A guide to
Cambridge Primary Mathematics
Introduction
Cambridge Primary Mathematics encourages life-long enthusiasm for analytical and rational thinking. Learners develop a holistic understanding of the subject, focusing on principles, patterns, systems, functions and relationships. They become confident using mathematics, and develop skills that they can apply to everyday situations.
Cambridge Primary Mathematics learners:
- engage in creative mathematical thinking to generate elegant solutions
- improve numerical fluency and knowledge of key mathematical concepts to make sense of numbers, patterns, shapes, measurements and data
- develop a variety of mathematical skills, strategies and a way of thinking that will enable them to describe the world around them and play an active role in modern society
- communicate solutions and ideas logically in spoken and written language using appropriate mathematical symbols, diagrams and representations
- understand that technology provides a powerful way of communicating mathematics, one which is particularly important in an increasingly technological and digital world.
Teaching Cambridge Primary Mathematics
We provide a wide range of practical resources, detailed guidance, innovative training and professional development so that you can give your learners the best possible experience of Cambridge Primary Mathematics.
We believe that for teaching and learning to be effective, there should be alignment between curriculum, pedagogy and assessment. We have designed Cambridge Primary Mathematics around this principle:
Curriculum – taken from Primary Mathematics Curriculum Framework
4Np.02 Use knowledge of place value to multiply and divide wholes numbers by 10 and 100
Pedagogy – 4Np.02 activity taken from the Stage 4 Scheme of Work
Ask learners:
- What happens to your numbers if you multiply them by 10?
- What happens to your numbers if you multiply them by 100?
Show learners the number 65 000 and ask them to represent it on a place value grid.
Then ask them to divide it by 10. They should notice that the number is now 10 times smaller. This is the inverse of multiplying 6500 by 10. Explore the effect of multiplying and dividing different numbers by 10 and 100, avoiding answers with decimal numbers.
Possible misconceptions:
Learners often incorrectly place a zero at the end of a number to show it has been multiplied by 10. Ensure that learners understand that multiplying a number by 10 means that the place value of every digit in the number increases by one place.
Assessment – question assessing 4Np.02 taken from a Stage 4 Progression Test
Complete these calculations:
363 x 10 =
64 000 ÷ 10 =
Curriculum Framework
The Cambridge Primary Mathematics Curriculum Framework is available to download on the Mathematics (0096) page of the Cambridge Primary support site. It provides a comprehensive set of learning objectives that give a structure for teaching and learning and can be used to assess learners’ attainment and skills development. The Curriculum Framework provides balanced coverage of mathematics skills and knowledge at the primary level.
We have divided the learning objectives into three main areas called ‘strands’, which run through every stage. Each strand is divided into ‘sub-strands’:
The strands within the curriculum are related and should be taught alongside each other. Thinking and Working Mathematically is not an independent strand. Instead, the Thinking and Working Mathematically characteristics should be integrated into the teaching of the other strands.
We have designed the learning objectives to make sure learners progress as they move from Stage 1 to Stage 6 and onwards into Cambridge Lower Secondary. You can download a Progression Grid, that outlines the progression for all learning objectives across all stages, from the Mathematics (0096) page of the Cambridge Primary support site.
In the Progression Grid, identify the stage that you will be teaching, and the prior knowledge that learners are expected to have. It is important to ensure that this prior knowledge is secure before moving on to new skills and knowledge.
Below are some examples of how knowledge, understanding and skills progress across the stages:
Curriculum Framework
The Cambridge Primary Mathematics Curriculum Framework is available to download on the Mathematics (0096) page of the Cambridge Primary support site. It provides a comprehensive set of learning objectives that give a structure for teaching and learning and can be used to assess learners’ attainment and skills development. The Curriculum Framework provides balanced coverage of mathematics skills and knowledge at the primary level.
We have divided the learning objectives into three main areas called ‘strands’, which run through every stage. Each strand is divided into ‘sub-strands’:
The strands within the curriculum are related and should be taught alongside each other. Thinking and Working Mathematically is not an independent strand. Instead, the Thinking and Working Mathematically characteristics should be integrated into the teaching of the other strands.
We have designed the learning objectives to make sure learners progress as they move from Stage 1 to Stage 6 and onwards into Cambridge Lower Secondary. You can download a Progression Grid, that outlines the progression for all learning objectives across all stages, from the Mathematics (0096) page of the Cambridge Primary support site.
In the Progression Grid, identify the stage that you will be teaching, and the prior knowledge that learners are expected to have. It is important to ensure that this prior knowledge is secure before moving on to new skills and knowledge.
Below are some examples of how knowledge, understanding and skills progress across the stages:
Learning objective examples | ||||||
---|---|---|---|---|---|---|
Strand | Stage 1 | Stage 2 | Stage 3 | Stage 4 | Stage 5 | Stage 6 |
Number | Understand and visualise that halves can be combined to make wholes. | Understand and visualise that wholes, halves and quarters can be combined to create new fractions. | Estimate, add and subtract fractions with the same denominator (within one whole). | Estimate, add and subtract fractions with the same denominator. | Estimate, add and subtract fractions with the same denominator and denominators that are multiples of each other. | Estimate, add and subtract fractions with different denominators. |
Geometry and Measure | Differentiate between 2D and 3D shapes. | Identify 2D and 3D shapes in familiar objects. | Recognise pictures, drawings and diagrams of 3D shapes. | Match nets to their corresponding 3D shapes. | Identify and sketch different nets for a cube. | Identify and sketch different nets for cubes, cuboids, prisms and pyramids |
Statistics and Probability | Describe data, using familiar language including reference to more, less, most or least to answer non-statistical questions and discuss conclusions. | Describe data, identifying similarities and variations to answer non-statistical and statistical questions and discuss conclusions. | Interpret data, identifying similarities and variations, within data sets, to answer non-statistical and statistical questions and discuss conclusions. | Interpret data, identifying similarities and variations, within and between data sets, to answer statistical questions. Discuss conclusions, considering the sources of variation. | Interpret data, identifying patterns, within and between data sets, to answer statistical questions. Discuss conclusions, considering the sources of variation. | Interpret data, identifying patterns, within and between data sets, to answer statistical questions. Discuss conclusions, considering the sources of variation, and check predictions. |
Pedagogy
The Curriculum Framework gives you a list of learning objectives for each stage. Our support materials then give you guidance on:
- the order in which to teach the objectives
- ways of grouping them
- how to split the objectives into smaller steps, and how to differentiate to make the work easier or harder
- suitable activities through which to teach
- ideas for active learning.
Other support materials include:
- Progression Grids
- Schemes of Work
- Teacher Guide
- Endorsed resources
- Training
Find and access these support materials, on the Mathematics (0096) page of the Cambridge Primary support site. You can find more general information about these support materials on the About Cambridge Primary page of the Cambridge Primary support site.
Thinking and Working Mathematically
We have designed Cambridge Primary Mathematics around the principle of Thinking and Working Mathematically. It has meaningful content that helps learners to develop a rich understanding of the subject.
Thinking and Working Mathematically supports the concepts and skills in all strands of the Cambridge Primary Mathematics curriculum. When learners think and work mathematically, they actively engage with their learning. They try to make sense of ideas and build connections between different facts, procedures and concepts. Learners who do not think and work mathematically can carry out processes that their teacher has shown them. However, they may not understand why the processes work or what the results mean. Noticing inconsistencies, patterns and particular representations encourages learners to think and work mathematically. Practice, reflection and questioning will help them to improve.
Thinking and Working Mathematically covers eight characteristics that are presented in four pairs:
- Specialising and Generalising
- Conjecturing and Convincing
- Characterising and Classifying
- Critiquing and Improving.
The four pairs of characteristics are represented in the Thinking and Working Mathematically Star.
The eight Thinking and Working Mathematically characteristics are all closely connected and interdependent. A high-quality task may include one or more of them. The characteristics give learners the language they need to think and work mathematically. They can then decide which mathematical knowledge, procedures and strategies they need to use to gain a deeper understanding of mathematical questions.
Choose a topic from the stage you are teaching and from the relevant Scheme of Work. Find activities that integrate Thinking and Working Mathematically characteristics.
Choose a Thinking and Working Mathematically characteristic, look at the Scheme of Work and find the stage you are teaching. Find opportunities throughout the year where the characteristic can be developed.
All primary stages use a three-step teaching approach:
- concrete
using objects to support understanding a new concept
- representational
transforming the concrete model to a pictorial representation of the same concept
- abstract
learning how the pictorial representation relates to conventional mathematical symbols and notations.
For example, when introducing the concept of addition, you can:
- concrete
use counters to show that two counters and one counter total three counters all together
- representational
draw circles to represent the counters, discovering that two circles and one circle total three circles all together
- abstract
show how the circles represent the symbols 2 + 1 = 3.
For some concepts, this three-step approach may take several weeks or months to complete.
For more information on the approaches to teaching and learning in Cambridge Primary Mathematics, refer to Section 3.4 of the Teacher Guide.
Assessment
We offer a range of optional assessments to help you prove and improve learning:
- Cambridge Primary Progression Tests check learners’ progress in Stages 3, 4, 5 and 6. They are updated annually and marked in school.
- Cambridge Primary Checkpoint can be used to monitor individual and group performance at the end of the primary programme. See how your learners are performing in comparison to the rest of their class and against an international benchmark. The tests are marked by Cambridge International.
Cambridge Primary Progression Tests (teacher marked)
Cambridge Primary Progression Tests help you to check your learners' progress. They provide detailed information about the performance of each learner for Stages 3, 4, 5 and 6 of the curriculum. The tests help teachers to compare the strengths and weaknesses of individuals and groups and share feedback with learners and parents. They are marked by teachers in your school and come with access to a unique reporting and analysis tool.
You can download sample Progression tests on the Mathematics (0096) page of the Cambridge Primary support site.
You can find general information more about Cambridge Primary Progression Tests on the About Cambridge Primary page of the Cambridge Primary support site.
Cambridge Primary Checkpoint (marked by Cambridge examiners)
Cambridge Primary Checkpoint tests skills, knowledge and understanding at the end of Stage 6 and helps you to measure achievement at the end of Cambridge Primary. The tests are marked by Cambridge International to provide an international benchmark of learner performance. Feedback reports show how a learner has performed in relation to the curriculum, their learning group, the whole school, and against all learners who have taken tests in that series around the world.
There are two Cambridge Primary Checkpoint exam series every year. To enter learners for the tests, your school exams officer needs to go to the Making entries area on Cambridge International Direct.
You can find more general information about Cambridge Primary Checkpoint on the About Cambridge Primary page of the Cambridge Primary support site.
Assessment
We offer a range of optional assessments to help you prove and improve learning:
- Cambridge Primary Progression Tests check learners’ progress in Stages 3, 4, 5 and 6. They are updated annually and marked in school.
- Cambridge Primary Checkpoint can be used to monitor individual and group performance at the end of the primary programme. See how your learners are performing in comparison to the rest of their class and against an international benchmark. The tests are marked by Cambridge International.
Cambridge Primary Progression Tests (teacher marked)
Cambridge Primary Progression Tests help you to check your learners' progress. They provide detailed information about the performance of each learner for Stages 3, 4, 5 and 6 of the curriculum. The tests help teachers to compare the strengths and weaknesses of individuals and groups and share feedback with learners and parents. They are marked by teachers in your school and come with access to a unique reporting and analysis tool.
You can download sample Progression tests on the Mathematics (0096) page of the Cambridge Primary support site.
You can find general information more about Cambridge Primary Progression Tests on the About Cambridge Primary page of the Cambridge Primary support site.
Cambridge Primary Checkpoint (marked by Cambridge examiners)
Cambridge Primary Checkpoint tests skills, knowledge and understanding at the end of Stage 6 and helps you to measure achievement at the end of Cambridge Primary. The tests are marked by Cambridge International to provide an international benchmark of learner performance. Feedback reports show how a learner has performed in relation to the curriculum, their learning group, the whole school, and against all learners who have taken tests in that series around the world.
There are two Cambridge Primary Checkpoint exam series every year. To enter learners for the tests, your school exams officer needs to go to the Making entries area on Cambridge International Direct.
You can find more general information about Cambridge Primary Checkpoint on the About Cambridge Primary page of the Cambridge Primary support site.