Probability measures the chance of something happening. Each different result is known as an outcome.

In this lesson we are looking at probability with rolling dice. We will figure out the probabilities of different outcomes that can occur when rolling a dice.

The list of all possible different outcomes is known as the sample space.

The sample space for rolling a dice is shown below.

The sample space for a dice is 1, 2, 3, 4, 5, 6.

A dice contains six sides, which each have an equal chance of occurring when the dice is rolled.

In the example below we are asked, “What is the probability of rolling a 1?”.

We know that there are 6 possible outcomes in total:

1, 2, 3, 4, 5 or 6

There is only one face of the dice with a ‘1’ on it.

The probability of rolling a one is   ¹ / ₆  .

There is only one face out of six faces that have a ‘1’ on it.

Here is another example.

“What is the probability of rolling a 3 on a dice?”

There is only one face that has a ‘3’.

1 out of 6 sides of the dice contain a ‘3’.

The probability of rolling a 3 is   ¹ / ₆  .

We can see that the probability of rolling any single number from 1 to 6 on a dice is   ¹ / ₆  .

In the example below we are asked, “What is the probability of rolling a 2 or a 5?”.

Looking at our dice sample space, we still have 6 total outcomes: 1, 2, 3, 4, 5 or 6.

We can see that ‘2’ and ‘5’ are two of these faces on the dice.

The probability of rolling a 2 or a 5 is   ² / ₆.

Two of the six faces are outcomes that we want.

In our sample space list we can see this:

1, 2, 3, 4, 5, 6

  ² / ₆   can be simplified to ¹ / ₃  by halving both the numerator and denominator of the fraction.

This means that on average, a 2 or 5 will appear on a dice every three times that the dice is rolled.

Here is another example of dice probability.

“What is the probability of rolling a number greater than 4?”.

The numbers greater than 4 are: ‘5’ and ‘6’.

This is 2 out of 6 possible outcomes and so the probability is   ² / ₆   .

Again this probability can be simplified to   ¹ / ₃ .  

It is important to be careful not to include the number ‘4 in this example.

4 is not greater than 4 and so, we do not include it.

‘5’ and ‘6’ are the only numbers on a dice that are greater than 4.

Here is another example.

“What is the probability of rolling a 3 or less?”.

In this example, we have the number 3 or the numbers less than 3.

So we have ‘3’ and the numbers ‘2’ and ‘1’.

This is different from the previous example because we are allowed to include 3 and the numbers below it.

The word or gives this away.

This is 3 out of the six possible outcomes.

On our sample space list we can see this as:

1, 2, 3, 4, 5, 6

The probability of rolling a 3 or less on a dice is   ³ / ₆.

3 is half of 6 and so   ³ / ₆ can be simplified to   ¹ / ₂.

When rolling a dice we can expect to roll a ‘3 or less’ half of the time.

In the example below we are asked, “What is the probability of rolling an odd number?”.

The odd numbers on a dice are: 1, 3 and 5

This is 3 out of the 6 numbers.

The probability is   ³ / ₆ .

This probability can be simplified to   ¹ / ₂.

Half of the numbers on a regular die are odd.

The opposite of rolling an odd number is to roll an even number.

There are 3 out of 6 outcomes on a dice that are even: 2, 4 and 6.

And so, the probability of rolling an even number on a dice is   ³ / ₆ .

We could have figured this probability out using out last example.

If   ³ / ₆ numbers on the dice are odd, then the remaining numbers are even.

³ / ₆ and   ³ / ₆ add to make   ⁶ / ₆, which is all 6 faces of our dice.

When we roll our dice, we expect an odd number half of the time and an even number the other half of the time.

In this lesson, we will look at placing missing decimals on a number line when counting in fifths.

One fifth as a decimal is 0.2

One fifth is double the size of one tenth.

One tenth is 0.1 and so, one fifth is 0.2, which is double the size of 0.1.

In the animation below, we have a number line ranging from zero to one.

To get from zero to one, there are ten steps. This means that we will be counting up in tenths, or 0.1s.

The first line on the scale corresponds to an increment of 0.1, which is the same as one tenth.

The second line is 0.2, which is two tenths.

The third line is 0.3, which is three tenths.

The fourth line is 0.4, which is four tenths.

The fifth line is 0.5, which is five tenths. This thicker line indicates that it is the halfway point between 0 and 1.

The sixth line is 0.6, which is six tenths.

The seventh line is 0.7, which is seven tenths.

The eighth line is 0.8, which is eight tenths.

The ninth line is 0.9, which is nine tenths.

The tenth line is 1, which is the same as ten tenths, or one whole.

We know that 5 lots of 0.2 makes a whole, or 1.

In the animation below, we have a scale ranging from zero to one. However, this time, to get from zero to one, we have five steps.

The scale is divided into five parts, or fifths. This means that we will be counting up in fifths, or 0.2s.

This is because, instead of taking ten steps, we are taking five steps. So, we need to cover twice the distance in each step. Therefore, instead of counting in 0.1s, we need to count in 0.2s.

The first mark on the scale is 0.2, which is the same as one fifth.

The second mark is 0.4, which is two fifths.

The third mark is 0.6, which is three fifths.

The fourth mark is 0.8, which is four fifths.

The fifth mark is 1, which is the same as five fifths, or one whole.

Below, we have a scale ranging from one to two and from two to three.

To get from one to two, there are five steps and to get from two to three there are five steps.

We are asked to label the values on the number line that are indicated by the arrows.

Because there are five steps from one to two and from two to three, we are counting in fifths, or 0.2s.

So, we can begin by counting up from one. We have 1.2, 1.4 and 1.6, which is our first answer.

Next, we can count on from two. We have 2.2 and 2.4, which is our second answer.

In the following example, the scale ranges from 25 to 27.

The thicker line in the centre is the halfway point. The number that is halfway between 25 and 27 is 26.

To get from 25 to 26, there are five steps. So, we are counting in 0.2s.

Starting from 25, we have 25.2 and 25.4, which is our first answer.

Starting from 26, we have 26.2, 26.4, 26.6 and 26.8, which is our second answer.

We could have also found the second answer by counting back in 0.2s from 27.

On the scale below, we are given the numbers 15.6, 15.8 and 16.

To get from 15.6 to 15.8 and from 15.8 to 16, we add 0.2. This tells us that we are counting in 0.2s.

We can begin by counting back from 15.6. we have 15.4 and 15.2, which is our first answer.

Continuing, we have 15, 14.8 and 14.6, which is our second answer.

Continuing to count back from 14.6, we have 14.4, 14.2 and 14, which is our third answer.

A pictogram is a chart which uses pictures to represent numbers. A pictogram is also known as a pictograph.

In the example below, each book drawn means that a person has read 1 book.

The pictogram example below shows the number of books read by each person.

We can count the number of books drawn next to each person’s name to find out how many each person read.

James read 3 books.

Sarah read 2 books.

Alex read 1 book.

Amy read 5 books.

Terry read 2 books.

This pictogram is useful because it is visual display of how many books each person read. It can be easier to quickly read and compare the information shown when compared to a list of numbers.

For example, we can easily interpret the pictogram to see who read the most and who read the least.

Amy read the most with 5 books.

Alex read the least with 1 book.

There is no need to read every number in the list to answer these questions. We simply need to look for the longest or shortest set of books to see who has read the most or least.

In the example below we are asked, “Who read the same number of books?”.

We look for the people with the same number of books drawn in each row.

Sarah and Terry both read 2 books.

In the next question we are asked, “Who read more than 2 books?”.

Both James and Amy both read more than 2 books.

When teaching the interpretation of pictograms, it is important to explain that 2 books is not more than 2 books.

It is a common mistake to include the people that read 2 books as part of this answer.

2 does not count as being more than 2. We only look at 3 or more books.

In the next example each time we draw a face, it represents 2 people who have attended a school club.

Since each face represents 2 people, drawing half a face is worth half of this.

Half of 2 people is 1 person.

So drawing one whole face is worth 2 people and drawing half a face is worth 1 person.

The list of what each drawing is worth on a pictogram is called the key.

The pictogram below shows the number of people who attended the club each day.

On Monday there are two whole faces drawn.

Each face is worth two people so we have two lots of two which is four.

On Tuesday we have half a face, which is worth 1 person.

On Wednesday we have a whole face, worth 2 people plus half a face, worth 1.

2 + 1 =3, so 3 people attended the club on Wednesday.

On Thursday there are 3 full faces which is three lots of 2.

We also have another half of a face which is worth 1 person.

In total on Thursday we have 7 people.

On Friday, we have 5 people attending the club and we are asked to draw the pictogram row to represent this.

5 is made up of 2 twos and a 1.

So we draw two full faces and one half a face.

In the example below we are counting the number of cars that use a car park each day.

We will draw one car for every 10 cars that we see.

Pictograms often use this because it is easier than drawing such a large amount of cars.

On Monday we have one car drawn, which is worth 10 cars.

On Tuesday we have two cars, which is two lots of ten cars. We have 20 cars parked on Tuesday.

On Wednesday we have one car drawn on the pictogram, worth 10 cars.

On Thursday we have 4 cars, which is worth four lots of 10, or 40 cars.

On Friday we have 3 cars drawn, which is worth 30.

In the example below, we are using the data read from the pictogram to see which day had the most cars parked.

The biggest number is 40 and this was on Thursday.

We can easily read the pictogram to see that Thursday has the most cars. We can see this from the image, rather than needing to read every number.

In the next example of interpreting a pictogram, we are now asked, “Which days were there less than 30 cars?”.

Remember that less than 30 does not include the number 30 itself. We need to look for numbers that are smaller than 30.

Monday, Tuesday and Wednesday all have fewer than 30 cars.

We know that for every car we draw on our pictogram, it is worth 10 cars in real life.

We can draw half a car to represent half of this amount.

If the whole car is worth 10, then half a car is worth half of 10.

Drawing half a car is worth 5 cars.

Here is the key for our pictogram.

We will use this key to draw a pictogram for the values in the example below.

On Monday we have 20 cars, which is simply two lots of 10.

We draw two full cars.

On Tuesday we have 10 cars, which is shown with one full car.

On Wednesday there are 5 cars parked so we draw half a car.

On Thursday there are 15 cars. 15 is made from one ten plus a five.

We draw one whole car and one half a car.

On Friday we have 25 cars. This is made of two tens and a five.

So we draw 2 whole cars and one half a car.

In the last example, we needed to draw half of the picture.

In the most complicated school examples, we can be asked to divide our picture up into quarters.

Below is a drink. The whole image represents four drinks.

If we draw half a drink, we are showing half of four.

Drawing half a drink is worth 2 drinks.

If we half this again we have a quarter.

A quarter of four drinks is 1.

Drawing a quarter of the drink picture is worth 1 drink.

Below is the key to be used in this pictogram.

We will use this key to read the following pictogram showing how many drinks each person drank.

William has two full drink pictures drawn.

Each full drink picture is worth 4 drinks, so William drank two lots of 4 drinks.

William drank 8 drinks.

Megan has a quarter drink picture. This is worth 1 drink.

Sammi has a full drink picture, worth 4 and a half drink picture, worth 2.

4 + 2 = 6 and so, Sammi drank 6 drinks.

Bruce has two full drink pictures, each worth 4 along with a quarter drink picture, worth 1.

4 + 4 + 1 = 9. Bruce drank 9 drinks.

Here is our final pictograph example with the same key.

Fred has a quarter drink picture, worth 1 drink.

Grace has a half drink image, worth 2 drinks.

Jack has a half drink image, worth 2 drinks plus a quarter drink image worth 1.

2 + 1 = 3 and so, Jack drank 3 drinks.

Kate has a full drink image, worth 4 drinks plus a quarter drink picture, worth 1 drink.

4 + 1 = 5 and so, Kate drank 5 drinks.

With these examples it is important to keep referring to the pictogram key and it can help to write the number that each image is worth on top of the images in the pictogram.

Once you have written the number on top of each image using the key, you can add up the values afterwards.

Each number is made up of digits.

The order of digits from least to greatest is:

0, 1, 2, 3, 4, 5, 6, 7, 8 and 9

A two-digit whole number is a number that is made up of two digits next to each other, with one digit in the tens column and one digit in the units column.

The smallest two-digit whole number is 10 and the largest is 99.

In this lesson we will learn how to compare the sizes of all numbers up to 100.

To compare the size of whole numbers use the following steps:

• A whole number is larger than another if it has more digits.
• If the number of digits in each number is the same, then look at the digits from left to right.
• If the left digit is larger in one number, then this is the largest number.
• If this digit is the same, compare the next digit along on the right.

In the example below we have 15 and 4.

We can count the number of digits in each number.

15 is a two-digit number because it is made of two digits: ‘1’ and ‘5’.

4 is a one-digit number because it is only made of one digit: ‘4’.

If a whole number has more digits than another whole number then it is larger.

15 is greater than 4.

This is because one-digit numbers are all smaller than 10 and all two digit numbers must contain at least one lot of 10.

We can see that 15 is greater than 4 just by counting the digits in this number.

This method will only work for whole numbers and will not work for decimal numbers.

We can use comparison symbols to write ‘greater than’ or ‘less than’ more easily and quickly.

• ‘<' is the comparion symbol which is read as 'less than'
• ‘>’ is the comparison symbol which is read as ‘greater than’

Therefore instead of writing:

15 is greater than 4

in words, it can be easier to just write:

15 > 4

To help remember which way around to write the comparison symbol, we can remember that the open end of ‘>’ or ‘<' is like an open crocodile's mouth.

The crocodile wants to eat the larger number.

An alternative way is to remember that the ‘pointy end’ of each symbol is like an arrowhead and we always point to the smaller number.

15 > 4

In the example below we have 18 and 38.

Both 18 and 38 have two digits and so we need to look at each place value column from left to right.

The first digit in each number is in the tens column.

‘1’ is a smaller digit than ‘3’

And so,

18 is less than 38

We can write this by replacing ‘less than’ with the comparison symbol for less than, which is: ‘<'.

18 < 38

Remember that the symbol points to the smaller number.

In this example 18 has ‘1’ in the tens column, which means that it is larger than 10 but less than 20.

38 has a ‘3’ in the tens column, which means that is is larger than 30 but less than 40.

In the example below we are comparing 61 and 29.

Both 61 and 29 are two-digit numbers.

We compare these numbers by comparing the size of each digit from left to right.

‘6’ is larger than ‘2’ and so 61 is greater than 29.

We write this as 61 > 29.

‘>’ is read as ‘greater than’ and we can remember this by thinking of the symbol as an arrow pointing at the smaller number of 29.

We were able to compare the two numbers by looking at the first digit.

We do not look at the second digit at all.

We know that 61 is larger than 60 because it has 6 tens.

We know that 29 is less than 30 because it does not have three tens. It only has 2 tens in the tens column.

In the next example of comparing two-digit numbers, we have 77 and 92.

‘7’ is less than ‘9’ and so 77 is less than 92.

We can write 77 < 92.

In the final example we are comparing 42 and 49.

Both numbers have 2 digits and so we begin by comparing the digits from left to right.

Both numbers have a ‘4’ in the tens digit.

Because the digit is the same we need to look at the next digit in both numbers to compare them.

42 has a ‘2’ in the units column.

49 has a ‘9’ in the units column.

2 is smaller than 9 in the order of digits.

And so, 42 is less than 49.

We write 42 < 49.

The comparison symbol points to the smaller number.

Both numbers are in the forties.

Both numbers have a 4 in the tens column which means that they are both greater than 40 but less than 50.

We had to look at the units column to decide which number was larger.

In this lesson we are ordering whole numbers between 1 and 100.

Here are the steps to order all whole numbers from smallest to largest:

• If the whole number has more digits than another, then it is larger.
• For whole numbers with the same number of digits, the larger number will have the larger first digit.
• If this digit is the same then compare the next digit to the right of this.

The order of the digits from smallest to largest is:

0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

In this lesson we are specifically looking at numbers with up to two digits and so we compare the tens place value column and if this digit is the same, then we compare the digits in the units column.

Below is an example of putting numbers in order.

We will use the steps above to begin ordering these numbers.

There is only one single-digit number, which is 4.

This means that it is the only number smaller than ten and so, it is the smallest.

We could imagine the number ‘4’ as ’04’. The digit in the tens column is ‘0’.

We now look at the numbers with a tens digit of ‘1’.

17 is the only number in this list with a ‘1’ in the tens column. So it comes next.

17 is the only number above that is larger than 10 but less than 20.

We have looked at numbers with a tens digit of ‘0’ and then ‘1’.

Next we look at the numbers in the list that have a tens digit of ‘2’.

21 and 28 both begin with a ‘2’.

Since both numbers both have the same tens digit, we move to the next digit on the right and compare these.

‘1’ is smaller than ‘8’ and so, 21 is smaller than 28.

Next we look at the numbers with a digit of ‘3’ in the tens column.

36 is the only number in this list with a tens digit of ‘3’. It is larger than 30 but less than 40.

We do not have any numbers that have a ‘4’ in the tens column.

This means that there are no numbers between 40 and 50.

We move on to look at the numbers that have a ‘5’ in the tens column: 58 and 59.

Since both of these two numbers have a ‘5’ in their tens column, we look at the next digit along to compare their sizes.

‘8’ is smaller than ‘9’ and so, 58 is smaller than 59.

The final number is 63 and it is the largest number because it has the largest digit in its tens column.

63 is the only number in our list that is greater than 60.

Below is the animation which summarises the ordering of these two-digit numbers

Here is another example of ordering a list of numbers from least to greatest.

We first consider the single-digit numbers which are less than 10.

We have 2 and 7.

We can look at our list of digits and see that 2 is smaller than 7.

Next we look at numbers larger than 10 but less than 20.

We look at numbers with a tens digit of ‘1’.

These numbers are: 11, 12 and 14.

These numbers all have a tens digit of ‘1’ and so we compare their units columns.

‘1’ is smaller than ‘2’ which is smaller than ‘4’.

Therefore 11 is smaller than 12 which is smaller than 14.

We have considered numbers with ‘0’ and ‘1’ tens.

Next we look at the numbers with a ‘2’ in the tens column.

We have 22, 25 and 29.

These three numbers all have two tens.

We put them in order by considering their units column on the right.

‘2’ is smaller than ‘5’ which is smaller than ‘9’.

Therefore 22 is smaller than 25 which is smaller than 29.

Below is the full animation of putting this list of numbers in order from least to greatest.

A tally is used to help count a number of objects and it is particularly useful for making a running total.

A tally mark is a line drawn as each new number is counted.

Below is a tally of the number of counters with a new tally mark drawn as each is counted.

To draw a tally, each number from 1 to 4 is drawn with a

, which is a line going from top to bottom.

The number 5 is represented as a tally by drawing a diagonal line across the first four lines.

Making a tally is useful for making a running total. In this example above we have three counters before a fourth counter is added. Updating the tally is easy because another line is simply drawn alongside the first three.

This tally method is easier than writing the number ‘3’ and then crossing it out or erasing it before writing the number ‘4’.

We can continue to count on using a tally past the number 5 as more counters are added.

5 is represented with a diagonal line across the first 4 lines. We only draw one diagonal line across each set of 4.

Once another counter is added, we have 6 counters and so we simply draw another vertical line alongside our group of 5.

We can continue to draw a vertical tally mark for each new number from 6 to 9.

The number 9 is represented as a tally with one group of 5 and four more vertical lines.

We can see that we have 4 free vertical lines.

So the next number will be represented as a tally with a diagonal line across.

Whenever there are 4 vertical lines as a tally, the next tally mark is a diagonal line across them.

The number 10 is in the five times table.

Every number in the five times table is represented with a diagonal line.

This method is used because it allows us to easily count larger numbers as a tally by counting up in groups of 5.

Below are the

shown in tally form. We do not count each individual tally mark, we simply count up in fives.

Each group that has a diagonal across it is a new number in the five times table.

These are:

5, 10, 15 and 20.

This method allows us to quickly count a tally.

Below is an example of reading a tally.

We know that the first group in the tally which contains a diagonal line is a group of 5.

To count this tally we simply count on from five.

We have three more vertical lines that are free following the group of five and so, we will count on three more from 5.

We have 6, 7 and then 8.

5 + 3 = 8.

And so, this tally represents 8.

We do not count each individual tally mark, we simply count on from 5.

Here is another example of reading a tally.

We have two groups of 5, which are the two groups of tally marks with diagonals across them.

2 lots of 5 are 10.

And so, we count on from 10.

We have one more free vertical line and therefore we count 1 more than 10, which is 11.

This tally represents 11.

We have seen that tallies are an easy way of representing numbers when counting.

Tally marks are easy to write and are often put into a chart before we count up the total.

A tally chart is a table of tally marks which are then counted. The total number is often called the frequency.

In the tally chart below, 4 people: Dennis, Jenny, Lisa and Ron have scored the following number of points in a game.

Since points in the game are awarded as the game is played, a running total is made. Remember that a tally is a very useful way of counting a running total.

Dennis has a group of 5 plus two more.

5 + 2 = 7 and so, Dennis scored 7.

Jenny scored 4, which is represented by four tally marks drawn as vertical lines.

Lisa has exactly three groups of 5.

3 x 5 = 15 and so, Lisa has a score of 15.

Ron scored 11.

Two groups of 5 are 10. Eleven is one more than 10 and so, we draw a single tally mark after the two groups of 5.

Below is another tally chart example which shows the number of people who prefer each colour.

The tally for red is shown as three tally marks, which means that 3 people prefer red.

The tally for blue is made of two groups of 5, plus 3 more tally marks.

Two lots of five is 10 and so, we can count on three from 10.

13 people prefer blue.

The tally for green is shown with one more tally mark following the group of 5.

One more than 5 is 6.

6 people prefer green.

The most popular colour is the colour that most people prefer.

We look for the biggest number in the frequency column.

13 is the biggest number and so, blue is the most popular colour.

In this final example we have a tally chart showing the number of goals scored by the following four people.

Josh has scored 4 goals as shown by 4 vertical tally marks.

Taylor has exactly two groups of 5. Two lots of five are ten.

Taylor has scored 10 goals.

Eddie has three lots of five and then two more.

Three lots of five are fifteen. Two more than 15 is 17.

Eddie has scored 17 goals.

Tom has scored two more than five.

Tom has scored 7 goals.

We are asked, “Who scored more than five goals?”.

The players who has more than five goals are Taylor, Eddie and Tom.

We can see that Josh is the only player who does not have a group of five. We can see that his tally does not have a diagonal line which would represent 5 goals.

We are asked, “How many did Josh and Taylor score in total?”.

We add the numbers shown for Josh and Taylor.

4 + 10 = 14 goals.

We can see that tally charts are a useful way to keep a record of points or scores. They may also be used for counting a running total.

You can make your own tally chart to show the number of cars that go past your house or the number of days that it rains this month.

In this lesson we are introducing the concept of describing direction using turns.

There are four possible types of turn that are first taught:

1. A quarter turn
2. A half turn
3. A Three-quarter turn
4. A full turn

The car in the example below is resting on a circle which is divided into four equal parts.

Each of these parts are known as quarters, since they are equal in size.

We will first look at a quarter turn.



In a quarter turn, one quarter of the full turn is made.

We can see that one of the four quarters of the circle has been shaded as the car rotates.

When the car is in line with the first new line that it comes to, it has made a quarter turn.

In school based questions or elsewhere, your child may not be given a circle with the lines dividing it into quarters.

When teaching quarter turns, we can draw in the quarters onto examples that do not have them to help visualise it more clearly. This can be done by drawing a simple cross.

If the object is facing upwards then a quarter turn will mean that the object is then facing left or right, depending which direction it turns.

The next turn we will look at is a half turn.

A half turn results in the object facing the opposite direction (or backwards) to the direction it was originally facing.



The car was originally facing upwards and so after half a turn, it is now facing downwards.

The reason that this is half a turn is that the car has rotated through half of the circle behind it. It is halfway around the full rotation. Another of these half turns will make a whole turn or full turn.

The car has turned through two of the four quarters of the circle behind it. Two out of four is the same as one half.

The next turn we will look at is a three-quarter turn.

Each of the lines that the car gets to as it rotates is one quarter of a turn.

We can see it sweeping out one quarter of the circle as it gets to each new grid line.



In a three-quarter turn, we turn through three of the four quarters.

The car rotates to be in line with the third line it comes to.

When teaching a three-quarter turn, we can count how many quarters have been shaded and show that it is equal to three. We can also show that this is opposite a one quarter turn.

The car is facing in the opposite direction to when it rotated a one quarter turn.

The car is one quarter turn away from being back to where it started.

The final turn is a full turn or whole turn.

In a full turn, the object rotates completely and is facing in the same direction to where it started.



The car has turned through all four quarters.

It has turned fully.

A full turn results in no overall change to the direction of the object compared to the beginning.

In this lesson we are introducing weight and how to compare the weight of two objects.

The weight of an object is a force that pushes downwards. You can feel the weight of lots of different objects when you hold them. It is the reason we find it difficult to lift some objects at all.

Below is a set of scales. Scales can be used to compare the weights of two objects.

We place a mass at one end of the scale. There is nothing on the other end.

The weight of the mass pushes down on this end of the scale and so this left side moves downwards.

This causes the other side to rise upwards.

When teaching weight to children, it can be helpful to have a physical set of scales to play with, so that your child can experience how it works for themself.

We do not need a large mass to push the scale downwards.

Since there is nothing at the one end, if anything is placed on the other end, it will push down on the scale.

We will put a pencil on the scale at one end.

The pencil pushes down on the left hand side of the scale, causing this side to move downward.

In the example below, we will place two objects on the scale.We will compare the weight of a tennis ball and a feather.

To compare the weight of two objects, they need to be on separate ends of the scales.

The side with the tennis ball moves downwards.

This has happened because the tennis ball pushes down on the scales more than the feather does.

We say that the tennis ball is heavier than the feather.

This means that is is more difficult to lift up than a feather.

The opposite way to say this is to say that the feather is lighter than the tennis ball.

This means that the feather is easier to lift up than the tennis ball.

When teaching weight and mass to children, we can consider them as being very similar, using the words almost interchangeably. However, the mass of an object measures how much matter is inside the object.

You can explain this with an empty and full box. The full box will be heavier and more difficult to move than the empty box because it has more matter inside it.

The weight of the tennis ball pushes downwards more than the weight of the feather. The mass of the tennis ball means that it is more difficult to move in any direction. We can try blowing a tennis ball and a feather and see that it is much easier to move the feather.

In these introductory examples, we simply need to decide which object is heavier by looking at the scales to see which side has been pushed down.

In this next example we will compare the weight of a book and a leaf.

The side with the book moves down causing the side with the leaf to move up.

The book is lower on the scale than the leaf.

Therefore, the book is heavier than the leaf.

And the leaf is lighter than the book.

Remember that the leaf only moves upwards because the book moves downwards pushing the leaf side upwards.

Some children may have the misconception that the leaf being light causes the scales to move upwards. The best way to overcome this misconception is to remove the book and see what happens when the leaf is on the scales alone.

If the leaf is on the scales alone with no book, then the leaf will push its side downwards. It does not cause the scale to rise up. Objects’ weights can only push downwards.

An object being ‘light’ only means that it is not ‘heavy’. Sometimes this word can confuse children who may associate it with balloons which actually may have an upwards force.

Objects always push downwards with their weight. Even feathers and leaves have a weight which pushes downwards.

In this last example, we compare the weights of a carrot and a strawberry.

The carrot pushes this side downwards, causing the strawberry side to move upwards.

The carrot has a larger weight than the strawberry.

The carrot is heavier than the strawberry.

The strawberry is lighter than the carrot.

When teaching and introducing weight to children it is important to consider real life examples so that the child can relate their understanding to what they have already experienced.

Simply holding two objects in each hand can be a way to feel and compare their weights.

If you do not have scales to use in this lesson, you can simply hold the objects and feel which is harder to lift.

Asking your child questions such as, “What do you think is heavier…?” or, “Why can’t you lift…?” will help them realise that they already have an understanding of some aspects of weight. They will probably already know that some objects are heavy and cannot be lifted.

Sometimes they may believe that an object’s weight is linked completely to its size.

This is true if the objects are the same material. For example, a larger rock will be heavier than a smaller rock or a larger person will be heavier than a smaller human. However it is important to explain that this is not always true when comparing different materials.

A small tennis ball may be heavier than an inflatable beach ball or you may have some toys that you can use to show this.

In this lesson we are describing objects as quicker or slower when comparing their speeds.

In the example below, the rabbit and the tortoise are having a race.

The animal that crosses the finish line first is the winner.

The rabbit crosses the finish line before the tortoise because it ran more quickly.

We say that the rabbit is quicker than the tortoise.

The opposite of quick is slow.

The tortoise is slower than the rabbit.

In the example below, we have a race between a bike and a car.

Which is the fastest?

The car crosses the finish line before the bike does.

And so, the car is quicker than the bike.

Or we can say that the bike is slower than the car.

Here is a race between a dog and a snail.

The dog is quicker than the snail because it crossed the finish line first.

The snail is slower than the dog because it crossed the finish line last.

Finally, we will look at this race between a plane and a helicopter.

The plane crosses the finish line before the helicopter and so, the plane is quicker than the helicopter.

And the helicopter is slower than the plane.

A quarter is one out of four equally sized parts.

A quarter is written as   ¹ / ₄   as a fraction and 0.25 as a decimal.

If a fraction of a shape fits into the whole shape exactly four times then it is a quarter.

The shape below is a square. To find a quarter of this square we will divide it into four equally sized parts.

The square shape is divided into four equally sized sections using the red cross shown, halving the square and halving it again.

We shade in one of these four sections to show that it is a quarter.

We have ‘one out of four’ equally sized parts and this can be written as a fraction as ¹ / ₄.

This fraction can be read as ‘one out of four’ and it also means 1 ÷ 4, which means that the one whole shape has been divided into 4.

In the example below we will find one quarter of a circle shape.

One quarter is one out of four equally sized parts and so we can see a quarter visualised above.

Again the red cross shown has been useful in finding this quarter as we were able to halve the shape and halve it again.

When teaching finding one quarter to children (a common year 1 primary school task), we usually start with easier shapes. We can first look to see if the shape can be halved and halved again by dividing it directly through the middle horizontally and vertically.

This will often be the case for many year 1 questions.

Again this hexagon shape can be quartered in this way, dividing it through the middle horizontally and vertically.

We have one out of four equally sized parts. The shaded region fits into the whole shape exactly four times and we can see that all of the four regions are equal in size.

When teaching quarters of shapes, it can be useful to show the shaded quarter fitting in exactly four times to fill the whole shape. You can fold the shape, or use tracing paper to make copies of the quarter to duplicate.

We can see this in the example of the circle below.

You can also think of this as doubling the shaded region and doubling it again. Doubling a quarter makes a half and then doubling a half makes a whole.

The same technique is shown for the quarter of the square shape below:

These shaded regions seen so far all fit exactly into the whole shape four times.

Sometimes we may be asked if a region is equal to a quarter or not.

A common mistake for children first introduced to quarters is that they may simply count 4 separate regions, without checking if the 4 regions are equal in size.

To be a quarter, the four regions must be equal in size.

Is the following region the same as the fraction of   ¹ / ₄   ?

We can fit 4 of the shaded regions together and we see that there is still space within the whole shape.

Four of the shaded regions do not fill the whole shape exactly and so this is not one quarter.

Since less than the whole shape is filled, the shaded region is less than one quarter.

Comparing the sizes of the regions, the shaded region is smaller than some of the other regions and so this is another way to see that this is less than one quarter.

We do not have 4 equally sized regions.

In the example below we are asked to decide if we have one quarter of the whole shape.

We do not have 4 equally sized sections and so, this is not a quarter.

We can place 4 of the parts together and they fill more than the whole shape. Therefore this is more than one quarter.

We can see that although we have four sections, the shaded section is larger than some of the others.