Splitting an angle in half
An angle is split exactly in half by a line from its corner, then the pieces are split in half again, one to three times in all. The student types an angle in degrees: the size of the marked piece when the whole angle is given, or the whole angle when one piece is given. The angle is drawn to size: as plain lines, as lines a child draws, as a paper wedge folded in half, as a piece of pizza cut from the tip, or as a flower bed split by paths from its corner.
Each split halves, so the student divides by 2 once for every split, or doubles to go back. In some questions only one of the two newest pieces is split each time, so the pieces end up different sizes: a half, a quarter and an eighth of the whole. Then the student has to see which split made the marked piece and undo only those splits. A student who doubles once for every split gets an angle far too big. The working halves or doubles one split at a time on the picture, then checks that the pieces add up to the whole angle.
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What changes each time
- The marked piece's angle from the whole angle, or the whole angle from the marked piece
- 1 to 3 splits, with every piece split each time or only one of the two newest, so the marked piece can come from any split
- Whole angles from 20° to 180° that halve to whole degrees every time, with no piece smaller than 6°
More shapes and angles practice
- Sides and corners of 2D shapes (Grade 2)
- Faces, edges and vertices (Grade 3)
- Sorting quadrilaterals (Grade 3)
- Turning and flipping letters (Grade 3)
- Counting squares of every size (Grade 3)
- Inside or outside the loop (Grade 3)
- Which piece fills the gap? (Grade 3)
- Symmetry on a grid (Grade 4)
- Rotations and reflections (Grade 4)
- Reading a protractor (Grade 4)
- Parallel and perpendicular lines (Grade 4)
- Parts of a circle (Grade 4)
- Draw without lifting your pencil (Grade 4)
- Can these sticks make a triangle? (Grade 4)
- Lines, rays and line segments (Grade 4)
- Counting line segments (Grade 4)
- Triangle from two circles (Grade 4)
- 3D shapes: side view (Grade 5)
- Rectangle in a quarter circle (Grade 5)
- Painted cube puzzle (Grade 5)
- Rope around the Earth (Grade 5)
- Can dominoes cover the board? (Grade 5)
- Most crossing points of straight lines (Grade 5)
- Equal radii: find the missing length (Grade 5)
- Angles in a circle (Grade 6)
- Congruent triangles: match the corners first (Grade 6)
- Vertically opposite angles (Grade 6)
- Inscribed circle in a right triangle (Grade 8)
- SSS and SAS: is it enough to prove congruence? (Grade 8)