Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

Hexpentas

Age 5 to 11
Challenge Level

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

Two by One

Age 7 to 11
Challenge Level

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

Shaping Up

Age 7 to 11
Challenge Level

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

Cereal Packets

Age 7 to 11
Challenge Level

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

Putting Two and Two Together

Age 7 to 11
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?

Map Folding

Age 7 to 11
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?

Coordinate Challenge

Age 7 to 11
Challenge Level

Use the clues about the symmetrical properties of these letters to place them on the grid.

Tri-five

Age 7 to 11
Challenge Level

Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

Cuboid-in-a-box

Age 7 to 11
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?

Cover the Tray

Age 7 to 11
Challenge Level

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

More Transformations on a Pegboard

Age 7 to 11
Challenge Level

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Nine-pin Triangles

Age 7 to 11
Challenge Level

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

Peg and Pin Boards

Age 5 to 11

This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.

Uncanny Triangles

Age 7 to 11
Challenge Level

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

Three Sets of Cubes, Two Surfaces

Age 7 to 11
Challenge Level

How many models can you find which obey these rules?

The Third Dimension

Age 5 to 11
Challenge Level

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

Multilink Cubes

Age 7 to 11
Challenge Level

If you had 36 cubes, what different cuboids could you make?

Making Cuboids

Age 7 to 11
Challenge Level

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

Egyptian Rope

Age 7 to 11
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?

Tri.'s

Age 7 to 11
Challenge Level

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

Brush Loads

Age 7 to 11
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.

Sticks and Triangles

Age 7 to 11
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?

Knight's Swap

Age 7 to 11
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?

Four Colours

Age 5 to 11
Challenge Level

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

Count the Trapeziums

Age 7 to 11
Challenge Level

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

Folded Number Line

Age 7 to 11
Challenge Level

When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.

Square Corners

Age 7 to 11
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?

Triangles All Around

Age 7 to 11
Challenge Level

Can you find all the different triangles on these peg boards, and find their angles?

Dice Stairs

Age 7 to 11
Challenge Level

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Dodecamagic

Age 7 to 11
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?

Cubes Here and There

Age 7 to 11
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?

Shunting Puzzle

Age 7 to 11
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

Age 7 to 11
Challenge Level

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

Chocs, Mints, Jellies

Age 7 to 11
Challenge Level

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

Painting Possibilities

Age 7 to 11
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. . . .

Creating Cubes

Age 7 to 11
Challenge Level

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

Make Pairs

Age 7 to 11
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.

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?

Wag Worms

Age 7 to 11
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

Age 7 to 11
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.

More and More Buckets

Age 7 to 11
Challenge Level

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

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?

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.

Triangles to Tetrahedra

Age 11 to 14
Challenge Level

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra 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?

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.

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.

Is a Square a Rectangle?

Age 7 to 11
Challenge Level

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

Buying a Balloon

Age 7 to 11
Challenge Level

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Calcunos

Age 7 to 11
Challenge Level

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