The White Rose answers have not been published yet so we'll see if I've made any mistakes...

Ch1

Star = 10

Heart = 17

Triangle = 0

Ch2

Tom has 75p

so pencils cost 10p each

Ch3

There are 6 possible 3 digit numbers each child can make

358, 385, 538, 583, 835 and 853

The difference has to be between 300 and 400

So **853** - **538** = 315

Ch4

Using the diagram I noticed the height of a rectangle is 3x the width so = 12cm. The length of the large rectangle is 12cm + 4cm + 4cm = 20cm.

The Perimeter (P) = 2 x (length + height)

P = 2 (20 + 12)

P = 64cm

Ch5

Width of 1 small rectangle = 112 div 7 = 16cm

length of small rectangle = 2 x width so L = 32cm

New shape = 15 x 32cm various ways to work out

10 x 32 = 320

5 x 32 = half of 320 = 160

15 x 32 = 320 + 160 = 480cm

Ch6

If you add the 3 pairs of shapes you get a height of 47.8cm which I noticed has 2 of each shape.

So divide by 2 to get a height of 23.9cm

Thankfully they didn't ask us to find the height of each shape!

Ch7

I noticed the smallest triangle was an isosceles and was1/2 of 1/4 the square so 1/8 total area

The other 2 triangles were right angled scalene and were1/2 of 1/2 the square so 1/4 total area

1/8 +1/4 + 1/4

1/8 + 2/8 + 2/8

= 5/8 area of square

Ch8

A bit confusing at first....

but shade 1:2 out of 30 squares so 10 green squares to 20 white squares

then

start again almost and shade 4 green: 1 white out of the 30 so 24 green to 6 white.

So Lisa had 10 shaded but needed 24 shaded. Therefore she shaded another **14**

Getting really challenging now...so well done if you had a go at these.

Ch9

I started by finding the fraction of the book read every day from the clues.

Monday 2/5 = 4/10 (so 6/10 left to read)

Tuesday 1/2 of 6/10 = 3/10 (3/10 left)

Wednesday 5/9 of 3/10 (remember the butterfly method?)

= 1/3 x 1/2 = 1/6

M + T + W + Th = WHOLE book

4/10 + 3/10 + 1/6 + **2/15 **= whole

Then I noticed LCM (Lowest Common Multiple) of 30

12/30 + 9/30 + 5/30 + 4/30 = whole book

so if there were 30 pages Mo read 4 pages more Tuesday than Wednesday BUT Mo read 68 pages more

If you drew a table headed with 9 and 5 and kept adding multiples of 9 and 5 until you eventually reached the 17th multiple you found Tuesday's page count was 153 and Wednesday's was 85 pages. Therefore you had to multiply the original denominator by 17. So 30 x 17 (various ways to do this) 3 x 17 =51 so 30 x 17 = 510

So there were 510 pages in the book.

Ch10

You may remember the area of a triangle is 1/2 of base x height.

Area of triangle = 126cm2

Then use your knowledge of coordinates to find the base is split into 2 parts - 5 and something?

The base from the y axis to B is 16cm

so base = 21cm

Then using pythagoras theorem the 2 sides AC and BC can be found

AC2 = height 122 + base 52

= 144 + 25

= 169

so AC = 13cm

BC found the same way = 20cm

so Perimeter P = 21 + 20 + 13 = **54cm**

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