Resources tagged with: Working systematically

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Broad Topics > Mathematical Thinking > Working systematically

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?

Nine-pin Triangles

Age 7 to 11 Challenge Level:

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

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?

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?

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?

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. . . .

Jigsaw Pieces

Age 7 to 11 Challenge Level:

How will you go about finding all the jigsaw pieces that have one peg and one hole?

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.

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.

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?

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?

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?

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?

Crack the Code

Age 7 to 11 Challenge Level:

The Zargoes use almost the same alphabet as English. What does this birthday message say?

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?

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?

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 if you have an ordered approach.

Three Sets of Cubes, Two Surfaces

Age 7 to 11 Challenge Level:

How many models can you find which obey these rules?

Professional Circles

Age 7 to 11 Challenge Level:

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

Finding All Possibilities Upper Primary

Age 7 to 11 Challenge Level:

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

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.

Home City

Age 7 to 11 Challenge Level:

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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?

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?

This Pied Piper of Hamelin

Age 7 to 11 Challenge Level:

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Seven Pots of Plants

Age 7 to 11 Challenge Level:

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

Paw Prints

Age 7 to 11 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?

Family Tree

Age 7 to 11 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.

Two by One

Age 7 to 11 Challenge Level:

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

Counting Cards

Age 7 to 11 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?

Symmetry Challenge

Age 7 to 11 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.

Tri.'s

Age 7 to 11 Challenge Level:

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

Ancient Runes

Age 7 to 11 Challenge Level:

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

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.

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?

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?

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.

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'.

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.

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?

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?

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?

Age 7 to 11 Challenge Level:

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

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?

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.

Counters

Age 7 to 11 Challenge Level:

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

Encouraging Primary Children to Work Systematically

Age 3 to 11

This article for primary teachers suggests ways in which to help children become better at working systematically.