# There are 366 different Starters of The Day, many to choose from. You will find below some starters on the topic of Investigations. A lesson starter does not have to be on the same topic as the main part of the lesson or the topic of the previous lesson. It is often very useful to revise or explore other concepts by using a starter based on a totally different area of Mathematics.

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### Investigations Starters: Work out the number of stamps needed to post a parcel. How many different ways can four people stand in line? Questions about the Small LEDs used to make up the digits on a calculator display. Use the flowchart to generate a sequence of numbers. Which number will reach 1 the fastest? A clock face containing only the number 4. Can you make a clock face containing any other single number? If all the students in this room shook hands with each other, how many handshakes would there be altogether? To find out whether a number is happy or not, square each of its digits, add the answers and repeat. If you end up with 1 the number is happy! How many other happy numbers can you find? A puzzle about the lifts in a hotel which serve floors based on the day of the week. Add together the dates of all the Thursdays in May this year. Which day sum is largest? Which numbers when multiplied by the number of letters in the word(s) of the number give square numbers? Arrange the numbers 1-9 to make three 3 digit numbers that add up to 999. Investigate three fractions which add together to give one fifth. Investigate three fractions which add together to give one ninth. Find other numbers that can be changed to 1 on a calculator using only the 4 key and any operation. A number puzzle suitable for children with a wide range of abilities. Calculate the areas of all the possible quadrilaterals that can be constructed by joining together dots on this grid. Arrange the numbers on the grid of squares so that the totals along each line of three squares are equal. Place the numbers on the triangle so that the totals along each of the sides are equal. Find calculations which written back to front give the same answer.

## Exercises #### Area Builder

An interactive workspace in which to make shapes using square tiles with given areas and perimeters. #### Area Two

How many different shapes with an area of 2 square units can you make by joining dots on this grid with straight lines? #### Aunt Lucy's Legacy

Decide which of the four schemes Aunt Lucy proposes will provide the most money. This investigation involves the sum of sequences as well as considering life expectancy. #### Aunt Sophie's Post Office

Investigate the ways of making up various postage amounts using 3p and 8p stamps. An online stamp calculator is provided for you to check your working. #### Beginning with One

Is it true that most numbers begin with the digit one? Think of numbers you see everyday and it is a surprising fact that so many of them begin with a one. Can you think why this is true? #### Braille

Investigate the possibility of redesigning the Braille alphabet to make it easier to learn. #### Calendar Maths Investigation

Investigate the connection between the numbers in a T shape drawn on this month's calendar. #### Cosmic Redshift

Investigate the number found by performing an algorithm on a three digit number. #### Crossing the River

Two men and two boys want to cross a river and they only have one canoe which will only hold one man or two boys. #### Decimal Products

Find two decimal numbers that add up to exactly one. What is the product of these two decimals? How many different badges can you make using three different coloured squares put together to make a rectangle? #### Dice Investigation

Throw two dice and multiply the scores. Investigate the different products you can obtain. What about adding? What about using three dice? #### Digit Sums and Multiples

Investigate numbers which are multiples of the sum of their digits. #### Digital Lights

Investigate the way small LEDs were used to make up the digits on a calculator display. #### Egg Box Investigation

In how many different ways can two eggs be arranged in an egg box? #### First Impressions

This activity will collect data about your first impressions of some optical illusions. You can then analyse the data to come to your own conclusions. #### Football Scores

If you know the final score of a football match, what might the half time score have been? #### Four Ever

Generate a number sequence based on the number of letters needed to spell the previous number. #### Frustration

A logic challenge requiring a strategy to update each of the numbers in a grid. #### Function Builder

An interactive function machine for patterns, numbers and equations. #### Graph Plotter

An online tool to draw, display and investigate graphs of many different kinds. #### Green Fingers

Choose the amount of liquid from each bottle needed to make the watermelon grow as big as possible. #### Halving

An open-ended investigation challenging pupils to find many different ways to you cut the shape in half. #### Handshakes

If everyone in this room shook hands with each other, how many handshakes would there be? #### Happy Numbers

To find out whether a number is happy square each of its digits, add the answers and repeat. End in one and the number is happy. #### Have you got change?

An investigation about making change for different amounts. #### House Painting

The houses in Mathsland are all three storeys tall. Each storey is painted using one colour. How many ways can the houses be painted? #### How Many Sides?

How many different polygons can you make on a 3 by 3 pin board? What about larger pin boards? #### Hula Hoops

If a number of Hula Hoops are dropped on the floor, what is the maximum number of regions they might form? #### Jugs

Can you make 4 litres if you only have 7 and 5 litre jugs? #### Lamp Posts

What is the greatest number of lamp posts that would be needed for a strange village with only straight roads? #### Largest Product

A drag and drop activity challenging you to arrange the digits to produce the largest possible product. #### Leapfrog

An investigation of the fewest number of moves required to make the blue and green frogs swap places. #### lnvestigating stamps

How many different postage amounts can you make with the given stamps? Investigate this amazing mind reading performance based on simple mathematical principles. #### Maxvoltray

Find the maximum volume of a tray made from an A4 sheet of paper. A practical mathematical investigation. #### Mystic Rose

Investigate the properties of the Mystic Rose by using this interactive diagram. #### Number Stairs

Find the relationships between the numbers on different size grids. #### Odd Dice

Take three dice. How many ways can they be turned so that they show only odd numbers on top? #### Palandromic numbers

How many steps does each number take to become palandromic? #### Pin Board

Rows and columns of dots that can be joined using straight lines to create shapes. #### Polygon Areas

Investigate polygons with an area of 4 sq. units. Investigate polygons with other areas. #### Prison Cell Problem

A number patterns investigation involving prisoners and prison guards. #### Reaction Time

When the numbers appear hit the correct button depending on whether the numbers are even or odd #### Rectangle Perimeters

The perimeter of a rectangle is 28cm. What could its area be? #### River Crossing

The traditional River Crossing challenge. Can you do it in the smallest number of moves? #### Rod Triangles

Using 12 rods of varying lengths how many different triangles can you make? #### Six Keys

Use just six keys on your calculator to make a given total. How many different ways can it be done? #### Snooker Investigation

Investigate a special snooker table with only four pockets. Which hole will the snooker ball fall into for various sized snooker tables? #### Songkran Game

Where should you stand in the circle to win the Songkran game? #### Steps

Investigate the numbers associated with this growing sequence of steps made from Multilink cubes. #### Take Baht

How many different ways can you make a given total with Thai coins? #### Tantrum

A game, a puzzle and a challenge involving counters being placed at the corners of a square on a grid. #### Tetrominoes

A tetromino is a shape made of four squares joined edge to edge. How many different tetrominoes are there? #### The Four Rules

See if you can make all of the numbers from 0 to 10 using four threes #### Traffic Jams

How many ways can three cars be lined up in a traffic jam? #### Transum Club

How many different colour schemes can you devise for the Transum Club Badge. #### Trapezia

Which numbers can be represented by groups of circles arranged in the shape of a trapezium? #### Trilett

A strategy game requiring you to select three words with a common letter before the computer does.

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