### NRICH PROBLEM SOLVING PLACE VALUE

Powers of numbers behave in surprising ways. This prompts the awareness that ‘five and five make ten’. Pupils’ Recording or Pupils Recording Age 5 to 14 This article, written for teachers, looks at the different kinds of recordings encountered in Primary Mathematics lessons and the importance of not jumping to conclusions! Various arrangements of counters on the ten-frames can be used to prompt different mental images of numbers and different mental strategies for manipulating these numbers, all in association with the numbers’ relationships to ten. Two and Two Age 11 to 14 Challenge Level: Take a look at some of these and try to explain why they are true.

In this square, look at the green square which contains the numbers 2, 3, 12 and Have a go at balancing this equation. Multiply Multiples 3 Age 7 to 11 Challenge Level: Age 7 to 11 Challenge Level: Additional frames full of ten counters can be used to show numbers over 19 so that children develop mental images of numbers based on their experiences with these resources. Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces?

In how many different ways can you do it?

## Place Value: the Ten-ness of Ten

Writing Digits Age 5 to 7 Challenge Level: Take any four digit number. For older students, we offer problems that focus on powers and indices. Age 11 to 14 Challenge Level: Watch our videos of multiplication methods that you may not have met before.

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Can you build it up? Did you get a multiple of 11? This prompts the awareness that ‘five and five make ten’. Dicey Operations for an adult and child.

Alien Counting Age 7 to 11 Challenge Level: Method in Multiplying Madness? Multiply Multiples 1 Age 7 to 11 Challenge Level: How quickly can you put back the numbers on the hundred square? Can you reconstruct the original multiplication?

Move the first digit to the end and move the rest along. Investigate the different ways these aliens count in this challenge. Once this type of thinking is established, the ten-frame is no longer needed.

Powers of numbers behave in surprising ways.

The Number Jumbler can always work out your chosen symbol. Choose four different digits from and put one in each box so that the resulting four two-digit numbers add to a total of How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in vwlue same order?

CRUEL ANGELS THESIS YUGIOH

# Place Value KS1 :

For more details about what we as teachers can do to support learners’ number sense and place value, including a range of classroom activities, see our related article and our Number Sense and Place Value Feature. All the Digits Age 7 to 11 Challenge Level: Age 7 to 11 Challenge Level: Other tags that relate to Number Sense Series: Age 5 to 11 Challenge Level: Register for our mailing list.

Light the Lights Age 5 to 7 Challenge Level: Try out this number trick.

plqce Alien Counting Age 7 to 11 Challenge Level: Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible? Take a look at some of these and try to explain why they are true.

# Numbers and the Number System :: Place value :

Register for our mailing list. Can you replace the letters with numbers? What happens with different starting numbers?