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U in a Pentagon

Age 11 to 14 Short Challenge Level:

Weekly Problem 18 - 2008
The diagram shows a regular pentagon. Can you work out the size of the marked angle?

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UKMT 2007

Content for UKMT 2007

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UKMT 2008

Resources to support UKMT 2008 Teacher Meeting presentations

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UKMT 2012 Teacher Meetings

Resources to accompany NRICH team presentations at UKMT 2012 Teacher Meetings.

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UKMT 2013 Teacher Meetings

Resources to accompany NRICH team presentations at UKMT 2013 Teacher Meetings.

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UKMT 2014 Teacher Meetings

Resources to accompany NRICH team presentations at UKMT 2014 Teacher Meetings.

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UKMT 2015 Teacher Meetings

Age 11 to 18

Resources to accompany NRICH team presentations at UKMT 2015 Teacher Meetings.

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UKMT 2016 Teacher Meetings

Resources to accompany NRICH team presentations at UKMT 2016 Teacher Meetings.

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Uncanny Triangles

Age 7 to 11 Challenge Level:

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

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Under the Ribbon

Age 14 to 16 Challenge Level:

A ribbon is nailed down with a small amount of slack. What is the largest cube that can pass under the ribbon ?

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Underground Mathematics

Age 16 to 18 Challenge Level:

Check out the new Underground Maths website

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Underground Mathematics

Age 16 to 18 Challenge Level:

Check out the new Underground Maths website

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Understanding Hypotheses

Age 14 to 18

This article explores the process of making and testing hypotheses.

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Understanding Information

Deepen your understanding of different types of information with these challenges.

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Understanding Information

Age 7 to 11

Deepen your understanding of different types of information with these upper primary challenges.

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Understanding Information

Age 5 to 7

These lower primary challenges focus on different types of information.

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Understanding Inverse Relationships

Age 11 to 18 Challenge Level:

The problems in this feature encourage students to consider inverses and working backwards to solve problems.

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Unequal Averages

Age 11 to 14 Challenge Level:

Play around with sets of five numbers and see what you can discover about different types of average...

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Unexpected Ordering

Age 5 to 7 Challenge Level:

Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?

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Uniform Sum?

Age 16 to 18 Challenge Level:

Is the sum or difference of two uniform random variables uniform?

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Uniform Units

Age 14 to 16 Challenge Level:

Can you choose your units so that a cube has the same numerical value for it volume, surface area and total edge length?

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Uniformly Unstable

Age 16 to 18 Challenge Level:

Invent shapes with different numbers of stable and unstable equilibrium points

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Unit Differences

Age 5 to 7 Challenge Level:

This challenge is about finding the difference between numbers which have the same tens digit.

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Unit Fractions

Age 11 to 14 Challenge Level:

Consider the equation 1/a + 1/b + 1/c = 1 where a, b and c are natural numbers and 0 < a < b < c. Prove that there is only one set of values which satisfy this equation.

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Unit Interval

Age 16 to 18 Short Challenge Level:

Can you prove our inequality holds for all values of x and y between 0 and 1?

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Unit Interval

Age 14 to 18 Challenge Level:

Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?

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Units

The Units collection of STEM resources

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Universal Time, Mass, Length

Age 16 to 18 Short Challenge Level:

Can you work out the natural time scale for the universe?

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Unlocking the Case

Age 7 to 11 Challenge Level:

A case is found with a combination lock. There is one clue about the number needed to open the case. Can you find the number and open the case?

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Unusual Long Division - Square Roots Before Calculators

Age 14 to 16 Challenge Level:

However did we manage before calculators? Is there an efficient way to do a square root if you have to do the work yourself?

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Unusual Polygon

Age 14 to 16 Short Challenge Level:

What is the perimeter of this unusually shaped polygon...

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Unusual Quadrilateral

Age 14 to 16 Short Challenge Level:

This quadrilateral has an unusual shape. Are you able to find its area?

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Up a Semitone?

Age 16 to 18 Challenge Level:

Fifth challenge cipher

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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 red dot affects its vertical and horizontal movement at each stage.

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Up and Down

Age 5 to 7 Challenge Level:

Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?

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Up and Down Donkey

Age 5 to 11 Challenge Level:

A number card game for 2-6 players.

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Up and Down Staircases

Age 7 to 11 Challenge Level:

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

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Up or Down?

Age 11 to 14 Challenge Level:

How high can you reach?

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Up, Down, Flying Around

Age 11 to 14 Challenge Level:

Play this game to learn about adding and subtracting positive and negative numbers

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Upper Primary Flash Interactives

Age 7 to 11

Flash interactives for upper primary.

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Upper Primary Games Using Counters

Age 7 to 11

Here are some games which use counters.

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Upper Primary Group-worthy Tasks

Age 7 to 11

Although almost any NRICH activity could be tackled in a group, these upper primary activities have been created specifically with group work in mind.

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Upper Primary Non-flash Interactives

Age 7 to 11

Non-Flash interactives for upper primary.

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Upper Primary Working Systematically KS2

Age 7 to 11 Challenge Level:

Activities for upper primary children which focus on working systematically.

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Upper Secondary - Complete Article Index

Age 14 to 18

The archive of our upper secondary student articles.

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Upper Secondary Latest

Latest content for Upper Secondary

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Upsetting Pitagoras

Age 14 to 18 Challenge Level:

Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2

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Useful Graphing Tools

A collection of useful graphing resources to support work on NRICH problems.

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Using Books: Maisy Goes Camping

Age 3 to 5

Read the book 'Maisy Goes Camping' by Lucy Cousins. Act out the story with some toys - is there room for one more in the tent? How many characters are in the tent now?

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Using Books: the Doorbell Rang

Age 3 to 5

Read the book 'The Doorbell Rang' by Pat Hutchins. Have a go at sharing out some cookies like the characters in the story!