If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
Can you hang weights in the right place to make the equaliser balance?
Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?
Use the number weights to find different ways of balancing the equaliser.
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.
If you were to set the X weight to 2 what do you think the angle might be?
Weekly Problem 35 - 2008
A child's box of bricks contains cubes, cones and spheres. Can you work out how many spheres will balance a single cone?
Attach weights of 1, 2, 4, and 8 units to the four attachment points on the bar. Move the bar from side to side until you find a balance point. Is it possible to predict that position?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
Imagine a very strange bank account where you are only allowed to do two things...
Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.
Who will be the first investor to pay off their debt?
Explore the mathematics behind the famous Wheatstone Bridge circuit.
A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?
Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.
An article which gives an account of some properties of magic squares.
You might have heard your teacher or another adult talk about 'algebra'. If you have tackled problems where there were missing numbers, then chances are you'll have been doing some algebraic. . . .
Algebra is only formally mentioned in the new National Curriculum at Year 6. However, we can encourage algebraic thinking from a much younger age. In her article, Anne Watson suggests ways of. . . .
You'll need to think a little differently to tackle the challenges in this feature. There might be missing numbers to find or patterns to notice and continue. You may not know how to begin each. . . .
This feature includes articles and tasks which will support you in encouraging algebraic thinking throughout primary school.
Try these activities to find out more about what it means to be thinking algebraically.
You'll need to think a little differently to have a go at the challenges in this feature. Don't be afraid to have a go and try something out!
Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?
Investigate different ways of making £5 at Charlie's bank.
You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?
Lower primary interactives
Resources to support the teaching and learning of moments of forces (M1)
Resources to support the teaching and learning of centres of mass
Given information about the mean, can you work out the missing numbers?
Here are some exciting activities for you - have a go at them and then see what happens if you change one of the little questions. You may be able to change it more than just once!
Resources shared at Mathematical Resilience Conference, March 2017
There are 12 identical looking coins, one of which is a fake. The counterfeit coin is of a different weight to the rest. What is the minimum number of weighings needed to locate the fake coin?
A simple method of defining the coefficients in the equations of chemical reactions with the help of a system of linear algebraic equations.
The lower primary tasks in this collection all focus on adding and subtracting.
Exploring balance and centres of mass can be great fun. The resulting structures can seem impossible. Here are some images to encourage you to experiment with non-breakable objects of your own.
Using balancing scales what is the least number of weights needed to weigh all integer masses from 1 to 1000? Placing some of the weights in the same pan as the object how many are needed?
You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?
Weekly Problem 47 - 2015
One of N coins is slightly heavier than the others. How large can N be if the coin can be determined with only two weighings with a set of scales?
Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?
In these activities, you can practise your skills with adding and subtracting. You can also solve problems about what happens when we add or subtract different numbers!
In these activities, you can practise your skills with adding and taking away. You can also solve problems about what happens when we add or take away different numbers!
Resources to accompany Charlie's workshop.
This article for teachers sets out some ideas for introducing children to some of the concepts at the root of mechanics.
Lynne suggests activities which support the development of primary children's algebraic thinking.