs puts each one in exactly one group, so only one member of each pair needs listing.
Both triangles on the trapezoid give 2 shapes.
With only three places to choose from, writing out every pair of places is quick and certain.
1.G.A.2Make A Systematic ListChaining one triangle onto the other adds only 1 shape.
Building the chain one triangle at a time keeps the list short, and drawing each result shows at a glance which ones repeat a shape already on the list.
1.G.A.2Make A Systematic ListTogether that is 2 + 1 = 3.
Once each new arrangement has been compared with the ones already listed by turning and flipping it, the list is finished and can be counted.
8.G.A.2Make A Systematic ListCheck which sides are even allowed to meet first, then turn and flip each new figure to see whether you have already made it.