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Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

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There are **308** NRICH Mathematical resources connected to **Being collaborative**, you may find related items under Mathematical mindsets.

Problem
Primary curriculum
Secondary curriculum
### Fractions in a Box

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Mystery Matrix

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Moons of Vuvv

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What's it Worth?

There are lots of different methods to find out what the shapes are worth - how many can you find?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Twenty Divided Into Six

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Numerically Equal

Can you draw a square in which the perimeter is numerically equal to the area?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pumpkin Pie Problem

Peter wanted to make two pies for a party. His mother had a recipe for him to use. However, she always made 80 pies at a time. Did Peter have enough ingredients to make two pumpkin pies?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Forgot the Numbers

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Egyptian Rope

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### How Many Times?

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Watch the Clock

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What's in a Name?

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Quadrilaterals

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Highest and Lowest

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Chances Are

Which of these games would you play to give yourself the best possible chance of winning a prize?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### In a Box

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Attractive Tablecloths

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### CD Heaven

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at each price?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### American Billions

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Two and Two

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Age 7 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Why 24?

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Summing Consecutive Numbers

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Have You Got It?

Can you explain the strategy for winning this game with any target?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Birthday Cakes

Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cubes Cut Into Four Pieces

Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?

Age 5 to 7

Challenge Level

Problem
Live Primary curriculum
Secondary curriculum
### Grouping Goodies

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Making Sticks

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Butterfly Flowers

Can you find two butterflies to go on each flower so that the numbers on each pair of butterflies adds to the number on their flower?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Puzzling Sweet Shop

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Chain of Changes

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?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### One Big Triangle

Make one big triangle so the numbers that touch on the small triangles add to 10.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 4 Dom

Use these four dominoes to make a square that has the same number of dots on each side.

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Colouring Triangles

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Biscuit Decorations

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 6 Beads

If you put three beads onto a tens/ones abacus you can make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Domino Square

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Five Coins

Ben has five coins in his pocket. How much money might he have?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Four Triangles Puzzle

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Let's Investigate Triangles

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Maze 100

Can you go through this maze so that the numbers you pass add to exactly 100?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Making Cuboids

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Making Boxes

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sweets in a Box

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Roll These Dice

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Chocolate

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

Age 7 to 14

Challenge Level