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There are 104 NRICH Mathematical resources connected to Mental calculations, you may find related items under Calculations and numerical methods.
Broad Topics > Calculations and numerical methods > Mental calculationsCan you each work out the number on your card? What do you notice? How could you sort the cards?
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Here is a chance to play a version of the classic Countdown Game.
In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Use the differences to find the solution to this Sudoku.
These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?
A resource to try once children are familiar with number lines, and they have begun to use them for addition. It could be a good way to talk about subtraction. Leah and Tom each have a number line. Can you work out where their counters will land?
The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on the intersections between two diagonally adjacent squares.
Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?
Can you hang weights in the right place to make the the number balance balanced?
Do you agree with Badger's statements? Is Badger's reasoning 'watertight'? Why or why not?
These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?
Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I know?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Practise your tables skills and try to beat your previous best score in this interactive game.
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
Find at least one way to put in some operation signs to make these digits come to 100.
What do you notice about these squares of numbers? What is the same? What is different?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Can you find two butterflies to go on each flower so that the numbers on each pair of butterflies adds to the number on their flower?
Make one big triangle so the numbers that touch on the small triangles add to 10.
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
Use these four dominoes to make a square that has the same number of dots on each side.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
Find all the numbers that can be made by adding the dots on two dice.
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
Can you go through this maze so that the numbers you pass add to exactly 100?
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?