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Using Non-Standard Problems to Challenge Pre-Conceptions

This paper explores the value of using problems as a way of challenging children’s mathematical pre-conceptions and problems' potential for extending their knowledge and understanding. It considers some non-standard problems taken from the NRICH website and examines them in the light of children's solutions and what children have said, or implied, about their thinking.

article

Making Sense of Positives and Negatives

11 to 14

This article suggests some ways of making sense of calculations involving positive and negative numbers.

problem

Three Way Mix Up

5 to 11

Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

problem

Alternative Record Book

14 to 18

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

problem

Stone Age Counting

5 to 7

What could these drawings, found in a cave in Spain, represent?

problem

Close to Triangular

14 to 16

Drawing a triangle is not always as easy as you might think!

problem

Favourite

Three Squares

5 to 11

What is the greatest number of squares you can make by overlapping three squares?

problem

Favourite

What's in a Name?

5 to 7

What do you notice about these squares of numbers? What is the same? What is different?

problem

Favourite

Caterpillars

5 to 7

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

problem

Favourite

At Right Angles

14 to 16

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?