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Symmetry - Year 4 Interactive Lesson and End of the Year Activities

Symmetry - Year 4 Interactive Lesson and End of the Year Activities

Subject: Mathematics

Age range: 7-11

Resource type: Lesson (complete)

Skoolmaths

Last updated

24 October 2023

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lines of symmetry year 4 reasoning and problem solving

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"Exploring Geometry: A Year 4 Digital Maths Activity Bundle"

Are you looking for a comprehensive and interactive resource to help your Year 4 students explore the world of geometry? Our "Exploring Geometry" digital maths activity bundle is the perfect solution! This bundle is designed to engage students in a variety of fun and interactive activities that cover key geometry concepts such as lines, angles, shapes, symmetry, and more. With a focus on both theoretical understanding and practical application, this resource will help students develop a strong foundation in geometry and enhance their problem-solving and critical thinking skills. All activities in the bundle are aligned with the Year 4 Maths curriculum and have been created with the latest pedagogical techniques in mind. The activities are interactive and engaging, making them suitable for both classroom and remote learning environments. The "Exploring Geometry" digital maths activity bundle is available for immediate download and is compatible with a wide range of devices, including laptops, tablets, and smartphones. With its comprehensive coverage of key geometry concepts, this bundle is an essential resource for teachers, homeschoolers, and parents looking to support their students' learning journey. Don't miss out on this opportunity to engage your students in the exciting world of geometry and give them the tools they need to succeed!

Year 4 Maths Bundle

This completely interactive Digital Home Learning Pack contains all the Year 4 programme of study directly mapped to the British National Curriculum and is designed for learners from ages 8 to 9. Lesson can be used as whole class teaching by teachers and at home by learners. **What is in this pack:** 2-D Shapes 3-D Shapes Area and perimeter of Rectilinear Shapes Coordinates in the First Quadrant Converting Decimals and Fractions Year 4 Handling Data - Interpreting and Presenting Data Year 4 place value - Ordering and Comparing Numbers Roman Numerals Year 4 Place Value - counting Symmetry Time and Timetable Units of Measurements Year 4 Place Value - Rounding Adding and Subtracting Fractions Divisibility Rules Equivalent Fractions Year 4 Number and place Value Addition and Subtraction Tons of Printable Worksheets and Lots More... Opening Instruction is included in each individual lessons.

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Lines of Symmetry

Teacher notes

Symmetry in 2D shapes

Unit 10 – 2 weeks

The PowerPoint file contains slides you can use in the classroom to support each of the learning outcomes for this unit, listed below. Geometry topics are not covered by the NCETM Primary Mastery Professional Development materials. Therefore, some slides for this unit have been additionally created to provide the high-level overview to address each learning outcome. However, they do not provide the level of detail seen in other units, so teachers will need to supplement slides with other high quality materials available to them. You should also refer to the national curriculum to ensure coverage. There are also links to the ready-to-progress criteria detailed in the DfE Primary Mathematics Guidance 2020 .

Classroom slides for this unit

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Resources tagged with: Symmetry

There are 71 NRICH Mathematical resources connected to Symmetry , you may find related items under Transformations and constructions .

lines of symmetry year 4 reasoning and problem solving

Always, Sometimes or Never? Shape

Are these statements always true, sometimes true or never true?

lines of symmetry year 4 reasoning and problem solving

Use the information on these cards to draw the shape that is being described.

lines of symmetry year 4 reasoning and problem solving

National Flags

This problem explores the shapes and symmetries in some national flags.

lines of symmetry year 4 reasoning and problem solving

Poly Plug Pattern

Create a pattern on the small grid. How could you extend your pattern on the larger grid?

lines of symmetry year 4 reasoning and problem solving

Exploded Squares

This practical activity challenges you to create symmetrical designs by cutting a square into strips.

lines of symmetry year 4 reasoning and problem solving

Attractive Rotations

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

lines of symmetry year 4 reasoning and problem solving

Counters in the Middle

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

lines of symmetry year 4 reasoning and problem solving

Reflector ! Rotcelfer

Can you place the blocks so that you see the reflection in the picture?

lines of symmetry year 4 reasoning and problem solving

Coordinate Challenge

Use the clues about the symmetrical properties of these letters to place them on the grid.

lines of symmetry year 4 reasoning and problem solving

Stringy Quads

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

lines of symmetry year 4 reasoning and problem solving

Octa-flower

Join some regular octahedra, face touching face and one vertex of each meeting at a point. How many octahedra can you fit around this point?

lines of symmetry year 4 reasoning and problem solving

Symmetry Challenge

How many symmetric designs can you make on this grid? Can you find them all?

lines of symmetry year 4 reasoning and problem solving

Shady Symmetry

How many different symmetrical shapes can you make by shading triangles or squares?

lines of symmetry year 4 reasoning and problem solving

Reflecting Squarely

In how many ways can you fit all three pieces together to make shapes with line symmetry?

lines of symmetry year 4 reasoning and problem solving

A Cartesian Puzzle

Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.

lines of symmetry year 4 reasoning and problem solving

Attractive Tablecloths

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".

lines of symmetry year 4 reasoning and problem solving

Witch of Agnesi

Sketch the members of the family of graphs given by y = a^3/(x^2+a^2) for a=1, 2 and 3.

lines of symmetry year 4 reasoning and problem solving

Folium of Descartes

Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.

lines of symmetry year 4 reasoning and problem solving

Logosquares

Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.

lines of symmetry year 4 reasoning and problem solving

Mean Geometrically

A and B are two points on a circle centre O. Tangents at A and B cut at C. CO cuts the circle at D. What is the relationship between areas of ADBO, ABO and ACBO?

lines of symmetry year 4 reasoning and problem solving

Colouring Triangles

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

lines of symmetry year 4 reasoning and problem solving

Symmetric Trace

Points off a rolling wheel make traces. What makes those traces have symmetry?

lines of symmetry year 4 reasoning and problem solving

Building Patterns

Can you deduce the pattern that has been used to lay out these bottle tops?

lines of symmetry year 4 reasoning and problem solving

Emmy Noether

Find out about Emmy Noether, whose ideas linked physics and algebra, and whom Einstein described as a 'creative mathematical genius'.

lines of symmetry year 4 reasoning and problem solving

Watch Those Wheels

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!

lines of symmetry year 4 reasoning and problem solving

What mathematical words can be used to describe this floor covering? How many different shapes can you see inside this photograph?

lines of symmetry year 4 reasoning and problem solving

Plot the graph of x^y = y^x in the first quadrant and explain its properties.

lines of symmetry year 4 reasoning and problem solving

An irregular tetrahedron has two opposite sides the same length a and the line joining their midpoints is perpendicular to these two edges and is of length b. What is the volume of the tetrahedron?

lines of symmetry year 4 reasoning and problem solving

Symmetrical Semaphore

Someone at the top of a hill sends a message in semaphore to a friend in the valley. A person in the valley behind also sees the same message. What is it?

lines of symmetry year 4 reasoning and problem solving

Hidden Meaning

What is the missing symbol? Can you decode this in a similar way?

Pattern Power

Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.

lines of symmetry year 4 reasoning and problem solving

Two Triangles in a Square

Given that ABCD is a square, M is the mid point of AD and CP is perpendicular to MB with P on MB, prove DP = DC.

Some local pupils lost a geometric opportunity recently as they surveyed the cars in the car park. Did you know that car tyres, and the wheels that they on, are a rich source of geometry?

lines of symmetry year 4 reasoning and problem solving

Tournament Scheduling

Scheduling games is a little more challenging than one might desire. Here are some tournament formats that sport schedulers use.

lines of symmetry year 4 reasoning and problem solving

Classifying Solids Using Angle Deficiency

Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry

lines of symmetry year 4 reasoning and problem solving

The Frieze Tree

Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?

Frieze Patterns in Cast Iron

A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.

lines of symmetry year 4 reasoning and problem solving

A red square and a blue square overlap. Is the area of the overlap always the same?

lines of symmetry year 4 reasoning and problem solving

Square Pizza

Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?

lines of symmetry year 4 reasoning and problem solving

Prime Magic

Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?

Rhombicubocts

Each of these solids is made up with 3 squares and a triangle around each vertex. Each has a total of 18 square faces and 8 faces that are equilateral triangles. How many faces, edges and vertices does each solid have?

lines of symmetry year 4 reasoning and problem solving

An equilateral triangle is sitting on top of a square. What is the radius of the circle that circumscribes this shape?

lines of symmetry year 4 reasoning and problem solving

The ten arcs forming the edges of the "holly leaf" are all arcs of circles of radius 1 cm. Find the length of the perimeter of the holly leaf and the area of its surface.

lines of symmetry year 4 reasoning and problem solving

Eight Dominoes

Using the 8 dominoes make a square where each of the columns and rows adds up to 8

lines of symmetry year 4 reasoning and problem solving

A Problem of Time

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?

lines of symmetry year 4 reasoning and problem solving

Maltese Cross

Sketch the graph of $xy(x^2 - y^2) = x^2 + y^2$ consisting of four curves and a single point at the origin. Convert to polar form. Describe the symmetries of the graph.

lines of symmetry year 4 reasoning and problem solving

Sketch the graphs for this implicitly defined family of functions.

lines of symmetry year 4 reasoning and problem solving

Find the shape and symmetries of the two pieces of this cut cube.

lines of symmetry year 4 reasoning and problem solving

This activity investigates how you might make squares and pentominoes from Polydron.

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Year 4 Lines of Symmetry Maths Challenge

Year 4 Lines of Symmetry Challenge

This Year 4 Lines of Symmetry Challenge checks children’s understanding of finding lines of symmetry. Children will help Matt to select the correct shapes to find a given number of lines of symmetry.

If you would like to access  additional resources which link to this maths challenge, you can purchase a subscription for only £5.31 per month on our sister site, Classroom Secrets .

Teacher Specific Information

This Year 4 Lines of Symmetry Challenge checks pupils’ understanding of finding lines of symmetry. Pupils will help Matt to select the correct shapes to find a given number of lines of symmetry.

National Curriculum Objectives

Properties of Shapes

Mathematics Year 4: (4G2b) Identify lines of symmetry in 2-D shapes presented in different orientations

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lines of symmetry year 4 reasoning and problem solving

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lines of symmetry year 4 reasoning and problem solving

Mathematical Reasoning™ Level B

Bridging the gap between computation and math reasoning.

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Forget boring math lessons and dreaded drill sheets.  This fun, colorful 352-page book uses engaging lessons with easy-to-follow explanations, examples, and charts to make first grade mathematical concepts easy to understand.  It can be used as a textbook or a comprehensive workbook with your textbook to teach the math skills and concepts that students are expected to know in first grade—and several concepts normally taught in second grade.  This book emphasizes problem-solving and computation to build for success in higher-level math and math assessments.

Every lesson is followed with a variety of fun, colorful activities to ensure concept mastery.  The lessons and activities spiral slowly, allowing students to become comfortable with concepts, but also challenging them to continue building their problem-solving skills.  This book teaches more than mathematical concepts; it teaches mathematical reasoning, so students learn to devise different strategies to solve a wide variety of math problems.  It is written to the standards of the National Council of Teachers of Mathematics. CONTENTS

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lines of symmetry year 4 reasoning and problem solving

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Key stage 1: mathematics test framework

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Updated 20 May 2024

lines of symmetry year 4 reasoning and problem solving

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This publication is available at https://www.gov.uk/government/publications/key-stage-1-mathematics-test-framework/key-stage-1-mathematics-test-framework

This test framework is based on the national curriculum programme of study (2014) for mathematics, introduced for teaching in schools from September 2014 and first assessed in the summer term 2016. The framework specifies the purpose, format, content and cognitive domain of the optional key stage 1 (KS1) mathematics tests; it is not designed to be used to guide teaching and learning.

This document has been produced to aid the test development process.

1.1 Purposes of STA optional assessments

The purpose of the optional assessments is to give schools access to test papers to support in the evaluation of pupil achievement and help to understand where they need additional support as they transition into key stage 2 (KS2).

While the Government encourages schools to administer the tests, there is no requirement to do so or to report results to parents or local authorities, and they will not be used for accountability purposes.

2 What is a test framework?

The purpose of the test framework is to provide the documentation to guide the development of the tests. The framework is written primarily for those who write test materials and to guide subsequent development and test construction. It is being made available to a wider audience for reasons of openness and transparency.

The framework includes those parts of the programme of study as outlined in the national curriculum (2014) that will be covered in the test (the content domain). The cognitive processes associated with the measurement of mathematics are also detailed in the cognitive domain.

The test framework also includes a test specification from which valid, reliable and comparable tests can be constructed each year. This includes specifics about test format, question types, response types, marking and a clear test-level reporting strategy.

By providing all of this information in a single document, the test framework answers questions about what the test will cover, and how, in a clear and concise manner. The framework does not provide information on how teachers should teach the national curriculum.

The test development process used by the Standards and Testing Agency (STA) embeds within it the generation of validity and reliability evidence through expert review and trialling. Given that the optional KS1 tests will be internally marked by teachers, an additional study to consider the reliability of marking will be undertaken as part of the ‘technical pre-test’ trial in the first year. The test framework does not provide detail of the validity and reliability of individual tests; this will be provided in the test handbook, which will be published on the Department for Education’s website following the administration of the test.

The test framework should be used in conjunction with the national curriculum (2014) and the annual ‘Optional KS1 tests guidance’ document.

3 Nature of the test

The KS1 mathematics test forms part of the optional assessment arrangements for pupils at the end of KS1.

The test is based on the national curriculum statutory programme of study (2014) for mathematics at KS1.

The mathematics test will cover the aspects of the curriculum that lend themselves to paper-based testing.

The optional KS1 mathematics test will be marked by teachers.

3.1 Population to be assessed

The KS1 tests are optional. They are made available to schools to support the evaluation of pupil achievement and help to understand where they need additional help as they transition into KS2.

3.2 Test format

The optional mathematics test comprises 2 components, which are presented to pupils as 2 separate test papers. The first paper is an arithmetic paper. The second paper presents a range of mathematical reasoning and problem-solving questions. The test is administered on paper.

The tests are designed to enable pupils to demonstrate their attainment and as a result are not strictly timed, since the ability to work at pace is not part of the assessment. However, elements within the curriculum state that pupils should be able to use quick recall of mathematical facts and the arithmetic paper is designed to assess some of these elements. Guidance will be provided to schools to ensure that pupils are given sufficient time to demonstrate what they understand, know and can do without prolonging the test inappropriately. Table 1 provides an indication of suggested timings for each component. The total testing time is approximately 55 minutes. If teachers or administrators change the time significantly, the test outcomes will be less reliable.

Table 1: Format of the test

3.3 resource list.

The resource list for the test is:

  • Paper 1: arithmetic – a pencil; ruler; rubber (optional)
  • Paper 2: mathematical reasoning – a pencil; a sharp, dark pencil for mathematical drawing; ruler (showing centimetres and millimetres); mirror; rubber (optional)

Pupils will not be permitted to use a calculator, tracing paper, number apparatus or other supporting equipment in either of the components.

4 Content domain

The content domain sets out the relevant elements from the national curriculum programme of study (2014) for mathematics at KS1 that are assessed in the optional mathematics test. The tests will, over time, sample from each area of the content domain.

The content domain also identifies elements of the programme of study that cannot be assessed in the KS1 tests (section 4.3). Attainment in these elements will be monitored through teacher assessment.

Tables 2 and 3 detail content from the national curriculum (2014). Elements from the curriculum are ordered to show progression across the years. The curriculum has been grouped into subdomains and these are detailed in the ‘strand’ column.

The numbering in Table 2 is not sequential because content that relates to KS2 has been removed from it.

4.1 Content domain referencing system

A referencing system is used in the content domain to indicate the year, the strand and the substrand - for example, ‘1N1’ equates to:

  • strand – Number and place value
  • substrand – 1

Table 2 shows the references for the strands and substrand, and Table 3 shows the progression across the years.

Table 2: Content domain strands and substrands

4.2 content domain for key stage 1 mathematics, table 3: content domain, 4.3 elements of the national curriculum that cannot be assessed fully.

The table below identifies areas that are difficult to fully assess in a paper-based format. Some of the points below may be partially assessed.

Table 4: Elements of the curriculum that cannot be assessed fully

5 cognitive domain.

The cognitive domain seeks to make the thinking skills and intellectual processes required for the optional KS1 mathematics test explicit. Each question will be rated against the 4 strands of the cognitive domain listed in sections 5.1 to 5.4 below to provide an indication of the cognitive demand.

The cognitive domain will be used during test development to ensure comparability of demand as well as difficulty for tests in successive years. The national curriculum (2014) aims of solving mathematical problems, fluency and mathematical reasoning are reflected within the cognitive domain.

5.1 Depth of understanding

This strand is used to assess the demand associated with recalling facts and using procedures to solve problems.

Questions requiring less depth of understanding require simple procedural knowledge, such as the quick and accurate recall of mathematical facts or the application of a single procedure to solve a problem.

At intermediate levels of demand, a question may require the interpretation of a problem or the application of facts or procedures. However, the component parts of these questions are simple and the links between the parts and processes are clear.

At a high level of demand, a greater depth of understanding is expected. Questions may require that facts and procedures will need to be used flexibly and creatively to find a solution to the problem.

Table 5: Depth of understanding - rating scale

5.2 computational complexity.

This strand is used to assess the computational demand of questions.

In questions with low complexity, there will be no numeric operation.

At an intermediate level of complexity, more than one numeric step or computation will be needed to solve the problem.

At a high level of complexity, questions will involve more than 2 processes or numeric operations.

Table 6: Computational complexity - rating scale

5.3 spatial reasoning and data interpretation.

This strand is used to assess the demand associated with the representation of geometrical problems involving 2-dimensional and 3-dimensional shapes, position and movement. This strand is also used to assess the demand associated with interpreting data.

There is a low level of demand when all the resources or information required to answer the question are presented within the problem (for example, counting the number of sides of a given 2-D shape).

At intermediate levels of demand, spatial reasoning will be needed to manipulate the information presented in the question to solve the problem (for example, find a line of symmetry on a simple shape or interpret a 2-D representation of a 3-D shape). Pupils may need to select the appropriate information in order to complete the problem (for example, from a table, chart or graph).

At the highest level of demand, there may be the need to use complex manipulation or interpretation of the information as part of the problem.

Table 7: Spatial reasoning and data interpretation - rating scale

5.4 response strategy.

This strand describes the demand associated with constructing a response to a question.

At a low level of demand, the strategy for solving a problem is given as part of the presentation of the problem.

At a lower intermediate level of demand, the strategy for solving a problem is clear. Very little construction is required to complete the task.

At an upper intermediate level of demand, there may be simple procedures to follow that will lead to completion of the problem.

At a high level of demand, the question will require that a simple strategy is developed (and perhaps monitored) to complete the task. The answer may need to be constructed, organised and reasoned.

Table 8: Response strategy - rating scale

6 test specification.

This section provides details of each test component.

6.1 Summary

The test comprises 2 components, which will be presented to pupils as 2 separate papers.

Table 9: Format of the test

6.2 breadth and emphasis.

The content and cognitive domains for the optional mathematics tests are specified in sections 4 and 5. The test will sample from the content domain in any given year. Although every element may not be included within each test, the full range of assessable content detailed in this document will be assessed over time. The questions in each test will be placed in an approximate order of difficulty.

The following sections show the proportion of marks attributed to each of the areas of the content and cognitive domains in a test.

6.2.1 Profile of content domain

Each of the 7 strands listed in Table 10 will be tested on a yearly basis and these will be present in the tests in the proportions shown.

Table 10 shows the distribution of marks across the content domain.

Table 11 shows the distribution of marks across the components of the test and by national curriculum element.

Table 10: Profile of content domain

Table 11: profile of marks by paper and curriculum element.

The total number of marks for both papers is 60.

6.2.2 Profile of cognitive domain

The cognitive domain is specified in section 5. The allocation of marks across each strand and demand rating is detailed in Table 12.

Table 12: Profile of marks by cognitive domain strand

6.3 format of questions and responses, 6.3.1 paper 1.

Paper 1 (arithmetic) will be comprised of constructed response questions, presented as context-free calculations. The arithmetic questions will each be worth one mark.

6.3.2 Paper 2

For Paper 2, mathematical reasoning problems are presented in a wide range of formats to ensure pupils can fully demonstrate mathematical fluency, mathematical problem solving and mathematical reasoning. There will be 6 aural questions at the start: one practice question and 5 test questions. These questions will help the pupils settle into the test; they will be placed in approximate order of difficulty. All questions may be read aloud, so that reading ability does not impair a pupil’s ability to demonstrate his or her mathematical attainment.

Paper 2 will include both selected response and constructed response questions.

Selected response questions, where pupils are required to select which option satisfies the constraint given in the question, will include question types such as:

  • multiple choice, where pupils are required to select their response from the options given
  • matching, where pupils are expected to indicate which options match correctly
  • true / false or yes / no questions, where pupils are expected to choose one response for each statement

Constructed response questions, where pupils are required to construct an answer rather than simply select one or more options, will include the following:

  • constrained questions, where pupils are required to provide a single or best answer; these might involve giving the answer to a calculation, completing a chart or table, or drawing a shape (for questions worth more than one mark, partial credit will be available)
  • less constrained questions, where pupils are required to communicate their approach to solving a problem

Questions in Paper 2 will comprise items presented in context and out of context.

6.4 Marking and mark schemes

The end of KS1 tests are optional and will be marked internally by teachers.

The mark schemes will give specific guidance for the marking of each question, together with general principles to ensure consistency of marking.

The mark schemes will provide the total number of marks available for each question and the criteria by which teachers should award the marks to pupils’ responses. Where multiple correct answers are possible, examples of different types of correct answer will be given in the mark schemes. Where applicable, additional guidance will indicate minimally acceptable and unacceptable responses. The mark schemes will provide a content domain reference, so it is possible to determine what is assessed in each question.

For all questions, the mark schemes will be developed during the test development process and will combine the expectations of experts with examples of pupils’ responses obtained during trialling.

For two-mark questions, where the correct answer has not been obtained, the mark scheme will indicate how marks can be awarded for correctly following a process or processes through the problem.

Within the mark schemes, examples of responses will be developed for ‘method’ questions. This is because the questions are open, leading to pupils giving a wide range of responses that are very close to the border between creditworthy or non-creditworthy. The additional examples help to improve marking reliability by providing examples of responses that fall just either side of the border of what is creditworthy or non-creditworthy.

6.5 Reporting

The raw score on the test (the total marks achieved out of the 60 marks available) will be converted into a scaled score using a conversion table. Scaled scores retain the same meaning from one year to the next. Therefore, a particular scaled score reflects the same standard of attainment in one year as in the previous year, having been adjusted for any differences in difficulty of the test.

Additionally, each pupil will receive an overall result indicating whether or not he or she has achieved the required standard on the test. A standard-setting exercise will be conducted on the first live test in 2016 to determine the scaled score needed for a pupil to be considered to have met the standard. This process will be facilitated by the performance descriptor in section 6.7, which defines the performance level required to meet the standard. In subsequent years, the standard will be maintained using appropriate statistical methods to translate raw scores on a new test into scaled scores with an additional judgemental exercise at the expected standard. The scaled score required to achieve the expected standard on the test will remain the same.

6.6 Desired psychometric properties

While the focus of the outcome of the test will be whether a pupil has achieved the expected standard, the test must measure pupils’ ability across the spectrum of attainment. As a result, the test must aim to minimise the standard error of measurement at every point on the reporting scale, particularly around the expected standard threshold.

The provision of a scaled score will aid in the interpretation of pupils’ performance over time, as the scaled score that represents the expected standard will be the same year-on-year. However, at the extremes of the scaled score distribution, as is standard practice, the scores will be truncated such that above or below a certain point all pupils will be awarded the same scaled score to minimise the effect for pupils at the ends of the distribution, where the test is not measuring optimally.

6.7 Performance descriptor

This performance descriptor describes the typical characteristics of pupils whose performance in the optional KS1 test is at the threshold of the expected standard. Pupils who achieve the expected standard in the tests have demonstrated sufficient knowledge to be well-placed to succeed in the next phase of their education, having studied the full KS1 programme of study in mathematics. This performance descriptor will be used by panels of teachers to set the standards on the new tests following their first administration in May 2016. It is not intended to be used to support teacher assessment, since it reflects only the elements of the programme of study that can be assessed in a written test (see content domain in section 4).

6.7.1 Overview

Pupils working at the expected standard will be able to engage with all questions within the test. However, they will not always achieve full marks on each question, particularly if working at the threshold of the expected standard.

Questions will range from those requiring recall of facts or application of learned procedures to those requiring understanding of how to use facts and procedures creatively to decide how to solve more complex and unfamiliar problems. There will be a variety of question formats including selected response, short answer and more complex calculations involving a small number of steps.

Question difficulty will be affected by the strands of the cognitive domain such as computational complexity and spatial reasoning and data interpretation. This should be borne in mind when considering the remainder of this performance descriptor, since pupils working at the threshold of the expected standard may not give correct responses to all questions. In cases where there are multiple interrelated computational steps and/or a need to infer new information or to visualise or represent a more abstract problem, some pupils may find the question difficult to understand in a test setting. This will be true even when the performance descriptor determines that a skill should be within the pupil’s capacity if working at the expected standard.

The following sections describe the typical characteristics of pupils in year 2 working at the threshold of the expected standard. It is recognised that different pupils will exhibit different strengths, so this is intended as a general guide rather than a prescriptive list. References in [square brackets] refer to aspects of the content domain specified in section 4.

6.7.2 Number

Pupils working at the expected standard are able to:

  • count in multiples of 2, 5 and 10, to 100, forwards and backwards [N1]
  • count forwards in multiples of 3 to 30 [N1]
  • count in steps of 10, to 100, forward and backward (for example, 97, 87, 77, 67, …) [N1]
  • read and write numbers to at least 100 in numerals, and make recognisable attempts to write numbers to 100 in words [N2]
  • use place value in whole numbers up to 100 to compare and order numbers, using less than (<), equals (=) and greater than (>) signs correctly [N2]
  • identify, represent and estimate numbers within a structured environment (for example, estimate 33 on a number line labelled in multiples of ten) [N4]
  • use place value and number facts to solve problems (for example, 60 – ▢ = 20) [N6]
  • use addition and subtraction facts [C1]
  • a two-digit number and ones (for example, 65 + 8, 79 – 6)
  • a two-digit number and tens (for example, 62 + 30, 74 – 20)
  • 2 two-digit numbers (for example, 36 + 41, 56 – 22)
  • 3 one-digit numbers (for example, 9 + 6 + 8) [C2]
  • use inverse operations to solve missing number problems for addition and subtraction (for example, given 9 + 5 = 14, complete 14 – ▢ = 9 and ▢ – 9 = ▢) [C3]
  • solve simple 2-step problems with addition and subtraction (for example, Ben has 5 red marbles and 6 blue marbles. He gives 7 of his marbles to a friend. How many marbles does he have left?) [C4]
  • recall and use multiplication and division facts for the 10 multiplication table using the appropriate signs (×, ÷ and =) (for example, 80 ÷ 10 = ▢) [C6, C7]
  • recall and use multiplication facts for the 2 and 5 multiplication tables and begin to recall and use division facts for the 2 and 5 multiplication tables using appropriate signs (×, ÷ and =) (for example, 2 × ▢ = 16, 5 × 6 = ▢) [C6, C7]
  • recognise odd and even numbers [C6]
  • solve problems involving multiplication and division (for example, Ben shares 15 grapes between 3 friends; how many grapes do they each receive?) [C8]
  • know that addition and multiplication of 2 small numbers can be done in any order (commutative) and subtraction of one number from another cannot (for example, 5 × 6 = 6 × 5, but 19 – 12 is not equal to 12 – 19) [C9]
  • recognise and find half of a set of objects or a quantity (for example, find 12 of 18 pencils) and begin to find 1/3 (one-third) or 1/4 (one-quarter) or 3/4 (three-quarters) of a small set of objects (for example, find 1/3 (one-third) of nine pencils) [F1]
  • recognise, find and name fractions 1/2 (one-half), 1/3 (one-third), 1/4 (one-quarter), 2/4 (two-quarters) and 3/4 (three-quarters) of a shape (for example, shade 1/4 (one-quarter) or 3/4 (three-quarters) of a square split into 4 equal rectangles, or shade 1/2 (one-half) of a symmetrical shape split into 8 equal parts [F1]
  • recognise the equivalence of 2 quarters and one half in practical contexts [F2]

6.7.3 Measurement

Pupils working at the expected standards are able to:

  • compare and order lengths, mass, volume / capacity (for example, 30 cm is longer than 20 cm [M1]
  • choose and use appropriate standard units to measure length / height in any direction (m / cm); mass (kg / g); temperature (°C); capacity (litres / ml) to the nearest appropriate unit (for example, the bucket contains 4 litres of water, scale marked every litre and labelled at 5 litres) using rulers, scales, thermometers and measuring vessels and begin to make good estimates (for example, the book is about 20 cm long) [M2]
  • recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value and find different combinations of coins to equal the same amounts of money (for example, find two different ways to make 48p) [M3]
  • recognise, tell and write the times: o’clock, half past and quarter past and quarter to the hour; draw hands on a clock face to show half past and o’clock times [M4]
  • begin to tell and write the time to 5 minutes, including quarter past / to the hour and draw hands on a clock face to show these times [M4]
  • solve problems in a practical context involving addition and subtraction of money of the same unit, including giving change (for example, Mrs Smith buys a cake for 12p and a biscuit for 5p; how much change does she get from 20p?) [M9]

6.7.4 Geometry

  • compare and sort common 2-D shapes (for example, semi-circle, rectangle and regular polygons such as pentagon, hexagon and octagon) and everyday objects, identifying and describing their properties (for example, the number of sides or vertices, and recognise symmetry in a vertical line) [G1, G2]
  • compare and sort common 3-D shapes (for example, cone, cylinder, triangular prism, pyramid) and everyday objects, identifying and describing their properties (for example, flat / curved surfaces, and beginning to count number of faces and vertices correctly) [G1, G2]
  • identify 2-D shapes on the surface of 3-D shapes and images of them (for example, a circle on a cylinder and a triangle on a pyramid) [G3]
  • order and arrange combinations of mathematical objects in patterns (for example, continue a repeating pattern such as: circle, circle, star, triangle, circle, circle, star, triangle, circle, ▢) [P1]
  • use mathematical vocabulary to describe position, direction (for example, left and right) and movement, including movement in a straight line, and distinguish between rotation as a turn, and in terms of right angles for quarter and half turns [P2]

6.7.5 Statistics

  • interpret simple pictograms (where the symbols show one-to-one correspondence), tally charts, block diagrams (where the scale is divided into ones, even if only labelled in multiples of 2) and simple tables [S1]
  • answer questions by counting the number of objects in each category and sorting the categories by quantity [S2]
  • answer questions about totalling and begin to compare simple categorical data (for example, when the pictures or blocks are adjacent) [S2]

6.7.6 Solve problems and reason mathematically

  • use place value and number facts to solve problems (for example, 40 + ▢ = 70) [N6,C1]
  • use inverse operations to solve missing number problems for addition and subtraction (for example, There were some people on a bus, six got off leaving seventeen people on the bus. How many were on the bus to start with?) [C3]
  • solve simple 2-step problems with addition and subtraction, which require some retrieval (for example, There are 12 kittens in a basket, 6 jump out and only 2 jump back in; how many are in the basket now?) [C4]
  • solve simple problems involving multiplication and division (for example, Ahmed buys 3 packs of apples. There are 4 apples in each pack. How many apples does he buy?) [C8]
  • solve problems with one or 2 computational steps using addition, subtraction, multiplication and division and a combination of these (for example, Joe has 2 packs of 6 stickers; Mina gives him 2 more stickers; how many stickers does he have altogether?) [C4, C8]
  • solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change (for example, Identify three coins with a total value of 24p or find the two items which cost exactly £1 altogether from a list such as: 70p, 40p, 50p and 30p) [M3, M9]

7 Diversity and inclusion

The Equality Act 2010 sets out the principles by which national curriculum assessments and associated development activities are conducted. During the development of the tests, STA’s test development division will make provision to overcome barriers to fair assessment for individuals and groups wherever possible.

National curriculum assessments will also meet Ofqual’s core regulatory criteria. One of the criteria refers to the need for assessment procedures to minimise bias: ‘The assessment should minimise bias, differentiating only on the basis of each learner’s ability to meet national curriculum requirements’ (Regulatory framework for national assessment, published by Ofqual 2011).

The optional end of KS1 mathematics test should:

  • use appropriate means to allow all pupils to demonstrate their mathematical fluency, solving problems and reasoning
  • provide a suitable challenge for all pupils and give every pupil the opportunity to achieve as high a standard as possible
  • provide opportunities for all pupils to achieve, irrespective of gender, disability or special educational need, social, linguistic or cultural backgrounds
  • use materials that are familiar to pupils and for which they are adequately prepared
  • not be detrimental to pupils’ self-esteem or confidence
  • be free from stereotyping and discrimination in any form

The test development process uses the principles of universal design, as described in the ‘Guidance on the principles of language accessibility in national curriculum assessments’ (New language accessibility guidance, published by Ofqual 2012).

In order to improve general accessibility for all pupils, where possible, questions will be placed in order of difficulty. As with all national curriculum tests, attempts have been made to make the question rubric as accessible as possible for all pupils, including those who experience reading and processing difficulties and those for whom English is an additional language, while maintaining an appropriate level of demand to adequately assess the content. This includes applying the principles of plain English and universal design wherever possible, conducting interviews with pupils and taking into account feedback from expert reviewers.

For each test in development, expert opinions on specific questions are gathered - for example, at inclusion panel meetings, which are attended by experts and practitioners from across the fields of disabilities and special educational needs. This provides an opportunity for some questions to be amended or removed in response to concerns raised.

Issues likely to be encountered by pupils with specific learning difficulties have been considered in detail. Where possible, features of questions that lead to construct irrelevant variance (for example, question formats and presentational features) have been considered and questions have been presented in line with best practice for dyslexia and other specific learning difficulties.

7.1 Access arrangements

The full range of access arrangements applicable to optional KS1 assessments as set out in the ‘Optional KS1 tests guidance’ will be available to eligible pupils as required.

Teachers are able to vary the administration arrangements for pupils according to their need. Where arrangements are varied, it should follow normal classroom practice for assessments of this type.

Appendix: Glossary of terminology used in the test framework

Independent review of key stage 2 testing, assessment and accountability (2011), Lord Bew.

Hughes S., Pollit A., & Ahmed A. (1998). ‘The development of a tool for gauging demands of GCSE and A-Level exam questions’. Paper presented at the BERA conference The Queens University Belfast.

Webb L. N. (1997). ‘Criteria for alignment of expectations and assessments in mathematics and science education’. Research Monograph No. 8. Council of Chief School Officers.

Smith M.S., Stein M.K. (1998). ‘Selecting and creating mathematical tasks: from research to practice’. Mathematics teaching in middle school 3 pp344–350.

About this publication

Who is it for.

This document is aimed primarily at those responsible for developing the optional KS1 national curriculum test in mathematics. It may also be of interest to schools with pupils in KS1 and other education professionals.

What does it cover?

The framework provides detailed information to ensure an appropriate test is developed, including the:

  • content domain
  • cognitive domain
  • test specification
  • test performance descriptors

Related information

Visit the  Standards and Testing Agency homepage  for all related information.

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IMAGES

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    Teachers' Resources. Symmetry Challenge printable sheet. In this activity, we are going to shade the squares of this grid with one colour to make different designs. There are a few rules that our designs need to follow: Whole squares have to be shaded, rather than parts of squares. Each design must have at least one line of symmetry.

  17. Symmetry in 2D shapes

    Pupils compose symmetrical shapes from two congruent shapes. 3. Pupils investigate lines of symmetry in 2D shapes by folding paper shape cut-outs. 4. Pupils find lines of symmetry in 2D shapes using a mirror. 5. Pupils reflect polygons in a line of symmetry. 6. Pupils reflect polygons that are dissected by a line of symmetry.

  18. PDF Year 4 Lines of Symmetry Reasoning and Problem Solving

    Title: Year 4 Lines of Symmetry Reasoning and Problem Solving.pdf Author: New User Created Date: 6/15/2020 6:25:25 PM

  19. PDF Shape

    Step 7 Lines of symmetry ... Year 4 | Summer term | Block 4 - Shape | Step 1 Notes and guidance In Year 3, children explored full, half and quarter turns, using the language of clockwise and anticlockwise. This small step ... Reasoning and problem solving No multiple possible answers Ron and Rosie each draw an angle.

  20. NRICH topics: Transformations and constructions Symmetry

    An irregular tetrahedron has two opposite sides the same length a and the line joining their midpoints is perpendicular to these two edges and is of length b. What is the volume of the tetrahedron? Age 14 to 16

  21. Year 4 Lines of Symmetry Maths Challenge

    Teacher Specific Information. This Year 4 Lines of Symmetry Challenge checks pupils' understanding of finding lines of symmetry. Pupils will help Matt to select the correct shapes to find a given number of lines of symmetry. If you would like to access additional resources which link to this maths challenge, you can purchase a subscription ...

  22. KS2 Maths: Finding lines of symmetry

    Explore lines of symmetry through karate. Ethan chops objects like pineapples to find lines of symmetry and uses a mirror to work out the results. Suitable for Key Stage 2, Early and 1st Level and ...

  23. Mathematical Reasoning™ Level B

    Mathematical Reasoning™ helps students devise strategies to solve a wide variety of math problems. This book emphasizes problem-solving and computation to build the math reasoning skills necessary for success in higher-level math and math assessments. Thi ... • Symmetry • Temperature • Time • Weight • Whole Numbers: Details

  24. Key stage 1: mathematics test framework

    At intermediate levels of demand, spatial reasoning will be needed to manipulate the information presented in the question to solve the problem (for example, find a line of symmetry on a simple ...

  25. Monty Hall problem

    Monty Hall problem. In search of a new car, the player chooses a door, say 1. The game host then opens one of the other doors, say 3, to reveal a goat and offers to let the player switch from door 1 to door 2. The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let ...

  26. Year 8 Math Assessment: Decimals, Fractions & Geometry

    View Year 8 Assessment 2 2023-24 (2).pdf from SCIENCE 123 at Sultan Qaboos University. ... A regular hexagon has • _____ sides the same length • _____ angles the same size • _____ lines of symmetry ... gain or lose any marks. These are here to stretch your thinking and problem solving skills, to encourage mathematical reasoning and ...

  27. Year 4 White Rose Maths: Complete a Symmetric Figure

    Teach students how to complete symmetrical patterns and shapes using this Diving into Mastery teaching pack. With fluency, reasoning, and problem-solving questions and tasks, this resource links to the National Curriculum aim: Complete a simple symmetric figure with respect to a specific line of symmetry. It also supports the White Rose small step: 'complete a symmetric figure', of the White ...

  28. Electronics

    Large language models (LLMs) have demonstrated remarkable capabilities in natural language processing tasks, including conversation, in-context learning, reasoning, and code generation. This paper explores the potential application of LLMs in radiological information systems (RIS) and assesses the impact of integrating LLMs on RIS development and human-computer interaction. We present ChatUI ...