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Broad Topics > Sequences, Functions and Graphs > Graphs

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Mathsjam Jars

Stage: 4 Challenge Level: Challenge Level:1

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

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Exploring Quadratic Mappings

Stage: 4 Challenge Level: Challenge Level:1

Explore the relationship between quadratic functions and their graphs.

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Exploring Simple Mappings

Stage: 3 Challenge Level: Challenge Level:1

Explore the relationship between simple linear functions and their graphs.

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Surprising Transformations

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

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?

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Translating Lines

Stage: 3 Challenge Level: Challenge Level:1

Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.

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Reflecting Lines

Stage: 3 Challenge Level: Challenge Level:1

Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.

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Immersion

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Various solids are lowered into a beaker of water. How does the water level rise in each case?

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Maths Filler

Stage: 4 Challenge Level: Challenge Level:1

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

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Equation Matcher

Stage: 5 Challenge Level: Challenge Level:1

Can you match these equations to these graphs?

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Real-life Equations

Stage: 5 Challenge Level: Challenge Level:1

Here are several equations from real life. Can you work out which measurements are possible from each equation?

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Diamond Collector

Stage: 3 Challenge Level: Challenge Level:1

Collect as many diamonds as you can by drawing three straight lines.

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Matchless

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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 ?

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Perpendicular Lines

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

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

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Parallel Lines

Stage: 3 Challenge Level: Challenge Level:1

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?

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Spaces for Exploration

Stage: 3 and 4

Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.

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Steady Free Fall

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you adjust the curve so the bead drops with near constant vertical velocity?

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Up and Across

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

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

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Speeding Up, Slowing Down

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

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

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How Far Does it Move?

Stage: 3 Challenge Level: Challenge Level:1

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

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Exponential Trend

Stage: 5 Challenge Level: Challenge Level:1

Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.

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Fence It

Stage: 3 Challenge Level: Challenge Level:1

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

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Walk and Ride

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

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

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Cubics

Stage: 4 and 5 Challenge Level: Challenge Level:1

Knowing two of the equations find the equations of the 12 graphs of cubic functions making this pattern.

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Parabolas Again

Stage: 4 and 5 Challenge Level: Challenge Level:1

Here is a pattern composed of the graphs of 14 parabolas. Can you find their equations?

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Parabella

Stage: 5 Challenge Level: Challenge Level:1

This is a beautiful result involving a parabola and parallels.

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Parabolic Patterns

Stage: 4 and 5 Challenge Level: Challenge Level:1

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.

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How Many Solutions?

Stage: 5 Challenge Level: Challenge Level:1

Find all the solutions to the this equation.

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More Realistic Electric Kettle

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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Interpolating Polynomials

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.

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What's That Graph?

Stage: 4 Challenge Level: Challenge Level:1

Can you work out which processes are represented by the graphs?

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Electric Kettle

Stage: 4 Challenge Level: Challenge Level:1

Explore the relationship between resistance and temperature

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Which Is Bigger?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

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Which Is Cheaper?

Stage: 4 Challenge Level: Challenge Level:1

When I park my car in Mathstown, there are two car parks to choose from. Which car park should I use?

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Quadratic Transformations

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Explore the two quadratic functions and find out how their graphs are related.

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More Quadratic Transformations

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Here are some more quadratic functions to explore. How are their graphs related?

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Guess the Function

Stage: 5 Challenge Level: Challenge Level:1

This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.

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Steve's Mapping

Stage: 5 Challenge Level: Challenge Level:1

Steve has created two mappings. Can you figure out what they do? What questions do they prompt you to ask?

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Alison's Mapping

Stage: 4 Challenge Level: Challenge Level:1

Alison has created two mappings. Can you figure out what they do? What questions do they prompt you to ask?

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Charlie's Mapping

Stage: 3 Challenge Level: Challenge Level:1

Charlie has created a mapping. Can you figure out what it does? What questions does it prompt you to ask?

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Graphic Biology

Stage: 5 Challenge Level: Challenge Level:1

Several graphs of the sort occurring commonly in biology are given. How many processes can you map to each graph?

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Four on the Road

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Four vehicles travel along a road one afternoon. Can you make sense of the graphs showing their motion?

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Curve Match

Stage: 5 Challenge Level: Challenge Level:1

Which curve is which, and how would you plan a route to pass between them?

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Curve Fitter

Stage: 5 Challenge Level: Challenge Level:1

Can you fit a cubic equation to this graph?

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Maths Filler 2

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you draw the height-time chart as this complicated vessel fills with water?

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Bio Graphs

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

What biological growth processes can you fit to these graphs?

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Graphical Interpretation

Stage: 4 Challenge Level: Challenge Level:1

This set of resources for teachers offers interactive environments to support work on graphical interpretation at Key Stage 4.

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Motion Sensor

Stage: 4 Challenge Level: Challenge Level:1

Looking at the graph - when was the person moving fastest? Slowest?

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Take Your Dog for a Walk

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

Use the interactivity to move Mr Pearson and his dog. Can you move him so that the graph shows a curve?

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You Tell the Story

Stage: 2 Challenge Level: Challenge Level:1

Can you create a story that would describe the movement of the man shown on these graphs? Use the interactivity to try out our ideas.

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Golden Construction

Stage: 5 Challenge Level: Challenge Level:1

Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.


The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.