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Resources tagged with Working systematically similar to Cover the Tray:

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

Cover the Tray

Stage: 2 Challenge Level:

These practical challenges are all about making a 'tray' and covering it with paper.

Halloween Investigation

Stage: 2 Challenge Level:

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

Celtic Knot

Stage: 2 Challenge Level:

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

Map Folding

Stage: 2 Challenge Level:

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

Counters

Stage: 2 Challenge Level:

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Two on Five

Stage: 1 and 2 Challenge Level:

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

Newspapers

Stage: 2 Challenge Level:

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

Two by One

Stage: 2 Challenge Level:

An activity making various patterns with 2 x 1 rectangular tiles.

Waiting for Blast Off

Stage: 2 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?

Knight's Swap

Stage: 2 Challenge Level:

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

Ice Cream

Stage: 2 Challenge Level:

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

Street Party

Stage: 2 Challenge Level:

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

3 Rings

Stage: 2 Challenge Level:

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

Sticks and Triangles

Stage: 2 Challenge Level:

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

Ribbon Squares

Stage: 2 Challenge Level:

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

Display Boards

Stage: 2 Challenge Level:

Design an arrangement of display boards in the school hall which fits the requirements of different people.

Shunting Puzzle

Stage: 2 Challenge Level:

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

Putting Two and Two Together

Stage: 2 Challenge Level:

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Single Track

Stage: 2 Challenge Level:

What is the best way to shunt these carriages so that each train can continue its journey?

Calcunos

Stage: 2 Challenge Level:

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

Cereal Packets

Stage: 2 Challenge Level:

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

Polo Square

Stage: 2 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.

Paw Prints

Stage: 2 Challenge Level:

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

Uncanny Triangles

Stage: 2 Challenge Level:

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

Family Tree

Stage: 2 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.

Square Corners

Stage: 2 Challenge Level:

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Zargon Glasses

Stage: 2 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?

Route Product

Stage: 2 Challenge Level:

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

A Square of Numbers

Stage: 2 Challenge Level:

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

Wag Worms

Stage: 2 Challenge Level:

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

Two Dots

Stage: 2 Challenge Level:

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

Seating Arrangements

Stage: 2 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

Stage: 2 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?

Make Pairs

Stage: 2 Challenge Level:

Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.

Count the Trapeziums

Stage: 2 Challenge Level:

How many trapeziums, of various sizes, are hidden in this picture?

How Many Times?

Stage: 2 Challenge Level:

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

Dodecamagic

Stage: 2 Challenge Level:

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

Plates of Biscuits

Stage: 2 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?

Arrangements

Stage: 2 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....?

Geoboards

Stage: 2 Challenge Level:

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

Combining Cuisenaire

Stage: 2 Challenge Level:

Can you find all the different ways of lining up these Cuisenaire rods?

The Moons of Vuvv

Stage: 2 Challenge Level:

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

Tri.'s

Stage: 2 Challenge Level:

How many triangles can you make on the 3 by 3 pegboard?

Fake Gold

Stage: 2 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?

Snails' Trails

Stage: 2 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?

A-magical Number Maze

Stage: 2 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!

The Pet Graph

Stage: 2 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?

Pasta Timing

Stage: 2 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?

Room Doubling

Stage: 2 Challenge Level:

Investigate the different ways you could split up these rooms so that you have double the number.

It Figures

Stage: 2 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?