Decimals and Percentages
Specimen Worksheets for Selected Aspects
Paul Harling
b recognise the number relationship between coordinates in the first quadrant of related points
Key Stage 2 (AT2)
Number: Programme of Study
1. Pupils should be given opportunities to:
a develop flexible and effective methods of
computation and recording, and use them with
understanding;
b use calculators, computers and a range of
other resources as tools for exploring number
structure and to enable work with realistic
data;
c develop the skills needed for accurate and
appropriate use of equipment
2. Developing an understanding of place value
and extending the number system
Pupils should be taught to:
a read, write and order whole numbers,
understanding that the position of a digit
signifies its value; use their understanding of
place value to develop methods of computation,
to approximate numbers to the nearest 10 or
100, and to multiply and divide by powers of 10
when there are whole-number answers;
b extend their understanding of the number
system to negative numbers in context,
decimals with no more than two decimal places
in the context of measurement and money:
c understand and use, in context, fractions and
percentages to estimate. describe and compare
proportions of a whole.
3. Understanding relationships between
numbers and developing methods of
computation
Pupils should be taught to:
a explore number sequences, e.g. counting in
different sizes of step, doubling and halving,
using a multiplication square, explaining
patterns and using simple relationships;
progress to interpreting, generalising and using
simple mappings, e.g. C=15n for the cost of n
articles at 15p, relating to numerical, spatial or
practical situations, expressed initially in words
and then using letters as symbols;
on a line or in a shape e.g. the vertices of a
rectangle, a graph of the multiples of 3:
c consolidate knowledge of addition and
Subtraction facts to 20;know the multiplication
Facts 10X10; develop a range of mental
methods for finding quickly from known facts
those that they cannot recall; use some
properties of numbers, including multiples,
factors and squares, extending to primes, cubes
and square roots;
d develop a variety of mental methods of
computation with whole numbers up to 100, and
explain patterns used; extend mental methods to
develop a range of non-calculator methods of
computation that involve addition and
subtraction of whole numbers. progressing to
methods for multiplication and division of up to
three-digit by two-digit whole numbers:
e understand multiplication as repeated addition,
and division as sharing and repeated
subtraction; use associated language and
recognise situations to which the operations
apply;
f understand and use the relationships between
the four operations, including inverses;
g extend methods of computation to include
addition and subtraction with negative numbers,
all four operations with decimals, and
calculating fractions and percentages of
quantities. using a calculator where appropriate:
h understand and use the features of a basic
calculator. interpreting the display in the context
of the problem, including rounding and
remainders.
4. Solving numerical problems
Pupils should be taught to:
a develop their use of the four operations to
solve problems, including those involving
money and measures, using a calculator where
appropriate:
b choose sequences of methods of computation
appropriate to a problem, adapt them and apply
them accurately;
c check results by different methods, including
repeating the operations in a different order or
using inverse operations; gain a sense of the size
of a solution, and estimate and approximate
solutions to problems.
Level Descriptions
Level 1
Pupils count, order, add and subtract numbers
when solving problems involving up to 10
objects.
They read and write the numbers involved,
Pupils recognise and make repeating patterns,
counting the number of each object in each
repeat.
Level 2
Pupils count sets of objects reliably, and use
mental recall of addition and subtraction facts to
10.
They have begun to understand the place value
of each digit in a number and use this to order
numbers up to 100.
They choose the appropriate operation when
solving addition and subtraction problems.
They identify and use halves and quarters, such
as half of a rectangle or a quarter of eight
objects.
They recognise sequences of numbers, including
odd and even numbers.
Level 3
Pupils show understanding of place value in
numbers up to 1000 and use this to make
approximations. They have begun to use decimal
notation and to recognise negative numbers, in
contexts such as money, temperature and
calculator displays,
Pupils use mental recall of addition and
subtraction facts to 20 in solving problems
involving larger numbers.
They use mental recall of the 2, 5 and 10
multiplication tables, and others up to 5x5, in
solving whole-number problems involving
multiplication or division, including those that
give rise to remainders.
Pupils use calculator methods where numbers
include several digits.
They have begun to develop mental strategies,
and use them to find methods for adding and
subtracting numbers with at least two digits.
Level 4
Pupils use their understanding of place value to
multiply and divide whole numbers by 10 or
In solving number problems. pupils use a range
of mental and written methods of computation
with the four operations. including mental recall
of multiplication facts up to 10x 10.
They add and subtract decimals to two places.
In solving problems with or without a calculator.
pupils check the reasonableness of their results
by reference to their knowledge of the context or
to the size of the numbers.
They recognise approximate proportions of a
whole and use simple fractions and percentages
to describe these.
Pupils explore and describe number patterns,
and relationships including multiple. factor and
square. They have begun to use simple formulae
expressed in words.
Pupils use and interpret co-ordinates in the first
quadrant.
Level 5
Pupils use their understanding of place value to
multiply and divide whole numbers and
decimals by 10. 100 and 1000.
They order. add and subtract negative numbers
in context.
They use all four operations with decimals to
two places.
They calculate fractional or percentage parts of
quantities and measurements, using a calculator
where appropriate.
Pupils understand and use an appropriate noncalculator method for solving problems that
involve multiplying and dividing any three-digit
by an two-digit number.
They check their solutions by applying inverse
operations or estimating using approximations.
They construct, express in symbolic form, and
use simple formulae involving one or two
operations.
Level 6
Pupils order and approximate decimals when solving
numerical problems and equations such as x2 = 20. using
trial-and improvement methods
Pupils are aware of which number to consider as 100
percent or a whole. In problems involving comparisons
and use this to evaluate one number as a fraction or
percentage of another. They understand and use the
equivalences between fractions. decimals and
percentages, and calculate using ratios in appropriate
situations.
When exploring number patterns, pupils find and
describe in words the rule for the next term or nth term
of a sequence where the rule is linear
They formulate and solve linear equations with whole
number coefficients
They represent mappings expressed algebraically,
interpreting general features and using graphical
representation in four
quadrants where appropriate
One point to you!
Matching Decimals
First to one
Square up
On the right line
Rounding decimals
Add it
Shortcuts
Copyright:
Paul Harling (Maths Plus series: Decimals and Percentages)(WLE)
Decimal move
..
You need a counter for each person who is playing and 2 minis from a set of M.A.B.
Instructions
•
•
•
•
•
2 to 4 people may play this game.
Take 2 minis from your M.A.B. set. ‘Mark the decimals 0.1 to 0.6 in blue on one of
them. Mark the decimals 0.7 to 1.2 in red on the other,
Each player takes it in turns to throw both dice.
Subtract the decimal on the blue die from the decimal on the red die. Your answer
will tell you how far to move on the chart.
The first player to reach 10 is the winner.
How to handle hundredths
Copyright: Paul Harling (Maths) Plus series: Decimals and Percentages)(WLE)
Race to the line!.
Play this game with a friend. You both need a
calculator.
Most of the numbers on the grid below are
sums of two different numbers from this set.
For example, 44•9 is the sum of 3•4 and 41•5.
But watch out! There are two hidden
‘bug’ numbers that cannot be found by adding
listed numbers.
To play the game you have to find which numbers from the list are
needed to make all five numbers in any1row, column or diagonal on
the grid. You race your friend to see who can work out a whole line first.
So look at the grid carefully
and choose which line you
are going to work out.
Then write down the five
calculations as quickly as you
can. Record like this.
44•9 = 3•4 + 4l•5
The first to finish wins, but
your partner can challenge
your answers!
Recurring decimals
Percentages
You need a dictionary, centimetre squared
paper, scissors and glue
I Use the dictionary to find the meaning of
each of these words.
century centenary centurion centenarian
2 On the squared paper draw a square 10 cm
by 10 cm. This large square is made up of
100 small squares.
Copy this pattern exactly onto your square.
Then cut it out and stick it in your book.
Now copy these sentences
underneath the pattern.
4 squares out of 100 are black.
4
/100 is black.
4 per cent is black.
20 squares out of 100 are grey.
20
/100 is grey.
20% is grey.
12 squares out of 100 are blue.
12
/100 is blue.
12%is blue.
3 Look back to your pattern.
a How many squares are not coloured?
b What fraction is this?
c What percentage is not coloured?
4 Write each of these percentages
in decimal form.
a 4% b 20% c 12%
Working percentages
Collect advertisements that include percentages.
They will have phrases and sentences like these
Pocket-money
percentages
Carefully trace this percentage wheel.
Each sector (part) is 10%
of the full circle.
The full circle is 100%.
These wheels show how six teenagers
use their pocket money. Each gets £1•5O a day.
I For each person, use the percentage wheel to work out:
a what percentage of the £1•50 is spent on each item.
b how much money is spent on each item.
2 If each person’s pocket money went up to
£2 a day, what would happen to:
a the percentage spent on each item?
b the amount of money spent on each item?
3 Imagine you have £5. How would you use it?
Draw and label a diagram to show what
you would buy, and the percentage and
amount of money you
would spend on each item.
ercentage puzzle
Play this game with a friend. You each
need a calculator with a % key, and a set
of counters. (The two sets of counters
should be different in colour.)
Rules
Take turns to:
• Choose a percentage and a number from these sets.
• Work out the chosen percentage of the chosen number. (Look back
to page 18 if you need help.)
• Find the result of the calculation on the grid below and cover it
with a counter.
The first player to get
a line of four counters wins.