Fun Maths – Games and Puzzles Five piece Tangram

Fun Maths – Games and Puzzles Four In One Jigsaw

Fun Maths – Games and Puzzles Calendar calculations

Using ALL FOUR of the digits in the above number just once each; using addition, subtraction, multiplication, division, brackets, decimal points,

square roots (squares only if there’s a 2) make each of the numbers below. Score 2 points if the 4 numbers are in order, 1 otherwise. How near 60 can you score?

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

Fun Maths – Games and Puzzles Hexiamonds

Fun Maths – Games and Puzzles 3 by 3 Squares

42

Fun Maths – Games and Puzzles

WONDERFUL 3 BY 3 SQUARESOver a thousand years ago, even before we adopted the Hindu-Arabic numeral system we now use, apparently the Chinese started to explore the problem of placing the integers 1 to 9 into a 3 by 3 grid, in such a way that in each of the 8 ways you could have three squares successively, 3 horizontal, 3 vertical, and 2 diagonal, the totals would be the same. They called this the Lo-Shu square. In Western mathematics it got called a Magic Square. Fig 1 is an empty one. Can you find a solution?

Figure 1

The process whereby someone new to this task can be helped to find it is a useful one for young learners to go through. It does not help if teacher just gives them a solution! This is an important issue in all 21st century mathematics teaching.

If we write down the numbers 1-9 in order, and find out their total [after all, if each of (say) the three rows totals the same, then each must be one third of the total of the 9 integers].

As we add the numbers, we arrive at a pattern the learners recognise: 1, 3, 6, 10, 15… the Triangular Numbers. This pattern provides an interesting diversion to talk about these,including why they are so called, and perhaps then how they relate to the Square numbers.

Although at first it may seem that many alternative solutions exist to the order 3 Magic Square, actually, all solutions, allowing for reflections and rotations, still make use of a single unique solution.

A possible strategy game, worth trying with a class (if they have not met the Lo-Shu square before) is for everyone to have a 3 by 3 grid. Teacher calls out the numbers 1 to 9 in random order and each person tries to fit it each number into their grid, in order to make as many as possible triples in a row column or diagonal add up to 15.

Two variations to explore of the Magic Square of order 3 follow.

42

Fun Maths – Games and Puzzles

WONDERFUL 3 BY 3 SQUARESOver a thousand years ago, even before we adopted the Hindu-Arabic numeral system we now use, apparently the Chinese started to explore the problem of placing the integers 1 to 9 into a 3 by 3 grid, in such a way that in each of the 8 ways you could have three squares successively, 3 horizontal, 3 vertical, and 2 diagonal, the totals would be the same. They called this the Lo-Shu square. In Western mathematics it got called a Magic Square. Fig 1 is an empty one. Can you find a solution?

Figure 1

The process whereby someone new to this task can be helped to find it is a useful one for young learners to go through. It does not help if teacher just gives them a solution! This is an important issue in all 21st century mathematics teaching.

If we write down the numbers 1-9 in order, and find out their total [after all, if each of (say) the three rows totals the same, then each must be one third of the total of the 9 integers].

As we add the numbers, we arrive at a pattern the learners recognise: 1, 3, 6, 10, 15… the Triangular Numbers. This pattern provides an interesting diversion to talk about these,including why they are so called, and perhaps then how they relate to the Square numbers.

Although at first it may seem that many alternative solutions exist to the order 3 Magic Square, actually, all solutions, allowing for reflections and rotations, still make use of a single unique solution.

A possible strategy game, worth trying with a class (if they have not met the Lo-Shu square before) is for everyone to have a 3 by 3 grid. Teacher calls out the numbers 1 to 9 in random order and each person tries to fit it each number into their grid, in order to make as many as possible triples in a row column or diagonal add up to 15.

Two variations to explore of the Magic Square of order 3 follow.

Fun Maths – Games and Puzzles MacMahon Squares Puzzle tiles

Fun Maths – Games and Puzzles MacMahon Squares – possible solutions

Fun Maths – Games and Puzzles Multiplication Mountains – 7x

9876543210 0 1 2 3 4 5 6 7 8 9 10 11

Units Seven Times Table

Tens

Fun Maths – Games and Puzzles Number Mastermind

Number of guess 1st 2nd 3rd 4th Result

1

2

3

4

5

6

7

8

9

10

11

12

Fun Maths – Games and Puzzles Plan to Score

27

© 2019 Association of Teachers of Mathematics

PLAN TO SCORE(a version of paper, knife, scissors)

This is a game for 2 players. A counter is used to represent a ball, starting at the middle point of a ‘pitch’. A possible warm up to this game (perhaps for younger players) is to have each player roll one die.

A more interesting, strategic, game has each player starting with an energy score of (say) 25. On each round, perhaps from having hands behind backs or with fists closed, players show 0, 1, 2, 3, 4 or 5 fingers. The number of fingers shown by each player is removed from their energy score.

If one person has outscored the other, by showing a higher number of fingers, than the counter/ball is moved one step towards the other’s goal. If the number of fingers shown by each player is the same the counter/ball stays where it is. On each further round the process is the same. Goals are scored when the counter reaches the goal. Play then restarts at the centre. The energy score is renewed after each kick-off.

There may need to be some strategic thinking because once a person reaches 0 energy, they cannot participate, or defend their goal. If both reach zero, then the game restarts with the counter/ball at the centre with a renewed energy score.

One can choose to play until a goal is scored, or to have 10 restarts; or, for example in a group tournament, allow draws e.g. for when both players reach zero without scoring.

Other variations might be to allow for two hands, i.e. 1-10 fingers able to be shown in each round, and with a larger energy score, 50, or even 100. For the latter it may be worth making the pitch a little larger with 2 extra landing points. Experience suggests that it is best to start with the smaller sized pitch and energy game first.

A possible warm up to this game (perhaps for younger players) that does not require strategy, nor uses the energy score addition/subtraction requirement, is to have each player roll one die.

25 25

0 : 0

Fun Maths – Games and Puzzles Target 21 board

9 8 7 6 5 4 3 2 1 0 Start

10

11

12 13 14 15 16 17 18 19 20 21 Finish

Fun Maths – Games and Puzzles Vertigo tiles

Fun Maths – Games and Puzzles Vertigo grid

Fun Maths – Games and Puzzles Square Triples resource

Fun Maths – Games and Puzzles Tetrahexes

Fun Maths – Games and Puzzles Tetrahexes grid

Fun Maths – Games and Puzzles a + 3b Game cards – 01

1 2 3

4 5 6

7

Fun Maths – Games and Puzzles a + 3b Game cards – 02

8 9 10

11 12 13

14

Fun Maths – Games and Puzzles a + 3b Game cards – 03

15 16 17

18 19 20

21

Fun Maths – Games and Puzzles a + 3b Game cards – 04

22 23 24

25 26 27

28

Fun Maths – Games and Puzzles The Elephant Walk

8765 �

1 2 3 4

8 976 10 �1 2 3 4 5

Fun Maths – Games and Puzzles Latin Square Game Board

1 2 3 4 5 6 7

4 3 7 1 6 2 5

2 4 5 3 7 1 6

7 1 2 6 3 5 4

5 6 4 2 1 7 3

6 7 1 5 4 3 2

3 5 6 7 2 4 1

Fun Maths – Games and Puzzles Latin Square Grid

Fun Maths – Games and Puzzles Latin Square Grids