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### Number and algebra

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### For younger learners

### Advanced mathematics

# Working Systematically - Lower Secondary

### Two and Two

### Summing Consecutive Numbers

### Isosceles Triangles

### American Billions

### M, M and M

### 1 Step 2 Step

### Can They Be Equal?

### Pick's Theorem

### Sticky Numbers

### Shady Symmetry

### Shifting Times Tables

### Peaches Today, Peaches Tomorrow...

### Charlie's Delightful Machine

### Nine Colours

### What's Possible?

### The Number Jumbler

### Consecutive Numbers

### The Remainders Game

### Missing Multipliers

### Fruity Totals

### 5 by 5 Mathdokus

### Number Daisy

### Cuboids

### Factors and Multiples Puzzle

### Going Round in Circles

### Overlaps

### Consecutive Seven

### Power Mad!

### How Many Miles to Go?

### Fence It

### Magic Letters

### Growing Surprises

### Days and Dates

### Farey Sequences

### Consecutive Negative Numbers

### Multiples Sudoku

### Gabriel's Problem

### Number Pyramids

### Stars

### Weights

### Keep it Simple

### Sociable Cards

### Can You Make 100?

### Counting Factors

### Where Can We Visit?

### Squares in Rectangles

### Alison's Quilt

### Triangles to Tetrahedra

### Add to 200

### Almost One

### Cinema Problem

### Elevenses

### How Steep Is the Slope?

### Forwards Add Backwards

### Funny Factorisation

### WipeoutLive

### What's it Worth?

### Shopping Basket

### Ben's Game

### Product Sudoku

### River Crossing

### Expenses

### Finding Factors

### Matchless

### Nutrition and Cycling

### Fair Shares?

### CD Heaven

### Difference Sudoku

### Partly Painted Cube

### Latin Numbers

### LCM Sudoku

### Surprising Transformations

### Which Is Cheaper?

### Painted Cube

### Warmsnug Double Glazing

### Training Schedule

### Symmetricality

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Age 7 to 16

Challenge Level

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Age 11 to 14

Challenge Level

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Age 11 to 14

Challenge Level

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Age 11 to 14

Challenge Level

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Age 11 to 14

Challenge Level

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Age 11 to 14

Challenge Level

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

Age 11 to 14

Challenge Level

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Age 14 to 16

Challenge Level

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Age 11 to 14

Challenge Level

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

Age 11 to 14

Challenge Level

How many different symmetrical shapes can you make by shading triangles or squares?

Age 11 to 14

Challenge Level

Can you find a way to identify times tables after they have been shifted up or down?

Age 11 to 14

Challenge Level

A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

Age 11 to 16

Challenge Level

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Age 11 to 16

Challenge Level

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Age 14 to 16

Challenge Level

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

Age 7 to 14

Challenge Level

The Number Jumbler can always work out your chosen symbol. Can you work out how?

Age 7 to 14

Challenge Level

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Age 7 to 14

Challenge Level

Play this game and see if you can figure out the computer's chosen number.

Age 7 to 14

Challenge Level

What is the smallest number of answers you need to reveal in order to work out the missing headers?

Age 7 to 16

Challenge Level

In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

Age 7 to 16

Challenge Level

Can you use the clues to complete these 5 by 5 Mathematical Sudokus?

Age 11 to 14

Challenge Level

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

Age 11 to 14

Challenge Level

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Age 11 to 14

Challenge Level

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

Age 11 to 14

Challenge Level

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

Age 11 to 14

Challenge Level

Can you find ways to put numbers in the overlaps so the rings have equal totals?

Age 11 to 14

Challenge Level

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

Age 11 to 14

Challenge Level

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Age 11 to 14

Challenge Level

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

Age 11 to 14

Challenge Level

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Age 11 to 14

Challenge Level

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

Age 11 to 14

Challenge Level

Can you find the connections between linear and quadratic patterns?

Age 11 to 14

Challenge Level

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Age 11 to 14

Challenge Level

There are lots of ideas to explore in these sequences of ordered fractions.

Age 11 to 14

Challenge Level

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Age 11 to 14

Challenge Level

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

Age 11 to 14

Challenge Level

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Age 11 to 14

Challenge Level

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Age 11 to 14

Challenge Level

Can you work out what step size to take to ensure you visit all the dots on the circle?

Age 11 to 14

Challenge Level

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Age 11 to 14

Challenge Level

Can all unit fractions be written as the sum of two unit fractions?

Age 11 to 14

Challenge Level

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

Age 11 to 14

Challenge Level

How many ways can you find to put in operation signs (+, −, ×, ÷) to make 100?

Age 11 to 14

Challenge Level

Is there an efficient way to work out how many factors a large number has?

Age 11 to 14

Challenge Level

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

Age 11 to 14

Challenge Level

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

Age 11 to 14

Challenge Level

Nine squares are fitted together to form a rectangle. Can you find its dimensions?

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

By selecting digits for an addition grid, what targets can you make?

Age 11 to 14

Challenge Level

Choose some fractions and add them together. Can you get close to 1?

Age 11 to 14

Challenge Level

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

Age 11 to 14

Challenge Level

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

Age 11 to 14

Challenge Level

On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

Age 11 to 14

Challenge Level

What happens when you add a three digit number to its reverse?

Age 11 to 16

Challenge Level

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

Age 11 to 16

Challenge Level

Can you do a little mathematical detective work to figure out which number has been wiped out?

Age 11 to 16

Challenge Level

There are lots of different methods to find out what the shapes are worth - how many can you find?

Age 11 to 16

Challenge Level

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Age 11 to 16

Challenge Level

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

Age 11 to 16

Challenge Level

The clues for this Sudoku are the product of the numbers in adjacent squares.

Age 11 to 18

Challenge Level

There is nothing half so much worth doing as simply messing about in boats...

Age 14 to 16

Challenge Level

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

Age 14 to 16

Challenge Level

Can you find the hidden factors which multiply together to produce each quadratic expression?

Age 14 to 16

Challenge Level

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

Age 14 to 16

Challenge Level

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

Age 14 to 16

Challenge Level

A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?

Age 14 to 16

Challenge Level

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at each price?

Age 14 to 16

Challenge Level

Use the differences to find the solution to this Sudoku.

Age 14 to 16

Challenge Level

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

Age 14 to 16

Challenge Level

Can you create a Latin Square from multiples of a six digit number?

Age 14 to 16

Challenge Level

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

Age 14 to 16

Challenge Level

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

Age 14 to 16

Challenge Level

When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?

Age 14 to 16

Challenge Level

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

Age 14 to 16

Challenge Level

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

Age 14 to 16

Challenge Level

The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?

Age 14 to 18

Challenge Level

Five equations and five unknowns. Is there an easy way to find the unknown values?