1 side of B is 4cm longer than 1 side of A. So 20cm, which is the sum of length of 1 side of A and 1 side of B, is equals to 4cm more than 2 sides of A. 2 sides of A + 4cm ＝ 20cm 2 sides of A ＝ 16cm 1 side of A ＝ 8cm

8 cm

B = A + 4. Thus 2A + 4 = 20.

A - length of square A B - length of square B

A+B =20 A = B-4 (B-4)+B =20 2B-4 = 20 2B =20+4 2B =24 B = 24/2 =12 A = 12-4 =8

Another way

the length 20 is a combination of the length of A and B. since A and B are squares the common side of A, B, and C is the same as the sum of side A and B. So 20 can be the common side plus another side of square A. Take away 4 from the total (16), you get twice the side of A :) so the side of A is 8:)

Wow! N this is p4 math!

Looks like algebra to me.

Thanks everyone!

Lol...tricky

I would find the factors of 117 first and see which 2 factors have a difference of 4 ....so the factors are 1,3,9,13,39,117 and the 2 numbers should be 9 and 13

Find the factors of 117, then 9 and 13 are The ones which difference is 4.

Thanks. Wuld u kindly advise how do we get the factors of 3x13 & 9x39 in the first place. Many thxs as I need to explain

I would teach using guess and check and listing. Let's list two numbers with difference of 4. I will also ask the child to consider which number they will start with first. For example is we use 1 and 5 will we get a number that is as big as 117? This is called smart guessing. A child can probably start from 6 and 10 and then slowly move his/her way upwards. Until the answer is reached. It's really only 4 or 5 guesses

3 x 39 = 117, 13 x 9 = 117

There are many ways to start to arrive at the factors that will depend on the level of the child and their experience. For me when I look at this question, the first thing I see is that the difference is 4 therefore the numbers are very close like 10x10 or 11x11. Of course both of these are not factors of 117 but it helps me think around the numbers. Next to think about the factors: we know it is not even, we know not divisible by 5. Thus start with 3 and 7. Hint: There is a faster way too. If a number is divisible by 3, then the sum of the digits must be divisible by 3 too. Eg. 1+1+7 = 9. Is 9 divisible 3? Yes, so 117 is divisible by 3. So look at 3 and look at 9.

Thanks to all. I solved the puzzle.

Guess and check 5x1 = 5 ( too low) 10 x 6= 60 15 X11 = 165 13 x 9 = 117

Alternate listing / G&C approach: 1st no. x 2nd no. (must be 4 more than the 1st) = Product 1 x 5 = 5 2 x 6 = 12 3 x 7 = 21 ... 9 x 13 = 117 Facebook's comment orientation -.-

Use guess and check

Convert Everything to markers

Thanks... very clear... ^-^

Draw model

It's much more easier

Why multiply by 5 n 6

Its the closest same multiple of 13 and 11

So mutilply by 5&6

For this question you need to understand a few concepts: 1) It is IF IF (gap and difference / short and excess) thus we are required to compare two sets of outcomes and then 'go back' to the actual numbers. 2) There is nothing in the question that remains constant. Ie Yellow changes, Green changes and the Total changes. When you recognise this, you can create a simple set of ratios (stuff in red box). Then choose one of many ways to solve from there. Aside from the above and the method I have shown, there is also cross multiply and simultaneous equations. Models can be drawn too, but for such questions it tends to be more challenging for most kids.