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Resources tagged with Working systematically similar to Building Blocks:

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

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The Third Dimension

Stage: 1 and 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Four Colours

Stage: 1 and 2 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Three Sets of Cubes, Two Surfaces

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

How many models can you find which obey these rules?

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Family Tree

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Wag Worms

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Whose Face?

Stage: 1 and 2 Challenge Level: Challenge Level:1

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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Cubes Here and There

Stage: 2 Challenge Level: Challenge Level:1

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?

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Penta Place

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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New House

Stage: 2 Challenge Level: Challenge Level:1

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?

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Brush Loads

Stage: 2 Challenge Level: Challenge Level:1

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.

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Two on Five

Stage: 1 and 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Plates of Biscuits

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

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Waiting for Blast Off

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Knight's Swap

Stage: 2 Challenge Level: Challenge Level:1

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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Painting Possibilities

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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. . . .

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Cereal Packets

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Making Cuboids

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Celtic Knot

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

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Mystery Matrix

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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Creating Cubes

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Shaping Up

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Two Dots

Stage: 2 Challenge Level: Challenge Level:1

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

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Broken Toaster

Stage: 2 Short Challenge Level: Challenge Level:1

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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Bunny Hop

Stage: 2 Challenge Level: Challenge Level:1

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

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Rabbits in the Pen

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Button-up Some More

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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Red Even

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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A Right Charlie

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you use this information to work out Charlie's house number?

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Count the Trapeziums

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Crack the Code

Stage: 2 Challenge Level: Challenge Level:1

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

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The Moons of Vuvv

Stage: 2 Challenge Level: Challenge Level:1

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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Seating Arrangements

Stage: 2 Challenge Level: Challenge Level:1

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

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Team Scream

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Make Pairs

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Shunting Puzzle

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Single Track

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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How Many Times?

Stage: 2 Challenge Level: Challenge Level:1

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

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Route Product

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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Octa Space

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

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Dice Stairs

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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It Figures

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Ice Cream

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Pasta Timing

Stage: 2 Challenge Level: Challenge Level:1

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?

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Dodecamagic

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Quadrilaterals

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Pouring the Punch Drink

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

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Fencing Lambs

Stage: 2 Challenge Level: Challenge Level:1

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

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Eight Queens

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Putting Two and Two Together

Stage: 2 Challenge Level: Challenge Level:1

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?

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Dart Target

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.