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Resources tagged with PM - Reasoning, Justifying. Convincing. Proof. similar to James's Code Challenge:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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Broad Topics > Secondary processes > PM - Reasoning, Justifying. Convincing. Proof.

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Seven Squares

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

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Take Three from Five

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

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Summing Consecutive Numbers

Stage: 3 Challenge Level: Challenge Level:1

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

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Painted Cube

Stage: 3 Challenge Level: Challenge Level:1

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

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Odds and Evens

Stage: 3 and 4 Challenge Level: Challenge Level:1

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

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Arithmagons

Stage: 3 Challenge Level: Challenge Level:1

Can you find the values at the vertices when you know the values on the edges?

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Route to Infinity

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you describe this route to infinity? Where will the arrows take you next?

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1 Step 2 Step

Stage: 3 Challenge Level: Challenge Level:1

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

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What Numbers Can We Make?

Stage: 3 Challenge Level: Challenge Level:1

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

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Number Pyramids

Stage: 3 Challenge Level: Challenge Level:1

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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Diminishing Returns

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

In this problem, we have created a pattern from smaller and smaller squares. If we carried on the pattern forever, what proportion of the image would be coloured blue?

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Marbles in a Box

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

In a three-dimensional version of noughts and crosses, how many winning lines can you make?

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Tilted Squares

Stage: 3 Challenge Level: Challenge Level:1

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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What's it Worth?

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

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Magic Letters

Stage: 3 Challenge Level: Challenge Level:1

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?