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Numeracy is one of the core aspects of education and is a key focus of raising attainment in Scotland.
Being confident with understanding numbers, manipulating numbers and applying numeracy skills to real life situations is the key focus of our teaching and learning in numeracy.
Developing our approaches to planning, teaching and assessing numeracy across the nursery and school has been a key focus over the last few years.
Please have a look below to learn more about what we do to make sure everyone has the opportunity to achieve success in numeracy.
At the beginning of our journey, we developed a shared understanding of what quality numeracy lessons look like. We have then used this to help us quality assure and moderate our numeracy teaching as well as plan next steps and targets for ourselves.
At the beginning of our journey, we developed a shared understanding of what quality numeracy lessons look like. We have then used this to help us quality assure and moderate our numeracy teaching as well as plan next steps and targets for ourselves.
To plan numeracy, we use a calendar and planning documents, which are underpinned by the Curriculum for excellence experiences and outcomes and benchmarks. They provide clarity over how to plan progressively and help us identify what achievement at the end of a stage or level looks like.
To plan numeracy, we use a calendar and planning documents, which are underpinned by the Curriculum for excellence experiences and outcomes and benchmarks. They provide clarity over how to plan progressively and help us identify what achievement at the end of a stage or level looks like.
Big Maths is a planning, assessment and teaching resource that develops mental maths skills from Pre-Nursery up to Primary 7.
Big Maths is a planning, assessment and teaching resource that develops mental maths skills from Pre-Nursery up to Primary 7.
We use Big maths across the school to help develop confidence with mental maths.
We use Big maths across the school to help develop confidence with mental maths.
We use the big maths planners to ensure clear progression of mental maths teaching.
We use the big maths planners to ensure clear progression of mental maths teaching.
We also use the big maths assessments to ensure that we are providing learning at the appropriate level for everyone.
We also use the big maths assessments to ensure that we are providing learning at the appropriate level for everyone.
A key part of big maths is celebrating success and every week we celebrate people who have been able to set a new high score for themselves or progressed to the next level.
A key part of big maths is celebrating success and every week we celebrate people who have been able to set a new high score for themselves or progressed to the next level.
In our numeracy lessons, there are three key ways we can communicate information about numbers: concrete, pictorial and abstract.
We provide opportunities for all learners to explore and develop confidence with all three.
Concrete
Concrete
Concrete materials are essential to help support learners to understand what numbers represent. Concrete refers to anything that you can physically handle or touch.
We provide a wide range of concrete resources in school and they are available in all numeracy lessons to support learners.
Some examples include numicon, counters, beads, diennes, cubes, blocks.
Concrete materials are essential in the early stages of learning about numeracy and for learners who are finding confidence in numeracy a challenge. However, everyone, no matter their age or ability, benefits from accessing concrete materials while doing numeracy learning.
Pictoral
Pictoral
Pictures and visuals are another essential approach to representing numbers and mathematical concepts.
Pictures help learners to visualise a problem and often help to give a context to the abstract theory of maths.
Pictorial is a key step to help learners go from maths using concrete materials to maths in abstract form.
Some examples include arrays, bar models, pictures of objects you can't hold e.g. wheels on a car.
Abstract
Abstract
Abstract numeracy is the use of symbols and numerals to represent mathematical problems or processes.
For example, the digit 3 is an abstract symbol that represents the amount after two and before four. It is an abstract concept that only has meaning if we know what three objects feels like in our hands or we can see three of something.
We should always be demonstrating the abstract approach during numeracy lessons, but it is the most sophisticated concept for learners to understand and gain mastery of.
Supporting abstract maths with concrete and pictorial approaches ensures that maths has a real life meaning and understanding.
Assessment is a key part of numeracy in our school. We use a wide range of robust assessments to ensure we have an accurate holistic understanding of our learner's ability in numeracy, but also so that we can assess specific mathematical concepts or skills.
Before we start a new piece of learning, we do an assessment of current knowledge/understanding and confidence. We do this in multiple ways such as active maths assessments, formal tests and pupil voice groups. Through this we can identify gaps in knowledge, misconceptions, areas of strength and key themes.
This information then informs our planning so that our lessons are appropriately challenging for all of our learners. Learners are also given a voice in planning the direction of their learning.
At the end of a block of teaching, we then do a post topic assessment to measure progress and identify next steps. We can again do this in various ways and will be tailored to meet the needs of our class or individual learners. Where appropriate, we adapt assessments to remove barriers to learning and to makes sure that the assessment is accessible to all learners, including those with Additional Support Needs or communication challenges.
Big maths also provides diagnostic assessments at the start of the blocks of learning, as well as weekly mental maths assessment data.
We also use a more formal, overall numeracy assessment 3 times a year. This is called PUMA. If you would like to know more about PUMA, please get in touch with a member of the School Leadership Team.
Please see below for some examples of questions we use in numeracy assessments.
All skills in numeracy are linked and knowledge in one area can help in many other areas. However, we group some areas of numeracy together and teach them in a specific order. This is so that we can build a base of knowledge that helps us with the next level of learning. If we have gaps in the knowledge in the first stage of the process, this can make it more challenging for us to develop confidence in the next concept.
There are two main categories in numeracy: Number skills and Beyond number.
The number skills are the basis of all numeracy and are taught in a specific order across the school year. We focus on one main number skills per term. The beyond number skills have topic specific concepts and language, but require you to use the knowledge from the number skills to fully master them. We have matched these topics with the number skills in a logical way e.g. time with fractions half past, quarter to etc.
Number skills
Number skills
Place value - what is the place of a number and how much does it represent.
Addition and subtraction
Multiplying and Dividing
Fractions, decimals and percentages.
At Second and Third level, we also include "expressions and equations".
Beyond Number skills
Beyond Number skills
Time
Money
Measurement
Information handling
Shape, position and movement
Patterns and relationships
Maths and it's impact on the world
Please see below for a brief description of each of the core numeracy concepts and key resources we use to teach them.
Place Value
Place Value
Understanding how numbers are made and what each digit means.
Read, write, and say whole numbers and decimals.
Recognise the value of each digit in a number (e.g. units, tens, hundreds)
Count forwards and backwards in different steps
Compare and order numbers, including decimals
Identify numbers before, after and between
Round numbers to nearest 10, 100, 1000 or decimal place
Partition numbers in different ways to understand structure
Addition and subtraction
Addition and subtraction
Learning how numbers are combined and separated.
Use mental and written strategies to add and subtract.
Know number facts (e.g. number bonds to 10, doubles and halves).
Estimate and check calculations.
Apply strategies to solve real-life problems (e.g. money, time, measures).
Understand the language of addition and subtraction (e.g. total, difference).
multiplying and dividing
multiplying and dividing
Developing knowledge of times tables and how numbers are shared or grouped.
Recall and use multiplication and division facts.
Use arrays, groups, and repeated addition to understand multiplication.
Divide using sharing and grouping methods.
Apply multiplication/division to solve word problems.
Understand the relationship between multiplication and division e.g. 2 x 3 = 6 is linked to with 6 / 3 = 2
Fractions decimals and percentages
Fractions decimals and percentages
Understanding parts of a whole in different forms.
Recognise and use common fractions (e.g. ½, ¼, ¾).
Find fractions of shapes and amounts.
Understand equivalent fractions. Identify fractions that are the same size as each other.
Read, write, and use decimal numbers.
Convert between fractions and decimals.
Understand percentages and make links to fractions and decimals.
Solve everyday problems using fractions, decimals, and percentages.
Expressions and equations (P2-P7 only)
Expressions and equations (P2-P7 only)
Introducing basic algebra and using symbols to represent values.
Understand and use mathematical symbols (+, –, ×, ÷, =)
Explore simple number sentences and solve for missing numbers
Use brackets and follow the correct order of operations
Begin to use letters or symbols to represent unknowns
Create and solve simple equations
Money
Money
Using money in real-life situations and developing financial understanding.
Identify coins and notes and use them to make amounts.
Add and subtract amounts of money.
Work out change from a given amount.
Budget and make decisions based on cost and value.
Compare prices and explore best value in everyday contexts.
Explore how businesses are run.
Understand how to make positive financial decisions.
Time
Time
Understanding how to read, measure, and use time.
Read clocks (digital and analogue) to the nearest hour, half hour, quarter hour, 5 minutes, 1 minute.
Use 12-hour and 24-hour time formats.
Understand and use calendars, days, months, and seasons.
Estimate and measure time durations.
Solve real-life problems involving time (e.g. timetables, durations).
Organise and plan time.
Measurement
Measurement
Measuring the world around us accurately.
Measure length, weight/mass, volume/capacity using non-standard units (e.g. cubes) and standard units (e.g. cm or kg)
Compare and estimate measurements.
Use appropriate tools to measure (e.g. ruler, scale, jug).
Convert between units (e.g. cm to m, ml to litres).
Apply measurement to real-life tasks (e.g. cooking, building, planning).
Information handling
Information handling
Collecting, organising, and interpreting information in the form of data.
Gather and sort information in tables, lists, and tally charts.
Display data using bar charts, pictograms, line graphs, etc.
Read and interpret different types of graphs and charts.
Use data to answer questions and draw conclusions.
Explore probability through real-life situations (e.g. chance, fairness).
Shape Position and Movement
Shape Position and Movement
Exploring the properties of shapes and how they move and fit together.
Identify and describe 2D shapes and 3D objects.
Explore angles, symmetry, and tessellation.
Use language of position and direction (e.g. left, right, clockwise).
Understand and use coordinates on grids.
Rotate, flip, and move shapes in space.
Patterns and Relationships
Patterns and Relationships
Recognising and working with patterns in numbers, shapes, and sequences.
Create, explain and continue number sequences and patterns.
Spot patterns in calculations to support mental maths.
Explore and predict repeating patterns in shapes and designs.
Investigate number relationships (e.g. odd/even, multiples, factors).
Maths and it's impact on the world
Maths and it's impact on the world
Understanding how maths is used in real life and the wider world.
Explore how maths helps us in everyday life (e.g. shopping, travel, budgeting).
Understand how different jobs and industries use maths.
Explore how important maths discoveries have impacted our lives e.g. engineering, sport, travel, medicine.
Develop confidence and positive attitudes towards using maths outside of lessons.
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