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Mental arithmetic

Example of cuisenaire rods and number line
Two Cuisenaire rods on a number line.
CThe buttons used to selct the Cuisinaire rods
Select the Cuisenaire rods by clicking on the above buttons.

D1: Cuisenaire Rods with number lines.
Useful for lots of mental arithmetic activities (also work on fractions and ratio).

The on and off buttonsThe on and off buttons.
Top: horizontal or vertical Cuisenaire rods.

Delete all the Cuisenaire rods, they can also be deleted individually by dragging to the bin.

Turn the numbers on or off.

Turn the grid on or off.


Turn the horizontal number line on or off. The number lines can be dragged up or down, or left or right.


Turn the vertical number line on or off.

Example of number line

Bar
The buttons

The buttons

D2: Find the difference between two numbers

Two numbers are shown on a number line. Drag the two numbers along the number line or click on 'change'.
Select the numbers on the number line by clicking on the appropriate button.
Coloured bars can be shown to indicate one way of working out the difference. Click on the button showing the coloured bars to hide or show them.
Click on the zoom button to zoom in or out. The number line can be dragged from side to side when it is magnified.
Click in the boxes to hide or show the numbers or difference.

D3: Find the total of two numbers

Same idea as above but shows the total of two numbers. 50 is the maximum size for each number. No zoom facility.

Link to the number grid
What are the hidden numbers?
Reveal a few numbers, the pupils have to identify some of the hidden ones.
D4: 100-grid activities
The buttons
This number grid can be used to identify hidden numbers. Click on a square to reveal the number. Useful for addition and subtraction activities using a normal 100-grid or number sequence activities using a random grid.

There are four types of number grid:
1 to 100, 1 in the top-left hand corner, 100 in the bottom-right.
100 to 1, 100 in the top-left hand corner, 1 in the bottom-right.
A random grid starting with smallest number in the top-left.
A random grid starting with highest number in the top-left.
Example of questions

Mental arithmetic 'tests' each comprising ten questions on addition, subtraction, multiplication, division, place value, sequences, fractions, measures, time and money.

D5: National Curriculum: level 3 'test 1'
D6: National Curriculum: level 3 'test 2'
: slightly more difficult

A mental arithmetic 'test' comprising ten questions on addition and subtraction.

D7: National Curriculum: level 3

Load the activity

D43: How many are on the bus?

People get on and off a bus. How many are on the bus?
Use the sliders to determine the speed of the bus, the maxium number of people gwetting on and off the bus and the number of stops.
Click the 'play button then watch people getting on and off the bus.

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Hidden numbers and missing numbers

Go to the hidden numbers.
Click on the polygon person to reveal the hidden number, click again to hide it.

 

Hide or show the number line.
Use this button to hide or show the number line.

 

 

 

 



 

Go to the hidden numbers.
Click on the polygon person to reveal the hidden number, click again to hide it.

 

 

 

 

 

 

 

Hidden numbers

D10: Hidden numbers 1
Lots of different addition and subtraction sums with one of the numbers hidden.
Click on the options buttons to change the sums. The option buttons generate the following types of sum:

The option buttons

1. Add small numbers
2. Add numbers less than 30
3. Add numbers less than 50
4. Subtract small numbers
5. Subtract numbers less than 30
6. Subtract numbers less than 50
7. Add or subtract small numbers
8. Add or subtract numbers less than 50
9. Add or subtract a multiple of 10 to or from a two-digit number, without crossing 100
eg 63 - 30, 47 + 30
10. Add or subtract a pair of multiples of 100, without crossing 1000 (with number line)
eg 600 - 300, 400 + 500
11. Add a single digit to a 'teens' number, or subtract a single digit from a 'twenties' number, crossing 20
eg 17 + 5, 25 - 8
12. Find a small difference between a pair of numbers lying either side of 20, or another multiple of 10
eg 63 - 58, 37 + ? = 45
13. Add or subtract a multiple of 10 to and from a two-digit number, crossing 100
14. Add or subtract a pair of multiples of 100 crossing 1000
15. Add or subtract 100 to or from any three-digit number, without crossing 1000
16. Add or subtract a single digit to or from a two-digit number, crossing the tens boundary
eg 58 + 7
17. Find a small difference between a pair of numbers lying either side of a multiple of 100 from 100 to 1000
eg 607 - 598
18. Add or subtract any pair of two-digit numbers

D16: Hidden numbers 2
Lots of different addition and subtraction sums with one of the numbers hidden.
Click on the options buttons to change the sums. The option buttons generate the following types of sum:
The option buttons

1. Add or subtract two-digit multiples of 10
2. Add or subtract a pair of multiples of 100, crossing 1000
eg 600 + 800
3. Add or subtract a multiple of 10 to or from a two or three-digit number, without crossing the hundres boundary
eg 672 - 50
4. Add a two or three digit-number to a multiple of 10, 100 or 1000
eg 300 + 234
5. Find what to add to a two or three-digit number to make 100 or the next higher multiple of 100
eg 456 + ? =500
6. Find what to add to a four-digit multiple of 100 to make the next higher multiple of 1000
eg 4100 + ? =5000
7. Add or subtract three-digit multiples of 10
eg 560 + 350
8. Add or subtract a single-digit multiple of 100 to or from a three or four-digit number, crossing 1000
eg 600 + 567
9. Add or subtract a three-digit multiple of 10 to or from a three-digit number, without crossing the hundreds boundary
eg 540 + 324
10. Find what to add to a decimal with units and tenths to make the next higher whole number
5.6 + ? = 6
11. Add or subtract four-digit multiples of 100
eg 3400 - 1800
12. Find what to add to a decimal with units, 10ths and 100ths to make the next higher whole number or 10th
eg 4.56 + ? = 4.6
13. Find what to add to a number to make 1.
eg 0.56 + ? = 1

D23: Add three 3-digit multiples of 100
700 + Missing number box + 500 = 1800

D42: Hidden Numbers flash cards
Please let us know if you think the options should be changed, eg more time for thinking?

Load the triangles resource

D44: Number triangles
This resource generates the random numbers to make the triangles work. It leaves one missing number.
Children generate the facts from the triangle. e.g. 5 x 7 = 56, 56 divided by 7 = 8 etc

Eight options.
Click on the tick button to show/hide all the answers. Click in the number facts boxes to reveal indiviual answers. Click in the triangle to reveal a missing number.
One or six triangles can be shown.

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Random number generator: target board

Link to the number generator
A screenshot of the number generator.

D30: A flexible whiteboard resource which generates 24 different sets of numbers; similar to a target board.

Options include:

Random numbers to 100
Random numbers -25 to 25
Totals, eg 27 and 24 and 51(27 + 24 = 51)
Differences, eg 65 and 36 and 29 (65 - 36 = 29)
Number bonds to 10, eg 6.1 and 3.9
Number bonds to 100, eg 66 and 34

The option buttonsSelect the type of numbers to be generated by clicking on the numbered buttons at the top.
1: random numbers to 100, 2: random numbers -25 to 25, 3: totals, 4: differences, 7: number bonds to 10, 8: number bonds to 100

The buttons usedThe colour of the number can be changed. Select one of 8 colours then click on a number.

The numbers can be put arranged in a grid, click this button arrange in a table
or arranged randomly, click this button arrange randomly

The numbers can be grouped by dragging them about.

The numbers can be discarded by dragging them to the bin.

Children can use the resource to match pairs:
eg 3x5 and 15 (times-tables 1)
eg 35 and 70 (doubles)

A clock starts when a set of numbers has been generated. The clock can be hidden or shown (click the green clock button). It can be stopped by clicking the 'stop the clock' button!
The clock can be used to see who can match the pairs in the quickest time.

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Missing symbols: use the symbols >, < and =
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link to worksheet

Decide which symbol to use

D31: >, < and =

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SAT-type questions
Link to activity

D11: Two cards are chosen. The numbers on the cards are added together. The result is rounded to the nearest 10. There might be more than one solution.
Click on the cards to show/hide the digits.

Link to activity

D12: Use the digit cards to make the sum correct. Arrange the digit cards to make two 2-digit numbers that add up to 100.

worksheet example

D32: Circle three numbers that add up to make....

worksheet example

D33: Use five cards to make this sum correct
Five numbers are shown and the answer to the sum.

Link to activity

Link to activity

Work out the differences between numbers.

D34: Small differences

D35: Multiples of 10 differences

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Solving problems
Solve puzzles and problems such as

Link to activity

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Link to activity

Missing number problem-solving activities

Sum, Difference and Product

D8: Two whole numbers
D9: Two decimal numbers
Two small numbers are generated, their sum, difference and product are worked out.
Hide the two numbers, can you work out what they are from their sum, product and difference?
Click on 'change' to generate two more numbers.
Hide the product, work out the two numbers from their sum and difference.

Hide the odd or even labels: is it possible to say whether a sum, product or difference will be odd or even?

Sum puzzle
Write a number in each circle so that the number in each square equals the sum of the two numbers on either side of it. There are many possible solutions for the square arithmagon. The answer sheet will give one set of solutions.

D36: Sum puzzle

Example of a 4x4 magic square

Complete the magic squares

D37: 3 x 3 magic square
D38: 3 x 3 magic square (more difficult)
D39: 4 x 4 magic square

Link to activity

Triangle puzzle
The three numbers on each side of the triangle must add up to the red target number.

D40: Triangle puzzle

Play darts
Use the number pad to decide on the score required then press the 'throw' button.

D41: Play Darts: Finish on a double or a bullseye

The dartboard usedUse this 1 to 10 dartboard to do some mental arithmetic. First decide on the finshing score then click on the 'throw' button. The darts can be dragged about and thrown by releasing the mouse button.

How many ways are there to finish on 37? 42? Remember the last dart thrown must be a double or a bullseye.

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