Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

Finding Fifteen

Age 7 to 11 Challenge Level:

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?

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?

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?

Professional Circles

Age 7 to 11 Challenge Level:

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

Encouraging Primary Children to Work Systematically

Age 3 to 11

This article for primary teachers suggests ways in which to help children become better at working systematically.

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.

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?

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?

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?

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In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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.

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?

A Right Charlie

Age 7 to 11 Challenge Level:

Can you use this information to work out Charlie's house number?

Home City

Age 7 to 11 Challenge Level:

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

Family Tree

Age 7 to 11 Challenge Level:

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

This Pied Piper of Hamelin

Age 7 to 11 Challenge Level:

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

All Seated

Age 7 to 11 Challenge Level:

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?

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.

Finding All Possibilities Upper Primary

Age 7 to 11 Challenge Level:

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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?

Ancient Runes

Age 7 to 11 Challenge Level:

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

Possible Pieces

Age 5 to 11 Challenge Level:

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

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?

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?

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?

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.

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?

Coins (2)

Age 7 to 11 Challenge Level:

What is the smallest number of coins needed to make up 12 dollars and 83 cents?

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.

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?

Pasta Timing

Age 7 to 11 Challenge Level:

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

Page Numbers

Age 7 to 11 Short Challenge Level:

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

Bean Bags for Bernard's Bag

Age 7 to 11 Challenge Level:

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?

Fake Gold

Age 7 to 11 Challenge Level:

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

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.

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?

Whose Face?

Age 5 to 11 Challenge Level:

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

Crack the Code

Age 7 to 11 Challenge Level:

The Zargoes use almost the same alphabet as English. What does this birthday message say?

Bunny Hop

Age 7 to 11 Challenge Level:

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

Polo Square

Age 7 to 11 Challenge Level:

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

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?

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.

Build it up More

Age 7 to 11 Challenge Level:

This task follows on from Build it Up and takes the ideas into three dimensions!

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?

Shape Times Shape

Age 7 to 11 Challenge Level:

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

Penta Primes

Age 7 to 11 Challenge Level:

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

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?

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?

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?

Fifteen Cards

Age 7 to 11 Challenge Level:

Can you use the information to find out which cards I have used?