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Challenge Maths:Solving Problems

We are learning to:

Use place value and number facts to solve problems.

Challenge 1

1) David has 5 counters to put on the abacus.

tens ones

What is the largest number he can make if he puts counters on each pole?

What is the smallest number he can make if he puts counters on each pole?

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2) Tilly has chosen the cards 1, 2 and 3. How many 2-digit even numbers can she make using these cards? Could she make more 2-digit even numbers if she chose 3 different numbers? Prove your answer.

1 2 3 4 5 6

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3) Tara is thinking of a number.

It is even The digit in the tens place is odd The digit in the ones is even. The sum of the digits is 9.

What is 10 more than this number?

David says:

Is he correct?

“There is only 1 answer for this problem.”

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Challenge 2

1010101010

10

1010

1010 10

10 101

11

1

11

111

111 1

4) Amy chose 3 counters. Billy chose 12 counters.

They both had counters worth the same amount.

What counters could Amy have chosen?

What counters could Billy have chosen?

5) Molly, Tara and Jake have guessed how many marbles are in a jar.

0 100

Molly says, “I think there are 25.” Tara says, “I think there are 35.” Jake says, “I think there are 61.”

There were 50 marbles in the jar. Who was closest?

Use the number-line to prove it.

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6) The price cards for these two toys have fallen off the shelf.

Rocket Scooter

The shopkeeper cannot remember how much the toys cost. He knows the rocket was cheaper and that both toys cost more than £10.

Can you find all possible pairs of prices?

1 2 3 4 £ £

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7) David has used the cards to make these two numbers.

19 63

1 3 6 9

Use the same cards. How many numbers can you make that will fit between these two numbers?

8) Tilly has these counters.

Tens Ones

How many more blue counters will she need to add before she can swap them all for a red counter?

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FeedbackChallenge 3

“How many even numbers can you make using exactly six counters?”

Will you be able to make more even numbers if you use exactly 8 counters?

1010101010

10

1010

1010 10

10 101

11

1

11

111

111 1

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9) Mrs Smith says:

Answers

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Challenge 1

1) 41 and 14

Challenge 2

4) Possible answers include: Amy chose 1 x 10 and 2 ones. Billy chose 12 ones.

Rocket Scooter

12 34

12 43

13 24

13 42

14 23

14 32

21 34

2) 2, 12 and 32 Yes. If 2, 4 and 6 are chosen. 24 26 42 46 62 64

3) No. 28, 46, 64, 82

5) Jake.

6) Rocket Scooter

21 43

23 41

24 31

34 41

34 42

34 43

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7) 31 36 39 61

8) 4

Challenge 3

9) 6 counters 4 6, 24, 42, 60 8 counters 5 8, 26, 44, 62, 80