May Challenge - Years 1 & 2

Button-up

My coat has three different buttons.
Sometimes, I do them up starting with the top button.  Sometimes, I start somewhere else.

How many ways can you find to do up my coat?

Think about:

What could you change about the buttoning? 
Do you always have to start in the same place? 
Do you think there are any more ways?  How do you know?

Solutions are to be completed by Thursday 26^th May.  Please post them into the Maths Challenge Box in the picture book library.

May Challenge - Years 3 & 4

Lighthouses

On the coast there are three lighthouses.

The first light shines for 3 seconds, then is off for 3 seconds.

The second light shines for 4 seconds, then is off for 4 seconds.

The third light shines for 5 seconds, then is off for 5 seconds.

All three lights have just come on together.

Questions:

1) When is the first time that all three lights will be off?

2) When is the next time that all three lights will come on at the same moment?

Hints:
Think about drawing three number lines (one for each lighthouse) to show when each light is on and off.  Be sure to match the three lines up so they are easy to compare.
Question 2 will require some careful work and perseverance if you use the number lines.  Alternatively, you may wish to think about the number of seconds between each turning on of  a light.  For example, the first lighthouse turns on every 6 seconds.  Think about how you could use your knowledge of multiples.

Solutions are to be completed by Thursday 26^th May.  Please post them into the Maths Challenge Box in the picture book library.

May Challenge - Years 5 & 6

Letter Land (Updated)

A to H represent the numbers from 0 to 7.

A + C = A   (Please note that I originally incorrectly published this sum as A + B = A)

F x D = F

B – G = G

A + H = E

B / H = G

E – G = F

Find the values of A, B, C, D, E, F, G and H.

Hints – Only read the hints once you have tried on your own first.

1) Solve for C and D first.

2)  Next solve for B and G.  You may need to consider a few possibilities.

April Solutions - Year 3 & 4

There were 11 solutions in total.  You need to work systematically to find them all.

April Solutions - Years 5 & 6

1. I am 48 (or even 104).

2. I am 26 now, and in 38 years I will be 64 (which is both a square number and a cube number).

3. I am 9 years old now.

A couple possible ways to solve question 3:

a) Create a table and test the possibilities one by one.

My age	Mum’s age		My age now	Mum’s age eight years ago	My age in 5 years time doubled
0	27
1	28		1	19	12
2	29		2	21	14
3	30		3	22	16
4	31		4	23	18
5	32		5	24	20
6	33		6	25	22
7	34		7	26	24
8	35		8	27	26
9	36		9	28	28
10	37
11	38
12	39

b) You could also solve an algebraic equation where x represents my age now.

x= my age now, so x + 27 is my mum’s age now.

x + 5 is my age in five years time.

2(x + 5) is my age in five years time doubled.

x + 27 – 8 is my mum’s age eight years ago.

So, 2(x+5) = x + 27 -8.

When you solve for x, you find that x=9.