Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

Penta Place

Age 7 to 11 Challenge Level:

Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?

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.

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.

Finding All Possibilities Upper Primary

Age 7 to 11 Challenge Level:

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

Tetrafit

Age 7 to 11 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?

Home City

Age 7 to 11 Challenge Level:

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

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?

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?

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?

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?

Count the Trapeziums

Age 7 to 11 Challenge Level:

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

Crack the Code

Age 7 to 11 Challenge Level:

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

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?

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.

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?

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.

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?

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.

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.

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'.

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. . . .

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.

Stairs

Age 5 to 11 Challenge Level:

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

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 on Five

Age 5 to 11 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?

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?

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?

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?

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.

Elf Suits

Age 7 to 11 Challenge Level:

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

Multilink Cubes

Age 7 to 11 Challenge Level:

If you had 36 cubes, what different cuboids could 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.

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.

Train Carriages

Age 5 to 11 Challenge Level:

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

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!

New House

Age 7 to 11 Challenge Level:

In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?

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.

Crossing the Town Square

Age 7 to 11 Challenge Level:

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

Quadrilaterals

Age 7 to 11 Challenge Level:

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

Cover the Tray

Age 7 to 11 Challenge Level:

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

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?

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?

Ribbon Squares

Age 7 to 11 Challenge Level:

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

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.

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?

School Fair Necklaces

Age 5 to 11 Challenge Level:

How many possible necklaces can you find? And how do you know you've found them all?

Street Party

Age 7 to 11 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.

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?

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?

Greater Than or Less Than?

Age 7 to 11 Challenge Level:

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?