### Two Numbers Under the Microscope

This investigates one particular property of number by looking closely at an example of adding two odd numbers together.

### Odd Times Even

This problem looks at how one example of your choice can show something about the general structure of multiplication.

### Walking Round a Triangle

This ladybird is taking a walk round a triangle. Can you see how much he has turned when he gets back to where he started?

# A Bag of Marbles

##### Age 5 to 7Challenge Level

We were particularly pleased with the kinds of answers and explanations that came with these solutions.We had many sent in and here are just two as a sample. First from Daniel at Englefield Green Infants School:

A. rough to feel and sparkley when rolling
B. rough to feel and dark inside
C. dark inside and sparkle when rolling
D dark inside and cold
E. cold, dark and rough
F. cold, sparkle when rolling, rough
G. rough, sparkle when rolling, dark inside
H. cold, rough
I. sparkle when rolling
J. sparkle when rolling, cold, dark inside.

On marbles that
sparkle when rolling but are dark inside - red and green
are cold to touch and feel rough - white and blue
are cold, but sparkle when rolling - white, red.

What colour(s) could be on a marble that
is cold - white
sparkles when rolling - red

The colour you would find on a cold, sparkly, dark and rough marble -
blue, green, red and white.

The second one is from Rebecca at Montsaye Community College:

Marbles -
A- would be rough to feel and Sparkles when it rolls
B- would be rough to feel and Dark inside
C- would Sparkle when it rolls and Dark on the inside
D- would be Dark on the inside and cold to touch
E- would be Cold to touch, Rough to feel and and Dark on the inside
F- would be Cold to touch, Rough to feeland Sparkle when it rolls
G- would Sparkle when it rolls, be Rough to feel and Dark on the inside
H- would be cold to touch and Rough to feel
I- would Sparkle when it rolls and be cold to touch
J- would Sparkle when it rolls, be cold to touch and dark on the inside

If I was making the Marbles-
If the Marble would Sparkle when it rolls and be dark on the inside I
would put Red and Green on it.
If the Marble would be cold to touch and Rough to feel I would put White
and Blue on it.
If the marble would be cold to touch and Sparkle when it rolls I would put
White and red on it.

If a Marble was cold it could be-
Just white,
White and Blue,
White and Green,
White and Red,
White and Blue and Red,
White and Blue and Green,
White and Red and Blue and Green.

If a Marble Sparkled when it rolled it could be-
Red.
Red and Blue,
Red and Green,
Red and White,
Red and Blue and White,
Red and Blue and Green,
Red and White and Green,
Red and White and Green and Blue.

If a Marble was cold, sparkly, dark and rough it would be-
White and Red and Green and Blue.

Other solutions came from;

Kristy at Singapore International School
Various un-named pupils from Buckingham College Preparatory School
Talia and Alex at Red Hill Field School
Saskia and Amrita at Jebal School
Rhea at Mason Middle School
Alaa at Gateway School
Lauren at Danesfield School
A girl called Charlie at Culford Preparatory School
Sarah at Seabrook High School
Sofia at Glenarm College
Samantha at Kaleen School
Libby, Patrick, Peter and Olivia at Danes Hill School
Marianne and Aramide at Clapham Manor School
Samantha at Driftwood Middle
and last but not least, Meghan and Kia

Well done everyone!