Calculator Activities for Key Stages 2 and 3

1 The answer is 2001, what was the question?

2 How many ways can you write an expression for 100 which only uses the same digit repeated and any operations?

for example

99 + (99 ÷ 99)

111 - 11

1111 ÷ 11 - 1

What about 2001?

3 In how may ways can you write an expression for 100 which uses any digit only once?

for example

98 + 2

87 + 13

12 ÷ 3 + 96

What about 2001?

4 Can you write an expression for 100 which uses all the digits?

What about 2001?

5 Can you calculate to 100 using exactly five operations?

for example enter:

10 + 20 = 30 (1)

30 x 5 = 150 (2)

150 ÷ 3 = 50 (3)

50 ÷ 2 = 25 (4)

25 x 4 = 100 (5)

Can you do it in a different way?

Can you do it with five different operations?

What about 2001?

6 In the centre of the flower is the number 100.

Put numbers in the first ring of ten petals so that the total of the numbers on the petals is one hundred. To find the numbers in each of the petals in the second ring add together the numbers in the two petals which touch it. Total the second ring of petals. Try with other numbers.

What about 2001?

7 Flick

In a game you have: 3 plastic cups numbered 1, 2 and 3and also 3 counters numbered 1, 2 and 3

Flick the counters so they land in the cups.

Your score is the total of the numbers in each cup multiplied by the number on the cup, the three results are added together.

e.g. 1 x (0) + 2 x (1 + 3) + 3 x (2) = 12

What possible scores can you obtain?

What could the scores be:

if the counters are numbered 2, 3 and 4, or 3, 4 and 5, or ...?

if the cups are numbered 2, 3 and 4, or 3, 4 and 5, or...

What could happen if you had more counters?

8 Deal It

You have 4 number cards and 3 operations cards.

Shuffle the 2 piles of cards.

Turn the 2 piles of cards face down.

Then select the cards, turning them up in the order:

number, operation, number, operation, number, operation, number.

Work out the answer.

for example: 8 + 12 - 15 + 5 = 10

What possible answers are there?

9 Deal and Add

Use 6 number cards,

for example: 12, 13, 17, 23, 34, 35.

Deal them into 2 equal piles.

12, 23 and 34

13, 35 and 17

Total each pile.

67 and 65

How many different answers could you obtain?

Try with cards which have consecutive numbers on them.

Try with more cards.

Try products.

10 Work It Out

A game for two or more players.

Equipment: 3 sets of cards,

set 1 - numbers 1 to 9

set 2 - numbers 10, 20, . . ., 90

set 3 - numbers 100, 200, . . ., 900

Player 1 enters a 3 figure number on a calculator.

Player 2 chooses six cards from any of the 3 sets, face down.

Using as many of the six numbers as possible, the player makes a total as near as possible to the number chosen.

If there are more than two players all of the others make up a total, the player with the nearest total (with the most cards) wins the round.

11 Simple Targets

Equipment: Number cards

for example, 11, 27, 30, 45, 56, 69, . . .

Shuffle, turn up the first card, enter it on the calculator,

Turn up the second card, enter an operation and a number to obtain the second number, without clearing the calculator display.

Continue for the third, etc.

If this is to be played by 2 players, they take it in turns to try to reach a target number, if she/he succeeds then they win that number card, otherwise it is put to the bottom of the pack.

Variation: use only multiplication and division

the answer must be correct to 1, 2 or 3 significant figures.

12

Is it true that the sum of three consecutive numbers is always divisible by three?

Is it true that the sum of five consecutive numbers is always divisible by five?

13

Which numbers can be expressed as the sum of consecutive counting numbers in 2, 3, 4, . . . ways?

for example:

15 = 7 + 8

or 15 = 4 + 5 + 6

or 15 = 1 +2 + 3 +4 + 5

15 can be expressed as a sum of consecutive counting numbers in 3 ways.

Do your answers differ if you can use 0 and negative numbers?

14

Is it true that the product of three consecutive numbers is always divisible by six?

15

What proportion of all the possible products of two consecutive numbers is divisible by 3?

What proportion of all the possible products of two consecutive numbers is divisible by 8?