A guide to
Cambridge Lower Secondary Mathematics
Introduction
Cambridge Lower Secondary Mathematics encourages life-long enthusiasm for analytical and rational thinking. Learners develop a holistic understanding of the subject, focussing on principles, patterns, systems, functions and relationships. They become confident using mathematics, and develop skills that they can apply to everyday situations.
Cambridge Lower Secondary 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 Lower Secondary 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 Lower Secondary Mathematics.
We believe that for teaching and learning to be effective, there should be alignment between curriculum, pedagogy and assessment. We have designed Cambridge Lower Secondary Mathematics around this principle:
Curriculum – taken from Lower Secondary Mathematics Curriculum Framework
8Nf.01 Recognise fractions that are equivalent to recurring decimals.
Pedagogy – 8Nf.01 activity taken from the Stage 8 Scheme of Work
Ask learners to convert the fractions 1/4, 1/5 and 1/8 into decimals by dividing the numerator by the denominator using a short division method. Then ask learners to convert 1/3 in the same way. They should discover that the answer will be a recurring decimal (0.33333…). Establish that this decimal can be written as 0.3 ̇. Ask learners to use their answer to write 2/3 as a decimal.
Using calculators, learners should investigate different unit fractions to see which ones give recurring answers and record their results in a table:
Learners should recognise that if a unit fraction, such as 1/11 , is equivalent to a recurring decimal, then proper fractions that are multiples of this unit fraction will also be equivalent to recurring decimals, i.e. 2/11, 3/11, 4/11, …,9/11 are also equivalent to recurring decimals.
Assessment – question assessing 8Nf.01 taken from a Stage 8 Progression Test
Curriculum Framework
The Cambridge Lower Secondary Mathematics Curriculum Framework is available to download on the Mathematics (0862) page of the Cambridge Lower Secondary 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 lower secondary level.
We have divided the learning objectives into four 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 ensure progression in learning from Stage 7 to Stage 9 and onwards into Cambridge Upper Secondary. You can download a Progression Grid, that outlines the progression for all learning objectives across all stages, from the Mathematics (0862) page of the Cambridge Lower Secondary 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 is an example of how knowledge, understanding and skills progress across the stages:
Curriculum Framework
The Cambridge Lower Secondary Mathematics Curriculum Framework is available to download on the Mathematics (0862) page of the Cambridge Lower Secondary 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 lower secondary level.
We have divided the learning objectives into four 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 ensure progression in learning from Stage 7 to Stage 9 and onwards into Cambridge Upper Secondary. You can download a Progression Grid, that outlines the progression for all learning objectives across all stages, from the Mathematics (0862) page of the Cambridge Lower Secondary 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 is an example of how knowledge, understanding and skills progress across the stages:
Learning objective examples | |||
---|---|---|---|
Strand | Stage 7 | Stage 8 | Stage 9 |
Number | Understand the relationship between squares and corresponding square roots, and cubes and corresponding cube roots. | Recognise squares of negative and positive numbers, and corresponding square roots. | Use knowledge of square and cube roots to estimate surds. |
Algebra | Understand and describe nth term rules algebraically (in the form n ± a, a × n where a is a whole number). | Understand and describe nth term rules algebraically (in the form n ± a, a × n, or an ± b, where a and b are positive or negative integers or fractions). | Understand and describe nth term rules algebraically (in the form an ± b, where a and b are positive or negative integers or fractions, and in the form n⁄a, n2, n3or n2 ± a, where a is a whole number). |
Geometry and Measure | Derive and use a formula for the volume of a cube or cuboid. Use the formula to calculate the volume of compound shapes made from cuboids, in cubic metres (m3), cubic centimetres (cm3) and cubic millimetres (mm3). | Use knowledge of area and volume to derive the formula for the volume of a triangular prism. Use the formula to calculate the volume of triangular prisms. | Use knowledge of area and volume to derive the formula for the volume of prisms and cylinders. Use the formula to calculate the volume of prisms and cylinders. |
Statistics and Probability | Understand and explain that probabilities range from 0 to 1, and can be represented as proper fractions, decimals and percentages. | Understand that complementary events are two events that have a total probability of 1. | Understand that the probability of multiple mutually exclusive events can be found by summation and all mutually exclusive events have a total probability of 1. |
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.
Our support materials include:
- Progression Grids
- Schemes of Work
- Teacher Guide
- Endorsed resources
- Training
Find and access these support materials, on the Mathematics (0862) page of the Cambridge Lower Secondary support site. You can find more general information about these support materials on the About Cambridge Lower Secondary page of the Cambridge Lower Secondary support site.
Thinking and Working Mathematically
We have designed Cambridge Lower Secondary 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 mathematical concepts and skills in all strands of the Cambridge Lower Secondary 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 consists of 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 mathematics 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 for the stage you are teaching. Find opportunities throughout the year where the characteristic can be developed.
For more information on the approaches to teaching and learning in Cambridge Lower Secondary 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 Lower Secondary Progression Tests can be used to check learners’ progress in Stages 7, 8 and 9. They are updated annually and marked in school.
- Cambridge Lower Secondary Checkpoint can be used to monitor individual and learners are performing in comparison group performance at the end of the Lower Secondary programme. See how your to the rest of their class and against an international benchmark. The tests are marked by Cambridge International.
Cambridge Lower Secondary Progression Tests (teacher marked)
Cambridge Lower Secondary Progression Tests help you to check your learners' progress. They provide detailed information about the performance of each learner for Stages 7, 8 and 9 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 find more general information about Cambridge Lower Secondary Progression Tests on the About Cambridge Lower Secondary page of the Cambridge Lower Secondary support site.
You can download sample Progression tests on the Mathematics (0862) page of the Cambridge Lower Secondary support site.
Cambridge Lower Secondary Checkpoint (marked by Cambridge examiners)
Cambridge Lower Secondary Checkpoint tests skills, knowledge and understanding at the end of Stage 9 and helps you to measure achievement at the end of Cambridge Lower Secondary. 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.
You can find more general information about Cambridge Lower Secondary Checkpoint on the About Cambridge Lower Secondary page of the Cambridge Lower Secondary support site.
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.
Assessment
We offer a range of optional assessments to help you prove and improve learning:
- Cambridge Lower Secondary Progression Tests can be used to check learners’ progress in Stages 7, 8 and 9. They are updated annually and marked in school.
- Cambridge Lower Secondary Checkpoint can be used to monitor individual and learners are performing in comparison group performance at the end of the Lower Secondary programme. See how your to the rest of their class and against an international benchmark. The tests are marked by Cambridge International.
Cambridge Lower Secondary Progression Tests (teacher marked)
Cambridge Lower Secondary Progression Tests help you to check your learners' progress. They provide detailed information about the performance of each learner for Stages 7, 8 and 9 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 find more general information about Cambridge Lower Secondary Progression Tests on the About Cambridge Lower Secondary page of the Cambridge Lower Secondary support site.
You can download sample Progression tests on the Mathematics (0862) page of the Cambridge Lower Secondary support site.
Cambridge Lower Secondary Checkpoint (marked by Cambridge examiners)
Cambridge Lower Secondary Checkpoint tests skills, knowledge and understanding at the end of Stage 9 and helps you to measure achievement at the end of Cambridge Lower Secondary. 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.
You can find more general information about Cambridge Lower Secondary Checkpoint on the About Cambridge Lower Secondary page of the Cambridge Lower Secondary support site.
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.