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# Always, Sometimes or Never? KS1

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Age 5 to 7

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

Thank you to everybody who sent in their thoughts about this task.

Tom from Clifton Hill Primary School in Australia sent in these solutions for the number statements:

Good ideas, Tom! Ayden from St John's College, Cardiff, Wales had some similar solutions, and also sent in their solutions for the shape statements:

The number statement cards are only either "always" and "sometimes". No cards are in the "never" section of the table.

When you add two numbers, you can change the order and the answer will be the same, so that card is true and is in the "always" section of the table. For example, 12+8=20, and 8+12=20. 31+74=105, and 74+31=105 too.

If you add 10 and take away 1, it is the same as adding 9, so that card is true and is in the "always" section of the table. For example, 0+10=10, and 10 - the answer for the previous sum - take away 1 (10-1) = 9. If you add 0 and 9 (0+9) =9, which is the same as the previous answer. In my opinion, adding 9 is quicker than adding 10 and taking away 1.

When you add 10 to a number, the answer is only sometimes a multiple of 10, so that card is in the "sometimes" section of the table. This statement is true if the number you are adding 10 onto is a multiple of 10, but is false if the number is not. For example, 30+10=40, which means this statement is true, but 43+10=53, which means this statement is false. It depends on the situation as it can be true or false.

When you subtract one number from another number, you can only sometimes change the order and the answer will be the same, so that card is in the

"sometimes" section of the table. This statement is true if the two numbers in your equation are equal, but false if they are not. For example, 9-9=0 and 9-9=0, which means this statement is true, but 4-3=1 and 3-4=(-1), which means this statement is false. It depends on the situation as it can be true or false.

Now to the shape statements. The shape statement cards are only either "always" and "sometimes". No cards are in the "never" section of the table.

Three sided shapes are called triangles, so that card is in the "always" section of the table. Proof in file attached, page 1.

Four sided shapes are only sometimes called squares, depending on the situation, so that card is in the "sometimes" section of the table. Proof in file attached, page 2.

When you cut a square in half, you only sometimes get a triangle, so that card is in the "sometimes" section of the table. Proof in file attached, page 3.

If you put two squares together, you only sometimes get a rectangle, so that card is in the "sometimes" section of the table. Proof in file attached, page 4.

3D shapes can only sometimes have more than 4 faces, so that card is in the "sometimes" section of the table. For example, some 3D shapes, like cylinders, have less than 4 faces, which suggests that this statement is false. However, other 3D shapes, like cubes, have more than 4 faces, which suggests that this statement is true. It can be true or false, as it depends on the situation.

You've thought about all of these statements really carefully, Ayden! Ayden's file of evidence goes into more detail about their reasoning on the shape statements.

Kanaa from Ganit Kreeda, Vicharvatika, India sent in these pictures explaining how they decided whether the shape statements were always, sometimes or never true:

Good ideas, Kanaa - I like the way you used examples and counter-examples to decide for each statement!

Thank you as well to the following children who sent in similar solutions to this problem: Ananya, Shivashree, Swara N., Ruhi, Mrunmayee, Aarav, Swara S., Kimaya, Atharva, Shruti, Amey, Avyuktth from Ganit Kreeda; Dean, Lucinda, Marley, Ava from Clifton Hill Primary School in Australia; and Dhruv from The Glasgow Academy in the UK.