Problem
Liam's longest inside segment is the diameter: 12 in.
The widest line across a circle is the diameter.
3.G.A.1Organize Information In More WaysThe compass opening from point to pencil is the radius (center to edge). Double it to get the diameter.
Diameter is twice the radius, so double the 7 in compass opening.
3.OA.C.7Organize Information In More WaysDoubling Mia's 7 in compass opening gives her circle's diameter, 7 x 2 = 14 in.
A diameter reaches from one edge, straight through the center, to the opposite edge, so it is one radius on each side of the center joined together.
The two radius pieces meet at the center with no gap and no overlap, so together they make up the whole diameter.
Both pieces run from the center out to the edge, so each one is a radius of Mia's circle.
Each half equals the one fixed radius length, 7 in, so the two halves are equal to each other.
Two equal 7 in pieces is 7 taken twice, which is 7 x 2 = 14.
Multiplying 7 by 2 just means adding together 2 equal groups of 7.
Noah's halving segment is also a diameter: 10 in.
Only a line through the center divides a circle into two equal halves; that line is the diameter.
3.G.A.1Organize Information In More WaysNow all three are diameters: Liam 12 in, Mia 14 in, Noah 10 in. The smallest diameter belongs to the smallest circle.
With the same measure for all three, the smallest number is the smallest circle.
3.OA.A.3Eliminate PossibilitiesTurn every clue into a diameter first -- once they match, the smallest number wins, just Grade 3 comparison!