Counting line segments
Lettered points sit in a row on a straight line, and the student types how many line segments have two of the points as their ends. Some questions ask for every segment. Others name one point and ask for the segments with it at one end, the segments that pass over it, or the segments that do not end at it.
The trap is counting each segment twice: segment AC is the same as segment CA, so 5 points make 10 segments, not 20. Counting from the left avoids it. The first point joins every point after it, the next joins the points after it, and so on, so 5 points give 4 + 3 + 2 + 1. A segment passes over a point when one end is on its left and the other on its right, so that count is left times right. The working draws each segment on the picture as it is counted.
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What changes each time
- Every segment, the ones with a given point at one end, the ones that pass over it, or the ones that do not end at it
- 3 to 8 points (4 to 8 when a point is named), lettered with a run of capitals that skips I and O
- Six settings: plain points, a ruled line, a chalk line, bus stops on a road, stations on a railway and trees along a path
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)
- Triangle from two circles (Grade 4)
- Splitting an angle in half (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)