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There are **104** NRICH Mathematical resources connected to **Mental calculations**, you may find related items under Calculations and numerical methods.

Problem
Primary curriculum
Secondary curriculum
### Sort Them Out (1)

Can you each work out the number on your card? What do you notice? How could you sort the cards?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Going Round in Circles

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

Age 11 to 14

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Dicey Operations

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Strike it Out

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Age 5 to 11

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Countdown

Here is a chance to play a version of the classic Countdown Game.

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Power Countdown

In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Find the Difference

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Difference Sudoku

Use the differences to find the solution to this Sudoku.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Shape Times Shape

These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Number Lines

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?

Age 5 to 7

Challenge Level

General
Primary curriculum
Secondary curriculum
### Integrated Sums Sudoku

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.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Domino Sorting

Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Number Balance

Can you hang weights in the right place to make the the number balance balanced?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### An Easy Way to Multiply by 10?

Do you agree with Badger's statements? Is Badger's reasoning 'watertight'? Why or why not?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Carrying Cards

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Consecutive Seven

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Finding Fifteen

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Tall Tower

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Mind Reading

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Square of Numbers

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Brown Family

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Ladybirds in the Garden

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?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Got It

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.

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Multiplication Tables - Matching Cards

Practise your tables skills and try to beat your previous best score in this interactive game.

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sealed Solution

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Super Shapes

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

Age 7 to 11

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Shapes on the Playground

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Twenty Divided Into Six

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Make 100

Find at least one way to put in some operation signs to make these digits come to 100.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What's in a Name?

What do you notice about these squares of numbers? What is the same? What is different?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Highest and Lowest

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Where Can We Visit?

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Butterfly Flowers

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?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### One Big Triangle

Make one big triangle so the numbers that touch on the small triangles add to 10.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Number Round Up

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.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Buying a Balloon

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 4 Dom

Use these four dominoes to make a square that has the same number of dots on each side.

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 2, 4, 6, 8

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Two Dice

Find all the numbers that can be made by adding the dots on two dice.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Domino Square

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Noah

Noah saw 12 legs walk by into the Ark. How many creatures did he see?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Maze 100

Can you go through this maze so that the numbers you pass add to exactly 100?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Roll These Dice

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?

Age 7 to 11

Challenge Level