Reasoning · Grade 3-2 Circles and Length
Problem
With E at 0, B sits at 8 and A at 16.
The diameter is two radii stacked, so the top point A is 8 + 8 = 16 cm above the bottom.
3.OA.A.1Draw A DiagramC is the midpoint of BE, so 4.
The center of a circle is exactly halfway between two opposite points on it, so C is the midpoint of B and E.
3.NF.A.1Identify SubproblemsThe centre of a circle sits exactly halfway between two opposite points on it, so C is the midpoint of B and E.
Both of those points sit one radius from the centre, and those two radii are the same length.
The two radii lie end to end with no gap and no overlap, so the whole distance is one radius doubled and half of it is the centre.
D is the midpoint of CE, so 2.
Each new circle is half as tall as the one above, so the centers 8, 4, 2 keep halving - an easy pattern to follow.
3.NF.A.1Look For A PatternSubtracting, AD is 16 − 2 = 14 cm.
Distance between two points on a line is just the bigger height minus the smaller one.
3.NBT.A.2Identify SubproblemsEach circle is half as tall as the one above, so the centers go 8, 4, 2 - then just subtract 2 from 16 to get 14 cm!