Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

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?

Rabbits in the Pen

Age 7 to 11
Challenge Level

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

On Target

Age 7 to 11
Challenge Level

You have 5 darts and your target score is 44. How many different ways could you score 44?

How Old?

Age 7 to 11
Challenge Level

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

How Much Did it Cost?

Age 7 to 11
Challenge Level

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

Hubble, Bubble

Age 7 to 11
Challenge Level

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

Adding Plus

Age 7 to 11
Challenge Level

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?

A Mixed-up Clock

Age 7 to 11
Challenge Level

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?

A-magical Number Maze

Age 7 to 11
Challenge Level

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!

Zargon Glasses

Age 7 to 11
Challenge Level

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Oh! Harry!

Age 7 to 11
Challenge Level

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

Pouring the Punch Drink

Age 7 to 11
Challenge Level

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.

The Pied Piper of Hamelin

Age 7 to 11
Challenge Level

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!

Seven Square Numbers

Age 7 to 11
Challenge Level

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.

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?

Spell by Numbers

Age 7 to 11
Challenge Level

Can you substitute numbers for the letters in these sums?

The Dice Train

Age 7 to 11
Challenge Level

This dice train has been made using specific rules. How many different trains can you make?

X Is 5 Squares

Age 7 to 11
Challenge Level

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

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.

Today's Date - 01/06/2009

Age 5 to 11
Challenge Level

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

Being Resourceful - Primary Number

Age 5 to 11
Challenge Level

Number problems at primary level that require careful consideration.

Prison Cells

Age 7 to 11
Challenge Level

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?

Dice and Spinner Numbers

Age 7 to 11
Challenge Level

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

Twenty Divided Into Six

Age 7 to 11
Challenge Level

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?

The Puzzling Sweet Shop

Age 5 to 11
Challenge Level

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?

Two Egg Timers

Age 7 to 11
Challenge Level

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?

Dart Target

Age 7 to 11
Challenge Level

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

Beads and Bags

Age 5 to 11
Challenge Level

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

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.

Fractions in a Box

Age 7 to 11
Challenge Level

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

Sealed Solution

Age 7 to 11
Challenge Level

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?

One to Fifteen

Age 7 to 11
Challenge Level

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

Code Breaker

Age 7 to 11
Challenge Level

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Multiply Multiples 3

Age 7 to 11
Challenge Level

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

Team Scream

Age 7 to 11
Challenge Level

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

Seating Arrangements

Age 7 to 11
Challenge Level

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

Two Primes Make One Square

Age 7 to 11
Challenge Level

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

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.

Greater Than or Less Than?

Age 7 to 11
Challenge Level

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

Five Coins

Age 5 to 11
Challenge Level

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

Sums and Differences 1

Age 7 to 11
Challenge Level

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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.

Octa Space

Age 7 to 11
Challenge Level

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

Rolling That Cube

Age 5 to 11
Challenge Level

My dice has inky marks on each face. Can you find the route it has taken? What does each face look like?

Reach 100

Age 7 to 11
Challenge Level

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.

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?

Sums and Differences 2

Age 7 to 11
Challenge Level

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

Different Deductions

Age 7 to 11
Challenge Level

There are lots of different methods to find out what the shapes are worth - how many can you find?

Route Product

Age 7 to 11
Challenge Level

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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 to have an ordered approach.