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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.)
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Activity 1 Decimals up to 2 d.p.
Ones Tenths Hundredths
0 3 2
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
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Activity 1 Decimals up to 2 d.p.
Ones Tenths Hundredths
0 3 2
0.1 0.01 0.010.1 0.1
There are 0 ones, 3 tenths, and 2 hundredths.The number is 0.32.
What number is represented on the place value chart?
45 – Decimals & Percentages
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Activity 1 Decimals up to 2 d.p.
Ones Tenths Hundredths
There are __ ones, __ tenths, and __ hundredths.The number is __.
0.1
0.1
0.10.01 0.01
0.010.1
How did you know what number it was??
What number is represented on the place value chart?
55 – Decimals & Percentages
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Activity 1 Decimals up to 2 d.p.
Ones Tenths Hundredths
0 4 3
There are 0 ones, 4 tenths, and 3 hundredths.The number is 0.43.
0.1
0.1
0.10.01 0.01
0.010.1
What number is represented on the place value chart?
65 – Decimals & Percentages
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Activity 1 Decimals up to 2 d.p.
1.52 0.49
0.37 0.88
Represent the numbers on a place value chart and complete the stem sentences.
75 – Decimals & Percentages
There are __ ones, __ tenths, and __ hundredths.The number is __.
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Activity 1 Decimals up to 2 d.p.
1.52
0.49
0.37
0.88
Represent the numbers on a place value chart and complete the stem sentences.
Ones Tenths Hundredths
1 5 2
0.1 0.1 0.1 0.1 0.1 0.01 0.011
Ones Tenths Hundredths
0 3 7
0.1 0.1 0.1 0.01 0.01 0.01 0.01 0.01 0.01 0.01
Ones Tenths Hundredths
0 4 9
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
Ones Tenths Hundredths
0 8 8
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
85 – Decimals & Percentages
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Activity 2 Decimals up to 2 d.p.
2.44 0.61
1.97 3.85
67.39
12.19
Make the numbers with place value counters and write down the value of the underlined digit.
95 – Decimals & Percentages
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Activity 2 Decimals up to 2 d.p.
2.44 0.61
1.97 3.85
67.39
12.19
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
105 – Decimals & Percentages
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Activity 3 Decimals up to 2 d.p.
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.
115 – Decimals & Percentages
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0.29 = 0.2 + 0.09 = 2 tenths and 9 hundredths
Activity 3 Decimals up to 2 d.p.
0.57 = 0.5 + 0.07 = 5 tenths and 7 hundredths
0.57 = 0.5 + 0.07 = 5 tenths and 7 hundredths
Fill in the missing numbers.
125 – Decimals & Percentages
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Reasoning 1 Decimals up to 2 d.p.
Malachi says there is only one way to partition 0.53.
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
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Reasoning 1 Decimals up to 2 d.p.
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
145 – Decimals & Percentages
0.53
0.5 0.03
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Reasoning 2 Decimals up to 2 d.p.
155 – Decimals & Percentages
Match each description to the correct number.
4.54
5.5
13.16
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.
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Reasoning 2 Decimals up to 2 d.p.
165 – Decimals & Percentages
Match each description to the correct number.
4.54
5.5
13.16
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.
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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.
175 – Decimals & Percentages
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Fluency & Reasoning Teaching Slides
Decimals as Fractions (1)
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Activity 1 Decimals as Fractions (1)
The fraction is the same as the decimal _______.
What fraction is shown in both representations?
1100
1100
1100
3100
195 – Decimals & Percentages
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Activity 1 Decimals as Fractions (1)
What fraction is shown in both representations?
1100
1100
1100
3100
The fraction is the same as the decimal 0.03.
205 – Decimals & Percentages
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Activity 2 Decimals as Fractions (1)
215 – Decimals & Percentages
If the whole bead string represents one whole, what decimal is represented by the highlighted part?
Can you represent this on a 100 square??
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Activity 2 Decimals as Fractions (1)
225 – Decimals & Percentages
30100
If the whole bead string represents one whole, what decimal is represented by the highlighted part?
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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
A B
C
D110
110
110
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Reasoning 1 Decimals as Fractions (1)
Which of the images below is the odd one out?
245 – Decimals & Percentages
0.1 0.10.1
0.1 0.2 0.3 0.4 0.50
A B
C
D110
110
110
B is the odd one out because it shows 14 or 0.25.
The other images show 0.3 or 310.
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Reasoning 2 Decimals as Fractions (1)
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
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Reasoning 2 Decimals as Fractions (1)
265 – 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?
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Reasoning 3 Decimals as Fractions (1)
Now complete the following part-whole models using fractions or decimals.
275 – Decimals & Percentages
60100
0.50 0.80
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Reasoning 3 Decimals as Fractions (1)
Now complete the following part-whole models using fractions or decimals.
285 – Decimals & Percentages
60100
0.50 0.8010100 or
0.1
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
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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?
Decimals as Fractions (1)
295 – Decimals & Percentages
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Fluency & Reasoning Teaching Slides
Decimals as Fractions (2)
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Activity 1 Decimals as Fractions (2)
Use this method to record equivalent decimals and fractions of the models in the next pages.
315 – Decimals & Percentages
0.5 = 510 = 50
100
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Activity 1 Decimals as Fractions (2)
325 – Decimals & Percentages
Model 1 Model 2
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Activity 1 Decimals as Fractions (2)
335 – Decimals & Percentages
Model 1 Model 2
0.29 = 291000.46 = 46
100
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Activity 1 Decimals as Fractions (2)
345 – Decimals & Percentages
Model 3
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Activity 1 Decimals as Fractions (2)
355 – Decimals & Percentages
Model 3
1.6 = 1610 = 160
100
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Activity 1 Decimals as Fractions (2)
365 – Decimals & Percentages
Model 4
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Activity 1 Decimals as Fractions (2)
375 – Decimals & Percentages
Model 4
3.47 = 347100
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Activity 2 Decimals as Fractions (2)
a b c d
2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3
385 – Decimals & Percentages
Write down the values of a, b, c, and d as a decimal and a fraction.
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Activity 2 Decimals as Fractions (2)
a b c d
2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3
395 – Decimals & Percentages
209100
or
2.09
245100
or
2.45
287100
or
2.87
291100
or
2.91
Write down the values of a, b, c, and d as a decimal and a fraction.
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Activity 3 Decimals as Fractions (2)
405 – Decimals & Percentages
Complete the table.
Concrete DecimalDecimal
(Expanded)Fractions Fraction
(Expanded)Words
2.41 2 + 0.4 + 0.01 2 41100 2+
410
+1
100
Two ones, four tenths, and one
hundredth
3.05 3 5100
1+910
+8
100
Three ones, five tenths, and two
hundredths
0.01
0.11
1 0.1
0.1
0.1
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Activity 3 Decimals as Fractions (2)
Concrete DecimalDecimal
(Expanded)Fractions Fraction
(Expanded)Words
2.41 2 + 0.4 + 0.01 2 41100 2+
410
+1
100
Two ones, four tenths, and one
hundredth
3.05 3 + 0.05 3 5100 3+
5100
Three ones, and five hundredths
1.98 1 + 0.9 + 0.08 198100
1+910
+8
100
One one, nine tenths, and
eight hundredths
3.52 3 + 0.5 + 0.02 352100
3+510
+2
100
Three ones, five tenths, and two
hundredths
0.01
0.11
1 0.1
0.1
0.1
415 – Decimals & Percentages
Complete the table.
0.01
0.01 0.01
0.01 0.01
1
11
1
11
0.1
0.1
0.1
0.1
0.1
0.01
0.01
10.1 0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.10.01
0.01 0.01
0.01 0.01
0.01
0.01 0.01
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Reasoning 1 Decimals as Fractions (2)
425 – Decimals & Percentages
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?
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Reasoning 1 Decimals as Fractions (2)
435 – Decimals & Percentages
1.52
0.49
0.37
0.88
Can you write the following numbers in at least three different ways?
Decimal (Expanded)
Fractions Fraction (Expanded)
Words
0.8 + 0.08 88100
810
+8
100
Eight tenths, and eight
hundredths.
1 + 0.5 + 0.02 1 52100 1 +
510
+2
100
One one, five tenths, and two
hundredths.
0.4 + 0.09 49100
410
+9
100Four tenths, and nine hundredths.
0.3 + 0.07 37100
310
+7
100
Three tenths, and seven
hundredths.
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Reasoning 2 Decimals as Fractions (2)
445 – Decimals & Percentages
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.?
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Reasoning 2 Decimals as Fractions (2)
455 – Decimals & Percentages
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:
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Reasoning 3 Decimals as Fractions (2)
465 – Decimals & Percentages
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.?
5
List all possible numbers you can make.
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Reasoning 3 Decimals as Fractions (2)
475 – Decimals & Percentages
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.
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Discuss
48
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.
Decimals as Fractions (2)
Year 5
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Fluency & Reasoning Teaching Slides
Understand Thousandths
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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.
505 – Decimals & Percentages
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2 wholes, 1 tenth, 5 hundredths, 6 thousandths.
Activity 1 Understand Thousandths
Rosie is using Base 10 to represent decimals.
3 tenths, 8 hundredths, and 2 thousandths
7.184
515 – Decimals & Percentages
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Activity 2 Understand Thousandths
___1
10
___1
10___1
10
___1
10___1
10
___1
10___1
10
___1
10___1
10
___1
10___1
10
1
1 ___1
1000___1
100___1
101 ___1
1000___1
100
___1
10___1
100___1
100
___1
100___1
100
___1
100___1
100
___1
100___1
100
___1
100___1
100
___1
101 ___1
1000___1
100
___1
100
= __ tenths1 ___1
10 = __ hundredths ___1
100 = __ thousandths
525 – Decimals & Percentages
Use the place value counters to help you fill in the final chart.
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Activity 2 Understand Thousandths
___1
10
___1
10___1
10
___1
10___1
10
___1
10___1
10
___1
10___1
10
___1
10___1
10
1
1 ___1
1000___1
100___1
101 ___1
1000___1
100
___1
10___1
100___1
100
___1
100___1
100
___1
100___1
100
___1
100___1
100
___1
100___1
100
___1
101 ___1
1000___1
100
___1
100
= 10 tenths1 ___1
10 = 10 hundredths ___1
100 = 10 thousandths
535 – Decimals & Percentages
___1
1000___1
1000
___1
1000___1
1000
___1
1000___1
1000
___1
1000___1
1000
___1
1000___1
1000
Use the place value counters to help you fill in the final chart.
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Activity 3 Understand Thousandths
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?
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Activity 3 Understand Thousandths
What has this hundred square been divided up into? How many thousandths are there in one hundredth?
555 – Decimals & Percentages
The hundred square has been divided by 10.
1 hundredth = 10 thousandths.1 tenth = 100 thousandths.
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Reasoning 1 Understand Thousandths
565 – Decimals & Percentages
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.?
0.1
0.01
0.0010.01 0.01
0.01 0.010.001
0.001
0.001
0.001
0.001
0.001
0.0010.001
=0.01 0.001
0.01 0.01
0.01 0.01
0.001
0.001
0.001
0.001
0.001
0.001
0.0010.0010.01
0.01 0.01
0.01 0.010.01
0.01 0.01
0.01
0.01
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Reasoning 1 Understand Thousandths
575 – Decimals & Percentages
Leanna thinks that the 2 numbers are equal.
0.1
0.01
0.0010.01 0.01
0.01 0.010.001
0.001
0.001
0.001
0.001
0.001
0.0010.001
=0.01 0.001
0.01 0.01
0.01 0.01
0.001
0.001
0.001
0.001
0.001
0.001
0.0010.0010.01
0.01 0.01
0.01 0.010.01
0.01 0.01
0.01
0.01
She is correct. We can exchange ten hundredth counters for a one tenth
counter.
0.159 = 1591000
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Reasoning 2 Understand Thousandths
585 – Decimals & Percentages
0.543 = 5 tenths, 4 hundredths, and 3 thousandths
= 510 +
4100 +
31000
= 0.5 + 0.04 + 0.003
0.752 0.3240.148
Write these numbers in three different ways:
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Reasoning 2 Understand Thousandths
595 – Decimals & Percentages
0.148 = 1 tenth, 4 hundredths, and 8 thousandths
= 110 +
4100 +
81000
= 0.1 + 0.04 + 0.008
Write these numbers in three different ways:
0.752 = 7 tenths, 5 hundredths, and 2 thousandths
= 710 +
5100 +
21000
= 0.7 + 0.05 + 0.002
0.324 = 3 tenths, 2 hundredths, and 4 thousandths
= 310 +
2100 +
41000
= 0.3 + 0.02 + 0.004
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Discuss
60
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
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Fluency & Reasoning Teaching Slides
Thousandths as Decimals
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Activity 1 Thousandths as Decimals
1 ___1
1000___1
100 1110
1100
11000
___1
101
11 ___1
100
7 ones, 4 tenths, 1 hundredth, and 3 thousandths
625 – Decimals & Percentages
Use the place value chart and counters to represent these numbers.
Write down the numbers as a decimal.?
A
B
C 5 291000
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Activity 1 Thousandths as Decimals
1 ___1
1000___1
100 1110
1100
11000
4 1 2 1
___1
101
11 ___1
100
635 – Decimals & Percentages
A
C 5 291000
4.121
7.413
5.029
7 ones, 4 tenths, 1 hundredth, and 3 thousandthsB
Use the place value chart and counters to represent these numbers.
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Activity 2 Thousandths as Decimals
645 – Decimals & Percentages
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
ba c
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Activity 2 Thousandths as Decimals
655 – Decimals & Percentages
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
b
2.018
or
2 181000
a c
2.042
or
2 421000
2.074
or
2 741000
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Reasoning 1 Thousandths as Decimals
665 – Decimals & Percentages
Jeff has 5 counters.He makes numbers using the place value chart.
At least 3 columns have counters in them.
1110
1100
11000
Can you record the numbers in different ways??
What is the largest and smallest number he can make with 5 counters?
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Reasoning 1 Thousandths as Decimals
675 – Decimals & Percentages
Jeff has 5 counters.He makes numbers using the place value chart.
At least 3 columns have counters in them.
1110
1100
11000Largest
1 1 1 ___1
100___1
10
1110
1100
11000Smallest
___1
100___1
10___1
1000___1
1000___1
1000
3.11
0.113
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Reasoning 2 Thousandths as Decimals
685 – Decimals & Percentages
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
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Reasoning 2 Thousandths as Decimals
695 – Decimals & Percentages
= 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.
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Reasoning 3 Thousandths as Decimals
705 – Decimals & Percentages
Three children are representing number 0.603
6031000
Who is correct? Explain why.?
Rosie Esin Malachi
310+
310+ 3
1000610
+3
1000
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Reasoning 3 Thousandths as Decimals
715 – Decimals & Percentages
Three children are representing number 0.603
6031000
Rosie Malachi
310+
310+ 3
1000610
+3
1000
They are all correct.
Rosie has recorded it as a fraction. Esin and Malachi have partitioned it differently.
Esin
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Discuss
72
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
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Fluency & Reasoning Teaching Slides
Rounding Decimals
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Activity 1 Rounding Decimals
1
1
0.1
0.1
0.1
1
0.1
Ones Tenths
1
1
0.1
0.1
0.1
1
0.1
Ones Tenths
1
0.1
745 – Decimals & Percentages
Complete the number lines and round the representations to the nearest whole number:
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Activity 1 Rounding Decimals
1
1
0.1
0.1
0.1
1
0.1
Ones Tenths
3 43.4
1
1
0.1
0.1
0.1
1
0.1
Ones Tenths
1
0.1
4 54.5
755 – Decimals & Percentages
Complete the number lines and round the representations to the nearest whole number:
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Activity 2 Rounding Decimals
765 – Decimals & Percentages
Use the number lines to round 4.24 to the nearest tenth and the nearest whole number.
4.24
4.2 4.25 4.3 4 4.5 5
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Activity 2 Rounding Decimals
4.2 4.25 4.3 4 4.5 5
775 – Decimals & Percentages
Use the number lines to round 4.24 to the nearest tenth and the nearest whole number.
4.24 4.244.2 4
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Activity 3 Rounding Decimals
1
1
0.1
0.1
0.1
1
0.1
Ones Tenths Hundredths
0.10.1
0.1
0.1
0.1
0.1
0.1
0.1
785 – Decimals & Percentages
Round each number to the nearest tenth and nearest whole number. Use number lines to help you.
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Activity 3 Rounding Decimals
1
1
0.1
0.1
0.1
1
0.1
Ones Tenths Hundredths
0.10.1
0.1
0.1
0.1
0.1
0.1
0.1
795 – Decimals & Percentages
3.53.483.4 43 3.48
Round each number to the nearest tenth and nearest whole number. Use number lines to help you.
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Activity 3 Rounding Decimals
1
1 0.1
1
Ones Tenths Hundredths
0.10.1
0.1
0.1
0.1
0.1
805 – Decimals & Percentages
1
1
Round each number to the nearest tenth and nearest whole number. Use number lines to help you.
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Activity 3 Rounding Decimals
1
1 0.1
1
Ones Tenths Hundredths
0.10.1
0.1
0.1
0.1
0.1
815 – Decimals & Percentages
5.1 65
1
1
5.2 5.165.16
Round each number to the nearest tenth and nearest whole number. Use number lines to help you.
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Reasoning 1 Rounding Decimals
825 – Decimals & Percentages
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?
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Reasoning 1 Rounding Decimals
835 – Decimals & Percentages
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.
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Reasoning 2 Rounding Decimals
845 – Decimals & Percentages
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.?
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Reasoning 2 Rounding Decimals
855 – Decimals & Percentages
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
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Reasoning 3 Rounding Decimals
865 – Decimals & Percentages
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?
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Reasoning 3 Rounding Decimals
875 – Decimals & Percentages
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?
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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
885 – Decimals & Percentages
5www.masterthecurriculum.co.uk
Fluency & Reasoning Teaching Slides
Order & Compare Decimals
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Activity 1 Order & Compare Decimals
11 0.1
0.01
0.01 0.01
0.01
0.01 0.001
0.1
0.1 11 0.1 0.001
0.1
0.1 0.001
0.001 0.001
905 – Decimals & Percentages
Use <, > or = to make the statements correct.
1 0.1
0.01
0.01 0.01
0.01
0.01 0.001
0.1
0.1
0.0010.1
12.52 ÷ 10
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Activity 1 Order & Compare Decimals
11 0.1
0.01
0.01 0.01
0.01
0.01 0.001
0.1
0.1 > 11 0.1 0.001
0.1
0.1 0.001
0.001 0.001
1 0.1
0.01
0.01 0.01
0.01
0.01 0.001
0.1
0.1 >0.0010.1
12.52 ÷ 10
915 – Decimals & Percentages
Use <, > or = to make the statements correct.
2.351 2.304
1.452 1.252
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Activity 2 Order & Compare Decimals
4.11 4.12
4.115 4 1121000 Four and 11 hundredths
925 – Decimals & Percentages
Place the numbers in ascending order on the number line.
Is it easier to convert fractions to decimals than decimals to fractions??
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Activity 2 Order & Compare Decimals
4.11 4.12
4.115 4 1121000 Four and 11 hundredths
935 – Decimals & Percentages
4.1154 1121000
Four and 11 hundredths
Place the numbers in ascending order on the number line.
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Activity 3 Order & Compare Decimals
945 – Decimals & Percentages
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
A
B
C
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Activity 3 Order & Compare Decimals
955 – Decimals & Percentages
Place in descending order.
0.6120.510.1120.001
11km8.001km7.5km
5.015km
34.9934.00920.11020.011
1 0
0.612 0.51 0.112 0.001
7.5km
5.015km8.001km11km
A
B
C
15 km 5 km
35 20
20.01120.11034.99
34.009
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Reasoning 1 Order & Compare Decimals
965 – Decimals & Percentages
Tia says:
4.137 is greater than 4.2 because 137 is
greater than 2.
Tia
Do you agree? Explain your answer.?
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Reasoning 1 Order & Compare Decimals
975 – Decimals & Percentages
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:
Tia
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Reasoning 2 Order & Compare Decimals
985 – Decimals & Percentages
Rosie says:
I have put some numbers into ascending order:
4.015
4 511000
4.105
4 51100
What can’t her number be??Rosie
Rosie has missed one number out.
What could her number be?
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Reasoning 2 Order & Compare Decimals
995 – Decimals & Percentages
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:
4.015
4 511000
4.105
4 51100
Rosie
Rosie says:
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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
1005 – Decimals & Percentages
5www.masterthecurriculum.co.uk
Fluency & Reasoning Teaching Slides
Understand Percentages
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Activity 1 Understand Percentages
Complete the sentence stem for each diagram.
There are ___ parts per hundred shaded. This is ___%
1025 – Decimals & Percentages
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Activity 1 Understand Percentages
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 %
1035 – Decimals & Percentages
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Activity 2 Understand Percentages
Pictorial Parts per hundred Percentage
There are 32 parts per hundred.
79%
Complete the table.
1045 – Decimals & Percentages
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Activity 2 Understand Percentages
Pictorial Parts per hundred Percentage
There are 32 parts per hundred.
32%
There are 79 parts per hundred.
79%
Complete the table.
1055 – Decimals & Percentages
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100%
?
? 100%
30%
Activity 2 Understand Percentages
1065 – Decimals & Percentages
Complete the bar models.
100%
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20%
100%
30%
Activity 2 Understand Percentages
1075 – Decimals & Percentages
Complete the bar models.
100%
50%
100%
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Reasoning 1 Understand Percentages
1085 – Decimals & 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 _ _ _ _.
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Reasoning 1 Understand Percentages
1095 – Decimals & Percentages
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:
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Reasoning 2 Understand Percentages
1105 – Decimals & Percentages
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%??
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Reasoning 2 Understand Percentages
1115 – Decimals & Percentages
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.
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Reasoning 3 Understand Percentages
1125 – Decimals & Percentages
Zach and Rosie each have 100 sweets.
Zach eats 55% of his.Rosie has 45 sweets left.
Who has more sweets left?
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Reasoning 3 Understand Percentages
1135 – Decimals & Percentages
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.
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Discuss
114
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
5www.masterthecurriculum.co.uk
Fluency & Reasoning Teaching Slides
Percentages as Fractions & Decimals
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Activity 1
Pictorial Percentage Fraction Decimal
There are 30 parts per hundred.
30%
30 out of 100
30100
30 hundredths
0.30
Percentages as Fractions & Decimals
Complete the table.
1165 – Decimals & Percentages
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Activity 1
Pictorial Percentage Fraction Decimal
Percentages as Fractions & Decimals
Complete the table.
1175 – Decimals & Percentages
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Activity 1
Pictorial Percentage Fraction Decimal
There are 55 parts per hundred.
55%
55 out of 100
55100
55 hundredths
0.55
Percentages as Fractions & Decimals
Complete the table.
1185 – Decimals & Percentages
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Activity 1
Pictorial Percentage Fraction Decimal
There are 8 parts per hundred.
8%
Percentages as Fractions & Decimals
Complete the table.
1195 – Decimals & Percentages
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Activity 1
Pictorial Percentage Fraction Decimal
There are 8 parts per hundred.
8%
8 out of 100
8100
8 hundredths
0.08
Percentages as Fractions & Decimals
Complete the table.
1205 – Decimals & Percentages
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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
1215 – Decimals & Percentages
Give your answer as a percentage and a decimal.
60400 = 15
100 = 15 % = 0.15
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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
1225 – Decimals & Percentages
Give your answer as a percentage and a decimal.
60400 = 15
100 = 15 % = 0.15
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1250
Activity 3 Percentages as Fractions & Decimals
1235 – Decimals & Percentages
Record the fractions as decimals and percentages.
98200
33300
76400
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1250
Activity 3 Percentages as Fractions & Decimals
1245 – Decimals & Percentages
Record the fractions as decimals and percentages.
98200
33300
76400
= 24100 = 24% = 0.24
= 49100 = 49% = 0.49
= 11100 = 11% = 0.11
= 19100 = 19% = 0.19
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Reasoning 1 Percentages as Fractions & Decimals
1255 – Decimals & Percentages
Esin says:
To convert a fraction to a percentage, you just need to put
a percent sign next to the numerator.
Esin
Is Esin correct? Explain your answer.?
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Reasoning 1 Percentages as Fractions & Decimals
1265 – Decimals & Percentages
Esin is incorrect.
This only works when the denominator is 100 because percent means parts
per hundred.
Esin says:
Esin
To convert a fraction to a percentage, you just need to put
a percent sign next to the numerator.
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Reasoning 2 Percentages as Fractions & Decimals
1275 – Decimals & Percentages
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?
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Reasoning 2 Percentages as Fractions & Decimals
1285 – Decimals & Percentages
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:
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Reasoning 3 Percentages as Fractions & Decimals
1295 – Decimals & Percentages
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??
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Reasoning 3 Percentages as Fractions & Decimals
1305 – Decimals & Percentages
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.
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Discuss
131
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?
Percentages as Fractions & Decimals
Year 5
5www.masterthecurriculum.co.uk
Fluency & Reasoning Teaching Slides
Equivalent Fractions, Decimals
and percentages (F.D.P.)
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Activity 1 Equivalent F.D.P.
1335 – Decimals & Percentages
Use a bead string to show:
What are these decimals as a percentage?What are they as a fraction? Can you simplify the fraction??
0.60
0.5
0.10
0.25
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Activity 1 Equivalent F.D.P.
1345 – Decimals & Percentages
Use a bead string to show:
0.60
0.5
0.10
0.25
= 60% = 60100 = 3
5
= 50% = 50100 = 1
2
= 10% = 10100 = 1
10
= 25% = 25100 = 1
4
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Activity 2 Equivalent F.D.P.
10% 10% 10% 10% 10% 10% 10% 10% 10% 10%
1355 – Decimals & Percentages
Use the bar model to convert the fractions into a percentages and decimals.
12
34
710
25
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Activity 2 Equivalent F.D.P.
10% 10% 10% 10% 10% 10% 10% 10% 10% 10%
1365 – Decimals & Percentages
Use the bar model to convert the fractions into a percentages and decimals.
12
34
710
25
50% = 0.5
75% = 0.75
70% = 0.7
40% = 0.4
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Activity 3 Equivalent F.D.P.
1375 – Decimals & Percentages
Draw arrows to show the position of each representation on the number line.
410
60%
0% 100%
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Activity 3 Equivalent F.D.P.
0% 100%
1385 – Decimals & Percentages
Draw arrows to show the position of each representation on the number line.
410
60%
40100
= 40%
30100
= 30%
60100
= 60%
75100
= 75%
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Reasoning 1 Equivalent F.D.P.
1395 – Decimals & Percentages
Sort the fractions, decimals and percentages into the correct column.
Less than 12 Equal to 12 Greater than 12
60%
Eight tenths
80 hundredths
100%
50%
13
2040
0.10
15%
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Reasoning 1 Equivalent F.D.P.
1405 – Decimals & Percentages
Sort the fractions, decimals and percentages into the correct column.
Less than 12 Equal to 12 Greater than 12
60%
Eight tenths
80 hundredths
100%
50%
13
0.10
15% 2040
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Reasoning 2 Equivalent F.D.P.
1415 – Decimals & Percentages
Zach has £45.
He spends 13 of his money on a jacket and 50% on toys.
How much does he have left?
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Reasoning 2 Equivalent F.D.P.
1425 – Decimals & Percentages
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
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Reasoning 3 Equivalent F.D.P.
1435 – Decimals & Percentages
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?
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Reasoning 3 Equivalent F.D.P.
1445 – Decimals & Percentages
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.
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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.
4__5
1455 – Decimals & Percentages