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Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
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?
Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.
A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
Are these games fair? How can you tell?
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
A collection of short Stage 3 and 4 problems on Posing Questions and Making Conjectures.
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Can you find the values at the vertices when you know the values on the edges?
What's the largest volume of box you can make from a square of paper?
If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
Which of these triangular jigsaws are impossible to finish?