Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

Magic Potting Sheds

Age 11 to 14
Challenge Level

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Number Sandwiches

Age 7 to 14
Challenge Level

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

Ladybird Box

Age 5 to 11
Challenge Level

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

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?

Difference

Age 7 to 11
Challenge Level

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

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?

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?

Junior Frogs

Age 5 to 11
Challenge Level

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Coded Hundred Square

Age 7 to 11
Challenge Level

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

A Square of Numbers

Age 7 to 11
Challenge Level

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

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?

Coins (2)

Age 7 to 11
Challenge Level

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

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.

Plates of Biscuits

Age 7 to 11
Challenge Level

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

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?

Colour in the Square

Age 7 to 16
Challenge Level

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

Games Related to Nim

Age 5 to 16

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

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?

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?

Arrangements

Age 7 to 11
Challenge Level

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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.

Waiting for Blast Off

Age 7 to 11
Challenge Level

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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.

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?

Twin Corresponding Sudokus II

Age 11 to 16
Challenge Level

Two sudokus in one. Challenge yourself to make the necessary connections.

Diagonal Product Sudoku

Age 11 to 16
Challenge Level

Given the products of diagonally opposite cells - can you complete this Sudoku?

Open Squares

Age 7 to 11
Challenge Level

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

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?

Broken Toaster

Age 7 to 11 Short
Challenge Level

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Twinkle Twinkle

Age 7 to 14
Challenge Level

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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?

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?

Seasonal Twin Sudokus

Age 11 to 16
Challenge Level

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

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?

Cinema Problem

Age 11 to 14
Challenge Level

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

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.

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.

Wallpaper Sudoku

Age 11 to 16
Challenge Level

A Sudoku that uses transformations as supporting clues.

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.

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?

Seven Flipped

Age 7 to 11
Challenge Level

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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?

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.

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?

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?

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?

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?

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?