Working systematically - Lower Secondary

problem

Dozens

Age

7 to 14

Challenge level

Can you select the missing digit(s) to find the largest multiple?

problem

Missing multipliers

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?

game

Favourite

The remainders game

Age

7 to 14

Challenge level

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

problem

Consecutive numbers

Age

7 to 14

Challenge level

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

problem

Two and two

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.

problem

Fruity totals

Age

7 to 16

Challenge level

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

problem

The Number Jumbler

Age

7 to 14

Challenge level

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

problem

5 by 5 Mathdokus

Age

7 to 16

Challenge level

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

problem

What's it worth?

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?

problem

On the edge

Age

11 to 14

Challenge level

If you move the tiles around, can you make squares with different coloured edges?

problem

Overlaps

Age

11 to 14

Challenge level

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

problem

Squares in rectangles

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?

problem

Parallelogram it

Age

11 to 16

Challenge level

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a parallelogram.

problem

Cuboid challenge

Age

11 to 16

Challenge level

What's the largest volume of box you can make from a square of paper?

problem

Shopping basket

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?

problem

Opposite vertices

Age

11 to 14

Challenge level

Can you recreate squares and rhombuses if you are only given a side or a diagonal?

problem

Square it

Age

11 to 16

Challenge level

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

problem

Perimeter challenge

Age

11 to 14

Challenge level

Can you deduce the perimeters of the shapes from the information given?

problem

Rhombus it

Age

11 to 16

Challenge level

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.

problem

Power mad!

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.

problem

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?

problem

Sending a parcel

Age

11 to 14

Challenge level

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

problem

River crossing

Age

11 to 18

Challenge level

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

problem

Product Sudoku

Age

11 to 16

Challenge level

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

problem

Multiples Sudoku

Age

11 to 14

Challenge level

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

problem

Reflecting squarely

Age

11 to 14

Challenge level

In how many ways can you fit all three pieces together to make shapes with line symmetry?

$Guess \my Quad$

problem

Guess my quad

Age

11 to 14

Challenge level

How many questions do you need to identify my quadrilateral?

problem

Factors and multiples puzzle

Age

11 to 14

Challenge level

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

problem

Keep it simple

Age

11 to 14

Challenge level

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

problem

Cinema problem

Age

11 to 14

Challenge level

A cinema has 100 seats. How can ticket sales make £100 for these different combinations of ticket prices?

problem

Changing areas, changing perimeters

Age

11 to 14

Challenge level

How can you change the area of a shape but keep its perimeter the same? How can you change the perimeter but keep the area the same?

problem

Consecutive seven

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?

problem

Growing surprises

Age

11 to 14

Challenge level

Can you find the connections between linear and quadratic patterns?

problem

Sticky numbers

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?

problem

Changing areas, changing volumes

Age

11 to 14

Challenge level

How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?

problem

Fence it

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?

problem

Completing quadrilaterals

Age

11 to 14

Challenge level

We started drawing some quadrilaterals - can you complete them?

problem

Funny factorisation

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?

problem

Shady symmetry

Age

11 to 14

Challenge level

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

problem

Efficient cutting

Age

11 to 14

Challenge level

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

problem

How steep is the slope?

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?

problem

How many miles to go?

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?

problem

Magic letters

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?

problem

Isosceles triangles

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?

problem

An equilateral triangular problem

Age

11 to 14

Challenge level

Take an equilateral triangle and cut it into smaller pieces. What can you do with them?

problem

Where can we visit?

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?

problem

Going round in circles

Age

11 to 14

Challenge level

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

problem

Farey sequences

Age

11 to 14

Challenge level

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

problem

Hidden squares

Age

11 to 14

Challenge level

Can you find the squares hidden on these coordinate grids?

problem

Stars

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?

problem

Gabriel's problem

Age

11 to 14

Challenge level

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

problem

Consecutive negative numbers

Age

11 to 14

Challenge level

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

problem

Nine colours

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?

problem

Shifting times tables

Age

11 to 14

Challenge level

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

problem

Number pyramids

Age

11 to 14

Challenge level

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

problem

Perimeter possibilities

Age

11 to 14

Challenge level

I'm thinking of a rectangle with an area of 24. What could its perimeter be?

problem

Triangles in circles

Age

11 to 14

Challenge level

Can you find triangles on a 9-point circle? Can you work out their angles?

problem

Can you make 100?

Age

11 to 14

Challenge level

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

problem

Cola can

Age

11 to 14

Challenge level

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

problem

Wipeout

Age

11 to 16

Challenge level

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

problem

Right angles

Age

11 to 14

Challenge level

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

problem

Alison's quilt

Age

11 to 14

Challenge level

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

problem

Days and dates

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...

problem

Growing rectangles

Age

11 to 14

Challenge level

What happens to the area and volume of 2D and 3D shapes when you enlarge them?

problem

Tilted squares

Age

11 to 14

Challenge level

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

problem

Making a difference

Age

11 to 14

Challenge level

How many different differences can you make?

problem

Shapely pairs

Age

11 to 14

Challenge level

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

problem

Almost one

Age

11 to 14

Challenge level

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

problem

Weights

Age

11 to 14

Challenge level

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

problem

Number daisy

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?

problem

Charlie's delightful machine

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?

problem

Peaches today, peaches tomorrow...

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?

problem

Triangles in a square

Age

11 to 14

Challenge level

What are the possible areas of triangles drawn in a square?

problem

How far does it move?

Age

11 to 14

Challenge level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects the distance it travels at each stage.

problem

Pocket money

Age

11 to 14

Challenge level

Which of these pocket money systems would you rather have?

problem

American billions

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...

problem

Sociable cards

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?

problem

Cryptarithms

Age

11 to 14

Challenge level

Can you crack these cryptarithms?

problem

Speeding up, slowing down

Age

11 to 14

Challenge level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its speed at each stage.

problem

Counting factors

Age

11 to 14

Challenge level

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

problem

M, M and M

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?

problem

Which solids can we make?

Age

11 to 14

Challenge level

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

problem

Ben's game

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?

problem

Add to 200

Age

11 to 14

Challenge level

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

problem

Up and across

Age

11 to 14

Challenge level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

problem

Summing consecutive numbers

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?

problem

Elevenses

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?

problem

1 step 2 step

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?

problem

Cuboids

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?

problem

Forwards add backwards

Age

11 to 14

Challenge level

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

problem

Semi-regular tessellations

Age

11 to 16

Challenge level

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

problem

Can they be equal?

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?

problem

Training schedule

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?