Subtraction facts are combinations of numbers written as subtraction sums involving a subtraction sign ‘-‘ and an equals sign ‘=’.

For example, 10 – 5 = 5 is a subtraction fact. It is a subtraction fact from 10, since 10 is the number that is being subtracted from.

Simple subtraction facts are taught in school alongside addition facts. It is useful to memorise the subtraction facts up to 10 because they will help when subtracting all larger numbers mentally.

To learn subtraction facts, it is easiest to learn the pairs of numbers that add to make the number that is being subtracted from.

In this lesson we will look at subtraction facts to 10, 9, 8 and 7.

Subtraction Facts to 10

Subtraction facts to 10 are subtractions from 10 that should be learnt. 10 will be the first number in the equation and it will be followed by a subtraction sign.

To learn the subtraction facts to 10, you need to know your number bonds to 10.

These are the pairs of numbers that add to make 10.

Here is the full list of number bonds to 10.

We can see that as the first number in each pair increases from 1 to 2, 2 to 3, 3 to 4 and 4 to 5, the second number decreases by one each time from 9 to 8, 8 to 7, 7 to 6 and 6 to 5.

When teaching subtraction facts to 10, it is important to show these number bonds and to look for this simple pattern. There are only 5 pairs of numbers to remember.

Here is an example of a subtraction fact to 10, with a missing number.

We have 10 – something = 8. We need to find the missing number.

Since the subtraction is from 10, we know to use the number bonds to 10 list to help us solve it.

The other number in the subtraction fact is 8.

We look at the list of number bonds to 10 and see that 2 + 8 = 10.

10 is 2 more than 8 and so if we take away 2 from 10 we will have 8.

10 – 2 = 8.

2 is our missing number.

It is easier to think ‘how much larger is 10 than 8’ to solve this subtraction fact problem.

The missing number is the difference between the two numbers that are in this subtraction sentence.

Here is another subtraction fact example.

The subtraction is from 10 and so, the number bonds to 10 will help to solve it.

10 – something = 9.

This missing number is how much larger 10 is than 9.

We can see that 1 + 9 = 10 and so, 10 is 1 larger than 9.

The missing number is 1.

To solve this subtraction from 10, we can simply look at the number bonds to 10 and see which number pairs with 9 to make 10. The missing number is this difference.

In this subtraction fact example, we want to know what 10 – 6 is equal to.

The answer is the difference between 10 and 6. It is the number that we need to add to 6 to make 10.

Using the number bonds, 4 + 6 = 10 and so 4 is the missing number.

Here is another subtraction from 10.

5 + 5 = 10 and so, 10 – 5 = 5.

When teaching subtraction from 10, it is best to try to learn the five number bonds to 10 soon after the concept has been grasped. This will help when moving on to subtracting mentally.

Here are some more subtraction from 10 questions.

The answers are as follows:

Subtraction Facts to 9

Subtraction facts to 9 are the sums made from a subtraction from 9. Because we are subtracting from 9, we use our number bonds to 9 to learn them.

Here are the number bonds to 9. The number bonds to 9 are the pairs of numbers that add to make 9.

The number bonds to 9 are 1 + 8, 2 + 7, 3 + 6 and 4 + 5.

Here is an example subtraction fact to 9 question. 9 – something = 3.

We are subtracting from 9 and so, we use our number bonds to 9.

We see that 3 + 6 = 9 and so, 9 is 6 more than 3.

We need to subtract 6 from 9 to make 3.

In this example we have a subtraction from 9 to get 7 as an answer.

The answer is the number that is subtracted from 9 to make 7.

Using the number bonds to 9, 2 + 7 = 9.

And so, 9 – 2 =7.

In this example we have 9 – 5.

We are subtracting from 9 and so, use our number bonds to 9 to solve this subtraction fact.

4 + 5 = 9 and so, 9 – 5 = 4.

Here are some example of subtraction facts from 9 questions with their answers.

Subtraction Facts to 8

A subtraction fact from 8 is a subtraction sum in which 8 is the number being subtracted from.

To learn the subtraction facts to 8, the number bonds to 8 will be used.

The four number bonds to 8 are 1 + 7, 2 + 6, 3 + 5 and 4 + 4.

In the example below we have 8 – something = 5.

3 + 5 = 8 and so, 8 – 3 = 5.

In this example we have 8 – something = 4.

4 + 4 = 8 and so, 8 is 4 more than 4.

8 – 4 = 4

In this subtraction fact to 8 question we have 8 – 6.

2 + 6 = 8 and so, 8 – 6 = 2.

Here are some further subtraction fact to 8 questions and answers.

Subtraction Facts to 7

Subtraction facts to 7 are subtraction sums in which the number being subtracted from is 7.

To learn the subtraction facts to 7, we will learn the pairs of numbers that add to make 7.

Here are the number bonds to 7.

The three number bonds to 7 are 1 + 6, 2 + 5 and 3 + 4.

In the example below we have a subtraction fact to 7 question.

7 subtract what number equals 5?

Using the number bonds to 7, we know that 2 + 5 = 7.

7 is 2 more than 5 and therefore 7 subtract 2 = 5.

The missing number is 2.

In this question we are asked which number is subtracted from 7 to make 3?

3 + 4 = 7 and so, 7 – 4 = 3.

The missing number is 4.

Here are some subtraction fact to 7 questions with their answers.

Skip Counting Up in Fives

To skip count by 5, add five to get to the next number. Keep adding 5 to each number to get to the next and do not count the numbers in between.

We start at zero and continue to add five to get to the next numbers.

When skip counting in fives from zero, the first few numbers are simply the numbers in the five times table.

We have: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95 and 100.

To teach skip counting to children it is useful to use a number grid to 100.

Below is a number grid showing skip counting in fives.

We can see that there is a pattern when skip counting in fives that can make it easy to learn.

Firstly, the numbers all fall into two columns on the number grid, which can be used to help children to find the next number in the pattern. It can help to say the numbers as you read them and even point at them on the number grid.

Secondly, the numbers all end in 5 and then 0.

When counting up in fives from zero, the numbers alternate between ending in 5 and ending in 0.

To learn the pattern easily, we can see that each group of ten has a number ending in 0 and then 5. After each pair of 0 and 5, we reach the next ten.

We have 0 and 5, 10 and 15, 20 and 25, 30 and 35, 40 and 45, 50 and 55, 60 and 65, 70 and 75, 80 and 85, 90 and 95 and then finally, 100.

The digit in the tens column increases by 1 after adding five to each number that ends in a 5.

We can use this pattern to skip count in fives from any number.

For example, we will start at 40 and skip count forward by 5.

We can use the same pattern before to help us. The numbers end in 0 and then 5. After each number ending in 5, the tens digit increases by 1.

We have 40 and 45, 50 and 55 and then 60 and 65.

There is a pair of numbers in each ten that end in a 0 and then a 5.

In this example we will count up in fives from 15.

15 ends in a 5 and so the next number will be in the next ten up and it will end in a 0 in the units column.

We have: 20 and 25, 30 and 35 followed by 40.

To practise skip counting by 5, we can use skip counting caterpillar worksheets.

We will add 5 to get to the next number along and write the numbers in each segment of the caterpillar.

We fill in the blank spaces between 5 and 85.

Here is the caterpillar worksheet being completed.

Skip Counting Backwards in Fives

To further practise skip counting by five, we can skip count backwards in fives.

We will start at 55 and skip count backwards by 5.

To skip count backwards in fives, subtract five each time to get to the next number.

Skip counting backwards can help to reinforce the forwards pattern.

Remember that we have numbers ending in 5 and then 0. There is a number ending in 5 and 0 for each ten.

Subtracting 5 from and number ending in 0 in the units column results in a number ending in 5 that has a tens digit that is one less than the previous number.

We have: 55 and 50, 45 and 40, 35 and 30, 25 and 20.

We will now look at an example of skip counting backwards in fives from 75.

Remember to count the numbers in pairs of number ending in 5 and 0 to help learn the pattern.

We have 75 and 70, 65 and 60, 55 and 50.

Here is another skip counting caterpillar worksheet to practise skip counting backwards in fives.

Here is the worksheet being completed, subtracting five each time to get to the next number.

What is Skip Counting by 10?

Skip counting by 10 means to count up in tens, adding ten each time. Do not say the numbers in between. Skip counting in tens is important because it allows us to count up more quickly than counting up in ones.

For example, skip counting in tens from zero we have 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100.

Below is an example of a blank skip counting caterpillar worksheet that you can use to practise skip counting. We will count up in tens to complete the caterpillar, writing a number in each segment.

Here is the completed caterpillar example.

How to Skip Count by 10

To skip count by 10, add 10 to get to the next number. This is most easily done by increasing the digit in the tens column of the number by 1. For example, skip counting in tens from 7, we have 7, 17, 27, 37, 47, 57, 67, 77, 87, 97.

The tens digit simply increases from 1 to 2 to 3 etc.

An alternative method for skip counting by 10 is to use a number grid to 100 and move down one row each time as you add 10.

We have: 7, 17, 27, 37, 47, 57, 67, 77, 87 and 97.

We stop at 97 because it is the last number in the pattern before 100 but we could keep counting on if we needed to.

We can see that the numbers all end in the same digit as the number we started on.

The numbers all end in 7 because we skip counted in tens starting at 7.

We simply add 1 more to the tens digit with each addition of 10.

Counting on in Tens from Any Number

To count on in tens from any number, add 10 to get to the next number. The easiest way to do this is to increase the digit in the tens column by 1 each time. For example, starting at 1, we have 11, 21, 31, 41, 51, 61, 71, 81 and 91.

To skip count in tens from any number, simply add one to the tens digit each time. The numbers will always end in the same digit in their ones column.

Remember that to add 10 on a number grid, simply move down one square.

Instead of starting at zero, we start at ‘1’.

Moving one square down the grid each time is adding ten. We have:

1, 11, 21, 31, 41, 51, 61, 71, 81 and 91.

We could continue skip counting in tens further if we needed to.

We can start at any number on the number grid and move down the column to help us skip count in tens. Remember that this number grid can be a useful teaching tool to help practise counting in tens.

We can choose any number on the number grid to count on in tens from.

For example, here is 46. We will count on in tens from 46.

We will start at 46 and move down from square to square, adding ten each time.

Again we simply increase the tens digit by one each time from 46 to 56, to 66 and so on.

46 ends in the digit ‘6’ in its units column and so, the other numbers in our skip counting pattern end in ‘6’ too.

Here is a blank skip counting caterpillar that we will complete together, skip counting up in tens from 11.

11 ends in the units digit of ‘1’ and so, the other numbers in the pattern will also end in a ‘1’.

In the following example, we are counting up in tens starting with 3.

All of the next numbers in the pattern will also end in 3.

Teaching Skip Counting by 10

To teach counting on in tens, it is helpful to use a number grid. Adding ten on a number grid simply involves moving down one row from the original number. Using the number grid it is possible to notice patterns more easily, showing how the digit in the tens column increases by 1 each time.

To skip count in tens, keep adding ten to get to the next number. To easily skip count in ten, increase the tens digit by one each time. The numbers will all end in the same digit in the units column.

Skip counting is a quicker way to count than counting in ones.

When teaching skip counting by 10 for the first time, it can be useful to use a number grid to 100 to help visualise the patterns in the numbers.

Starting from zero, we can add ten to get to 10.

We continue to add 10 each time and get: 20, 30, 40, 50, 60, 70, 80, 90 and 100.

We can see that every time that we add ten to a number on the number grid, we move one square downwards.

We started with ‘0’ and counted up in tens. When skip counting by 10 from zero, the numbers are all in the ten times table.

We can see a pattern that all of the numbers end in the same digit in the units column. The numbers all end in zero.

When teaching skip counting by 10, it is important to point out that adding ten to a number increases its tens digit by 1 each time.

We can see the pattern in the tens digits increasing from 1 to 2, to 3 and so on. 100 is 10 tens.

Skip Counting by 10 Backwards

To skip count backwards by 10, subtract 10 each time. Subtracting 10 on the number grid results in moving one square up each time. The digit in the tens column will decrease by 1 each time.

For example, from 42 counting backwards, we have 42, 32, 22, 12 and 2. The digit in the tens column decreases by 1 each time from 4 to 3 to 2 to 1 to 0.

We can find 42 on the number grid to 100.

To subtract 10 on the number grid, we move up the grid to the square directly above the number we are currently in.

42 ends in a ‘2’ and so the other numbers in the pattern will also end in a ‘2’.

Counting backwards, we have 42, 32, 22, 12 and 2.

We do not continue to subtract 10 because 2 is less than 10 and there are no further squares shown above 2 on the number grid.

Here is another example.

Skip counting backwards in tens, starting at 100 we have 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0.

To skip count backwards in tens subtract ten to get to the next new number. The units column will remain the same but the tens column will decrease by one each time. The numbers will all end in the same digit.

We can use skip counting caterpillar worksheets to practise skip counting backwards.

Here is a blank example for skip counting backwards.

Here is the caterpillar worksheet being completed by skip counting backwards in tens.

We can see that the numbers in the caterpillar worksheet for skip counting backwards are the same as skip counting forwards. Skip counting backwards can be useful for practising the patterns seen when skip counting forwards.

When teaching skip counting, it is important to first practise skip counting forwards before moving on to skip counting backwards using the same numbers.

Here is another skip counting worksheet in which we count backwards in tens from 99.

When teaching skip counting by 10 it is helpful to say the numbers as you count forwards and backwards, emphasising the numbers that remain the same in each pattern.

What is the Point of Skip Counting?

Skip counting helps us to look for patterns in numbers and to build a better understanding of the relative size of numbers. Skip counting is a form of repeated addition where the answers form the times tables. Thus, skip counting helps us to learn the times tables. Learning how to add on and subtract by skip counting forwards and backwards also reinforces our ability to do addition and subtraction.

In general, skip counting reinforces our confidence with working with numbers. Multiplication, division, addition and subtraction are all improved by first learning how to skip count forwards and backwards by a range of different numbers.

Here is an example of skip counting backwards by 10 from 92.

We simply subtract ten to get to each number, which is the same as decreasing the tens digit by 1 each time.

92 ends in a ‘2’ in the units column. The coming numbers in the patter will also end in ‘2’ but the digit in the tens column will decrease by 1 each time.

The pattern learnt through this process allows us to then learn how to subtract ten from any number.

It helps us understand how the different numbers relate to each other in size.

There are 60 minutes in an hour and 24 hours in a day.

To work out the number of minutes in a time given in hours, multiply the number of hours by 60.

To convert a time in days to a time in hours, multiply the time in days by 24.

We will look at some examples of how to convert hours to minutes and days to hours further in this lesson.

Converting Hours to Minutes

The largest hand on an analogue clock is called the minute hand. The smallest line on the scale of a clock face is worth one minute. It takes one minute for the minute hand to move between each of the smallest lines shown.

The smaller hand is the hour hand.

The day starts with both hands on the clock face pointing upwards to the 12.

We can count how many minutes there are until the minute hand reaches the number ‘1’.

The number ‘1’ is 5 lines away from the ’12. There are five minutes between the ’12’ and the ‘1’ on the clock.

We can count the minutes as the hand moves: 1, 2, 3, 4, 5.

Each number that is written on the clock face is separated by 5 minutes.

Each written number on the clock face has a slightly larger line. Every time the minute hand reaches a new number, another five minutes have passed.

This means that we can skip count in fives instead of counting every single minute mark shown.

We can multiply the number written on the clock face by 5 to see how many minutes have passed.

2 x 5 = 10 and so, when the minute hand points at the 2, ten minutes have passed.

3 x 5 = 15 and so, when the minute hand points at the 3, fifteen minutes have passed.

Continuing to count in fives we have: 20, 25, 30, 35, 40, 45, 50, 55 and finally we reach 60 once the minute hand returns to the top.

It has taken 60 minutes for the minute hand to rotate fully around the clock to return to its original position.

There are 60 minutes in an hour. We can see that 12 x 5 = 60. The minute hand points at ’12’.

No matter where the minute hand starts, it will take 60 minutes to return to the same starting position, which is one hour later.

Once we know that there are 60 minutes in an hour, it is easy to find how many minutes there are in two hours.

We could continue to count on from 60 minutes in fives until the minute hand has rotated fully to make another hour.

We can see that another 60 minutes has passed in the second hour.

The first hour was 60 minutes and the second hour was another 60 minutes.

60 + 60 = 120

In total two hours is 120 minutes.

However, when teaching converting hours to minutes it is easiest to multiply the number of hours by 60.

2 hours is 2 lots of 60 minutes and so, the total time is 60 x 2.

Multiplying by 60 may seem a little daunting for a child because it is a much larger number than those in the times tables.

Fortunately, multiplying by 60 is a relatively rare calculation in primary school mathematics, predominantly featuring in this time topic.

The easiest way to multiply by 60 is to multiply by 6 using times tables and then to multiply by 10 afterwards.

We can use this trick to find the number of minutes in 3 hours.

We need to calculate 60 x 3.

We can use the fact that 6 x 3 = 18.

60 x 3 = 180, which is ten times larger.

There are 180 minutes in three hours.

Similarly we can work out the number of minutes in four hours by multiplying 60 by 4.

6 x 4 = 24 and so, 60 x 4 = 240.

There are 240 minutes in 4 hours.

Since there are 60 minutes in a whole hour, we can halve this amount to find the minutes in every half hour.

Half of 60 is 30 and so, there are 30 minutes in half an hour.

We can halve this again to find one quarter. There are 15 minutes in a quarter of an hour.

For example: How many minutes are in 2 and a half hours?

We can work out the number of minutes in 2 hours and then add the half hour separately at the end.

2 x 60 = 120 and so, there are 120 minutes in two hours.

The extra half an hour is 30 minutes.

12 + 3 = 5 and so, 120 + 30 = 150.

There are 150 minutes in 2 and a half hours.

Converting Days to Hours

A new day begins at twelve o’clock in the morning, which can be written as 0:00 am.

This means that we are at the start of the day because zero hours have passed.

Noon is the middle of the day at 12:00 pm. It is also called midday.

Each day there are 12 hours before noon and 12 hours after noon.

For times that are before noon, we write ‘am’ after the time. The ‘am’ is a short way of telling us that this time is in the morning.

For times that are after noon we write ‘pm’ after the time. This is a short way to tell us that the time is after noon.

‘am’ is short for ‘Ante-Meridiem’, which is Latin for ‘before noon’.

‘pm’ is short for ‘Post-Meridiem’, which is Latin for ‘after noon’.

We can see that the clock only has 12 numbers and that the day has 24 hours. Each number on the clock face will be pointed at twice, once in the morning and once in the afternoon. To tell the two times apart we need to write ‘am’ or ‘pm’ after the times.

In this example we will calculate how many hours there are in 2 days.

We use the fact that there are 24 hours in one day.

To find the number of hours in 2 days, we multiply 24 by 2.

The easiest way to multiply 24 by two is to double each digit separately, since both digits are less than 5.

2 x 2 = 4 and 4 x 2 = 8.

Therefore 24 x 2 = 48.

There are 48 hours in two days.

We can find the number of hours in any given amount of days by multiplying 24 by the number of days.

Similarly we can find the number of hours in half a day.

If there are 24 hours in a whole day, we can halve this amount to see that there are 12 hours in half a day.

We already knew that there were 12 hours in the morning and 12 hours in the afternoon. 12 hours in each half of the day.

Using the fact that there are 24 hours in a whole day and 12 hours in half a day, it is possible to work out other combinations for converting days into hours.

For example, how many hours are there in a day and a half?

To calculate this, it is easiest to work out the days and the half days separately and add them at the end.

There are 24 hours in one day and 12 hours in half a day.

24 + 12 = 36 and so, there are 36 hours in a day and a half.

When the calculations involve larger and larger numbers, it can be best to teach this topic by encouraging written methods of addition or multiplication.

Temperature is a measure of how hot something is. The larger the temperature, the hotter it is. The lower the temperature, the cooler it is.

To measure temperature we use a plastic rod called a thermometer. A thermometer contains a liquid called mercury. The mercury expands as it gets warmer and the hotter it is, the more the mercury rises upwards through the thermometer tube.

There are numbers on the side of the thermometer scale which help us to record the temperature. The temperature on a thermometer is the number which the mercury is in line with.

Here is an animation showing the temperature on a thermometer rising as it gets warmer.

Temperature is measure in degrees Celsius.

We can write degrees with the symbol ‘°’ for short.

We write Celsius with a ‘C’ for short.

So to write temperature in degrees Celsius we write °C after the number.

On the thermometer shown in the image above, the numbers on the scale go up in fives.

The mercury is in line with the number 15, which means that the temperature reading is 15 °C.

To compare temperatures we read the temperature and the the larger reading will be the warmer temperature.

To calculate the difference between two temperatures subtract the smaller temperature from the larger temperature.

In this example, we will compare the temperatures on two different days.

The thermometer is in line with 5 °C on Monday.

The thermometer is in line with 10 °C on Tuesday.

To find the difference in temperature between the two days, we subtract the smaller temperature from the larger temperature.

10 – 5 = 5

The difference in temperature is 5 °C.

It is 5 °C warmer on Tuesday than it is on Monday.

We can also see that the thermometer is one increment higher on the scale on Tuesday compared to Monday.

Each increment is worth 5 °C on this thermometer.

In this next example we will compare the temperatures inside and outside a house.

This time, the increments on the thermometer are going up in twos. The numbers on the side of the thermometer go up in twos.

The thermometer is in line with 8 °C outside.

The thermometer is in line with 18 °C inside.

Because the temperature is a larger number inside compared to outside, we say it is warmer inside compared to outside.

The difference in temperature is found by subtracting the smaller number from the larger number.

18 – 8 = 10

And so, the difference in temperature is 8 °C.

We can say that it is 8 °C warmer inside compared to outside.

We can see that the mercury is higher up the thermometer when it is warmer.

To compare the temperature easily, we can just look to see on which thermometer the mercury is the highest.

In this example we will compare the temperatures in two cities.

Again the scale on the thermometer is going up in twos.

The thermometer is in line with 26 °C in Sydney.

The thermometer is directly between 22 °C and 24 °C in London.

The number directly half way between 22 and 24 is 23.

The temperature in London is 23 °C.

26 °C is larger than 23 °C and so, it is warmer in Sydney than in London.

The mercury on the thermometer is higher in Sydney compared to London.

The difference in temperature is found by subtracting the lower temperature from the larger temperature.

26 – 23 = 3

And so, the temperature in Sydney is 3 °C higher than in London.

We can also write that 26 °C > 23 °C to say that ’26 °C is greater than 23 °C’.

The ‘>’ sign reads as ‘greater than’.

The ‘>’ sign reads as ‘less than’.

The open end of the sign always opens out to face the larger number and the closed tip of the sign points at the smaller number.

In this next example we will compare temperatures at night and day.

The thermometer is in the daytime is 2 °C above 15 °C.

15 + 2 = 17

The thermometer in the daytime is therefore at 17 °C.

The thermometer in the nighttime is 3 °C above 5 °C.

5 + 3 = 8

The nighttime temperature is therefore at 8 °C.

17 °C is larger than 8 °C and so, it is warmer in the daytime than at nighttime.

We can write 17 °C > 8 °C. The ‘arrow’ of this sign points at the smaller temperature.

The difference in temperature is 17 – 8, which equals 9.

We can say that it is 9 °C warmer in the day than at night.

What is Skip Counting by 3?

Skip counting by 3 means to count up in threes rather than ones. To get from one number to the next, simply add three each time. You skip out 2 numbers each time and only count the 3rd number.

Skip counting is a faster way to count than simply counting up in ones.

Skip counting by 3 means to add three to get to the next number, skipping two numbers out in the process.

Skip counting up in threes from zero we have:

0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 …

Since there is not a clear pattern, a number grid can be a helpful teaching tool for teaching skip counting by three.

When teaching skip counting by three using a number grid, it can be helpful to first shade or colour in the numbers before counting them.

With a number grid, it is easy to see which numbers are coming next and to see that we are skipping out two numbers each time.

Before looking at skip counting in threes with larger numbers we will look at the numbers up to 30 to see a pattern in the digits.

Adding three each time from zero, we get the 3 times table:

0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

To notice a pattern in the three times table, we can look at the digit in the units column for these numbers:

0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

With 30 we are back to a units digit of ‘0’.

In the same way that 0 + 3 = 3, 30 + 3 = 33.

The following numbers will have the same digit in the units column as those just seen.

In the first ten numbers, we had:

0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Continuing to add three, we get:

30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60

We have the same original ten numbers but we have added ’30’ to each of them.

When teaching skip counting by three, simply learning the first ten numbers first will help to learn the next set.

Adding a ‘3’ to the tens column of the digits above, we get:

60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90

The trickiest part of adding 3 is when we cross each multiple of 10.

It is worth teaching the following patterns in skip counting by 3.

• Adding three to a number ending in 9 results in a number ending in 2.

For example: 9 + 3 = 12, 39 + 3 = 42 and 69 + 3 = 72.

• Adding three to a number ending in 8 results in a number ending in 1.

For example: 18 + 3 = 21, 48 + 3 = 51 and 78 + 3 = 81.

• Adding three to a number ending in 7 results in a number ending in 0.

For example: 27 + 3 = 30, 57 + 3 = 60 and 87 + 3 = 90.

We can use these tips for skip counting by 3 to complete the following skip counting caterpillar.

He can complete the skip counting caterpillar worksheet by adding three to each number and counting up.

We will now look at skip counting backwards in threes.

When teaching skip counting, it is first best to introduce skip counting forwards. Once familiar with the numbers, skip counting backwards is useful for practising the concept.

To skip count backwards by 3, subtract three from each number. We keep subtracting three until we get to zero.

Starting at 30 and subtracting three we get:

30, 27, 24, 21, 18, 15, 12, 9, 6, 3 and 0.

We can practise skip counting backwards using a skip counting caterpillar worksheet shown below.

We start at 90 and subtract three from each number to count down in threes.

Here is the completed skip counting caterpillar worksheet.

You can download and print these skip counting caterpillar worksheets as PDF files above.

What is Skip Counting by 2?

Skip counting by 2 means to count up in twos rather than in ones. This is a quicker way to count because we only need to count every other number. We skip out the numbers in between.

Skip counting is important because it is faster than counting in ones and it is an important skill that helps to build a deeper understanding of multiplication, division, addition and subtraction.

We will use skip counting to help count the number of teddy bears in the introduction example below.

Counting the number of bears by counting in ones we have: 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.

Instead, these bears can be counted in twos. We can pair them up and add two at a time.

Skip counting in twos we have: 2, 4, 6, 8, 10.

We only had to count five numbers: 2, 4, 6, 8 and 10.

It was faster to skip count by 2. We did not say the numbers in between: 1, 3, 5, 7 or 9.

How to Skip Count in Twos

To skip count in twos, keep adding two to get to the next number. Alternatively, simply count every other number.

To skip count by 2 from an even number, repeat the digits 0, 2, 4, 6, 8 and increase the tens digit by 1 each time.

To skip count by 2 from an odd number, repeat the digits 1, 3, 5, 7, 9 and increase the tens digit by 1 with each cycle.

When skip counting by 2 from zero we can notice a pattern.

We have the numbers: 0, 2, 4, 6, 8

and then: 10, 12, 14, 16, 18

We can see that the numbers end in the digits: 0, 2, 4, 6, 8, which is a pattern which repeats over and over again.

The 0, 2, 4, 6, 8 digit pattern repeats once it reaches the end.

Once we get to 8 and add two, we get to 10. 10 ends in 0, which is back to the start of the 0, 2, 4, 6, 8 sequence.

We can see that the pattern of 0, 2, 4, 6, 8 digits is repeated but with 10 added to every number.

To continue skip counting by 2, simply repeat the 0, 2, 4, 6, 8 pattern, increasing the tens digit by 1 each time.

So we have 0, 2, 4, 6, 8 with a ‘1’ digit in front to show that we have added a ten.

We have 10, 12, 14, 16, 18.

Then we repeat 0, 2, 4, 6 8 but with a ‘2’ in front.

We have 20, 22, 24, 26, 28.

We then will have a ‘3’ in the tens and the 0, 2, 4, 6, 8 pattern in the units.

We have 30, 32, 34, 36, 38.

We can continue this pattern with ‘4’ in the tens, ‘5’ in the tens etc.

If we started at one instead of zero, then we see a different pattern.

Here is how to skip count in twos with odd numbers. To skip count in twos with odd numbers, we simply say each odd number and miss out the even numbers.

1 + 2 = 3

3 + 2 = 5

5 + 2 = 7

7 + 2 = 9

We can see that we have the pattern of digits: 1, 3, 5, 7, 9.

Continuing to add 2, we have: 11, 13, 15, 17, 19.

We can see that these numbers end in the digits: 1, 3, 5, 7 and 9, just like the first row of numbers.

This is the alternative pattern that we will see with skip counting by 2.

If we start with an odd number then we have the pattern: 1, 3, 5, 7, 9 in the digits.

The tens digit will increase by 1 each time we cycle through this pattern of digits.

We will see the 1, 3, 5, 7, 9 pattern with a ‘2’ digit in front in the tens column.

This will be 21, 23, 25, 27, 29.

After this we have the 1, 3, 5, 7, 9 pattern with a ‘3’ in the tens digit in front.

This is 31, 33, 35, 37, 39.

This pattern will continue on with 41, 43, 45, 47, 49 and then 51, 53, 55, 57, 59, then 61, 63, 65, 67, 69 and so on.

How to Teach Skip Counting by 2

To Teach skip counting by 2, it is useful to start by using real-life objects and grouping them into pairs. Start by counting up from zero in ones but do not say the odd numbers. Eventually move on to starting at numbers that are larger than zero and odd numbers.

For example, we will introduce skip counting by twos with counting the number of teddy bears here.

Starting from zero and adding two each time we have: 2, 4, 6.

The general idea behind skip counting by 2 is to only say every other number. Once this is understood, it is helpful to practise skip counting with larger numbers. Lots of practice is recommended and skip counting worksheets like the ones below are useful.

Below is a skip counting caterpillar that we can fill with numbers by skip counting in twos.

We can complete the skip counting caterpillar by adding 2 to each number. Since we are skip counting in twos from zero, we will have the 0, 2, 4, 6, 8 pattern repeating with each tens digit.

Here is the completed skip counting caterpillar worksheet answers.

When teaching skip counting, it is important to pick out patterns early on and use these to help memorise the numbers.

Children will enjoy picking out the repeating pattern and it can be helpful to chant or sing the patterns as you teach the numbers. We can also use number grids to show the patterns and you can point at each number as it comes up.

It is also helpful to break down the patterns, teaching a string of numbers at a time, pausing and then repeating the string of numbers. For example, we can count 20, 22, 24, 26, 28, then pause and then count 30, 32, 34, 36, 38, pause then count 40, 42, 44, 46, 48 and so on.

Skip Counting by 2 Backwards

To skip count backwards by 2, simply subtract 2 each time to get to the next number. Skip counting backwards in twos is like counting backwards in ones but only saying every other number. It is easiest to learn how to skip count forwards in twos before learning to skip count backwards.

We will now look at skip counting backwards by 2.

We will have the same number pattern as before but we will be subtracting 2 each time as we go backwards.

When teaching skip counting, it is easiest to teach skip counting forwards first and then introduce skip counting backwards as a way to practise using the exact same number patterns.

In this example, we will have the number pattern 0, 2, 4, 6, 8 but backwards.

Starting at 8, we will then have 6, 4, 2, 0.

We will have the same pattern of 8, 6, 4, 2, 0 when we count back from 18.

We have: 18, 16, 14, 12, 10.

We can see the digits repeat this pattern.

We will now practise skip counting by 2 backwards using a skip counting caterpillar worksheet.

Below is a blank skip counting caterpillar that we can use to count backwards from 60.

We will take away two each time we skip count backwards.

Here is the example of the skip counting caterpillar worksheet being completed.

Here are the answers to the skip counting caterpillar worksheet.

To skip count in twos from zero, the digits in the units column will move from 0, 2, 4, 6, 8 and repeat with each new tens digit.

To skip count backwards in twos with these same numbers, the digits will decrease in the same pattern of 8, 6, 4, 2, 0.

In this lesson we are looking at strategies for adding 3 single-digit numbers.

How to Add 3 Numbers

3 Numbers can be added in any order. Choose two of the numbers and write down the answer before adding the final number to this result. Some strategies for adding 3 numbers are:

• Start by adding the 2 smallest numbers.
• Try and make a number bond to 10.
• Try to add two numbers to make 9.
• Try and make a double.

We will look at these strategies below.

In the example below we are adding three numbers, 2 + 3 + 1.

We will represent each number with a counter.

2 + 3 + 1 makes a total of 6.

We can write the sum in a different order as 1 + 2 + 3.

1 + 2 + 3 = 6.

We can see that we still have the same total and so, it does not matter in which order we add the numbers.

We can use this to choose which numbers to add first in our sums.

In the example below, we have 6 + 1 + 2.

Because the order that we add three numbers does not matter, we can start by adding the two smaller numbers first.

1 + 2 = 3 and so, we can replace ‘1 + 2’ with ‘+3’.

6 + 1 + 2 is the same as 6 + 3.

We can then work out this sum.

6 + 3 = 9

and so,

6 + 1 + 2 = 9

Here is another example of adding three numbers.

We have 5 + 2 + 3.

We will use the same strategy as before and start by adding the two smaller numbers.

2 + 3 = 5

We now can replace the ‘2 + 3’ with a ‘+5’.

The sum is now 5 + 5.

5 + 5 = 10

We might recognise 5 and 5 as a pair of number bonds to ten, which leads us to another strategy.

We can try and make 10 in our sum by looking for number bonds to ten.

We will look at another example of adding three single-digit numbers, where we can use this strategy.

We have 1 + 9 + 5.

We look for two numbers in this sum that add to make 10.

We notice that 1 + 9 = 10 and so, we can replace ‘1 + 9’ with ‘+10’.

The three number sum of 1 + 9 + 5 becomes 10 + 5.

Adding 10 to a single-digit number is relatively easy as it is as simple as putting a ‘1’ digit in front of it.

This will always be the case when adding 10 to a single-digit whole number because the units (or ones) digit has not changed, we have simply added a 10.

Remember that we can add these three numbers in any order and so we can look for any pair in the entire sum that add to make 10.

Here is 6 + 7 + 3.

We can see that 7 + 3 = 10.

The 3 number sum of 6 + 7 + 3 becomes 6 + 10.

We can add 10 to 6 quite easily because the answer will end in 6 too. It is 16.

6 + 7 + 3 = 16.

Here we have the example of adding the three single-digit numbers 8 + 9 + 2.

We can see that 8 + 2 = 10.

We can replace the ‘8 + 2’ with ‘+10’.

We now have 9 + 10 which equals 19.

Not every three number addition will have a number bond to ten. We can look for one and if there is one then we can use that strategy. If not, then we must try another addition strategy.

In this example we have 5 + 7 + 4.

None of these numbers make a pair to 10.

We can try making 9 instead.

We can see that 5 + 4 = 9.

We can replace the ‘5 + 4’ with a ‘+9’ in our sum, so that we have 7 + 9.

We can add 9 to numbers by adding 10 and subtracting 1.

We can do this by putting a ‘1’ digit in front and lowering the units digit by 1. We are adding 9 to 7 and so the answer will end in one less than 7. It will end in 6.

7 + 9 = 16.

And so,

5 + 7 + 4 = 16.

We will again use this strategy in the example below.

We have 4 + 1 + 8.

We cannot make 10 and so we will try and make 9.

We notice that 1 + 8 = 9 and so, we will replace ‘1 + 8’ with ‘+9’ in our sum.

We now have the sum of 4 + 9 which is 13.

In the following example we cannot add two numbers to make 10 or to make 9.

Instead we look at our original strategy for adding three numbers, which is to add the two smallest numbers first.

We have 8 + 5 + 3.

We can add 5 + 3 to make 8 and our sum becomes 8 + 8.

8 + 8 = 16.

We can work this out since we have two eights in the sum of 8 + 8.

This is the same as two eights and so 8 + 8 = 2 times 8.

We can simply double 8 to get our answer of 16.

This is another strategy we can use to add three numbers, which is to try and make a double.

We will use this strategy in our final example of 6 + 3 + 3.

We can see that 3 + 3 = 6, which is the same as the first number in our three number sum.

This means that 6 + 3 + 3 is the same as 6 + 6.

Doubling 6 gives us 12 and so 6 + 3 + 3 = 12.

These are just some strategies that we can use to help us to add three single-digit numbers.

It helps to know number bonds and number facts (specifically the addition of two single-digit numbers that give an answer larger than 10) when breaking these three number sums down into smaller chunks.

Below is a spinner. The arrow is spun and the number that it lands on is the score that we receive. This number is called the outcome.

The list of all possible outcomes is called the sample space.

We make a list of all of the numbers that the spinner can land on and we do not need to write each outcome more than once.

The sample space for this spinner is:

1, 2, 3 and 5

Probability measures how likely it is that something will happen.

We can write probability in words, as a decimal, a percentage or a fraction. We tend to write whichever is easiest

In this lesson we will be writing the probability as a fraction because spinners are divided into equal sections.

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

We can write probability as:   ^{the number of desired outcomes} / _{the number of total outcomes}   .

There are 8 sections on the spinner in total. So the number of total outcomes is 8.

We write our probability as a fraction out of 8.

Now we count how many of these 8 sections contain a ‘1’.

There are 3 ones on the spinner.

3 out of 8 parts contain a ‘1’.

The probability of spinning a 1 is   ³ / ₈   .

This means that we can expect the spinner to spin a ‘1’ three times if it is spun eight times.

We will now look at the probability of spinning a ‘2’.

There are 2 sections on the spinner that contain a ‘2’.

The probability of spinning a 2 is   ² / ₈   .

The probability of spinning a 3 is also   ² / ₈   .

Spinning a 2 and spinning a 3 are equally likely on this spinner because there is the same probability of each outcome occurring.

The probability of spinning a 5 is   ¹ / ₈   .

We have filled our sample space with the probabilities of spinning each outcome.

We can check that our fractions all add up to   ⁸ / ₈   or one whole.

We can see that   ² / ₈   can be simplified to   ¹ / ₄   .

This means that we can expect a 2 a quarter of the times that the spinner is spun.

We can also expect a 3 a quarter of the times that the spinner is spun.

We can show the probabilities in our sample space on a probability scale.

The probability scale is a line drawn between zero and one.

A probability of zero means that there is zero chance of the outcome occurring.

Something with a probability of zero is impossible.

A probability of 1 whole means that the outcome is certain.

A probability of one half is in the middle of zero and one.

A probability of one half means that the outcome occurs half of the time.

We can use this to describe our outcomes.

Anything that occurs less than half of the time we describe as unlikely.

Anthing that occurs more than half of the time we describe as likely.

The outcomes of the spinner are all fractions out of 8.

We can label their positions on the probability scale by dividing the scale into eight equal parts.

We can see that spinning a 1 is the most likely outcome because it has the biggest probability of occurring.

When teaching probability, a common misconception is that if something is the most likely then we will expect it to occur most of the time.

However we can see that all of the outcomes are unlikely to occur because they are all less than   ¹ / ₂   .

Below is a new example with a spinner divided into 5 equally sized sections.

The probability of spinning a one can be written as a fraction.

One out of five sections contain a ‘1’ and so, the probability of spinning a one is   ¹ / ₅   .

Because 1 is less than half of 5, this outcome can be described as unlikely.

The probability of spinning a two is   ³ / ₅   .

Because this fraction is greater than one half, this outcome can be described as likely.

The following example asks, “What is the probability of spinning a 1 or a 3?”.

We look at how many outcomes are either a ‘1’ or a ‘3’.

There are two sections on the spinner that are a ‘1’ or a ‘3’.

The probability of spinning a 1 or a 3 is   ² / ₅   .

Two is less than half of five and so this outcome is unlikely.

In the example below we are asked for the probability of spinning a number greater than 1.

The numbers 2 and 3 are both greater than 1.

We cannot include 1 as we are asked for numbers that are strictly greater than 1.

There are four sections on the spinner that contain numbers greater than 1.

The probability of spinning a number greater than 1 is   ⁴ / ₅   .

Since this fraction is much larger than one half, we can describe the outcome as very likely.