 # Maths for Key Stage 2: a teacher's guide

December 6, 2021

Maths for Key Stage 2: a teacher's guide to making the abstract more concrete.

## 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

## 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.

## 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.

## What is included in KS2 Maths?

Below is a list of the concepts included in KS2 Maths Curriculum (from Years 3 to 6):

• Partition, order and rounded numbers up to three decimal places;
• Multiples and factors;
• Negative numbers;
• Square numbers;
• Prime numbers (up to 100);
• Cube numbers;
• Key skills of Addition, subtraction, division and multiplication of numbers (up to four digits);
• Ratio and proportion;
• Finding equivalents between percentages, decimals and simple fractions;
• Basic algebra;
• The arithmetic practice of BODMAS and use of brackets;
• Discussions of math problems involving percentages, division with fractions, non-unit fractions and decimals;
• Regular practice of reading and plotting coordinates;
• Measurement and drawing of acute, right, obtuse, and reflex angles;
• Problem-solving and logic skills of calculating area and perimeter;
• Calculating the sum of angles on a straight line, around a point, and in a quadrilateral and triangle;
• Maths skills of symmetry;
• Procedural knowledge of visualising and describing 3D and 2D shapes;
• Measuring mass, length, and capacity;
• Geometry - Properties Of Shape;
• Conversion of measuring units;
• Calculating time intervals and telling the time using a 12- or 24-hour clock;
• Essential practice exercises of creating and interpreting bar charts, line graphs, pictograms and pie charts;
• Practice activities of calculating the mean, and average;
• By the end of Year 6, the students are expected to have an ideal practice and solid grip on times tables (12-multiplication tables).

## 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.

## 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. Step 1/6     ## Enhance outcomes across your school  Step 2/6
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## 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

## 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.

## 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.

## What is included in KS2 Maths?

Below is a list of the concepts included in KS2 Maths Curriculum (from Years 3 to 6):

• Partition, order and rounded numbers up to three decimal places;
• Multiples and factors;
• Negative numbers;
• Square numbers;
• Prime numbers (up to 100);
• Cube numbers;
• Key skills of Addition, subtraction, division and multiplication of numbers (up to four digits);
• Ratio and proportion;
• Finding equivalents between percentages, decimals and simple fractions;
• Basic algebra;
• The arithmetic practice of BODMAS and use of brackets;
• Discussions of math problems involving percentages, division with fractions, non-unit fractions and decimals;
• Regular practice of reading and plotting coordinates;
• Measurement and drawing of acute, right, obtuse, and reflex angles;
• Problem-solving and logic skills of calculating area and perimeter;
• Calculating the sum of angles on a straight line, around a point, and in a quadrilateral and triangle;
• Maths skills of symmetry;
• Procedural knowledge of visualising and describing 3D and 2D shapes;
• Measuring mass, length, and capacity;
• Geometry - Properties Of Shape;
• Conversion of measuring units;
• Calculating time intervals and telling the time using a 12- or 24-hour clock;
• Essential practice exercises of creating and interpreting bar charts, line graphs, pictograms and pie charts;
• Practice activities of calculating the mean, and average;
• By the end of Year 6, the students are expected to have an ideal practice and solid grip on times tables (12-multiplication tables).

## 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.

## 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.