Word Problems: Learning to Choose the Operation Before Calculating
Why pupils add every number in the problem, and how to teach them to understand the situation before calculating.
Read the articleParallel or Perpendicular: Why Pupils Mix Them Up
Neatly upright lines hide the real concept. How to help pupils identify and check parallel and perpendicular lines.
Many pupils can identify two parallel lines in their textbook, then fail as soon as the figure is turned. The difficulty lies less in the words than in the mental images built from a few very similar examples.
The prototype trap
If perpendicular lines are almost always drawn with one horizontal and one vertical line, pupils remember the position and not the relationship. As soon as both lines are tilted, they no longer recognize them. In the same way, two horizontal lines look parallel without any checking, while two slanted ones seem much less so.
So vary the orientations from the start. A single figure, drawn on a sheet of paper that you rotate, shows that the relationship doesn’t change when the position does.
Lines that haven’t met yet
Another misunderstanding: “they don’t cross, so they’re parallel.” In a drawing, two lines may seem never to meet simply because the drawing stops. Have pupils extend the lines with a ruler, or measure the gap in two places. If it changes, they will eventually cross.
Three ways to check
- The set square for perpendicular lines: place it on one line, and the other must follow its edge exactly.
- Measuring the gap for parallel lines: the distance must be the same at several points.
- Folding to make a right angle without a tool: fold a sheet of paper twice, laying the first fold along itself.
The aim is for “by eye” to stop being an acceptable answer: every statement should be something you can check.
Start from the world around us
A window frame, the rungs of a ladder, a crosswalk: the environment offers plenty of examples. Ask pupils to find a pair of parallel lines and a pair of perpendicular lines in the classroom, then to prove it with a set square.
Line HuntIdentify and draw parallel or perpendicular lines, with a virtual set square.See the game
A four-stage progression
- Observe and sort pairs of lines, in every orientation.
- Check with a set square and by measuring the gap.
- Recognize these relationships in objects and scenes.
- Draw a parallel or perpendicular line through a given point.
Drawing comes last because it depends on understanding the relationship. A pupil who still mixes up the two ideas will gain nothing from doing more constructions.
Shape HuntShapes scroll along three lanes. Tap the right ones before they get away.See the game