List

Working systematically - Lower Secondary

Fruity Totals
problem

Fruity totals

Age
7 to 16
Challenge level
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In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

The Number Jumbler
problem

The Number Jumbler

Age
7 to 14
Challenge level
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The Number Jumbler can always work out your chosen symbol. Can you work out how?

5 by 5 Mathdokus
problem

5 by 5 Mathdokus

Age
7 to 16
Challenge level
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Can you use the clues to complete these 5 by 5 Mathematical Sudokus?

Two and Two
problem

Two and two

Age
7 to 16
Challenge level
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How many solutions can you find to this sum? Each of the different letters stands for a different number.

The Remainders Game
game
Favourite

The remainders game

Age
7 to 14
Challenge level
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Play this game and see if you can figure out the computer's chosen number.

missing multipliers
problem

Missing multipliers

Age
7 to 14
Challenge level
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What is the smallest number of answers you need to reveal in order to work out the missing headers?
Consecutive Numbers
problem

Consecutive numbers

Age
7 to 14
Challenge level
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An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Dozens
problem

Dozens

Age
7 to 14
Challenge level
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Can you select the missing digit(s) to find the largest multiple?

Making a difference
problem

Making a difference

Age
11 to 14
Challenge level
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How many different differences can you make?
Isosceles Triangles
problem

Isosceles triangles

Age
11 to 14
Challenge level
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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?

Consecutive negative numbers
problem

Consecutive negative numbers

Age
11 to 14
Challenge level
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Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Charlie's delightful machine
problem

Charlie's delightful machine

Age
11 to 16
Challenge level
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Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Shady Symmetry
problem

Shady symmetry

Age
11 to 14
Challenge level
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How many different symmetrical shapes can you make by shading triangles or squares?
Cryptarithms
problem

Cryptarithms

Age
11 to 14
Challenge level
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Can you crack these cryptarithms?
Stars
problem

Stars

Age
11 to 14
Challenge level
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Can you work out what step size to take to ensure you visit all the dots on the circle?
Funny Factorisation
problem

Funny factorisation

Age
11 to 16
Challenge level
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Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
Sociable Cards
problem

Sociable cards

Age
11 to 14
Challenge level
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Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
How Many Miles To Go?
problem

How many miles to go?

Age
11 to 14
Challenge level
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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?
Add to 200
problem

Add to 200

Age
11 to 14
Challenge level
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By selecting digits for an addition grid, what targets can you make?
Triangles in circles
problem

Triangles in circles

Age
11 to 14
Challenge level
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Can you find triangles on a 9-point circle? Can you work out their angles?

Weights
problem

Weights

Age
11 to 14
Challenge level
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Different combinations of the weights available allow you to make different totals. Which totals can you make?
Where can we visit?
problem

Where can we visit?

Age
11 to 14
Challenge level
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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?
Which solids can we make?
problem

Which solids can we make?

Age
11 to 14
Challenge level
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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?

Farey Sequences
problem

Farey sequences

Age
11 to 14
Challenge level
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There are lots of ideas to explore in these sequences of ordered fractions.
Forwards Add Backwards
problem

Forwards add backwards

Age
11 to 14
Challenge level
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What happens when you add a three digit number to its reverse?
Right angles
problem

Right angles

Age
11 to 14
Challenge level
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Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

Parallelogram It
problem

Parallelogram it

Age
11 to 16
Challenge level
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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.

Nine Colours
problem

Nine colours

Age
11 to 16
Challenge level
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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?
Number Pyramids
problem

Number pyramids

Age
11 to 14
Challenge level
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Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Overlaps
problem

Overlaps

Age
11 to 14
Challenge level
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Can you find ways to put numbers in the overlaps so the rings have equal totals?
Shapely pairs
problem

Shapely pairs

Age
11 to 14
Challenge level
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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...

Rhombus It
problem

Rhombus it

Age
11 to 16
Challenge level
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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.

m, m and m
problem

M, M and M

Age
11 to 14
Challenge level
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If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

River Crossing
problem

River crossing

Age
11 to 18
Challenge level
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There is nothing half so much worth doing as simply messing about in boats...
How far does it move?
problem

How far does it move?

Age
11 to 14
Challenge level
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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.

Elevenses
problem

Elevenses

Age
11 to 14
Challenge level
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How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Opposite vertices
problem

Opposite vertices

Age
11 to 14
Challenge level
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Can you recreate squares and rhombuses if you are only given a side or a diagonal?

Tilted Squares
problem

Tilted squares

Age
11 to 14
Challenge level
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It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Guess \my Quad
problem

Guess my quad

Age
11 to 14
Challenge level
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How many questions do you need to identify my quadrilateral?

Speeding up, slowing down
problem

Speeding up, slowing down

Age
11 to 14
Challenge level
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Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its speed at each stage.

Can they be equal?
problem

Can they be equal?

Age
11 to 14
Challenge level
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Can you find rectangles where the value of the area is the same as the value of the perimeter?

Number Daisy
problem

Number daisy

Age
11 to 14
Challenge level
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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?
Peaches today, Peaches tomorrow...
problem

Peaches today, peaches tomorrow...

Age
11 to 14
Challenge level
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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?
Growing Surprises
problem

Growing surprises

Age
11 to 14
Challenge level
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Can you find the connections between linear and quadratic patterns?
Up and across
problem

Up and across

Age
11 to 14
Challenge level
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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.

Cuboid challenge
problem

Cuboid challenge

Age
11 to 16
Challenge level
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What's the largest volume of box you can make from a square of paper?

American Billions
problem

American billions

Age
11 to 14
Challenge level
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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...
Completing Quadrilaterals
problem

Completing quadrilaterals

Age
11 to 14
Challenge level
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We started drawing some quadrilaterals - can you complete them?

Semi-regular Tessellations
problem

Semi-regular tessellations

Age
11 to 16
Challenge level
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Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Days and Dates
problem

Days and dates

Age
11 to 14
Challenge level
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Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Power mad!
problem

Power mad!

Age
11 to 14
Challenge level
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Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Changing areas, changing perimeters
problem

Changing areas, changing perimeters

Age
11 to 14
Challenge level
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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?

Ben's Game
problem

Ben's game

Age
11 to 16
Challenge level
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Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
Squares in rectangles
problem

Squares in rectangles

Age
11 to 14
Challenge level
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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?
Multiples Sudoku
problem

Multiples Sudoku

Age
11 to 14
Challenge level
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Each clue in this Sudoku is the product of the two numbers in adjacent cells.

1 Step 2 Step
problem

1 step 2 step

Age
11 to 14
Challenge level
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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?
Changing areas, changing volumes
problem

Changing areas, changing volumes

Age
11 to 14
Challenge level
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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?

Cuboids
problem

Cuboids

Age
11 to 14
Challenge level
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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?

Counting Factors
problem

Counting factors

Age
11 to 14
Challenge level
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Is there an efficient way to work out how many factors a large number has?
Keep it simple
problem

Keep it simple

Age
11 to 14
Challenge level
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Can all unit fractions be written as the sum of two unit fractions?

What's it worth?
problem

What's it worth?

Age
11 to 16
Challenge level
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There are lots of different methods to find out what the shapes are worth - how many can you find?

On the Edge
problem

On the edge

Age
11 to 14
Challenge level
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If you move the tiles around, can you make squares with different coloured edges?

Gabriel's Problem
problem

Gabriel's problem

Age
11 to 14
Challenge level
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Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Product Sudoku
problem

Product Sudoku

Age
11 to 16
Challenge level
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The clues for this Sudoku are the product of the numbers in adjacent squares.

Summing Consecutive Numbers
problem

Summing consecutive numbers

Age
11 to 14
Challenge level
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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?

Shopping Basket
problem

Shopping basket

Age
11 to 16
Challenge level
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The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Magic Letters
problem

Magic letters

Age
11 to 14
Challenge level
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Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Square It
problem

Square it

Age
11 to 16
Challenge level
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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.

Can you Make 100?
problem

Can you make 100?

Age
11 to 14
Challenge level
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How many ways can you find to put in operation signs (+, −, ×, ÷) to make 100?
Factors and Multiples Puzzle
problem

Factors and multiples puzzle

Age
11 to 14
Challenge level
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Using your knowledge of the properties of numbers, can you fill all the squares on the board?
Sticky Numbers
problem

Sticky numbers

Age
11 to 14
Challenge level
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Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
Triangles to Tetrahedra
problem

Triangles to tetrahedra

Age
11 to 14
Challenge level
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Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Hidden Squares
problem

Hidden squares

Age
11 to 14
Challenge level
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Can you find the squares hidden on these coordinate grids?

Sending a Parcel
problem

Sending a parcel

Age
11 to 14
Challenge level
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What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

Alison's quilt
problem

Alison's quilt

Age
11 to 14
Challenge level
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Nine squares are fitted together to form a rectangle. Can you find its dimensions?
How steep is the slope?
problem

How steep is the slope?

Age
11 to 14
Challenge level
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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?

Reflecting Squarely
problem

Reflecting squarely

Age
11 to 14
Challenge level
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In how many ways can you fit all three pieces together to make shapes with line symmetry?

Perimeter Possibilities
problem

Perimeter possibilities

Age
11 to 14
Challenge level
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I'm thinking of a rectangle with an area of 24. What could its perimeter be?

Consecutive Seven
problem

Consecutive seven

Age
11 to 14
Challenge level
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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?
Almost One
problem

Almost one

Age
11 to 14
Challenge level
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Choose some fractions and add them together. Can you get close to 1?
Going round in circles
problem

Going round in circles

Age
11 to 14
Challenge level
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Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
Cinema Problem
problem

Cinema problem

Age
11 to 14
Challenge level
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A cinema has 100 seats. How can ticket sales make £100 for these different combinations of ticket prices?

Wipeout
problem

Wipeout

Age
11 to 16
Challenge level
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Can you do a little mathematical detective work to figure out which number has been wiped out?
Fence it
problem

Fence it

Age
11 to 14
Challenge level
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If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Pocket money
problem

Pocket money

Age
11 to 14
Challenge level
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Which of these pocket money systems would you rather have?
Shifting Times Tables
problem

Shifting times tables

Age
11 to 14
Challenge level
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Can you find a way to identify times tables after they have been shifted up or down?

Pick's Theorem
problem

Pick's theorem

Age
14 to 16
Challenge level
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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.
Fair Shares?
problem

Fair shares?

Age
14 to 16
Challenge level
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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?
Partly Painted Cube
problem

Partly painted cube

Age
14 to 16
Challenge level
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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?
Funnel
problem

Funnel

Age
14 to 16
Challenge level
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A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?

What's Possible?
problem

What's possible?

Age
14 to 16
Challenge level
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Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
LCM Sudoku
problem

LCM Sudoku

Age
14 to 16
Challenge level
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Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

Which is cheaper?
problem

Which is cheaper?

Age
14 to 16
Challenge level
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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?
Parabolic Patterns
problem

Parabolic patterns

Age
14 to 18
Challenge level
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The illustration shows the graphs of fifteen functions. Two of them have equations $y=x^2$ and $y=-(x-4)^2$. Find the equations of all the other graphs.

Training schedule
problem

Training schedule

Age
14 to 16
Challenge level
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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?
Squirty
problem

Squirty

Age
14 to 16
Challenge level
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Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.

Finding factors
problem

Finding factors

Age
14 to 16
Challenge level
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Can you find the hidden factors which multiply together to produce each quadratic expression?

Painted Cube
problem

Painted cube

Age
14 to 16
Challenge level
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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?
CD Heaven
problem

CD Heaven

Age
14 to 16
Challenge level
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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?