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Resources tagged with Working systematically similar to Rectangles with Dominoes:

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

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?

Tangram Tangle

Stage: 1 Challenge Level:

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

Two by One

Stage: 2 Challenge Level:

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

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?

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?

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?

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?

Single Track

Stage: 2 Challenge Level:

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

Display Boards

Stage: 2 Challenge Level:

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

Open Boxes

Stage: 2 Challenge Level:

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

Triangle Edges

Stage: 1 Challenge Level:

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

Inside Triangles

Stage: 1 Challenge Level:

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

Tessellate the Triominoes

Stage: 1 Challenge Level:

What happens when you try and fit the triomino pieces into these two grids?

Cover the Camel

Stage: 1 Challenge Level:

Can you cover the camel with these pieces?

Painting Possibilities

Stage: 2 Challenge Level:

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

Tri.'s

Stage: 2 Challenge Level:

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

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?

Egyptian Rope

Stage: 2 Challenge Level:

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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?

Nine-pin Triangles

Stage: 2 Challenge Level:

How many different triangles can you make on a circular pegboard that has nine pegs?

We'll Bang the Drum

Stage: 1 Challenge Level:

How many different rhythms can you make by putting two drums on the wheel?

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?

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?

Tetrafit

Stage: 2 Challenge Level:

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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.

Are You Well Balanced?

Stage: 1 Challenge Level:

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Cover the Tray

Stage: 2 Challenge Level:

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

Coloured Squares

Stage: 1 Challenge Level:

Use the clues to colour each square.

Three Ball Line Up

Stage: 1 Challenge Level:

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Hexpentas

Stage: 1 and 2 Challenge Level:

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

Routes 1 and 5

Stage: 1 Challenge Level:

Find your way through the grid starting at 2 and following these operations. What number do you end on?

Red Even

Stage: 2 Challenge Level:

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Dienes' Logiblocs

Stage: 1 Challenge Level:

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

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.

Three Sets of Cubes, Two Surfaces

Stage: 2 Challenge Level:

How many models can you find which obey these rules?

One to Fifteen

Stage: 2 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?

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....?

Stage: 2 Challenge Level:

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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.

Cuisenaire Counting

Stage: 1 Challenge Level:

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

Coded Hundred Square

Stage: 2 Challenge Level:

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

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?

Room Doubling

Stage: 2 Challenge Level:

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

Eight Queens

Stage: 2 Challenge Level:

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

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?

Cuboid-in-a-box

Stage: 2 Challenge Level:

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

Building with Rods

Stage: 2 Challenge Level:

In how many ways can you stack these rods, following the rules?

Stage: 2 Challenge Level:

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

Cubes Here and There

Stage: 2 Challenge Level:

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

Combining Cuisenaire

Stage: 2 Challenge Level:

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