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#### Resources tagged with Investigations similar to NRICH Starter Problem Selection:

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### There are 61 results

Broad Topics > Using, Applying and Reasoning about Mathematics > Investigations

### Few and Far Between?

##### Stage: 4 and 5 Challenge Level:

Can you find some Pythagorean Triples where the two smaller numbers differ by 1?

### 9 Hole Light Golf

##### Stage: 1, 2, 3, 4 and 5 Challenge Level:

We think this 3x3 version of the game is often harder than the 5x5 version. Do you agree? If so, why do you think that might be?

### Bent Out of Shape

##### Stage: 4 and 5 Challenge Level:

An introduction to bond angle geometry.

### Mach Attack

##### Stage: 5 Challenge Level:

Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.

### Operating Machines

##### Stage: 5 Challenge Level:

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

### Sextet

##### Stage: 5 Challenge Level:

Investigate x to the power n plus 1 over x to the power n when x plus 1 over x equals 1.

### Witch's Hat

##### Stage: 3 and 4 Challenge Level:

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

### Take Ten Sticks

##### Stage: 3 and 4 Challenge Level:

Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?

### Reaction Rates!

##### Stage: 5

Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...

### Number Chains

##### Stage: 5 Challenge Level:

Find all the periodic cycles and fixed points in this number sequence using any whole number as a starting point.

### Odd Stones

##### Stage: 4 Challenge Level:

On a "move" a stone is removed from two of the circles and placed in the third circle. Here are five of the ways that 27 stones could be distributed.

### What Salt?

##### Stage: 5 Challenge Level:

Can you deduce why common salt isn't NaCl_2?

### The Power of Dimensional Analysis

##### Stage: 4 and 5

An introduction to a useful tool to check the validity of an equation.

### Diamonds Aren't Forever

##### Stage: 5 Challenge Level:

Ever wondered what it would be like to vaporise a diamond? Find out inside...

### Modelling Assumptions in Mechanics

##### Stage: 5

An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.

### Carbon Footprints

##### Stage: 4 Challenge Level:

Is it really greener to go on the bus, or to buy local?

### Stirling Work

##### Stage: 5 Challenge Level:

See how enormously large quantities can cancel out to give a good approximation to the factorial function.

### CSI: Chemical Scene Investigation

##### Stage: 5 Challenge Level:

There has been a murder on the Stevenson estate. Use your analytical chemistry skills to assess the crime scene and identify the cause of death...

### Big and Small Numbers in Physics

##### Stage: 4 Challenge Level:

Work out the numerical values for these physical quantities.

### Smoke and Daggers

##### Stage: 5 Challenge Level:

We all know that smoking poses a long term health risk and has the potential to cause cancer. But what actually happens when you light up a cigarette, place it to your mouth, take a tidal breath. . . .

### Electromagnetism

##### Stage: 5

Read all about electromagnetism in our interactive article.

### Big and Small Numbers in Chemistry

##### Stage: 4 Challenge Level:

Get some practice using big and small numbers in chemistry.

### Alternative Record Book

##### Stage: 4 and 5 Challenge Level:

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

### Robot Camera

##### Stage: 4 Challenge Level:

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

### A Rational Search

##### Stage: 4 and 5 Challenge Level:

Investigate constructible images which contain rational areas.

### Designing Table Mats

##### Stage: 3 and 4 Challenge Level:

Formulate and investigate a simple mathematical model for the design of a table mat.

### Track Design

##### Stage: 4 Challenge Level:

Where should runners start the 200m race so that they have all run the same distance by the finish?

### Big and Small Numbers in the Physical World

##### Stage: 4 Challenge Level:

Work with numbers big and small to estimate and calculate various quantities in physical contexts.

### Genetic Intrigue

##### Stage: 5

Dip your toe into the fascinating topic of genetics. From Mendel's theories to some cutting edge experimental techniques, this article gives an insight into some of the processes underlying. . . .

##### Stage: 5

Read about the mathematics behind the measuring devices used in quantitative chemistry

### Perfect Eclipse

##### Stage: 4 Challenge Level:

Use trigonometry to determine whether solar eclipses on earth can be perfect.

### Big and Small Numbers in the Living World

##### Stage: 3 and 4 Challenge Level:

Work with numbers big and small to estimate and calculate various quantities in biological contexts.

### Clear as Crystal

##### Stage: 5 Challenge Level:

Unearth the beautiful mathematics of symmetry whilst investigating the properties of crystal lattices

### Escape from Planet Earth

##### Stage: 5 Challenge Level:

How fast would you have to throw a ball upwards so that it would never land?

### Spokes

##### Stage: 5 Challenge Level:

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.

### Peeling the Apple or the Cone That Lost Its Head

##### Stage: 4 Challenge Level:

How much peel does an apple have?

### Problem Solving: Opening up Problems

##### Stage: 1, 2, 3 and 4

All types of mathematical problems serve a useful purpose in mathematics teaching, but different types of problem will achieve different learning objectives. In generalmore open-ended problems have. . . .

### The Invertible Trefoil

##### Stage: 4 Challenge Level:

When is a knot invertible ?

### A Different Differential Equation

##### Stage: 5 Challenge Level:

Explore the properties of this different sort of differential equation.

### Twizzles Venture Forth

##### Stage: 4 Challenge Level:

Where we follow twizzles to places that no number has been before.

### Geometry and Gravity 1

##### Stage: 3, 4 and 5

This article (the first of two) contains ideas for investigations. Space-time, the curvature of space and topology are introduced with some fascinating problems to explore.

### Eight Ratios

##### Stage: 4 Challenge Level:

Two perpendicular lines lie across each other and the end points are joined to form a quadrilateral. Eight ratios are defined, three are given but five need to be found.

### Snookered

##### Stage: 4 and 5 Challenge Level:

In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?

### Two Regular Polygons

##### Stage: 4 Challenge Level:

Two polygons fit together so that the exterior angle at each end of their shared side is 81 degrees. If both shapes now have to be regular could the angle still be 81 degrees?

### Spiroflowers

##### Stage: 5 Challenge Level:

Analyse these repeating patterns. Decide on the conditions for a periodic pattern to occur and when the pattern extends to infinity.

### There's Always One Isn't There

##### Stage: 4 Challenge Level:

Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.

### Chance of That

##### Stage: 4 and 5 Challenge Level:

What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?

##### Stage: 4 and 5 Challenge Level:

Some of our more advanced investigations

### Taking Trigonometry Series-ly

##### Stage: 5 Challenge Level:

Look at the advanced way of viewing sin and cos through their power series.

### Scale Invariance

##### Stage: 5 Challenge Level:

By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.