Maths for Key Stage 2: a teacher's guide

What is taught in Maths for Key Stage 2?

The term Key Stage 2 (KS2) is used for a child's second stage of primary education. It encompasses the class years 3, 4, 5 and 6. In KS2, children are generally aged between 7 and 11 years. Key Stage 1 is about building up basic knowledge and skills and introducing subjects to a child and Key Stage 2 develops these skills further and builds on a deeper understanding of the topics. We have provided details of what your child will be studying in Mathematics for Key Stage 2.

In KS2 Maths, children gain much more confidence and accuracy in knowledge of Mathematics: they learn to add, subtract, multiply and divide. Also, they solve problems and do mental maths using money, time, and other mathematical concepts. Disadvantaged pupils might benefit from concrete, pictorial, abstract methods of teaching. More confident pupils might be able to take on the curriculum without any additional scaffolding. Using concrete approaches can certainly help reduce pupil misconceptions and are encouraged to be used in Maths up into key stage 3. 

KS2 Students will also start to build connections between what their previous learning and more complicated mathematics such as decimals and fractions. Key mathematical teaching methods you might want to try include:

- Quick-fire practice Maths questions

- SATS-style practice papers

- Edtech programs that 'gameify' the learning experience

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Lower key stage 2 Mathematics – Years 3 and 4

The primary focus of teaching mathematics in primary schools lower key stage 2 is to make children increasingly fluent with the four operations and whole numbers,  including the concept of place value and number facts. At the lower key stage 2  –  years  3  and  4 children develop valuable written and mental mathematics methods and do calculations correctly with increasingly large whole numbers. Children build their ability to solve a wide range of problems, including decimal place values and simple fractions.

Children in primary schools should draw with increasing correctness and build mathematical reasoning so they can evaluate shapes with their properties, and correctly demonstrate the relationship between them. Children learn to use measuring instruments correctly and make connections between numbers and measures. Before year 4 ends, children are expected to have memorised their 1 to 12 multiplication tables. Their work needs to demonstrate fluency and precision. Using their increasing knowledge of spelling and word reading, KS2 students must spell and read mathematical vocabulary with accuracy and confidence.

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Upper key stage 2 Mathematics – years 5 and 6

The primary focus of teaching maths in upper key stage 2 is to extend students' understanding of the place value and number system to include larger digits. At this level, students build connections between division and multiplication with percentages, decimals, ratios and fractions. At the Upper key stage 2 level, students build their skills of problem-solving using complex arithmetic and mental methods of calculation. Depending on the arithmetical understanding, students are introduced to the concepts of algebra which to solve a variety of problems.

Teaching algebra and geometry extend and consolidate students' conceptual knowledge of numbers. While teaching students, classroom teachers need to make sure that the students categorize shapes with highly complex geometry - properties and geometry - position that they must know the vocabulary they need to define them. By the end of studying upper Key Stage Two Maths in year 6, students must gain fluency in written techniques for all of the four operations, including long division and multiplication, and in using decimals, fractions, and percentages. Pupils must pronounce, read and spell mathematical terminologies correctly.

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What is included in KS2 Maths?

This curriculum encompasses a wide range of concepts and skills essential for developing mathematical proficiency and problem-solving abilities.

Number and Place Value

Children will learn to partition, order, and round numbers up to three decimal places. This includes understanding and using multiples, factors, negative numbers, square numbers, and prime numbers up to 100. Cube numbers and mastering the key operations of addition, subtraction, multiplication, and division with numbers up to four digits are also covered.

Fractions, Decimals, and Percentages

Students will explore finding equivalents between percentages, decimals, and simple fractions. They will engage in discussions involving math problems related to percentages, division with fractions, non-unit fractions, and decimals, enhancing their understanding of these concepts.

Ratio and Proportion

The curriculum includes lessons on ratio and proportion, where children learn to compare quantities and understand the relationships between different parts of a whole.

Algebra

Basic algebra is introduced, helping students understand and use simple algebraic expressions and equations. They will practice arithmetic operations following BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction) rules.

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Geometry and Measurement

In geometry, students will measure and draw acute, right, obtuse, and reflex angles. They will calculate the sum of angles on a straight line, around a point, and in various shapes such as quadrilaterals and triangles. The curriculum also includes lessons on symmetry, visualizing and describing 3D and 2D shapes, and understanding the properties of shapes.

Measurement topics cover mass, length, and capacity, as well as converting between different units of measurement. Students will also learn to calculate time intervals and tell the time using both 12-hour and 24-hour clocks.

Data Handling

The curriculum involves creating and interpreting bar charts, line graphs, pictograms, and pie charts. Students will practice calculating the mean and average, developing their ability to analyze and represent data effectively.

Problem-Solving and Logical Reasoning

Throughout the curriculum, there is a strong emphasis on problem-solving and logic skills. Students will tackle various mathematical problems, learning to apply their knowledge in practical situations.

Times Tables

By the end of Year 6, students are expected to have a solid grasp of times tables up to 12, ensuring they can recall multiplication facts quickly and accurately.

The KS2 Maths Curriculum is comprehensive, ensuring that students develop a well-rounded understanding of mathematics, preparing them for more advanced concepts in secondary school. This structured approach not only builds foundational skills but also encourages critical thinking and practical application of mathematical concepts.

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Building Mathematical Proficiency in Key Stage 2

Building mathematical proficiency in Key Stage 2 (KS2) is a crucial task for educators, with a particular focus needed on supporting disadvantaged pupils. As teachers, we're often concerned with the performance of pupils in national curriculum tests, commonly referred to as SATs, and naturally so. With the right strategies, we can effectively enhance the attainment of pupils in maths, with tangible improvement seen in maths assessments.

A comprehensive approach can be broken down into the following steps:

1. Reinforce Core Skills: Regular practice of foundational skills such as times tables is critical. This can be done using a variety of engaging activities, not just rote learning. For example, incorporating times tables into games can increase both engagement and retention.
2. Focus on Key Topics: Some mathematical concepts carry more weight in the national curriculum assessments. Make sure to dedicate adequate time and resources to these key topics.
3. Implement Regular Teacher Assessments: These can be used to track progress and identify any gaps in understanding. The timely feedback provided after teacher assessments can significantly impact pupil scores and overall performance.
4. Support for Disadvantaged Pupils: Special attention should be given to disadvantaged pupils who may lack the support and resources available to their peers. This can be done through targeted interventions, additional tutoring, and personalised learning plans.

According to a Department for Education report, in 2019, the majority of pupils, about 67% of all eligible pupils, reached the expected standard in Maths. However, a significant gap was observed between disadvantaged and non-disadvantaged pupils, underlining the importance of targeted efforts.

In the words of educational researcher Robert Marzano, "If students are not learning, then we must teach in a different way." As we navigate the journey of KS2 Maths instruction, let's remember this, continually refining our teaching to meet the evolving needs of our pupils.

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How to develop children's interest in Maths for key stage 2

Some topics can be easily related to everyday life, but there are common misconceptions that maths is only present in the practice papers, question books and in the classroom. This can make KS2 Maths seem a pointless and redundant exercise, and something which children can forget about soon after the school bell rings.

It may become easier to teach mathematics to pupils if children would start to see how KS2 Maths is used in everyday life. They wouldn't see maths topic as irrelevant or useless subject. Mathematics is indeed not only found in books for pupils, but we also apply maths very frequently in our everyday life. From journey planning to shopping, and from checking the time to seeing how far do we live from the school, maths is everywhere.

When excellent teachers show children, how we can use KS2 Maths in real life e.g. how long it takes to reach a friend's house? or how many plates are there in the kitchen cupboard? These will create opportunities for pupils to see how mathematics relate to our real life. To make children motivated to learn KS2 Maths, we must use mathematical knowledge for fun practice or while talking about things that are of individual pupils interest. For example, if they love baking we can help them explore mathematical concepts such as weighing and measuring ingredients and checking the baking time. Or, if they love to play football, we can indicate how to check statistics such as how many points their team needs to reach the top of the scoreboard.

KS2 or grade 3-6 pupils continue to study the core subjects started in key stage 1 i.e. Maths, English, Science, Computer, Geography, History, Technology, Design, Art and Music, RE and PE. Also, they might learn a foreign language, and their teacher will also help build personal and social skills such as nutrition and cooking. Before reaching the level of secondary school, pupils may be beginning to use more advanced math concepts and skills such as analytical and critical thinking and more advanced language of algebra.

If this is an area of interest there are some brilliant books that untangle the knotty issue of maths. As a parent, you might be interested in utilising a study book with mark scheme. In our opinion, thousands of pupils would benefit from understanding mathematical concepts using concrete tools. Number concepts don't necessarily have to remain abstract if you use the right kind of tool.

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Key Papers on Key Stage Two Mathematical Teaching Best Practices

The reviewed studies highlight the importance of reflective practices, thorough understanding of geometry, fine-grain assessments, and strengthening content knowledge for effective mathematical teaching at Key Stage Two. Additionally, incorporating hands-on, activity-based learning can enhance student engagement and comprehension in mathematics.

1. Teachers' Beliefs and Practices in Relation to their Beliefs about Questioning at Key Stage 2

This study examines the relationship between teachers' beliefs and their practices in using questioning at Key Stage 2. It reveals that teachers use a variety of questioning skills that they may not always be aware of, suggesting the importance of reflective practices to enhance teaching efficacy (Şahin, Bullock, & Stables, 2002).

2. Foundation Phase Teachers' (Limited) Knowledge of Geometry

This study investigates the conceptual understanding of shapes among student teachers. It finds that many student teachers have limited knowledge of basic geometry and emphasizes the need for re-learning these concepts to ensure effective teaching in primary education (Luneta, 2014).

3. Fine Grain Assessment of Students’ Mathematical Understanding: Participatory and Anticipatory Stages in Learning a New Mathematical Conception

This research explores the process of constructing new mathematical concepts and highlights the importance of fine-grain assessment to gauge students' understanding. The study emphasizes the need for tasks that assess and support students' progression in understanding complex concepts such as fractions (Tzur, 2007).

4. Strengthening Pre-Service Teachers’ Mathematical Content Knowledge

This paper discusses the self-perceptions of pre-service teachers regarding their readiness to teach mathematics. It underscores the necessity for strengthening both content knowledge and pedagogical content knowledge to ensure effective teaching practices in primary and secondary education (Hine, 2015).

5. Maths Homework for Key Stage 2: Activity-Based Learning

This resource provides a selection of hands-on, pencil-free activities for Key Stage 2 students to extend learning at home. The activities encourage learning through discussion and practical exercises, utilizing everyday resources to reinforce mathematical concepts (Parfitt, Forster, & McGowan, 2010).

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