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Engaging Maths

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Number Novelties Mathematical Novelties

Mathemagic

• Combines the beauty of

mathematical structure with the entertainment value of a trick

Choose a number between 1 and 63. Tell me if it appears on this chart.

• Using the numbers 1, 2, 4 and 8

and addition, stomp to make all the numbers from 1 to 15.

Number Stomp

 Using the numbers 1, 2, 4 and 8

and addition, stomp to make all the numbers from 1 to 15.

Human Computer

Stand side by side Each student represents a number Raise or lower hand to switch on/off

Tricky Table

9 7 5 11 7 5 3 9 13 11 9 15 8 6 4 10

Tricky Table

9 7 5 11 7 5 3 9 13 11 9 15 8 6 4 10

Tricky Table

9 7 5 11 7 5 3 9 13 11 9 15 8 6 4 10

Tricky Table

9 7 5 11 7 5 3 9 13 11 9 15 8 6 4 10

Tricky Table

9 7 5 11 7 5 3 9 13 11 9 15 8 6 4 10

Tricky Table

• Add the four circled numbers.
• 9 + 11 + 3 + 10 = 33
• Check your total against that of your

neighbour

How to create a Tricky Table

+ 5 3 1 7 4

9 7 5 11

2

7 5 3 9

8

13 11 9 15

3

8 6 4 10

Finding the Magic Number

• Add all the numbers on the outside of

the table

• 5 + 3 + 1 + 7 + 4 + 2 + 8 + 3 = 33

Create a Tricky Table

+

Try a Multiplication Table

x

Thrice Dice

• Roll three dice
• Stack on top of each other
• Magician reveals the total
• Add the numbers showing on the five

faces that are touching.

Double Dice

Instruction Dice

Throw two dice (blue, red) Multiply the two top numbers 4 x 2 Multiply the two bottom numbers 3 x 5 Multiply the top of the blue die by the bottom of red die 4 x 5 Multiply the top of the red die by the bottom of the blue die 3 x 2 Add the four numbers

The answer

49

The algebra behind the trick

• If we call the numbers on the top of each die

a and b, then the numbers on the bottom of the dice will be 7 - a and 7 - b.

• Consider the steps
• Multiplying top numbers a x b = ab

Algebra cont

• Multiplying bottom numbers

(7 - a)(7 - b) = 49 - 7a - 7b + ab

• Multiplying top by bottom

a(7 - b) = 7a - ab

• Multiplying bottom by top

b(7 - a) = 7b – ab

• Combining the results
• (ab) + (49 - 7a - 7b + ab) + (7a - ab) + (7b - ab)
• Simplified leaves 49.

Mobius Bands

• You will need a strip of paper about as

long and as wide as a ruler.

• Give it a half twist and join
• Cut lengthways
• What happens?

Number Words

• Choose a number (54)
• Write it in words (fifty four)
• Count the letters (9)
• Write it in words (nine)
• Count the letters …

Card Shark

• Requires 26 cards
• Split the 26 cards into a pile of 10

and a pile of 16

• Ask a friend to choose a card from the pile of

16 and place it on top of the pile of 10 to make eleven cards.

• Place the remaining 15 cards on top of the

eleven cards.

• Deal to find the secret card

Card Shark Deal

L R L R L R Once 26 cards are dealt face down, discard the 13 cards in the left pile. Collapse the right hand row, preserving the order of the cards. Continue until one card left

Crazy Calculator

• Enter a three-digit number into a calculator

(237)

• multiply by 7
• multiply by 11
• multiply by 13 …
• Start with a three-digit number, repeat and

divide by 7, 11, 13.

Triple treat

• Choose a two-digit number (39)
• Repeat three times (393 939)
• Divide by 13
• Divide by 21
• Divide by 37.

1089

Choose a three-digit number where the hundreds digit is at least two more than the units digit. 461 Reverse the digits 164 Subtract 461 – 164 = 297 Reverse the digits of the answer and then add this number to the answer 792 + 297 = Try another three-digit number and see what happens

1089

• Try
• 1089 x 1
• 1089 x 2
• 1089 x 3
• 1089 x 4 …

1089 with algebra

• The same pattern 900 + 180 + 9 is generated

because of the initial restrictions of the puzzle.

• We can represent this using some algebra
• If a, b and c represent the digits in the original

number we get 100a + 10b + c –(100c + 10b + a) = 99a – 99c or 99(a – c)

• We know that a and c can only represent single-digit

numbers and they cannot be equal because of the

• riginal restrictions.

1089

• The differences will be restricted to

multiples of 99, that is 198, 297, 396, 495, 594, 693, 792 and 891

• When the numbers are reverse and

added it leads to the following combinations 99 + 990, 198 + 891, 297 + 792 …

Think of a Number

• Choose a number
• Double it
• Add ten
• Treble it (3 x)
• Subtract 30
• Divide by six
• 6 (a)
• 12 (2a)
• 22 (2a + 10)
• 66 (6a + 30)
• 36 (6a)
• #

Think of a Number II

• Choose a number
• Add 20
• Double it
• Subtract 10
• Halve it
• Subtract the number

you started with

• 6 (a)
• 26 (a + 20)
• 52 (2a + 40)
• 42 (2a + 30)
• 21 (a + 15)
• #

Domino Trick

• Ask your partner to choose a domino piece

(without you seeing)

• Multiply one of the numbers shown on the

domino by 5

• Add 6 to the result
• Double your answer
• Add the number on the other half of the

domino

• Ask your partner to tell you his/her final

number

Working out the original numbers

• Subtract 12 to find the two numbers

that were on the original domino

• Could use two dice