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5Fluency & Reasoning Teaching Slides

Decimals & Percentages

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Fluency & Reasoning Teaching Slides

Decimals up to 2 decimal

places (2 d.p.)

masterthecurriculum.co.uk

Activity 1 Decimals up to 2 d.p.

Ones Tenths Hundredths

0.1 0.01 0.010.1 0.1

There are __ ones, __ tenths, and __ hundredths.The number is __.

What number is represented on the place value chart?

How did you know what number it was??35 – Decimals & Percentages

0.1 0.01 0.010.1 0.1

There are 0 ones, 3 tenths, and 2 hundredths.The number is 0.32.

45 – Decimals & Percentages

0.10.01 0.01

0.010.1

How did you know what number it was??

There are 0 ones, 4 tenths, and 3 hundredths.The number is 0.43.

0.10.01 0.01

0.010.1

1.52 0.49

0.37 0.88

Represent the numbers on a place value chart and complete the stem sentences.

0.1 0.1 0.1 0.1 0.1 0.01 0.011

0.1 0.1 0.1 0.01 0.01 0.01 0.01 0.01 0.01 0.01

0.1 0.1 0.1 0.01 0.01 0.01 0.01 0.01 0.01 0.010.1 0.01 0.01

0.1 0.1 0.1 0.01 0.01 0.01 0.01 0.01 0.010.1 0.01 0.010.1 0.1 0.1 0.1

2.44 0.61

1.97 3.85

Make the numbers with place value counters and write down the value of the underlined digit.

2.44 0.61

1.97 3.85

Make the numbers with place value counters and write down the value of the underlined digit.

4 hundredths 6 tenths 7 ones

1 one 8 tenths 1 ten

0.57 = __ + 0.07 = _________ and 7 hundredths

0.57 = 0.5 + __ = 5 tenths and ______________

How many other ways can you partition 0.57??

0.29 = 0.2 + 0.09 = 2 tenths and 9 hundredths

Fill in the missing numbers.

Reasoning 1 Decimals up to 2 d.p.

Malachi says there is only one way to partition 0.53.

0.5 0.03

Prove that Malachi is incorrect by finding at least 3 different ways of partitioning 0.53.?135 – Decimals & Percentages

Malachi says there is only one way to partition 0.53.

Possible ways of partitioning:

0.53 = 0.4 + 0.13 0.53 = 0.3 + 0.23 0.53 = 0.2 + 0.330.53 = 0.51 + 0.02 0.53 = 0.35 + 0.18 0.53 = 0.1 + 0.43

0.5 0.03

Match each description to the correct number.

1.73My number has the same amount of tens and tenths.

My number has one decimal place

My number has 4 hundredths.

My number has seven tenths.

Match each description to the correct number.

1.73My number has the same amount of tens and tenths.

My number has one decimal place

My number has 4 hundredths.

My number has seven tenths.

Discuss

How many ones/tenths/hundredths are in the number? How do you write this as a decimal? Why?

What is the value of the __ in the number ___?

When do we need to use zero as a place holder?

How can you partition decimal numbers in different ways?

Decimals up to 2 d.p.

Decimals as Fractions (1)

Activity 1 Decimals as Fractions (1)

The fraction is the same as the decimal _______.

What fraction is shown in both representations?

The fraction is the same as the decimal 0.03.

If the whole bead string represents one whole, what decimal is represented by the highlighted part?

Can you represent this on a 100 square??

If the whole bead string represents one whole, what decimal is represented by the highlighted part?

Reasoning 1 Decimals as Fractions (1)

Which of the images below is the odd one out?

Explain why.?235 – Decimals & Percentages

0.1 0.10.1

0.1 0.2 0.3 0.4 0.50

Which of the images below is the odd one out?

0.1 0.10.1

0.1 0.2 0.3 0.4 0.50

B is the odd one out because it shows 14 or 0.25.

The other images show 0.3 or 310.

How many different ways can you complete the part-whole model using fractions or decimals?

Create another part-whole model like the one above for your partner to complete.?255 – Decimals & Percentages

100100

0.25 75100 or 34 or 0.75

How many different ways can you complete the part-whole model using fractions or decimals?

Now complete the following part-whole models using fractions or decimals.

0.50 0.80

Now complete the following part-whole models using fractions or decimals.

0.50 0.8010100 or

25100 or 0.25

There are various possible answers.This is only one of

the many possibilities.

25100 or 0.25

25 or 0.4

15 or 0.2

15100 or 0.15

5100 or 0.05

Discuss

What does the whole grid represent?

What can you use to describe the equal parts of the grid?

How would you convert a fraction to a decimal?

What does the decimal point mean?

Can the fraction be simplified?

How can you prove that the decimal __ and the fraction __ are the same?

Use this method to record equivalent decimals and fractions of the models in the next pages.

0.5 = 510 = 50

Model 1 Model 2

0.29 = 291000.46 = 46

Model 3

1.6 = 1610 = 160

Model 4

3.47 = 347100

a b c d

2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

Write down the values of a, b, c, and d as a decimal and a fraction.

a b c d

2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

209100

245100

287100

291100

Write down the values of a, b, c, and d as a decimal and a fraction.

Complete the table.

Concrete DecimalDecimal

(Expanded)Fractions Fraction

(Expanded)Words

2.41 2 + 0.4 + 0.01 2 41100 2+

Two ones, four tenths, and one

hundredth

3.05 3 5100

Three ones, five tenths, and two

hundredths

Concrete DecimalDecimal

(Expanded)Fractions Fraction

(Expanded)Words

2.41 2 + 0.4 + 0.01 2 41100 2+

Two ones, four tenths, and one

hundredth

3.05 3 + 0.05 3 5100 3+

Three ones, and five hundredths

1.98 1 + 0.9 + 0.08 198100

One one, nine tenths, and

eight hundredths

3.52 3 + 0.5 + 0.02 352100

Three ones, five tenths, and two

hundredths

Complete the table.

0.01 0.01

10.1 0.1

0.10.01

0.01 0.01

2.35 = 2 ones, 3 tenths, and 5 hundredths

1.52 0.49 0.370.88

Can you write the following numbers in at least three different ways?

Decimal (Expanded)

Fractions Fraction (Expanded)

0.8 + 0.08 88100

Eight tenths, and eight

hundredths.

1 + 0.5 + 0.02 1 52100 1 +

One one, five tenths, and two

hundredths.

0.4 + 0.09 49100

100Four tenths, and nine hundredths.

0.3 + 0.07 37100

Three tenths, and seven

hundredths.

Zach says:

To convert a fraction to a decimal, take the numerator and put it after

the decimal point.

E.g. 22100 = 0.22.

Write two examples of converting fractions to decimals to prove that this does not always work.?

Zach is incorrect.

• 2100 is not equal to 0.2

• 4210 is not equal to 0.42

To convert a fraction to a decimal, take the numerator and put it after

the decimal point.

E.g. 22100 = 0.22.

Zach says:

Use the digits 1, 2, and 3 to complete the decimal number.

Write the decimals as mixed numbers.Choose three numbers and write them in words.?

List all possible numbers you can make.

515.23 = 15 23

100 = one ten, five ones, two tenths, three hundredths.

15.32 = 15 32100 = one ten, five ones, three tenths, two hundredths.

25.13 = 25 13100 = two tens, five ones, one tenth, three hundredths.

25.31 = 25 31100 = two tens, five ones, three tenths, one hundredth.

35.21 = 35 21100 = three tens, five ones, two tenths, one hundredth.

35.12 = 35 12100 = three tens, five ones, one tenth, two hundredths.

Use the digits 1, 2, and 3 to complete the decimal number.

Discuss

In the number 1.34 what does the 1 represent, what does the 3 represent, what does the 4 represent?

Can you represent this number in a different way, and another, and another?

On the number line, where can you see tenths? Where can you see hundredths?

On the number line, tell me another number that is between c and d. Now give your answer as a fraction.

Tell me a number that is not between c and d.

Year 5

Understand Thousandths

Use Base 10 to build:

• 2 wholes, 1 tenth, 5 hundredths, 6 thousandths• 3 tenths, 8 hundredths, and 2 thousandths• 7.184

Activity 1 Understand Thousandths

= 1 whole = 1 tenth = 1 hundredth = 1 thousandth

Rosie is using Base 10 to represent decimals.

2 wholes, 1 tenth, 5 hundredths, 6 thousandths.

Rosie is using Base 10 to represent decimals.

3 tenths, 8 hundredths, and 2 thousandths

10___1

1 ___1

1000___1

100___1

101 ___1

1000___1

10___1

100___1

101 ___1

1000___1

= __ tenths1 ___1

10 = __ hundredths ___1

100 = __ thousandths

Use the place value counters to help you fill in the final chart.

10___1

1 ___1

1000___1

100___1

101 ___1

1000___1

10___1

100___1

101 ___1

1000___1

= 10 tenths1 ___1

10 = 10 hundredths ___1

100 = 10 thousandths

1000___1

Use the place value counters to help you fill in the final chart.

How many thousandths are in one tenth??545 – Decimals & Percentages

What has this hundred square been divided up into? How many thousandths are there in one hundredth?

The hundred square has been divided by 10.

1 hundredth = 10 thousandths.1 tenth = 100 thousandths.

Reasoning 1 Understand Thousandths

Leanna thinks that the 2 numbers are equal.

Do you agree? Explain your thinking.Can you write this amount as a decimal and as a fraction.?

0.0010.01 0.01

0.01 0.010.001

0.0010.001

=0.01 0.001

0.01 0.01

0.0010.0010.01

0.01 0.01

0.01 0.010.01

0.01 0.01

Leanna thinks that the 2 numbers are equal.

0.0010.01 0.01

0.01 0.010.001

0.0010.001

=0.01 0.001

0.01 0.01

0.0010.0010.01

0.01 0.01

0.01 0.010.01

0.01 0.01

She is correct. We can exchange ten hundredth counters for a one tenth

counter.

0.159 = 1591000

0.543 = 5 tenths, 4 hundredths, and 3 thousandths

= 510 +

4100 +

= 0.5 + 0.04 + 0.003

0.752 0.3240.148

Write these numbers in three different ways:

0.148 = 1 tenth, 4 hundredths, and 8 thousandths

= 110 +

4100 +

= 0.1 + 0.04 + 0.008

Write these numbers in three different ways:

= 710 +

5100 +

= 0.7 + 0.05 + 0.002

= 310 +

2100 +

= 0.3 + 0.02 + 0.004

Discuss

If 4 tenths = 0.4, 4 hundredths = 0.04, what is 4 thousandths equal to?

Using the place value charts:How many tenths are in a whole?

How many hundredths are there in 1 tenth?Using place value counters complete the final chart.

How many thousandths are in 1 hundredth?

Understand Thousandths

Year 5

Thousandths as Decimals

Activity 1 Thousandths as Decimals

1 ___1

1000___1

100 1110

11 ___1

7 ones, 4 tenths, 1 hundredth, and 3 thousandths

Use the place value chart and counters to represent these numbers.

Write down the numbers as a decimal.?

C 5 291000

1 ___1

1000___1

100 1110

4 1 2 1

11 ___1

C 5 291000

7 ones, 4 tenths, 1 hundredth, and 3 thousandthsB

Use the place value chart and counters to represent these numbers.

The arrows are pointing to different numbers.

Write each number as a decimal and then as a mixed number.?

2 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.1

The arrows are pointing to different numbers.

2 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.1

2 181000

2 421000

2 741000

Reasoning 1 Thousandths as Decimals

Jeff has 5 counters.He makes numbers using the place value chart.

At least 3 columns have counters in them.

Can you record the numbers in different ways??

What is the largest and smallest number he can make with 5 counters?

Jeff has 5 counters.He makes numbers using the place value chart.

At least 3 columns have counters in them.

11000Largest

1 1 1 ___1

100___1

11000Smallest

100___1

10___1

1000___1

Symbols have been used to represent two different numbers.Write down the value of each as a mixed number and as a

decimal.

= 110 = 1

100 = 11000= 1

= 110 = 1

100 = 11000= 1

= 2 1321000 = 2.132

= 1 2141000 = 1.214

Symbols have been used to represent two different numbers.Write down the value of each as a mixed number and as a

decimal.

Three children are representing number 0.603

6031000

Who is correct? Explain why.?

Rosie Esin Malachi

310+ 3

1000610

Three children are representing number 0.603

6031000

Rosie Malachi

310+ 3

1000610

They are all correct.

Rosie has recorded it as a fraction. Esin and Malachi have partitioned it differently.

Discuss

What number is represented?

How will you show this on the place value chart? How many ones/tenths/hundredths/thousandths do you have?

Where would 2.015 be positioned on the number line? How many thousandths do you have?

How do you record this as a mixed number?

Thousandths as Decimals

Year 5

Rounding Decimals

Activity 1 Rounding Decimals

Ones Tenths

Complete the number lines and round the representations to the nearest whole number:

Ones Tenths

3 43.4

Ones Tenths

4 54.5

Complete the number lines and round the representations to the nearest whole number:

Use the number lines to round 4.24 to the nearest tenth and the nearest whole number.

4.2 4.25 4.3 4 4.5 5

Use the number lines to round 4.24 to the nearest tenth and the nearest whole number.

4.24 4.244.2 4

0.10.1

Round each number to the nearest tenth and nearest whole number. Use number lines to help you.

0.10.1

3.53.483.4 43 3.48

0.10.1

5.1 65

5.2 5.165.16

Reasoning 1 Rounding Decimals

Tia is measuring a cardboard box with a ruler that measures in centimetres and milimetres.

She measures it to the nearest cm and writes the answer as 37cm.

What is the smallest length the cardboard box could be?

She measures it to the nearest cm and writes the answer as 37cm.

What is the smallest length the cardboard box could be?

Smallest : 36.5 cm

Tia is measuring a cardboard box with a ruler that measures in centimetres and milimetres.

Leanna is thinking of a number.

Rounded to the nearest whole, her number is 5.

Rounded to the nearest tenth, her number is 4.8.

Leanna

Write down at least 4 different numbers that she could be thinking of.?

Leanna is thinking of a number.

Rounded to the nearest whole, her number is 5.

Rounded to the nearest tenth, her number is 4.8.

Possible answers :

4.75 4.814.76 4.824.77 4.834.78 4.84

4.79Leanna

Is there more than one option? Explain why.?

A number between 11 and 20 with 2 decimal places rounds to the same number when rounded to one decimal place and when rounded to the

nearest whole number.

What could this be?

The whole number can range from 11 to 19 and the decimal places can range from either ___.01 to ___.04 or ___ .95 to ___ .99.

A number between 11 and 20 with 2 decimal places rounds to the same number when rounded to one decimal place and when rounded to the

nearest whole number.

What could this be?

Discuss

What number do the ones and tenths counters represent?

How many decimal places does it have?

When rounding to the nearest one decimal place, how many digits will there be after the decimal point?

Where would 4.25 appear on both number lines?

What is the same and what is different about the two number lines?

Rounding Decimals

Order & Compare Decimals

Activity 1 Order & Compare Decimals

11 0.1

0.01 0.01

0.01 0.001

0.1 11 0.1 0.001

0.1 0.001

0.001 0.001

Use <, > or = to make the statements correct.

0.01 0.01

0.01 0.001

0.0010.1

12.52 ÷ 10

11 0.1

0.01 0.01

0.01 0.001

0.1 > 11 0.1 0.001

0.1 0.001

0.001 0.001

0.01 0.01

0.01 0.001

0.1 >0.0010.1

12.52 ÷ 10

Use <, > or = to make the statements correct.

2.351 2.304

1.452 1.252

4.11 4.12

4.115 4 1121000 Four and 11 hundredths

Place the numbers in ascending order on the number line.

Is it easier to convert fractions to decimals than decimals to fractions??

4.11 4.12

4.115 4 1121000 Four and 11 hundredths

4.1154 1121000

Four and 11 hundredths

Place the numbers in ascending order on the number line.

Place in descending order.

Check your answers using a place value chart.?

0.51 0.612 0.112 0.001

7.5km 5.015km 8.001km 11km

34.99 20.011 34.009 20.110

Place in descending order.

0.6120.510.1120.001

11km8.001km7.5km

5.015km

34.9934.00920.11020.011

0.612 0.51 0.112 0.001

5.015km8.001km11km

15 km 5 km

20.01120.11034.99

34.009

Reasoning 1 Order & Compare Decimals

Tia says:

4.137 is greater than 4.2 because 137 is

greater than 2.

Do you agree? Explain your answer.?

4.137 is greater than 4.2 because 137 is

greater than 2.

Tia is incorrect because 2 tenths is greater than 137 thousandths.

Tia says:

Rosie says:

I have put some numbers into ascending order:

4 511000

4 51100

What can’t her number be??Rosie

Rosie has missed one number out.

What could her number be?

Rosie has missed one number out.

What could her number be?

It could be:4.052, 4.053, 4.103, 4.106, etc.

It cannot be a number below 4.015 or a number above 4.51.

I have put some numbers into ascending order:

4 511000

4 51100

Rosie says:

Discuss

What number is represented by the place value counters?

_____ is greater/less than ____ because….

Explain how you know.

Can you build the numbers using place value counters?

How can you use these concrete representations to compare sizes?

Order & Compare Decimals

Understand Percentages

Activity 1 Understand Percentages

Complete the sentence stem for each diagram.

There are ___ parts per hundred shaded. This is ___%

Complete the sentence stem for each diagram.

There are 4 parts per hundred shaded.

This is 4 %

There are 24 parts per hundred shaded.

This is 24 %

Pictorial Parts per hundred Percentage

There are 32 parts per hundred.

Complete the table.

Pictorial Parts per hundred Percentage

Complete the table.

? 100%

Complete the bar models.

Reasoning 1 Understand Percentages

Malachi has spilt ink on his hundred square.

Complete the sentence stems to describe what percentage is shaded.

It could be _ _ _ _.

It must be _ _ _ _.

It can’t be _ _ _ _.

Malachi has spilt ink on his hundred square.

Complete the sentence stems to describe what percentage is

shaded.

It could be 24%.

It must be less than 50%.

It can’t be 10%.

Possible answers:

Zach, Tia, and Leanna all did a test with 100 questions.

Leanna got 7 more questions correct than Zach.

Name Score Percentage

Zach 65 out of 100

Tia 75%

Leanna

Complete the table.How many more marks did each child need to score 100%??

Name Score Percentage

Zach 65 out of 100 65%

Tia 75 out of 100 75%

Leanna 72 out of 100 72%

Zach needs 35.Tia needs 25.

Leanna needs 28.

Zach, Tia, and Leanna all did a test with 100 questions.

Leanna got 7 more questions correct than Zach.

Zach and Rosie each have 100 sweets.

Zach eats 55% of his.Rosie has 45 sweets left.

Who has more sweets left?

Zach eats 55% of his.Rosie has 45 sweets left.

Who has more sweets left?

Neither.

They both have an equal number of sweets left.

Zach and Rosie each have 100 sweets.

Discuss

How many parts is the square split in to?

How many parts per hundred are shaded/not shaded?

Can you represent this percentage differently?

Look at the bar model, how many parts is it split into?

If the bar is worth 100%, what is each part worth?

Understand Percentages

Year 5

Percentages as Fractions & Decimals

Activity 1

Pictorial Percentage Fraction Decimal

30 out of 100

30 hundredths

Complete the table.

Activity 1

Complete the table.

Activity 1

55 out of 100

55 hundredths

Complete the table.

Activity 1

Complete the table.

Activity 1

8 out of 100

8 hundredths

Complete the table.

Leanna has used 60ml of her shampoo. Her shampoo bottle holds 400ml of shampoo.

What proportion of the shampoo has she used?

Activity 2 Percentages as Fractions & Decimals

Give your answer as a percentage and a decimal.

60400 = 15

100 = 15 % = 0.15

Leanna has used 60ml of her shampoo. Her shampoo bottle holds 400ml of shampoo.

What proportion of the shampoo has she used?

Give your answer as a percentage and a decimal.

60400 = 15

100 = 15 % = 0.15

Record the fractions as decimals and percentages.

= 24100 = 24% = 0.24

= 49100 = 49% = 0.49

= 11100 = 11% = 0.11

= 19100 = 19% = 0.19

Reasoning 1 Percentages as Fractions & Decimals

Esin says:

To convert a fraction to a percentage, you just need to put

a percent sign next to the numerator.

Is Esin correct? Explain your answer.?

Esin is incorrect.

This only works when the denominator is 100 because percent means parts

per hundred.

Esin says:

To convert a fraction to a percentage, you just need to put

a percent sign next to the numerator.

Solve:

At a cinema, 610 of the audience are adults.

The rest of the audience is made up of boys and girls.

There are three times as many boys as girls.

What percentage of the audience are boys?

At a cinema, 610 of the audience are adults.

The rest of the audience is made up of boys and girls.

There are three times as many boys as girls.

What percentage of the audience are boys?

40% are children.So 30% are boys and 10% are girls.

Solve:

3 children have each read 240 pages of their own books.

Malachi’s book has 500 pages.Tia’s book has 300 pages.

Rosie’s book has 400 pages.

What fraction and percentage of their books have they read? How much in decimals?

Who has read the most of their books??

Malachi’s book has 500 pages.Tia’s book has 300 pages.

Rosie’s book has 400 pages.

What fraction and percentage of their books have they read? How much in decimals?

Malachi has read 240500, 48%, or 0.48.

Tia has read 240300, 80%, or 0.8.

Rosie has read 240400, 60%, or 0.6.

Tia has read the most of her book.

3 children have each read 240 pages of their own books.

Discuss

What do you notice about the percentages and the decimals?

What’s the same and what’s different about percentages, decimals and fractions?

Can you convert any percentage into a decimal and a fraction?

Year 5

Equivalent Fractions, Decimals

and percentages (F.D.P.)

Activity 1 Equivalent F.D.P.

Use a bead string to show:

What are these decimals as a percentage?What are they as a fraction? Can you simplify the fraction??

Use a bead string to show:

= 60% = 60100 = 3

= 50% = 50100 = 1

= 10% = 10100 = 1

= 25% = 25100 = 1

10% 10% 10% 10% 10% 10% 10% 10% 10% 10%

Use the bar model to convert the fractions into a percentages and decimals.

10% 10% 10% 10% 10% 10% 10% 10% 10% 10%

Use the bar model to convert the fractions into a percentages and decimals.

50% = 0.5

75% = 0.75

70% = 0.7

40% = 0.4

Draw arrows to show the position of each representation on the number line.

0% 100%

Draw arrows to show the position of each representation on the number line.

Reasoning 1 Equivalent F.D.P.

Sort the fractions, decimals and percentages into the correct column.

Less than 12 Equal to 12 Greater than 12

Eight tenths

80 hundredths

Sort the fractions, decimals and percentages into the correct column.

Less than 12 Equal to 12 Greater than 12

Eight tenths

80 hundredths

15% 2040

Zach has £45.

He spends 13 of his money on a jacket and 50% on toys.

How much does he have left?

Zach has £45.

He spends 13 of his money on a jacket and 50% on toys.

How much does he have left?

£45 – £15 – £22.5 = £7.5

Tia is playing a maths game.

Here are her scores at three different levels.

Level A – 330 points out 440.Level B – 280 out of 350.Level C – 60 points out of 120.

At which level did she have a higher success rate?

Tia is playing a maths game.

Here are her scores at three different levels.

Level A – 330 points out 440.Level B – 280 out of 350.Level C – 60 points out of 120.

At which level did she have a higher success rate?Level A – 75%Level B – 80%Level C – 50%

Tia had a higher success rate on level B.

Discuss

How many hundredths is each bead worth? How does this help you convert the decimals to fractions and percentages?

How many hundredths is the same as 0.1?

What fractions does the bar model show? How does this help to convert them to percentages?

Which is closer to 100%, or 50%? How do you know?

Equivalent F.D.P.

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