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Being Curious - Primary Teachers

Being Curious is part of our Developing Mathematical Mindsets - Primary Teachers collection. 

In Nurturing Students' Curiosity, we offer you support and advice on how to encourage your learners to be curious mathematicians.

All humans are naturally curious, and good mathematicians get excited by new ideas and are keen to explore and investigate them. As teachers, we want to nurture our learners' mathematical curiosity so they grow into creative, flexible problem-solvers. One way to nurture this curiosity is by providing the right hook to draw learners in.

We hope that the problems below will exploit learners' natural curiosity and provoke them to ask good mathematical questions.

You can browse through the Number, Measures, Geometry or Statistics collections, or scroll down to see the full set of problems below.

Shaping It
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Shaping It

Age
5 to 11
Challenge level
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These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.
If the World Were a Village
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If the World Were a Village

Age
5 to 11
Challenge level
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This activity is based on data in the book 'If the World Were a Village'. How will you represent your chosen data for maximum effect?

Five Steps to 50
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Five Steps to 50

Age
5 to 7
Challenge level
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Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?
Next-door Numbers
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Next-door Numbers

Age
5 to 7
Challenge level
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Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?
Eightness of Eight
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Eightness of Eight

Age
5 to 7
Challenge level
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What do you see as you watch this video? Can you create a similar video for the number 12?
Digit Addition
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Digit Addition

Age
5 to 11
Challenge level
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Try out this number trick. What happens with different starting numbers? What do you notice?

Magnifying glass
problem
Favourite

Number Detective

Age
5 to 11
Challenge level
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Follow the clues to find the mystery number.

Light the Lights
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Light the Lights

Age
5 to 7
Challenge level
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Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

Colouring Triangles
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Favourite

Colouring Triangles

Age
5 to 7
Challenge level
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Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

Chain of Changes
problem
Favourite

Chain of Changes

Age
5 to 7
Challenge level
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Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

Ring a Ring of Numbers
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Ring a Ring of Numbers

Age
5 to 7
Challenge level
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Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Little Man
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Little Man

Age
5 to 7
Challenge level
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The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?
More Numbers in the Ring
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More Numbers in the Ring

Age
5 to 7
Challenge level
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If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
Brush Loads
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Brush Loads

Age
7 to 11
Challenge level
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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.

Nice or Nasty
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Nice or Nasty

Age
7 to 14
Challenge level
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There are nasty versions of this dice game but we'll start with the nice ones...
Subtraction Surprise
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Subtraction Surprise

Age
7 to 14
Challenge level
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Try out some calculations. Are you surprised by the results?
Statement Snap
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Statement Snap

Age
7 to 14
Challenge level
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You'll need to know your number properties to win a game of Statement Snap...
Tumbling Down
problem
Favourite

Tumbling Down

Age
7 to 11
Challenge level
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Watch this animation. What do you see? Can you explain why this happens?

Triangle transformation
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Triangle transformation

Age
7 to 14
Challenge level
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Start with a triangle. Can you cut it up to make a rectangle?
Fruity Totals
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Fruity Totals

Age
7 to 16
Challenge level
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In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

The Number Jumbler
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The Number Jumbler

Age
7 to 14
Challenge level
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The Number Jumbler can always work out your chosen symbol. Can you work out how?
Consecutive Numbers
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Consecutive Numbers

Age
7 to 14
Challenge level
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An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Your number is...
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Your number is...

Age
7 to 14
Challenge level
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Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?
Number Differences
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Favourite

Number Differences

Age
7 to 11
Challenge level
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Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Two Clocks
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Two Clocks

Age
7 to 11
Challenge level
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These clocks have only one hand, but can you work out what time they are showing from the information?

Three neighbours
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Three neighbours

Age
7 to 14
Challenge level
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Take three consecutive numbers and add them together. What do you notice?
Pouring Problem
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Pouring Problem

Age
7 to 11
Challenge level
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What do you think is going to happen in this video clip? Are you surprised?

Curious number
problem
Favourite

Curious number

Age
7 to 11
Challenge level
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Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?