1. Forty Towers
4 different coloured blocks are arranged to make a tower How many different orders are there? What further questions might you pose?

2. Square Grids
On the 4 by 4 dotty grid, draw a quadrilateral by connecting 4 dots. What questions might you pose? Explore one or more of them.

3. 1
Frogs
The frogs are restless – they all want to change places

4. 2
Frogs
At the moment they’re all sat on their lily pads, green frogs on green lily pads and purple frogs on purple ones, separated by the golden lily (which they can land on).
However… the green frogs want to be on the purple lily pads and the purple frogs want to be on the green lily pads…

5. 3
Frogs
If there’s an empty lily pad next to a frog, he or she can slither across to it. Frogs can also jump over just one frog at a time to an empty lily pad. …and they can’t go backwards…

6. 4
Frogs
Can you help them out? How many moves will it take?

7. Six Circles
Is it possible to place the digits 1, 2, 3, 4, 5, 6 in the circles so that sum of the numbers on each side of the triangle is the same?
From Holton on Problem Solving

8. Lines, Crossovers and Regions
What’s the maximum number of crossovers that can be created when you draw 4 straight lines?

9. Max Box
Starting with a 20cm x 20cm square of card, cut out a square from each corner and fold up to make an open box. What is its volume?

10. Ice Creams
I’m going to eat a ‘2 scoop’ ice cream. How many options do I have if there is a choice of:
Vanilla (not much of a choice!)
Vanilla and Chocolate
Vanilla, Chocolate and Strawberry
Vanilla, Chocolate, Strawberry and Mint ??

11. Opposite Corners
Starting with a 100 square, draw a 2x3 rectangle around some numbers.
What’s the difference between the products of the numbers in opposite corners? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100

12. How many rectangles?
A rectangle is divided up using horizontal and vertical lines. How many rectangles are there? Note that one possible rectangle has been coloured in.