Rounding to the Nearest Hundred

Rounding to the Nearest Hundred

videolesson.JPG

Rounding to the Nearest Hundred Calculator

How to Round to the Nearest Hundred

Look at the digit in the tens column.

If it is 4 or less, round down. If it is 5 or more, round up.

How to round to the nearest hundred

To round up, increase the hundreds digit by one and set the following digits to zero.

To round down, keep the hundreds digit the same and set the following digits to zero.

  • Rounding to the nearest 100 means to write the multiple of 100 that is nearest to the number.
  • Either the hundreds digit will remain the same or it will increase by one.
  • 379 is in between 300 and 400, so the options are to round down to 300 or round up to 400.
  • To decide whether to round up or down, look at the digit in the tens column.
  • If the digit is 4 or less, round down.
  • If the digit is 5 or more, round up.
  • This is because 350 is halfway between 300 and 400.
  • 379 has a 7 as its tens digit, which is ‘5 or more’.
  • This means that 379 rounds up to 400.
  • This means that 379 is nearer to 400 than 300.
  • Always look at the tens digit to decide how to round a number to the nearest hundred.

videolesson.JPG

example of rounding 849 to the nearest hundred

  • 849 has an 8 as its hundreds digit so we can choose to round down to 800 or round up to 900.
  • We look at the digit in the tens column, which is 4.
  • This digit is ‘4 or less’ and so we round down.
  • 849 rounds down to 800.
  • This means that 849 is nearer to 800 than 900.
  • We can see that it is just before 850, which is the halfway point between 800 and 900.

practiseqs.JPG

Rounding to the Nearest Hundred Game

Click on the link below to practise rounding to the nearest hundred with this interactive game.

Rounding to the Nearest Hundred Game

Rounding to the Nearest Hundred Worksheets and Answers

Rounding Numbers to the Nearest Hundred

How to Round to the Nearest Hundred

To round to the nearest hundred:

  1. Look at the tens digit of the number.
  2. If it is 5 or more, increase the hundreds digit by 1.
  3. If it is 4 or less, keep the hundreds digit the same.
  4. Set the tens and ones digits to zero.

For example, round 379 to the nearest hundred.

how to round off to the nearest hundred

Look at the tens digit of the number

The tens digit of 379 is 7.

Decide if it is ‘5 or more’ or ‘4 or less’

7 is ‘5 or more’ and so, the hundreds digit is increased by 1.

The hundreds digit of 379 is increased from 3 to 4.

Set the tens and ones digits to zero

To round 379 number up, increase the hundreds digit by 1 and set the other digits to zero.

Increase the 3 to a 4 and change the 7 and 9 to a zero.

379 rounded to the nearest hundred is 400.

This means that 379 is closer to 400 than it is to 300. This is because 379 is larger than 350, which is the halfway point between 300 and 400.

Here are some examples of rounding numbers to the nearest hundred.

Number Rounded to the Nearest Hundred
197 200
320 300
449 400
450 500
2337 2300
84390 84400

Here is another example of rounding to the nearest hundred.

Round 628 to the nearest hundred.

The first step is to look at the tens digit, which is 2.

2 is ‘4 or less’ and so 628 is rounded down.

example of rounding 628 down to the nearest hundred

To round down to the nearest hundred, keep the hundreds digit the same but change the other ones and tens digits to zero.

The 6 in the hundreds column remains the same but the 2 and the 8 are set to zero.

628 rounds down to 600 when rounded to the nearest hundred.

Here is another example. Round 849 to the nearest hundred.

The hundreds digit is 8 and so, the choice is to keep 8 as 8, or round it up to a 9. 849 is in between 800 and 900.

First look at the tens digit, which is 4.

4 is ‘4 or less’ and so round down.

Rounding to the nearest hundred example of 849

Keep the 8 as an 8 and then set the remaining digits to zero.

849 rounds down to 800 when rounded to the nearest hundred.

When teaching rounding to the nearest hundred, it is important to follow the simple process of looking at the tens digit only to decide whether to round up or down.

Do not look at any other digits beyond the tens digit to decide how to round to the nearest hundred.

In the example of 849, we only look at the digit of 4. This tells us to round down.

A common mistake is to look beyond the 4. Some people will look at the 9 and round the 4 up to become a 5. They will then use this 5 to round up to 900.

This of course, is the wrong answer and we cannot use other digits to decide on rounding.

We can see from the number line that 849 is nearer to 800 than 900, so it must round down to 800. 849 is on the left of 850, which is the halfway mark.

What does Rounding to the Nearest Hundred Mean?

Rounding a number to the nearest hundred means to write down the multiple of 100 that is nearest to the number. If the nearest multiple of 100 is larger than the original number, this is called rounding up. If the nearest multiple of 100 is smaller than the original number, this is called rounding down.

It is useful to round a number to the nearest hundred when estimating numbers. Sometimes it is easier to say that there were ‘about 200 people in a room’ instead of actually counting them all.

For example, we have the number 30 below.

It is nearer to zero than it is to 100.

rounding 30 down to the nearest hundred

This means that 30 rounds down to zero when rounded to the nearest hundred.

Here is the number 60.

We can see that 60 is closer to 100 than it is to zero.

rounding 60 up to the nearest hundred of 100

This time, 60 rounds up to 100 instead of 0.

Here we have 50.

50 is directly in between 0 and 100. It is not nearer to 0 or 100 because it is exactly in between them both.

we round 50 up when rounding to the nearest 100

We have to decide whether to round 50 up or down.

We decide to round 50 up to 100 because we can make a rule for rounding.

51, 52, 53, 54, 55, 56, 57, 58 and 59 are all nearer to 100 than they are to 0.

If also round 50 up then we can say that if the tens digit is 5 or more, then we round up.

Even if we have a number like 50.1, it is nearer to 100 than it is to 0. If there is any other number added to 50, it is nearer to 100 and so, it is easiest to say that 50 rounds up.

rule for rounding to the nearest hundred

The rule for rounding to the nearest hundred is to look at the tens digit.

If it is 5 or more, then round up.

If it is 4 or less, then round down.

The rule for rounding to the nearest hundred is to consider the number formed by the digits in the tens and ones columns. If the number is 0-49, round down. If the number is 50-99, round up.

Here is the number 52.

example of how to round 52 to the nearest hundred.

The digit in the tens column of 52 is 5. 52 has 5 tens in it.

5 is ‘5 or more’ and so we round it up. When first teaching rounding to the nearest hundred it is important to explain that we are actually writing down the nearest number in the 100 times table to the number we have.

Number lines can be a useful way to introduce the concept of rounding as it allows us to see the size of each number and where it is in relation with other numbers.

Once this concept is understood, it is recommended to just look at the tens digit to decide on how to round.

Rounding to the Nearest Hundred on a Number Line

To round to the nearest hundred on a number line, write the number to be rounded between the multiples of 100 that are either side of it. Then mark halfway between the multiples of 100, where the last two digits are 50. If the original number is to the left of 50, round down and if it is to the right of 50, round up.

50 is halfway between 0 and 100. The halfway point between each hundred is marked by a 50.

For example, round 3161 to the nearest hundred.

Even though we have thousands in this number, we still follow the same steps as before.

We look at the tens digit, which is 6.

6 rounds 3161 up to the next hundred because 6 is ‘5 or more’.

Rounding a number to the nearest hundred example of 3161

We currently have a 1 in the hundreds column. To round up, this 1 increases to a 2 and the digits after this are set to zero.

3161 rounds up to 3200.

We previously has 31 hundreds and now we have 32 hundreds.

This means that 3161 is nearer to 3200 than it is to 3100.

Here is an example of rounding 4982 to the nearest hundred.

Rounding to the nearest hundred means that we write down the nearest multiple of 100 to our number.

We have 49 hundreds in 4982. This means that we decide between rounding to 49 hundreds and 50 hundreds.

4982 is in between 4900 and 5000.

We look at the tens digit, which is 8.

how to round a number to the nearest hundred example of 4982

8 is ‘5 or more’ and so, we round up.

We increase 49 hundreds to 50 hundreds.

4982 rounds up to 5000. This means that 4982 is nearer to 5000 than it is to 4900.

4982 is larger than 4950. 4950 is halfway between 4900 and 5000.

Examples of Rounding to the Nearest Hundred

Here are some examples of rounding to the nearest hundred:

Example Tens Digit / Rounding Rounded to the Nearest Hundred
234 3 is less than 5, so round down 200
289 8 is 5 or more, so round up 300
250 5 is 5 or more, so round up 300
34 3 is less than 5, so round down 0
72 7 is 5 or more, so round up 100
1462 6 is 5 or more, so round up 1500
5914 1 is less than 5, so round down 5900
6987 9 is 5 or more, so round up 7000
nextlesson.JPG

Now try our lesson on Rounding Decimals to the Nearest Whole Number where we learn how to round a decimal to the nearest whole number.

Subtraction on an Empty Number Line

Subtraction on an Empty Number Line

videolesson.JPG

subtraction on a number line 84 - 31

  • To subtract using the empty number line method, first draw a blank number line.
  • Mark the largest number on the right of the number line.
  • 84 is the number we are subtracting from so we write this first.
  • The number we are subtracting is broken down into its tens and ones.
  • 31 has 3 tens and 1 one.
  • We subtract the tens first, in this case we make 3 subtractions in jumps of 10.
  • 10 is easy to subtract because the ones digit remains the same but we decrease the tens digit by 1.
  • 84 – 10 = 74, 74 – 10 = 64 and then 64 – 10 = 54.
  • We now show the subtraction of the 1 unit with a smaller jump.
  • 54 – 1 = 53
  • This jump strategy is used to break down an subtraction and show the process visually.

Mark the number being subtracted from on the right of a number line.

Make jumps in tens and then ones to break down the subtraction.

videolesson.JPG

example of how to subtract using an empty number line 97 - 64

  • 97 is the number we are subtracting from so we mark it on the right of the number line.
  • 64 contains 6 tens and 4 ones.
  • We can subtract 6 tens directly by decreasing the tens digit by 6.
  • 9 – 6 = 3 and so, 97 – 60 = 37.
  • We show the subtraction with a jump to the left on our number line from 97 to 37.
  • We now subtract the 4 ones.
  • 7 – 4 = 3 and so, 37 – 4 = 33.
  • We draw a smaller jump from 37 to 33 on the number line.

practiseqs.JPG

Subtraction on a Number Line Worksheets and Answers

Subtraction on an Empty Number Line

What is the Empty Number Line Strategy?

The empty number line strategy is a method which shows an addition or subtraction visually, using jumps in tens or ones.

The empty number line strategy is also known as the jump strategy, open number line or blank number line strategy. The empty number line strategy is useful because it helps people to visualise the size of each number in the different stages in their calculation.

In this lesson we will use the empty number line strategy for subtraction.

Here is an example of a 2-digit subtraction using a number line.

We have 56 – 11.

The number line is important in breaking down the subtraction and showing the relative size of each number.

We need to subtract 11 so we break it down into 10 and 1.

2-digit subtraction on a number line of 56 - 11

We subtract the ten and then the one separately.

Write the values after each subtraction on the number line. This helps to keep a running record of the calculation. The numbers written help us to visualise the size of each number and improves our ability to estimate and check our work.

Here is another example of using the blank number line method.

We have 84 – 31.

Subtraction on a number line can be performed in several ways. There is no one correct way to break the subtraction down.

When first teaching subtraction on a number line, it is useful to break the subtraction down into tens and ones.

We can break this subtraction of 31 into 3 tens and 1 one.

Here we subtract 10 three times.

teaching subtraction on a number line by subtracting in tens and ones

We then subtract the one.

When teaching subtraction on a number line, it is easier to subtract smaller numbers. Subtracting 10 is easy as it is just the tens digit that decreases by 1. Subtracting 1 is also easy.

Whilst the subtractions are easy, 4 jumps were needed to subtract 31.

As we progress with the method, we can use fewer and fewer jumps.

A common strategy is to break the subtraction down into multiples of 10 and 1.

31 is made of 3 tens and 1 one.

We could have done the subtraction by taking away 30 and then taking away 1.

Jump Subtraction 3

We can see that this is a different way of using the empty number line strategy. Fewer jumps were used but the final answer is the same.

Subtraction using a Number Line

To subtract using a number line, use the following steps:

  1. Draw a blank number line with no numbers written.
  2. Write the number you are subtracting from on the right hand side of this line.
  3. Read the digit in the tens column of the number being subtracted.
  4. Subtract this digit from the tens digit of your original number.
  5. Draw an arrow jump left going from the original number to this answer.
  6. Read the digit in the ones column of the number being subtracted.
  7. Subtract this digit from the ones digit of the previous answer.
  8. Draw an arrow jump left from the previous answer to this new answer.

Here is an example of subtracting a 2-digit number using an open number line.

We have 97 – 64.

The first step is to draw the blank number line.

The second step is to mark the number we are subtracting from on the right hand side. We mark 97.

subtracting 2 digit numbers on a number line in steps

The third step is to read the tens digit of 64, which is 6. We will subtract 6 tens.

The fourth step is to subtract the 6 from the tens digit of 97.

9 – 6 = 3 and so, 97 – 60 = 37.

The fifth step is to draw this subtraction on the number line using a jump.

The sixth step is to read the ones digit of 64, which is 4.

The seventh step is to subtract this digit from the ones digit of 37.

7 – 4 = 3 and so, 37 – 4 = 33.

Here is another example of working out a 2-digit subtraction on a number line using the jump strategy.

We have 82 – 54.

We can show the subtraction of the tens digit with one jump.

8 – 5 is 3 and so, 82 – 50 = 32.

using the jump strategy for subtraction on a number line

In this example we can see that if we went to subtract the 4 in one go, it can be a little difficult for some students.

This is because 4 is larger than 2 and subtracting 4 from 32 involves crossing the tens barrier at 30.

It may be easier to subtract the 4 from 32 in 4 separate jumps of 1.

32 – 4 = 28 and so, 82 – 54 = 28.

nextlesson.JPG

Now try our lesson on Comparing 2-Digit Numbers with Greater Than and Less Than where we learn how to compare two numbers.

Jump Strategy for Addition

Jump Strategy for Addition

videolesson.JPG

Jump Strategy Addition of 33 + 21

  • To add numbers with the jump strategy first draw a blank number line.
  • Mark the largest number on the left of the number line.
  • 33 is larger than 21 so we mark 33.
  • We break the addition down into tens and units.
  • 21 has 2 tens and 1 unit.
  • We add the two tens first by drawing two jumps of 10.
  • 10 is easy to add because the units digit remains the same but we increase the tens digit by 1.
  • 33 + 10 = 43 and then 43 + 10 = 53.
  • We now show the addition of the 1 unit with a smaller jump.
  • The jump strategy is used to break down an addition and show the process visually.

Start with the largest number marked on a number line.

Make jumps in tens and then ones to break down the addition.

videolesson.JPG

Example of using the jump strategy for the addition of 45 + 32

  • 45 is the larger number so we mark it on the left of the blank number line.
  • 32 contains 3 tens.
  • We can add 3 tens in one go by increasing the tens digit by 3.
  • 4 + 3 = 7 and so, 45 + 30 = 75.
  • We draw an arrow jump to the right on our number line from 45 to 75.
  • 32 contains 2 units.
  • 5 + 2 = 7 and so, 75 + 2 = 77.
  • We draw a smaller jump from 75 to 77 on the number line.

practiseqs.JPG

Jump Strategy Addition Worksheets and Answers

The Jump Strategy for Addition

What is the Jump Strategy for Addition?

The jump strategy is a visual method in which an addition is performed by adding the tens and ones separately in jumps. A blank number line is drawn and each addition is shown using arrow jumps.

Here is an example of an addition that will be performed using the jump strategy.

We have 33 + 21.

The jump strategy is also known as the blank number line strategy or empty number line strategy. This is because we start with a blank number line.

Jump Strategy on a blank number line for adding 33 + 21

We can see that we split the addition of 21 into adding 2 tens and 1 one. When teaching the jump strategy, it is important to understand how numbers can be partitioned into tens and ones.

We show the addition of the 2 tens with two separate jumps of 10 on our number line.

33 + 10 = 43

43 + 10 = 53

When teaching the jump strategy, we use these jumps to reinforce how the addition is broken down. We have 2 tens in 21 and so we have two jumps.

After adding the 2 tens, we add the 1 one.

53 + 1 = 54 We show the addition of 1 using a smaller jump than the addition of 10.

When first introducing the jump strategy for addition, we can refer back to the number itself and show how it corresponds to the number of jumps that we have.

21 contains 2 jumps of ten and 1 jump of 1.

As you become more fluent with the strategy, we can reduce the method to only 2 jumps.

We have the same example, this time making the jump of 20 in one go.

blank number line strategy for addition with jumps shown on the number line.

Instead of adding 2 jumps of 10, we can add 20 in one go. This is quicker and takes up less space on the number line.

The jump strategy is used to break down an addition into separate chunks. The jump strategy is useful because it provides a visual picture for the addition.

It is easy to see how many parts of the number we have added because each addition is shown as an extra jump.

The number line helps to provide a frame of reference to see how the size of the answer compares with the original number.

Whilst it is not the most efficient method for addition, the process can help to build understanding of addition, number size and partitioning.

Teaching Addition using the Jump Strategy

To add using the jump strategy, use the following steps:

  • Draw an empty number line.
  • Mark the largest number in the addition on the left side of this line.
  • Look at the tens digit of the smaller number and add this digit to the tens digit of the larger number.
  • Draw an arrow from the larger number to the right and write the answer to this addition below it.
  • Look at the ones digit of the smaller number and add this digit to the ones digit of the larger number.
  • Draw an arrow from the previous answer to the right and write this new answer below it.

We will use these steps to add 45 + 32 using the jump strategy.

We draw an empty number line.

45 is larger than 32, so we start with 45 marked on the left of this number line.

Jump Strategy for the addition of 45 + 32

32 contains 3 tens and 2 units. 3 tens is 30.

We draw an arrow from 45 to the right.

Adding tens is easy because the units digit remains the same. We just increase the tens column. To add 3 tens, we add 3 to the 4 tens in 45.

4 + 3 = 7 and so, 45 + 30 = 75.

We can see that the tens digit increased by 3 from 4 to 7. The units digit remained as 5.

We then add the 2 ones.

75 + 2 = 77

Therefore 45 + 32 = 77.

We added the tens and then added the ones.

We can also add the 3 tens as 3 individual jumps of 10 and then add the 2 ones as 2 individual jumps of one.

Jump Strategy in parts shown on an empty number line

Here is another example of addition using a blank number line.

We have 12 + 39.

39 is larger than 12 and so, we start with 39 marked on the left of the number line.

The reason for this is that it is easier to add 12 to 39 than it is to add 39 to 12.

Jumps to add 12 is shorter and involves smaller numbers than jumps which as 39.

Teaching addition using the jump Strategy example

12 contains just 1 ten and 2 ones.

39 + 10 = 49

Adding ten is easy because both numbers end in 9 and we simply increase the 3 to a 4.

We could add the 2 ones in one go, however 9 + 2 = 11. Additions that cross a tens value are typically more difficult.

49 + 2 = 51 but it can be easier to show this as two separate jumps of 1.

When teaching the jump strategy, it is important to be able to choose between jumping in separate, many groups of ten or one and jumping all of the tens or ones in one go.

nextlesson.JPG

Now try our lesson on Addition using the Compensation Strategy where we learn how to use the compensation strategy to add two numbers.

Division Sentences

Division Sentences

videolesson.JPG

What is a division sentence?

  • A division sentence is a mathematical way to show how an amount is shared.
  • Here we have 18 counters in total.
  • We share the counters into 6 equal groups.
  • There are 3 counters in every group.
  • We write the total amount first, which is 18.
  • The division sign, ÷, means to share the amount before it by the amount after it.
  • 6 is the number of groups, so we write a 6 after the division sign.
  • There are 3 counters in each group so we write a 3 after the equals sign, =.
  • 18 ÷ 6 = 3 means that 18 shared into 6 equal groups gives us 3 in every group.
  • Division sentences with whole numbers start with the largest number.

The larger number is written before the division sign.

The number of groups comes after the division sign and the number in each group comes after the equals sign.

videolesson.JPG

Example of writing a division sentence

  • Ten marbles are put into 5 bags.
  • The total number of marbles is 10 and so, we write this number first.
  • We then write the division sign, ÷.
  • We are sharing the marbles into 5 parts and so, we write 5 after the division sign.
  • 10 marbles shared into 5 is written as 10 ÷ 5.
  • We then write an equals sign followed by the number of marbles in each bag.
  • There are 2 marbles in each bag.
  • 10 ÷ 5 = 2 means that 10 shared into 5 equal parts gives us 2 in each group.
  • The division sentence is 10 ÷ 5 = 2.

practiseqs.JPG

Division Sentences Worksheets and Answers

Division Sentences

What is a Division Sentence?

A division sentence is made up of 3 numbers, a division sign and an equals sign. The first number, before the division sign, tells us the total amount being shared. The second number, after the division sign, tells us how many groups we are sharing the amount into. The third number, after the equals sign, tells us the number in each group after the division.

20 ÷ 5 = 4 is an example of a division sentence. It contains three numbers, a division sign and an equals sign.

20 ÷ 5 = 4 means that 20 shared into 5 equal groups would give us 4 in each group.

We can teach division sentences using arrays of counters. We can circle groups of counters to group them.

Below we have 20 counters.

Division sentence for an array of 20 counters.

We share the counters into 5 equal groups. This means that we must have the same number of counters in each group.

There are 4 counters in each of the 5 groups.

The division sentence 20 ÷ 5 = 4 represents this problem.

example of writing a division sentence

The first number is 20, which is the total number of counters. We always write the total number of objects we are sharing first.

The second number is the number of groups we have. When teaching division sentences, we can circle the groups with a pencil, or if using real counters, we can put them into pots. We can then count the number of groups or pots.

The final number after the equals sign is the number in each group. We can count the number of counters in each circle. If we put the counters in each pot, we can count these.

Parts of a division sentence

There are 3 parts to a typical division sentence.

The first part is the number being shared. The second part is the number of groups the total is shared into. A division sign, ÷, separates the first and second parts.

The third part is the number in each group. An equals sign separates the second and third parts.

The first, largest number in a division is called the multiple.

The other two numbers in a division sentence are called factors. The two factors can be multiplied together to make the multiple.

Here is another example of a division sentence.

We have 18 ÷ 6 = 3.

This division sentence means that 18 shared into 6 equal groups gives us 3 in each group.

Again we will teach this division with counters. It is a good idea to introduce division to your child using physical models.

Teaching division using counters

18 is the total number and the largest number. This will go first in our number sentence.

The number of groups is 6.

The number of counters in each group is 3.

When teaching writing division sentences, it is useful to use physical counters and write the division sentence as you go. We can count the number of counters in total as the first step before writing this number down. We can share the counters equally into pots and count the number of pots. The final number is the number of counters in each pot.

Following these steps keeps the numbers in the division sentence in the correct order.

A division sentence for 20 ÷ 5 = 4 with the parts of the division shown

The number 20 is the multiple and the smaller numbers, 5 and 4 are the factors.

The two factors can multiply together to make the multiple.

parts of a division sentence

How to Write a Division Sentence

To write a division sentence use the following steps:

  1. Write down the total number being shared or divided first.
  2. Next write the division sign, ÷.
  3. After the division sign, write down the number of groups the amount is being shared into.
  4. Next write the equals sign, =.
  5. Finally, write the number in each group after the objects have been shared.

As long as we use whole numbers, the largest number in a division sentence will come first.

Here is an example of writing a division sentence for a word problem.

Ten marbles are put into 5 bags.

Writing a division sentence for a word problem

The first step is to write the total number being shared, which is 10.

The second step is to write a division sign, ÷.

The third step is to write the amount of groups. This is the number of bags the marbles will be put into. We have 5.

The fourth step is two write an equals sign, =.

The fifth step is to write the number in each group. By placing the marbles into 5 equal groups we can see that there are 5 in each group.

The division sentence is 10 ÷ 5 = 2.

This sentence means that 10 shared into 5 equal groups gives us 2 in each group.

Here is another example of writing a division sentence for a word problem.

12 apples are shared between 4 children.

writing a division for a word problem example

Remember that the largest number in the division sentence will come first.

We are sharing 12 objects between 4 people.

We write 12 ÷ 4.

Each child gets 3 and so, our answer to the division is 3.

12 ÷ 4 = 3 means that 12 apples shared between 4 children gives each child 3 apples.

Here is an example of writing a division.

16 birds are put into groups of 4.

forming a division sentence for a word problem example with birds

The largest number is the total. We have 16 birds so we write this first.

The number after the division sign is the number of groups.

We have 16 ÷ 4, which means 16 birds shared into 4 equal groups.

We count how many birds in each group to get our answer, after the equals sign.

There are 4 birds in each group and so, 16 ÷ 4 = 4.

nextlesson.JPG

Now try our lesson on Short Division without Remainders where we learn how to use the short division method for dividing numbers.

Multiplication Sentences

Multiplication Sentences

videolesson.JPG

Multiplication sentence for an array of 3 x 5

  • An array is a rectangular collect of objects which represent a multiplication.
  • We have 3 rows of 5 counters.
  • We have 3 equal groups of 5 or 3 lots of 5.
  • The multiplication sign, ×, means lots of.
  • 3 lots of 5 can be written as 3 × 5.
  • A multiplication sentence is made up of 3 numbers, a multiplication sign, × and an equals sign, =.
  • The number before the × sign tells us how many groups we have.
  • The number after the × sign tells us how many are in each group.
  • The number at the end, after the equals sign is the total number of items.
  • There are 15 counters in total so we write 3 × 5 = 15.

The larger number comes after the equals sign and tells us how much we have in total.

The number before the multiplication sign is how many groups we have and the number after the sign is how many in each group.

videolesson.JPG

Example of writing a multiplication sentence

  • We will write a multiplication sentence to describe how many wings we have in total.
  • There are 3 butterflies, so we write 3 in front of the multiplication sign.
  • There are 2 wings on each butterfly and so, the 2 goes after the multiplication sign.
  • There are 6 wings in total on the 3 butterflies so we write 6 after the equals sign.
  • The multiplication sentence is 3 × 2 = 6.
  • We can read this as 3 lots of 2 is 6.

practiseqs.JPG

Multiplication Sentences Worksheets and Answers

Multiplication Sentences

What is a Multiplication Sentence?

A multiplication sentence is made up of 3 numbers. The first number, before the multiplication sign tells us how many equal groups we have. The second number, after the multiplication sign tells us how many are in each group. The 3rd number comes after the equals sign and is how many there are in total.

An example of a multiplication sentence is 3 × 5 = 15. The multiplication sentence is made up of 3 numbers. 2 next to the multiplication sign and one at the end, after the equals sign.

Example of a multiplication sentence

This multiplication sentence means 3 lots of 5 makes a total of 15.

It is helpful to remember that when writing multiplication sentences for whole numbers, the largest number goes at the end, after the equals sign.

A multiplication sentence is a mathematical way to write the total number of objects that are in equal groups.

For example, below we have 3 butterflies.

Each butterfly has 2 wings.

To find the total number of wings we add the 2 wings on the first butterfly to the 2 wings on the second butterfly to the 2 wings on the third butterfly.

If we add 2 + 2 + 2 we get 6. There are 6 wings in total.

what is a multiplication sentence example for children

It is easier to think of this as 3 groups of 2 wings. Each butterfly has 2 wings and there are 3 butterflies.

We can say that we have 3 lots of 2, which is 6 in total.

The multiplication sign is ×. The multiplication sign is used instead of writing ‘lots of’ or ‘equal groups of’.

SO we can write 3 × 2 = 6, which means that 3 lots of 2 is equal to 6. It is quicker, easier and takes up less space to write compared to writing the multiplication sentence in words.

Writing Multiplication Sentences for Arrays

There are 2 multiplication sentences that can be written for an array. To write a multiplication sentence for an array use the following steps:

  1. Count the number of rows and write this number.
  2. Write the multiplication sign, ×.
  3. Count the number of columns and write this number after the multiplication sign.
  4. Write an equals sign, =.
  5. Count the total number of objects in the array and write this number after the equals sign.
  6. To find the other multiplication sentence, switch the two numbers either side of the multiplication sign.

Arrays are often used to teach multiplication. An array is a rectangular collection of objects (usually counters) arranged in equal rows and columns.

Here is an example of a multiplication array.

We have 5 counters in each row.

How to write a multiplication sentence for an array of 3 times 5.

We have 3 rows of 5 in the array. Every row contains 5 counters.

We can say that we have 3 rows of 5. Because every row in the array has the same number of counters, we can say that we have 3 ‘equal groups of’ 5 or simply, 3 ‘lots of’ 5.

When writing a multiplication sentence for this array, we can replace the words ‘lots of’ with a multiplication sign, ×.

We can write 3 × 5 to mean 3 equal lots of 5.

The number after the equals sign tells us how many counters we have in total in the array. If we count all of the counters, we can see that we have 15.

The multiplication sentence for this array is written as 3 × 5 = 15.

A multiplication sentence showing multiples and factors for 3 × 5 = 15

This multiplication sentence means 3 lots of 5 makes a total of 15.

When writing a multiplication sentence with whole numbers, the two smaller numbers come first and go next to the multiplication sign. The larger number comes last, after the equals sign.

In a multiplication sentence, the two numbers either side of the multiplication sign are called factors and the number after the equals sign is called the multiple.

If you wrote the two smaller numbers the other way around as 5 × 3 = 15 instead of 3 × 5 =15, this does not matter when talking about this array.

It would mean 5 lots of 3. We can still think of this array as representing 5 lots of 3 because we have 5 columns, each containing 3 counters.

We have 3 rows containing 5 counters or 5 columns each containing 3 counters.

So for this array, the multiplication sentences are:

3 × 5 = 15 or

5 × 3 = 15.

The total must come after the equals sign.

Here is another example of writing a multiplication sentence for an array.

In this array we have 4 counters in each column.

We have 6 columns.

There are 6 columns of 4. Because there are an equal number of counters in each column, we can write this as a multiplication.

Write a multiplication sentence for an array example with 24 counters

We have 6 lots of 4. Remember that we can replace the words lots of with a multiplication sign.

We can write the multiplication sentence for this array as 6 × 4 = 24.

There are 24 counters in total. We can count the counters individually our repeatedly add 4 + 4 + 4 + 4 + 4 + 4 to get 24.

6 × 4 = 24 means that 6 lots of 4 makes a total of 24.

The first number tells us how many groups we have. The second number tells us how many are in each group and the final number tells us how many there are in total.

Multiplication sentence example of 6 × 4 = 24

The two numbers being multiplied are called factors and the number at the end after the equals sign is called the multiple.

Factors multiply together to make a multiple.

Remember that when writing a multiplication sentence for an array, there are two possible options.

We have 6 columns of 4 or 4 rows of 6.

We can switch the two numbers either side of the multiplication sign.

We have 6 × 4 = 24 or

4 × 6 = 24.

How to write Multiplication Sentences

To write a multiplication sentence use the following steps:

  1. Count the number of equal groups and write this number down.
  2. Write a multiplication sign.
  3. Count the number of objects in each group and write this number after the multiplication sign.
  4. Write an equals sign.
  5. Count the total number of objects and write this number after the equals sign.

Here is an example of writing a multiplication sentence to describe a problem.

We have 2 ladybirds and there are 6 legs on each ladybird.

In total there are 12 legs.

We are asked to write a multiplication sentence to show how many legs there are in total.

Write a multiplication sentences for the model example

The first step is count the number of equal groups. The legs are in two groups. Each ladybird is a group of legs.

We have 2 groups, so we write 2.

There are 6 legs in each ladybird, so 6 legs in each group.

2 lots of 6 legs can be written as 2 × 6.

If we count the total number of legs, we can see that there are 12.

This total number goes after the equals sign.

The multiplication sentence to describe this problem is 2 × 6 = 12. It means 2 lots of 6 legs is 12 legs.

Here is another example of writing a multiplication sentence for a problem.

We have 5 bunches of flowers and in each bunch there are 4 flowers.

If we count the individual flowers, there are 20 in total.

Multiplication Sentences example of counting flowers

We can say that we have 5 groups of 4 flowers.

We can write this as 5 × 4.

The total number of flowers goes at the end, after the equals sign.

The multiplication sentence is 5 × 4 = 20.

nextlesson.JPG

Now try our lesson on Order of Multiplication where we learn that it does not matter in which order we multiply two numbers.

Times Tables Flashcards

Share on Google Classroom:

Choose a particular times table to practise:

×

×

=

Radius and Diameter

Radius and Diamater

videolesson.JPG

what is the radius of a circle

  • The centre of the circle is shown with a small black dot.
  • The radius is the name for any line that goes between the centre and the edge of a circle.
  • The radius of a circle can go in any direction.
  • Every radius on the same circle will always be the same length.
  • This is because the distance from the centre to the edge is always the same for each circle.

What is the diameter of a circle

  • The diameter is any line that goes from one side of a circle to the other and it must pass through the centre of the circle.
  • The diameter is twice as long as the radius.
  • We say that Diameter = 2 × Radius.
  • If we know the length of the radius, we can double it to get the length of the diameter.
  • If we know the length of the diameter, we can halve it to get the length of the radius.

The radius is any line from the centre to the edge of a circle.

The diameter is any line from one side of a circle to the other, passing through the centre.

videolesson.JPG

how to get the diameter from the radius

  • The diameter of a circle is twice as long as the radius.
  • To get from the radius to the diameter, we multiply the radius by 2.
  • The radius is 4 cm.
  • 2 × 4 cm = 8 cm.
  • The diameter is 8 cm long.
  • We can see that a radius connected to another radius can make a diameter.

videolesson.JPG

practiseqs.JPG

Radius and Diameter Worksheets and Answers

Radius and Diameter

What is the Radius of a Circle?

The radius of a circle is any line connecting the circle’s centre to its edge.

The radius is half the distance from one side of a circle to the other and so, it is half of the diameter.

radius of a circle

It does not matter which direction the radius is in. This means that each circle can have many different lines which are the radius.

Here is another example of a radius shown on the same circle.

radius example 2

Here is another example of a radius, again shown on the same circle.

radius example

To say more than one radius we say radii.

We can see that all radii are the same length. This is because every radius is simply the distance from the centre to the outside edge.

Radius and Diameter 1

What is the Diameter of a Circle?

The diameter of a circle is any line that passes from one side of the circle to the other, through the centre of the circle.

The diameter is twice as long as the radius of a circle.

diameter 2

The diameter passes straight across a circle but it must go directly through the centre point.

It does not matter in which direction the diameter goes, however the diameter must be a continuous straight line. It cannot change direction.

There are many different diameters a circle can have. Here is another example of a diameter.

diameter

The diameter is the longest

chordAny line connecting two points on the edge of a circle.
of a circle because it goes directly through the centre of the circle.

This is the Diameter of a circle

How to get the Diameter from the Radius

The diameter is twice the length of the radius. Therefore if you know the radius, multiply it by 2 to find the diameter.

We can say that the diameter = 2 × radius.

For example, if the radius is 4 cm long, then we can multiply this by 2 to find the diameter.

How to get the diameter if we know the radius

2 × 4 cm = 8 cm and so, the diameter of this circle is 8 cm long.

We can see that two 4 cm radii make a diameter that is 8 cm long.

If we are told the radius of a circle, we simply double it to find the diameter.

This is because the radius is half way across the circle from the centre, whereas the diameter is the whole way across the circle passing through the centre.

How to get the Radius from the Diameter?

The radius of a circle is half of its diameter. If we know the diameter, we halve it to find the radius.

We can say that radius =   1 / 2   × diameter.

For example, in this circle the diameter is 10 m.

10 m is the distance from one side to the other, passing through the centre of the circle.

how to get the diameter if we know the radius

The radius is half of this distance.

The radius is   1 / 2   × 10.

Half of 10 is 5 and so, the radius is 5 m long.

This is because the diameter is the whole way across but the radius is only half the way across.

The relation that the radius is half the diameter and the diameter is double the radius is always true for all circles.

nextlesson.JPG

Now try our lesson on What is the Volume of a Cuboid? where we learn how to find the volume of a cuboid.

Reflecting Shapes

Reflecting Shapes

videolesson.JPG

How to reflect Shapes

  • Reflecting a shape means to flip the shape over a mirror line.
  • The mirror line is shown as a dashed line.
  • The shape is now facing the opposite direction to before.
  • Every point on the shape is as far away from the mirror line as it was before.
  • To reflect a shape we move the corners and then join them together at the end.
  • The reflected shape image is the same size and shape as the original object.

The corners of a reflected shape are the same distance away from the mirror line.

The shape image is now facing the opposite direction to the original object.

videolesson.JPG

Example of reflecting a shape in a mirror line

  • To reflect the arrow in the mirror line we first mark the corners.
  • We count how many squares each point is from the mirror line.
  • The reflected point will be the same distance away from the mirror line but on the other side of the line.
  • The tip of the arrow is 4 squares to the left of the line so its reflection will be 4 squares right of the line.
  • The end of the arrow is 1 square left of the line so its reflection will be one square right of the line.
  • Once all of the corners have been reflected, we connect them to complete our reflected image.
  • The original object was pointing left but the reflected image is pointing right.

videolesson.JPG

practiseqs.JPG

Reflecting Shapes Worksheets and Answers

Reflecting Shapes

What does Reflecting a Shape Mean?

Reflecting a shape simply means to flip it over a mirror line. Each point in the shape is moved to the other side of the mirror line but remains the same distance away from the line.

The reflected image will now be facing in the opposite direction to the original object.

what reflection in a mirror line means

The mirror line is the line that the shape is reflected in. It also called a line of reflection.

We can see in this example above that the arrow is pointing left to begin with. After it has been reflected in the mirror line, it now points right.

The end of the arrow is still one square away from the mirror line and the tip of each arrow is 4 squares away from the mirror line.

Reflecting an arrow in a mirror line

After reflecting a shape, each point on the shape is the same distance away from the line of reflection but on the other side of the mirror line.

How to Reflect a Shape in a Mirror Line

To reflect a shape in a mirror line use the following steps:

  1. Mark the corners of the shape.
  2. Place a ruler on one of these corners and on the mirror line so that the ruler is at right angles to the mirror line.
  3. Measure how far away the corner is from the mirror line.
  4. Without moving the ruler, measure this same distance from the mirror line but on the other side of the line.
  5. This is the position of the reflected corner.
  6. Repeat this for each corner of the shape.
  7. Join the reflected corners together to create the reflected image of the shape.

Here is an example of reflecting a triangle in a line or reflection.

The first step is to mark each of the corners of the triangle.

We then use a ruler to measure how far away each corner is from the mirror line. When reflecting shapes on a grid, we can simply count the number of squares each corner is away from the mirror line.

how to reflect a shape in a line

The corner nearest to the mirror line is 1 square to the left of the line.

Its reflection is 1 square to the right of the mirror line.

The other two corners of the triangle are 3 squares to the left of the mirror line and so, their reflection will be 3 squares to the right of the mirror line.

Once all corners have been reflected, the final step is to connect them with a ruler.

The original shape is called the object and the reflected shape is called the image.

Here is another example of reflecting a shape on a grid in a vertical mirror line.

The first step is to mark the corners of the trapezium.

We count how far away from the mirror line each point is and reflect it the same distance to the other side of the line.

Reflecting a trapezium in a line on a grid

The two corners nearest to the mirror line are 2 squares to the left of the line. Their reflection will be 2 squares to the right of the line.

The other two corners furthest from the mirror line are both 4 squares left of the line. So their reflection will be 4 squares to the right of the line.

The reflected image is the same size and shape as the original object. It is just facing in the opposite direction.

We will now look at some examples of reflecting a shape in a horizontal mirror line.

Here we have a parallelogram.

The first step is to mark all of the corners of the parallelogram.

The second step is to count how far each corner is away from the mirror line. This time the points are above the mirror line and so we count how far above the mirror line each point is.

The reflected points will go below the line.

Reflecting a parallelogram on a grid in a horizontal mirror line

The two corners of the shape nearest to the line of reflection are 1 square above the line.

Their reflection is 1 square below the line.

The two corners of the shape furthest from the line of reflection are 3 squares above the line.

Their reflection is 3 squares below the line.

We can see that the reflected image is the same size and shape as the original object.

Here is another example of reflecting a shape on a grid in a horizontal mirror line.

We can see that this shape will have a lot of corners. If this is the case it might be easier to reflect part of the shape and then draw the rest of it in afterwards.

Below we have a cross and so, we will reflect the central square of the cross and draw the rest of it in afterwards.

Reflecting a shape without tracing paper

The central square of the cross is 3 squares above the mirror line.

We can reflect the central square to 3 squares below the mirror line.

Now we can draw the rest of the cross.

The central square has a square next to each of its sides. We can simply add a square next to each side of this central square to complete our cross.

This method is easier than copying every corner across.

Teaching Reflections in a Mirror Line

When first teaching reflections, it is helpful to have a small mirror to show how the reflected shape will look.

It is most helpful to do this with shapes such as arrows or triangles that are not symmetrical. That way, we can show how the shape has been reflected and how its orientation has changed. Shapes like arrows or triangles can be seen to be pointing in the opposite direction to before. If we use rectangles and squares, they will look the same because they are symmetric and we will be unable to see this effect.

We can also show reflections by folding paper.

We can use paint to colour in the inside of the original shape. Whilst the paint is still wet, we can fold the paper down the mirror line and press the two sides together.

The wet paint will leave the reflection of the shape on the other side of the mirror line when you open the paper up.

It can be helpful to look at lines of symmetry in everyday objects or photographs, which can act in a similar way to lines of reflection.

Below we have a picture of the Taj Mahal, with a mirror line down its centre.

reflectional symmetry of the taj mahal

We can see that each tower is the same distance away from the mirror line on each side.

We can also look for reflections in mirrors or reflections in water.

Below is a picture of some city buildings reflected in water.

teaching reflections using water

We can see that the reflected image is the same distance below the surface of the water as the original object.

nextlesson.JPG

Now try our lesson on Translating Shapes where we learn how to translate different shapes.

Translating Shapes

Translating Shapes

videolesson.JPG

what does translating a shape mean?

  • Translating a shape means to move it.
  • When a shape is translated it does not rotate or change size.
  • Every point on the shape moves the same distance in the same direction.
  • A translation 3 right means that the whole shape moves 3 squares right from its original position.
  • When translating a shape it is easiest to move all of its corners first.
  • Each corner of the shape has moved 3 squares to the right.

Translating a shape means to move it without changing its size or orientation.

All points in the shape move by the same amount in the same direction.

videolesson.JPG

example of translating a triangle

  • Translating the triangle 4 right and 1 down means to move the whole triangle 4 squares right and 1 square down.
  • First mark the corners of the shape.
  • Move all of the corners 4 squares to the right one corner at a time.
  • Mark each corner after we have moved it 4 squares right.
  • We then move each of the three corners 1 square down.
  • We join the corners together to make our final shape.
  • The triangle that has moved 4 right and 1 down is called the image.

videolesson.JPG

practiseqs.JPG

Translating Shapes Worksheets and Answers

Translating Shapes

What does Translating a Shape Mean?

Translating a shape means to move it without rotating it or changing its size. All points in the shape move by exactly the same distance in the same direction.

The original shape is called the object and the shape that has been translated is called the image.

For example, translating a shape 3 right means to move it 3 squares right.

what does translating a shape mean?

We can move the rectangle 3 squares to the right by sliding it right one square at a time.

When teaching translations it is important to emphasise that we move each corner of the shape. We can see that each corner of the translated shape is 3 squares to the right of where it started.

translating a shape

A common mistake is to believe that the translated shape and the original shape should be separated by the amount we are translating the shape by. We can see that although we have translated this shape by 3 squares to the right, there is only 1 square separating the original object and the translated image.

It is important that we move each corner separately.

We can see that each corner has been moved 3 squares to the right.

Here is another example of translating a square 5 left.

This means that we will move every point on the square 5 squares left.

We can see that every point inside the shape has moved 5 squares left. Every point in the shape has moved the same distance in the same direction.

Translating Shapes means that each point moves the same distance in the same direction

Rather than moving each point inside the shape, we can just move the corners of the shape and then join them together to form the outside of the shape.

How to Translate Shapes

To translate a shape follow these steps:

  1. Mark all the corners of the shape.
  2. Move each corner to its new position by the amount given.
  3. Join these corners together to draw the shape in its new position.

Here is an example of translating a triangle 2 up.

The first step is to mark the three corners of the triangle.

We then move each corner of the triangle 2 squares up. We can move the three corners one by one.

Translating a triangle 2 up

We can see that the final image and the original object are the same size and shape. The shape did not rotate and remained in the same orientation.

Here is an example of translating a rectangle 4 down.

This means that we will move all of the corners of the rectangle 4 squares down.

We can move the bottom left corner of the shape 4 squares down.

Translating Shapes 3

We know that the bottom right corner will be in line with the bottom left corner.

We know that when a shape is translated it does not change size. The original object was 2 squares long and so, the image will also be 2 squares long.

We can count up two squares from the bottom corners of the image to find the top corners.

We can see that with simple shapes, we can just move one corner and then draw the rest of the shape in because the image will be the same size as the original object. This can be quicker than moving every corner one by one.

In school questions in both primary and secondary school, the translations we are asked to make will involve horizontal and vertical movements. It is rare that we will be asked to translate a shape diagonally.

Here is an example of translating a shape both vertically and horizontally.

We will translate this square 3 right and 2 down.

When asked to translate a shape both horizontally and vertically, complete the horizontal translation first and then move these points in the vertical direction separately.

We first move each of the corners of the square 3 squares to the right.

Translating a square vertically and horizontally

We mark the position of the corners after they have been translated 3 squares right.

We then move these corners 2 squares down to their final position.

We connect the corners to create the final image.

Here is an example of translating a rectangle 2 left and 6 up.

We mark all of the corners and move them all 2 squares left first.

example of translating shapes on a grid

We can mark these points on our grid and then translate them 6 up.

We can then join these points to get our final image. We can erase the points that we drew to help us.

In this example of translating shapes on a grid, we are asked to translate this triangle 4 right and 1 down.

Translating Shapes on a grid example of translating a triangle

We first move the corners of the triangle 4 squares right and mark their new positions.

We can then move these points 1 down to obtain the final image position.

nextlesson.JPG

Now try our lesson on Classifying Angles where we learn how to describe an angle as acute, obtuse or reflex.

Fractions of Shapes: Interactive Questions

Fractions of Shapes: Interactive Questions Return to video lesson on Fractions of Shapes

Share on Google Classroom:

What is the shaded fraction shown below?

blankspace
blank
fractionline
 

 

blank

error: Content is protected !!