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Resources tagged with Working systematically similar to Subtraction Surprise:

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Broad Topics > Using, Applying and Reasoning about Mathematics > Working systematically

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Consecutive Negative Numbers

Age 11 to 14 Challenge Level:

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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More Magic Potting Sheds

Age 11 to 14 Challenge Level:

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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Multiply the Addition Square

Age 11 to 14 Challenge Level:

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

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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

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Maths Trails

Age 7 to 14

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

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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?

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The Moons of Vuvv

Age 7 to 11 Challenge Level:

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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Multiplication Squares

Age 7 to 11 Challenge Level:

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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Spell by Numbers

Age 7 to 11 Challenge Level:

Can you substitute numbers for the letters in these sums?

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Multiply Multiples 2

Age 7 to 11 Challenge Level:

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

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Two and Two

Age 11 to 14 Challenge Level:

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

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Multiply Multiples 3

Age 7 to 11 Challenge Level:

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

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Football Sum

Age 11 to 14 Challenge Level:

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

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How Old Are the Children?

Age 11 to 14 Challenge Level:

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

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ABC

Age 7 to 11 Challenge Level:

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

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Take Three Numbers

Age 7 to 11 Challenge Level:

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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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"?

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Trebling

Age 7 to 11 Challenge Level:

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

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Sweets in a Box

Age 7 to 11 Challenge Level:

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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Neighbours

Age 7 to 11 Challenge Level:

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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American Billions

Age 11 to 14 Challenge Level:

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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Sticky Numbers

Age 11 to 14 Challenge Level:

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

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Ben's Game

Age 11 to 14 Challenge Level:

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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Being Resourceful - Primary Number

Age 5 to 11 Challenge Level:

Number problems at primary level that require careful consideration.

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Pole Star Sudoku 2

Age 11 to 16 Challenge Level:

This Sudoku, based on differences. Using the one clue number can you find the solution?

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Curious Number

Age 7 to 11 Challenge Level:

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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A First Product Sudoku

Age 11 to 14 Challenge Level:

Given the products of adjacent cells, can you complete this Sudoku?

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Mystery Matrix

Age 7 to 11 Challenge Level:

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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9 Weights

Age 11 to 14 Challenge Level:

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

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Product Sudoku

Age 11 to 14 Challenge Level:

The clues for this Sudoku are the product of the numbers in adjacent squares.

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Integrated Product Sudoku

Age 11 to 16 Challenge Level:

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

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All the Digits

Age 7 to 11 Challenge Level:

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

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Six Is the Sum

Age 7 to 11 Challenge Level:

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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It Figures

Age 7 to 11 Challenge Level:

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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Consecutive Numbers

Age 7 to 14 Challenge Level:

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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Number Detective

Age 5 to 11 Challenge Level:

Follow the clues to find the mystery number.

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Window Frames

Age 5 to 14 Challenge Level:

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

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Roll These Dice

Age 7 to 11 Challenge Level:

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?

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The Pet Graph

Age 7 to 11 Challenge Level:

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

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Button-up Some More

Age 7 to 11 Challenge Level:

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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Seven Pots of Plants

Age 7 to 11 Challenge Level:

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

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Shape Times Shape

Age 7 to 11 Challenge Level:

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

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Calendar Cubes

Age 7 to 11 Challenge Level:

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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Ordered Ways of Working Upper Primary

Age 7 to 11 Challenge Level:

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

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Summing Consecutive Numbers

Age 11 to 14 Challenge Level:

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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Arranging the Tables

Age 7 to 11 Challenge Level:

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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Weights

Age 11 to 14 Challenge Level:

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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Snails' Trails

Age 7 to 11 Challenge Level:

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

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Journeys in Numberland

Age 7 to 11 Challenge Level:

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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Symmetry Challenge

Age 7 to 11 Challenge Level:

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.