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#### Resources tagged with Working systematically similar to Square Corners:

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

### 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?

### 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?

### 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?

### 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?

##### Stage: 2 Challenge Level:

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

### Making Cuboids

##### Stage: 2 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?

### 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?

### 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.

### 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. . . .

### Creating Cubes

##### Stage: 2 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.

### 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?

### 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?

### 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?

### Single Track

##### Stage: 2 Challenge Level:

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

### 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.

### 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?

### 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.

### 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?

##### 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.

### 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?

### Chocs, Mints, Jellies

##### Stage: 2 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?

### Combining Cuisenaire

##### Stage: 2 Challenge Level:

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

### 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.

### Three Sets of Cubes, Two Surfaces

##### Stage: 2 Challenge Level:

How many models can you find which obey these rules?

### 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?

### Display Boards

##### Stage: 2 Challenge Level:

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

### Cover the Tray

##### Stage: 2 Challenge Level:

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

### 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?

### 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....?

### Two by One

##### Stage: 2 Challenge Level:

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

### Counting Cards

##### Stage: 2 Challenge Level:

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

### Tri.'s

##### Stage: 2 Challenge Level:

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

### 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?

### 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?

### Shaping Up

##### Stage: 2 Challenge Level:

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

### 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?

### 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?

### 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?

### Polydron

##### Stage: 2 Challenge Level:

This activity investigates how you might make squares and pentominoes from Polydron.

### Arranging the Tables

##### Stage: 2 Challenge Level:

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

### Calendar Cubes

##### Stage: 2 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

##### Stage: 2 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.

##### Stage: 2 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?

### Rabbits in the Pen

##### Stage: 2 Challenge Level:

Using the statements, can you work out how many of each type of rabbit there are in these pens?

### 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?

### 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?

### 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?

### Symmetry Challenge

##### Stage: 2 Challenge Level:

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.