# 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.

December 6, 2021

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

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

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.

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.

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 (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:

**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.**Focus on Key Topics**: Some mathematical concepts carry more weight in the**n****ational curriculum assessments**. Make sure to dedicate adequate time and resources to these key topics.**Implement Regular Teacher Assessments**: These can be used to track progress and identify any gaps in understanding. The timely feedback provided after teacher assessment**s**can significantly impact pupil scores and overall performance.**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.

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.

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

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.

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.

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 (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:

**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.**Focus on Key Topics**: Some mathematical concepts carry more weight in the**n****ational curriculum assessments**. Make sure to dedicate adequate time and resources to these key topics.**Implement Regular Teacher Assessments**: These can be used to track progress and identify any gaps in understanding. The timely feedback provided after teacher assessment**s**can significantly impact pupil scores and overall performance.**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.

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.