Essentials of Numeracy

For

counting

Comparing and

ordering

Using

number lines

Odd/even

Knowing + and -

facts to 20

Knowing x and ÷

facts to 20

Remainders and

rounding

Calculations

with negatives

Calculations with

fractions, decimals,

percentages

Measures

of spread

Decision Trees

Reading scales

Length

Mass

Time

2D/3D Shapes

(and the way they

behave)

Properties

Symmetry

Handling Information

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.

Interpreting

Information

Charts:

Pie and Bar

Data in lists

and tables

Graphs

and Charts

Comparing

Sets of Data

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:

• Make sure we get the best deal when shopping
• Compare options for a holiday

Using

probability scale

Probability

Measures

of average

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’.

Estimating

probability from

statistical

information

Discrete data

Experimental

probability

Types of

Data

Processing

Data

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

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.

Continuous data

Venn diagrams

Shape, Space and Measures

Being Numerate

Numbers

(and the Number System)

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.

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.

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.

Infinite

- million

- beyond

0-20

0-100

0-1000

Estimate

Measure

and draw

Whole

Numbers

Making and

drawing

Imperial/

Metric

Temperature

Identify

structures

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

Identify information

needed to carry out

the task

Square

Break down a

problem or task

into smaller parts

Standard units of

measurement

Factors and

multiples

Be systematic

ANGLES

Prime

Problem

Solving

Reasoning

Capacity

Simple positional

language

Interpret solutions

in context

of a problem

Attitudes of Mind

Search for

pattern

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

Area/perimeter

Sequences

and Patterns

Size and

Order

Reading and

writing (symbols)

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

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

Shape and

Space

Measurement

Develop logical

thinking

Translation

Make mental

estimates to check

reasonableness

of answers

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.

Use angle

to describe

position and

movement

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

As labels

Reflection

Zero as a

place holder

Rotation

Using

numbers

Place Value

Ratio and

proportion

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.

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

Numbers

"In Between"

Whole Numbers

Predict and

Check

Volume

Coordinates to

describe position

Select and

use measuring

instruments

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.

Solving problems with shape, space

and measures

Money

context

Measures

Decision

Making

For

measuring

Interpret

numbers and

read scales

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.

Fractions

Decimals

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.

Estimation

Percentages

Use geometrical

notation

and symbols

correctly

Choose

appropriate

strategies

Choose

tools and

equipment

Select and use

appropriate

skills to solve

geometrical

problems

Identify

relevant

information

Operations and Calculations

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.

Mental methods to 100

Whole numbers to

1000 and beyond

Addition and

Subtraction

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.

Inverse

operations

Number

Operations

Effective Use

of Calculators

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

Reasonableness

of answers

Inter-

relationships

Order of

operations

Multiplication and Division

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

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