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# Essentials of Numeracy

Use the arrows or press 'autoplay' to take a pre-plotted tour of the Essentials. Alternatively use your mouse to zoom in and out on the topics that interest you most. Keywords: Numeracy, Essentials, Being Numerate, Numeracy across the Curriculum.
by

## National Numeracy

on 5 December 2013

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#### Transcript of Essentials of Numeracy

Subtraction
Mental methods to 100
Whole numbers to
1000 and beyond
Knowing + and -
facts to 20
Calculations with
fractions, decimals,
percentages
Reasonableness
Inter-
relationships
Effective Use
of Calculators
Calculations
with negatives
Remainders and
rounding
Multiplication and Division
Knowing x and ÷
facts to 20
Order of
operations
Number
Operations
Inverse
operations
Operations and Calculations
Shape, Space and Measures
ANGLES
Measure
and draw
Estimate
Use angle
to describe
position and
movement
2D/3D Shapes
(and the way they
behave)
Symmetry
Simple positional
language
Properties
Making and
drawing
Standard units of
measurement
Length
Imperial/
Metric
Temperature
Mass
Capacity
Time
Area/perimeter
Measurement
Shape and
Space
Translation
Reflection
Rotation
Select and
use measuring
instruments
Interpret
numbers and
Volume
Solving problems with shape, space
and measures
Use geometrical
notation
and symbols
correctly
Select and use
appropriate
skills to solve
geometrical
problems
Coordinates to
describe position

Handling Information
Interpreting
Information
Charts:
Pie and Bar
Data in lists
and tables
Using
probability scale
Estimating
probability from
statistical
information
Experimental
probability
Decision Trees
Venn diagrams
Continuous data
Measures
of average
Measures
Discrete data
Comparing
Sets of Data
Graphs
and Charts
Probability
Processing
Data
Types of
Data
Being Numerate
Be willing to solve problems
involving number, data or
measurement.

Persevere and try different
approaches; don't give up

Develop self-confidence
Become comfortable
with numbers

Choose
tools and
equipment
Identify
relevant
information
Choose
appropriate
strategies
Decision
Making
Identify information
needed to carry out
Identify
structures
Be systematic
Search for
pattern
Develop logical
thinking
Reasoning
Problem
Solving
Predict and
Check
Break down a
into smaller parts
Interpret solutions
in context
of a problem
Make mental
estimates to check
reasonableness
Numbers
(and the Number System)

Odd/even
Square
Factors and
multiples
Prime
Zero as a
place holder
Money
context
Estimation
Measures
Fractions
Percentages
Decimals
Ratio and
proportion
For
counting
For
measuring
Using
number lines
0-20
0-100
0-1000
Comparing and
ordering
writing (symbols)
As labels
Using
numbers
Numbers
"In Between"
Whole Numbers
Place Value
Sequences
and Patterns
Whole
Numbers
Size and
Order

A problem is a question that needs a solution. First we understand the problem by looking at the information carefully, deciding which parts are important, then we choose the best approach.

This may mean drawing a picture, using a graph, breaking down the problem into smaller parts, or other approaches.

We need a rough idea of a likely solution to check if an answer looks right or not.

Everyday uses:
Finding the cheapest and quickest way to travel to work
Deciding how to best arrange things in a room
Reasoning is looking for patterns and relationships then using general rules to help us find answers.

We estimate what answers will look like, then check answers to see if they look right, or, if not, whether we need to try again. Once we are happy, we need to be able to explain our reasoning.

Everyday uses:
Making sense of what is happening around us
Choosing how to solve problems
Addition is finding the total, or sum, by combining two or more numbers.

Subtraction is taking one number away from another and finding the difference between the two numbers.

It is helpful to know by heart the answers to addition and subtraction questions with numbers up to 20, and to know how to estimate and get the answers with bigger numbers, fractions, decimals and negative numbers.

Decision making starts with understanding information, deciding which parts are relevant and finding more details if needed.

We use reasoning to make choices and predict the likely outcome so that we can check results and see if we have made the best decisions.

Everyday uses:
Deciding on offers in a supermarket,
At work, where most decisions are in some way based on numbers.

We use numbers to show quantities.

We use them for counting, labelling, measuring and ordering.

Everyday uses:
Counting money
Calling somebody's mobile
Catching the right bus
A whole number is a quantity of separate objects.

We first learn about numbers up to ten, then a hundred, then a thousand, until we can use numbers of any size.

Everyday uses:
Recognising the right house number
Telling each other the time
Choosing an amount on a cash machine
Knowing the date
Our number system is based on the number ten. Using only ten symbols (0,1,2,3,4,5,6,7,8,9 - called digits) we can write any number of any size.

Place value is the value given to the place or position of a digit in a number. The place value of a digit shows if it means units, tens, hundreds or more.

In decimal numbers the place value of a digit represents a part of the whole number, such as tenths, hundredths and thousandths.

Everyday uses:
Handling money: 1p, 10p, £1 and £10 all have different values because the 1 is in a different place for each.
A sequence is a set of numbers or objects which follow a rule. A pattern is a repeated sequence.

Examples are lists of odd or even numbers, halves or doubles, and prime numbers. Spotting sequences and patterns lets us predict what comes next.

Everyday uses:
Budgeting for the month
Knowing when the bus is due
A fraction is a way of writing a number that is part of a whole. The top number (numerator) is how many parts you have. The bottom number (denominator) is how many equal parts the whole is divided into.

A decimal number uses a decimal point as a separator after a digit showing a whole number, then more digits as a way of showing values less than one.

Percentage, shown by %, means parts per 100.

These are all ways of showing numbers in between whole numbers and quantities less than one whole, for example 1/2 is the equivalent of 0.5 and also the equivalent of 50%. One and a half is the equivalent of 1.5 and also 150%.

Money is a good way of understanding percentages as for instance 50% of £1 is 50p.
Multiplication is adding the same amount a number of times. The symbol 'x' means multiplication.

Division is splitting into equal parts or groups.
The symbol ‘÷’ means division.

Everyday uses:
Working out how to feed a group of people: 5 people want 2 eggs each, 2 x 5 = 10 eggs
sharing something or splitting a bill
The most common operations are addition, subtraction, multiplication and division. Operations are used to find out or 'calculate' an answer.

Everyday uses:
We mix operations a lot in everyday life, eg: if we want to provide 2 cans for each of 4 people, but already have 3 in the fridge, we multiply 2 by 4, then subtract 3, to learn that we need to buy 5 more cans.
You can use a calculator to do operations. They are useful when working with big numbers or more complicated calculations.

We need to know when and how to use a calculator. It is often quicker to do simpler calculations mentally. If we use a calculator we need to know in which order to enter the information and when to use the memory function.

It is important to estimate the solution so that we can tell if the answer shown by the calculator is sensible, or if an error has been made.

Everyday uses:
Budgeting at home
Producing information at work
Graphs are pictures that show data in a clear way. Charts show data in lists or as tables.

The best kind of graph is chosen to show the info being looked at, eg: a line graph, pie chart, bar graph or tally chart. The right choice of graph depends on the type of data represented and helps us understand and reason quickly.

Everyday uses:
showing energy efficiency or train performance
How the 'ask the audience' question went
Data is a collection of facts or information, such as values or measurements. Comparing data is looking at how two sets of data are the same or different.

We work out the average of a set of values to get a figure which is typical of the set of numbers.

Everyday uses:
Compare options for a holiday
Processing data is about understanding data and sorting it out so that you can to use it to make decisions.

We choose the best way of showing data to help with this, including tally charts, decision trees, and flow charts.

Everyday uses:
Doing surveys
Making sense of any large amount of information
Probability is the chance that a particular event will occur. This could be certain, likely, unlikely, impossible.

If an event is certain, its probability is one in one (1). If it is impossible, its probability is zero (0).

The probability of getting heads when we toss a coin is 1 in 2 as there are 2 possible outcomes. Therefore the probability of getting heads is described as one half, or a 50% chance.

Everyday uses:
Talking about probability in a general way, eg: ‘it’s probably going to rain’,
or ‘you don’t have much chance of making it to the station in time’.
Numerical data can be Discrete ( can be counted) or Continuous (usually needs to be measured).

Discrete data deals with separate items and whole numbers, for example, how many people are in the swimming pool?

Continuous data is used for measurement, for example, 'how tall am I?' 'how much do I weigh?' and are usually not whole numbers.

A measurement is a number showing the size or amount of something. There are different systems of measurement such as metric and imperial. Imperial is still used for some things (eg pints or miles), and metric is used for others (eg metres or kilograms).

Everyday uses:
Measuring age, warmth, price, height, weight, distance, volume, speed, calories etc
Gathering and comparing information.
Shape describes how an object looks, how it is laid out.

2-D (two dimensional) shapes like squares, circles, triangles and rectangles.are 'flat' (and are only represented as pictures).

3-D (three dimensional) shapes like cubes, spheres, boxes and cylinders have 'depth' (and can be seen and touched as physical objects).

Everyday uses:
Designing buildings, household appliances, and objects
Drawing things to scale.
We can solve problems using shape, space and measure.

This often involves using angles which are measures of the amount of turn. We also use an understanding of the properties of shapes such as triangles to help us solve problems.

Everyday uses:
Parking a car
Designing bridges to take the right weight
Working out if a new sofa will fit in the living room.
Being Numerate is being able to use maths to make sense of information in order to solve problems and make
informed decisions. Most decisions are in some way based on numbers.

This area includes Reasoning, Problem Solving & Decision Making.
Numbers are the symbols and words we use to express quantities.

We use them for counting, labelling, measuring and ordering.

This area is made up of Using Numbers, Whole Numbers, Size & Order, Place Value, Sequences & Patterns and Numbers in between Whole Numbers.
We compare the size of numbers to other numbers and we order numbers according to their size or the quantity they represent.

We compare whole numbers, fractions, decimals, percentages and negative numbers.

Everyday uses:
Knowing that £5.60 is more than £4.60
Knowing that size 4 shoes are smaller than size 6 shoes
Operations & Calculations are activities used to solve numerical problems.

We split this area into Addition & Subtraction, Multiplication & Division, Number Operations and Effective use of Calculators.
Handling information is about understanding different kinds of data and knowing how best to use it.

This area includes Graphs & Charts, Comparing Sets of Data, Types of Data, Processing Data, and Probability.
Shape, Space and Measures is about understanding the properties of shapes and how to use numbers to show their size.

We use measures to quantify all aspects of our lives.

We split this area into Measurement, Shape & Space and Solving Problems with Shape, Space & Measures.
Infinite
- million
- beyond
Attitudes of Mind
www.nationalnumeracy.org.uk/essentialsofnumeracy