Download Decimals Answers

Assessing Understanding of
Place Value and Decimals (with Answers)
1
6351
The 3 stands for 3 hundreds
a)
635
The 3 stands for 3
Tens
B)
635 200
The 3 stands for 3
Ten thousands
Answers
2
0.137
The 3 stands for 3 Hundredths
a)
0.3
The 3 stands for 3
Tenths
B)
0.340
the 3 stands for 3
Tenths
c)
0.613
The 3 stands for 3
Thousandths
3
Write in figures:
a)
Three hundred and seventy
370
b)
Six hundred thousand and eighty two
600 082
4
Write in words as you would say it:
a)
7040
b)
130 000
c)
0.39
Seven thousand and forty
One hundred and thirty thousand
Point three nine (not point thirty
nine)
Adapted from Brown, M., Hart K., & Kuchemann, D., (1984). Chelsea Mathematics Diagnostic Tests Place Value and Decimals. Windsor, England: NFER-Nelson.
1
5
Add ten:
a)
4796
4806
b)
0.15
10.15
6
Add one hundred:
a)
23 627
23 727
b)
19 740
19 840
7
Add one tenth:
a)
4.273
4.373
b)
3.9
4
8
Subtract one hundred:
a)
783
b)
50 000
683
49 900
Adapted from Brown, M., Hart K., & Kuchemann, D., (1984). Chelsea Mathematics Diagnostic Tests Place Value and Decimals. Windsor, England: NFER-Nelson.
2
9
a)
30
40
This number is
38
Give the next answers as decimals
b)
6
7
This number is
6.8
c)
.
3.7
This number is
3.8
3.74
d)
17
e)
18
17.65
This number is
his number is about
5
.
6
5.2
This number is
f)
9
his number is about
.
This number is about is
10
9.3
Adapted from Brown, M., Hart K., & Kuchemann, D., (1984). Chelsea Mathematics Diagnostic Tests Place Value and Decimals. Windsor, England: NFER-Nelson.
3
10
This meter counts the people going into a rugby match.
0
6
3
9
9
After one more person has gone in the meter will read:
0
6
4
0
0
11
The number that is 3 less than 26 000 is
25 997
12
For the answer to a maths problem Sandra got 3.70 and Billy got
3.7
Is there any difference between the answers?
No
3.70 means 3 ones plus 7 tenths and 0
hundredths. And 3.7 means 3 ones plus 7 tenths.
So they are the same.
Why?
Adapted from Brown, M., Hart K., & Kuchemann, D., (1984). Chelsea Mathematics Diagnostic Tests Place Value and Decimals. Windsor, England: NFER-Nelson.
4
13
a)
Draw a ring around the bigger of the two numbers:
0.65 or 0. 7
5 hundredths is less than 1 tenth.
So 6 tenths plus 5 hundredths is less than 7 tenths.
Why is it the bigger?
b)
For each pair, draw a ring around the bigger number.
i
30 100
or
30 095
ii
8.55
or
8.5
iii
3.06
or
3.5
14
Six tenths as a decimal is 0.6
a)
How would you write as decimals:
i
four hundredths
0.04
ii
eleven thousandths
0.011
iii
eleven tenths
1.1
b)
Four tenths is the same as
……………. hundredths
a)
Write down any number between:
15
b)
i
3000 and 4000
ii
3100 and 3200
iii
0.3 and 0.4
iv
0.31 and 0.32
eg
eg
eg
eg
3467
3109
0.378
0.3156
How many different numbers could you write which lie
between 0.31 and 0.32?
An infinite number.
16
Adapted from Brown, M., Hart K., & Kuchemann, D., (1984). Chelsea Mathematics Diagnostic Tests Place Value and Decimals. Windsor, England: NFER-Nelson.
5
This is 1 square unit
a)
The area shaded is
1.3
square units.
a)
b)
The area shaded is
1.43
square units.
1.06
square units.
c)
b)
The area shaded is
c)
Adapted from Brown, M., Hart K., & Kuchemann, D., (1984). Chelsea Mathematics Diagnostic Tests Place Value and Decimals. Windsor, England: NFER-Nelson.
6
17
Multiply by ten
a)
30
3
b)
4.17
41.7
Multiply by one hundred
c)
21 700
217
3.2
320
f)
5.7
0.057
h)
16
d)
Divide by one hundred
e)
14
1400
Divide by twenty
g)
1.2
24
0.8
18
Draw a ring around the one in each pair that gives the bigger
answer.
a)
8 x 4
or
8  4
b)
8 x 0.4
or
8  0.4
c)
0.8 x 0.4
or
0.8  0.4
Adapted from Brown, M., Hart K., & Kuchemann, D., (1984). Chelsea Mathematics Diagnostic Tests Place Value and Decimals. Windsor, England: NFER-Nelson.
7
19
a)
Add
357
+ 984
b)
12.4 + 2.7
1412
– 675
d)
9.34 – 5.28
=
15.1
1341
c)
Subtract
=
4.06
737
20
a)
30 x 400
=
12 000
b)
5 x 0.2
=
1
c)
0.2 x 0.4
=
0.08
d)
80 ÷ 4
=
20
e)
80 ÷ 0.4
=
200
21
a)
b)
Draw a ring around the number nearest in size to:
i
167
100
67
170
150
200
ii
3.9
4
40
3
30
1
iii
0.17
0.1
10
0.2
20
0
Draw a ring around the number nearest in size to the answer.
(Do not work out the answer.)
i
2.9 x 7
0.002
0.02
0.2
2
20
200
ii
0.29 x 7
0.002
0.02
0.2
2
20
200
iii 59 ÷ 180
0.003
0.03
0.3
3
30
300
Adapted from Brown, M., Hart K., & Kuchemann, D., (1984). Chelsea Mathematics Diagnostic Tests Place Value and Decimals. Windsor, England: NFER-Nelson.
8
22
Draw a ring around the calculation you would need to do to find
the answer.
a)
The price of mince is $8.75 for each kilogram.
What is the cost of a packet of mince that weighs 0.58 kg?
b)
c)
8.75 + 0.58
0.58 ÷ 8.75
8.75 ÷ 0.58
0.58 – 8.75
8.75 – 0.58
0.58 x 8.75
The cost of a large bag of rice weighing 12.5 kilograms is
$10.95
What should be the price of one kilogram of rice?
12.5 + 10.95
10.95 ÷ 12.5
12.5 ÷ 10.95
10.95 – 12.5
12.5 – 10.95
10.95 x 12.5
My car can go 11.8 kilometres on each litre of petrol on a
motorway.
How many kilometres can I expect to travel on 25.65 litres?
11.8 + 25.65
25.65 ÷ 11.8
11.8 ÷ 25.65
25.65 – 11.8
11.8 – 25.65
25.65 x 11.8
Adapted from Brown, M., Hart K., & Kuchemann, D., (1984). Chelsea Mathematics Diagnostic Tests Place Value and Decimals. Windsor, England: NFER-Nelson.
9
Assessing Understanding of
Place Value and Decimals
Determining Level of Attainment
Level
1
Description of
Item Numbers
Level
Place-value in whole
3a, 10, 13bi, 15ai,
numbers up to
15aii, 17a
thousands
2
Decimals – tenths
3
Decimals –
hundredths,
thousandths etc
4
5
6
Criterion for Level
Attainment
2a, 9b, 13biii, 16a,
21aii
2b, 9c, 11, 13a,
14ai, 15aiii, 15aiv,
16b
7a, 7b, 9d, 9e, 16c,
17b, 17c, 21aiii,
21bi, 22c
Decimals – relation
with adjacent place
on left
Decimals- more
complex relations
between places.
Decimals as the
result of division;
infinite number of
decimals
4/6
3/5
5/8
6/10
1b, 14aiii, 14b, 17d,
17f, 20e
4/6
15b, 17g, 17h,
21biii
3/4
Attainment for 12 year olds
π
Percentage
0
17%
1
17%
2
22%
3
20%
4
9%
5
9%
6
6%
Adapted from Brown, M., Hart K., & Kuchemann, D., (1984). Chelsea Mathematics Diagnostic Tests Place Value and Decimals. Windsor, England: NFER-Nelson.
10