Resources tagged with: Place value

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Broad Topics > The Number System and Place Value > Place value

Chocolate Maths

Age 11 to 14 Challenge Level:

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

More Mathematical Mysteries

Age 11 to 14 Challenge Level:

Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . .

How Many Miles to Go?

Age 11 to 14 Challenge Level:

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

Seven Up

Age 11 to 14 Challenge Level:

The number 27 is special because it is three times the sum of its digits 27 = 3 (2 + 7). Find some two digit numbers that are SEVEN times the sum of their digits (seven-up numbers)?

Reversals

Age 11 to 14 Challenge Level:

Where should you start, if you want to finish back where you started?

The Number Jumbler

Age 7 to 14 Challenge Level:

The Number Jumbler can always work out your chosen symbol. Can you work out how?

Quick Times

Age 11 to 14 Challenge Level:

32 x 38 = 30 x 40 + 2 x 8; 34 x 36 = 30 x 40 + 4 x 6; 56 x 54 = 50 x 60 + 6 x 4; 73 x 77 = 70 x 80 + 3 x 7 Verify and generalise if possible.

Think of Two Numbers

Age 11 to 14 Challenge Level:

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

Read This Page

Age 11 to 14 Challenge Level:

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

Two and Two

Age 11 to 16 Challenge Level:

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Cayley

Age 11 to 14 Challenge Level:

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Eleven

Age 11 to 14 Challenge Level:

Replace each letter with a digit to make this addition correct.

Mini-max

Age 11 to 14 Challenge Level:

Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers. . . .

Football Sum

Age 11 to 14 Challenge Level:

Find the values of the nine letters in the sum: FOOT + BALL = GAME

Always a Multiple?

Age 11 to 14 Challenge Level:

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

Repeaters

Age 11 to 14 Challenge Level:

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

Please Explain

Age 11 to 14 Challenge Level:

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .

Three Times Seven

Age 11 to 14 Challenge Level:

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

How Can I Support the Development of Early Number Sense and Place Value?

Age 3 to 11

This article for primary teachers expands on the key ideas which underpin early number sense and place value, and suggests activities to support learners as they get to grips with these ideas.

Trebling

Age 7 to 11 Challenge Level:

Can you replace the letters with numbers? Is there only one solution in each case?

Big Powers

Age 11 to 16 Challenge Level:

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

Just Repeat

Age 11 to 14 Challenge Level:

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

Arrange the Digits

Age 11 to 14 Challenge Level:

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

Double Digit

Age 11 to 14 Challenge Level:

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . .

Power Mad!

Age 11 to 14 Challenge Level:

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Which Scripts?

Age 7 to 11 Challenge Level:

There are six numbers written in five different scripts. Can you sort out which is which?

Reach 100

Age 7 to 14 Challenge Level:

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Back to the Planet of Vuvv

Age 11 to 14 Challenge Level:

There are two forms of counting on Vuvv - Zios count in base 3 and Zepts count in base 7. One day four of these creatures, two Zios and two Zepts, sat on the summit of a hill to count the legs of. . . .

Ordering

Age 5 to 11

This set of activities focuses on ordering, an important aspect of place value.

Less Is More

Age 5 to 11 Challenge Level:

Use your knowledge of place value to try to win this game. How will you maximise your score?

Subtraction Surprise

Age 7 to 14 Challenge Level:

Try out some calculations. Are you surprised by the results?

Legs Eleven

Age 11 to 14 Challenge Level:

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

More Upper Primary Activities on Number Sense and Place Value

Age 7 to 11

More upper primary number sense and place value tasks.

Number Sense and Place Value

Age 5 to 11

This feature aims to support you in developing children's early number sense and understanding of place value.

Amount

Age 5 to 11

These tasks will help learners develop their understanding of place value, particularly giving them opportunities to express numbers as amounts.

Tis Unique

Age 11 to 14 Challenge Level:

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

Basically

Age 11 to 14 Challenge Level:

The number 3723(in base 10) is written as 123 in another base. What is that base?

Position

Age 5 to 11

One of the key ideas associated with place value is that the position of a digit affects its value. These activities support children in understanding this idea.

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!

Place Value: the Ten-ness of Ten

Age 3 to 11

This article develops the idea of 'ten-ness' as an important element of place value.

Journeys on the Gattegno Tens Chart

Age 5 to 11

Alf describes how the Gattegno chart helped a class of 7-9 year olds gain an awareness of place value and of the inverse relationship between multiplication and division.

Dicey Addition

Age 5 to 11 Challenge Level:

Who said that adding couldn't be fun?

Multiply Multiples 3

Age 7 to 11 Challenge Level:

Have a go at balancing this equation. Can you find different ways of doing it?

Writ Large

Age 11 to 14 Challenge Level:

Suppose you had to begin the never ending task of writing out the natural numbers: 1, 2, 3, 4, 5.... and so on. What would be the 1000th digit you would write down.

Multiply Multiples 2

Age 7 to 11 Challenge Level:

Can you work out some different ways to balance this equation?

Multiply Multiples 1

Age 7 to 11 Challenge Level:

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Round the Three Dice

Age 7 to 11 Challenge Level:

What happens when you round these three-digit numbers to the nearest 100?

Nice or Nasty for Two

Age 7 to 14 Challenge Level:

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.

Round the Dice Decimals 1

Age 7 to 11 Challenge Level:

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

Becky's Number Plumber

Age 7 to 11 Challenge Level:

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?