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Resources tagged with Working systematically similar to Diagonal Sums:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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

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Worms

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

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Spell by Numbers

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you substitute numbers for the letters in these sums?

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Six Is the Sum

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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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Coded Hundred Square

Stage: 2 Challenge Level: Challenge Level:1

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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Reach 100

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Dice in a Corner

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

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All the Digits

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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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Fractions in a Box

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

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A Mixed-up Clock

Stage: 2 Challenge Level: Challenge Level:1

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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Money Bags

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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Prompt Cards

Stage: 2 Challenge Level: Challenge Level:1

These two group activities use mathematical reasoning - one is numerical, one geometric.

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Today's Date - 01/06/2009

Stage: 1 and 2 Challenge Level: Challenge Level:1

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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Plants

Stage: 1 and 2 Challenge Level: Challenge Level:2 Challenge Level:2

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

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Five Coins

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Ben has five coins in his pocket. How much money might he have?

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Multiply Multiples 2

Stage: 2 Challenge Level: Challenge Level:1

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

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Two Primes Make One Square

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you make square numbers by adding two prime numbers together?

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Oh! Harry!

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

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Adding Plus

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

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Seven Square Numbers

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

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Rabbits in the Pen

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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Multiply Multiples 1

Stage: 2 Challenge Level: Challenge Level:1

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

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Buying a Balloon

Stage: 2 Challenge Level: Challenge Level:1

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?

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Two Egg Timers

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

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Magic Vs

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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Arranging the Tables

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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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Four Colours

Stage: 1 and 2 Challenge Level: Challenge Level:2 Challenge Level:2

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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Bean Bags for Bernard's Bag

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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Page Numbers

Stage: 2 Short Challenge Level: Challenge Level:1

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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Difference

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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Twenty Divided Into Six

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Trebling

Stage: 2 Challenge Level: Challenge Level:1

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

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A-magical Number Maze

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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Take Three Numbers

Stage: 2 Challenge Level: Challenge Level:1

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

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Sitting Round the Party Tables

Stage: 1 and 2 Challenge Level: Challenge Level:1

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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A Square of Numbers

Stage: 2 Challenge Level: Challenge Level:1

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

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ABC

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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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Pouring the Punch Drink

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

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Roll These Dice

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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 possibilities that could come up?

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Prison Cells

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

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The Puzzling Sweet Shop

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

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Area and Perimeter

Stage: 2 Challenge Level: Challenge Level:1

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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All Seated

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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The Pied Piper of Hamelin

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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A Shapely Network

Stage: 2 Challenge Level: Challenge Level:1

Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.

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Ladybird Box

Stage: 1 and 2 Challenge Level: Challenge Level:2 Challenge Level:2

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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Sealed Solution

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Journeys in Numberland

Stage: 2 Challenge Level: Challenge Level:1

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

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It's All about 64

Stage: 2 Challenge Level: Challenge Level:1

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

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Train Carriages

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

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Polo Square

Stage: 2 Challenge Level: Challenge Level:1

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.