Magic Squares ** to ***

A magic square is a square grid where the numbers in each horizontal, vertical and diagonal line add to the same number.  This number is called the magic number.  Try to complete these magic squares.

 Magic Square 15:

	7
9
4

Magic number = 15

Use the numbers 1 to 9 (although 4, 7 and 9 have already been placed for you).

 Magic Square 34:

7		9
	11		16
	6
	13	8	1

Magic number = 34

Use the numbers 1 to 16

Magic Square 111:

	18				23
	25		27	22	31
34	9	1	10		21
6		30	28		16
	14	29	8	20
		15	35	17	13

Magic number = 111

Use the numbers 1 to 36

Test your perseverance:  Complete this magic square so that it has a magic number of 12.  Fill in the squares using the numbers 0 to 8.  It will require some trial and improvement.

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3

Helpful Hint:  Draw the 3x3 grid.  Then cut out little squares of paper with the numbers on them so you can move them around on the grid to try different possibilities until you find the solution.

0

1

2

3

4

5

6

7

8

 

Target *

Instructions:

Choose a number between 25 and 55.

Take turns placing a marker on top of the numbers on the board below.

Each time add the number to the running total.

Each square can be used only once.

Try to be the player to reach the target exactly.

  

 

 

5	5	5	5	5
4	4	4	4	4
3	3	3	3	3
2	2	2	2	2
1	1	1	1	1

 

 

Variation: 

• For younger children choose a smaller target number and perhaps only use a board with 1s, 2s and 3s.
• Pick a number and work backwards to 0.

 

 

Helpful Hint:

You can use a counter on a Hundreds Square to keep track of your sum.  It may also help you to see how much more you would like to add on.

 

The Correct Order Solution

a)  2  4  1  3

b)  4  3  1  2

c)  2  3  1  5  4     or      4  3  1  5  2

Rabbit Problem Solution

Apologies...  I just realized that I didn't post the solution to the rabbit problem last week.  Here it is:


It takes the rabbit 28 days to climb out of the hole.

 

The first thing to notice is that the act of climbing and sliding can be greatly simplified.  Instead of thinking of going up 3 metres and down 2 metres every day, you can just think about it as going up 1 metre.  So every day the rabbit goes up 1 metre – which should mean that it takes her 30 days to get out, 1 metre each day.  But the reason it does not is that on the day the rabbit actually gets out, she doesn’t slip back down 2 metres.  The rabbit saves itself two days, and it only takes 28 days.

The Correct Order ****

You need to place the numbers in the correct order according to the clues given.  For each problem the numbers may not be in the place that relates to their value.  For example, 1 cannot be in the first position, 2 cannot be in the second place, 3 cannot be in the third place…and so on.

 a) Using 1  2  3  and  4:

• The four is directly to the right of the two.
• The first number and the last number add up to five.

b) Using 1  2  3  and  4:

• The even numbers are not next to each other.
• The 1 is directly to the right of the 3.

c) Using 1  2  3  4  and  5:

• The first and fifth cards add to 6.
• The third and fourth cards add to 6.
• The second and third cards add to 4.

Helpful tip:  Write the numbers on little pieces of paper (or use playing cards) so that you can move them around easily as you try out your ideas.

 

Make Fifteen **

Equipment:    

• calculator
• 20 counters (of keep a tally of points)

 Instructions:

• Player 1 enters any number 0-20 on the calculator and hands the calculator to Player 2, and says “Make 15.”
• Player 2 looks at the display and thinks of a number that can be added or subtracted from the displayed number to make a total of fifteen.
• Player 2 presses + or -, the number to be added or subtracted, and =.
• If the answer is 15, Player 2 earns one counter.  If the answer is not 15, Player 2 does not score.
• Players reverse roles.
• The first player to earn 10 counters wins the game.

 Variation:

• Player take turns to “Make Eight,” “Make Twelve,” “Make Twenty,” etc.

Rabbit Problem Hint

The answer is not 30.  Think carefully about what happens near the end of the rabbit’s climb to the top.