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### Number and algebra

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### Advanced mathematics

# Exploring Problem Solving, Reasoning and Fluency in a Geometrical Context

### Inside Triangles

### Seeing Squares

### Poly Plug Rectangles

### Jig Shapes

### Nine-pin Triangles

### Brush Loads

### Square Corners

### Stringy Quads

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These tasks, which are part of our Jaunts into Geometry Feature, offer geometrical contexts in which to explore the three aims of the primary National Curriculum for mathematics.

Age 5 to 7

Challenge Level

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

Age 5 to 11

Challenge Level

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Age 5 to 11

Challenge Level

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

Age 5 to 11

Challenge Level

Can you each work out what shape you have part of on your card? What will the rest of it look like?

Age 7 to 11

Challenge Level

How many different triangles can you make on a circular pegboard that has nine pegs?

Age 7 to 11

Challenge Level

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

Age 7 to 11

Challenge Level

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Age 7 to 11

Challenge Level

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!