• Understanding of positive integers and their properties.
• Knowledge of the number line with positive integers.
• Familiarity with the concept of commutativity and associativity in addition.
• Understanding the relationship between addition and subtraction as inverse operations.

• Performing addition of positive integers using mental math, written methods, and calculators.
• Performing subtraction of positive integers, including exchanging across place values.
• Simplifying expressions involving the addition and subtraction of multiple positive integers.
• Solving word problems involving the addition and subtraction of positive integers.
• Checking the correctness of addition and subtraction calculations by using inverse operations.

• Understanding of place value in decimal numbers (tenths, hundredths, thousandths, etc.).
• Knowledge of how to read and write decimal numbers.
• Familiarity with the concept of rounding decimal numbers to a specified place value.
• Understanding the relationship between decimals and fractions.
• Knowledge of decimal equivalence and comparison.

• Adding and subtracting positive decimals using mental math, written methods, and calculators.
• Comparing and ordering positive decimals.
• Rounding decimals to a given number of decimal places.
• Converting between decimals and fractions.
• Solving word problems involving addition and subtraction of positive decimals.
• Estimating results of decimal operations by rounding.

• Understanding of standard units of measurement for length (millimeters, centimeters, meters, kilometers).
• Knowledge of units for mass (grams, kilograms) and capacity (milliliters, liters).
• Familiarity with the concept of time units (seconds, minutes, hours, days).
• Understanding of the metric system and its prefixes (milli-, centi-, kilo-).
• Knowledge of how to convert between different units of measurement within the metric system.

• Measuring length, mass, and capacity using appropriate tools and units.
• Converting between different units of measurement (e.g., centimeters to meters, grams to kilograms).
• Estimating measurements and making comparisons between different units.
• Solving word problems involving units of measurement, including unit conversions.
• Applying units of measurement in real-life contexts, such as calculating distances or quantities 

• Understanding of different types of angles (acute, obtuse, right, straight, reflex).
• Knowledge of key angle properties (e.g., angles on a straight line sum to 180°, angles around a point sum to 360°).
• Familiarity with complementary (add up to 90°) and supplementary angles (add up to 180°).
• Understanding of vertically opposite angles.

• Measuring angles accurately using a protractor.
• Identifying and classifying angles based on their size.
• Calculating unknown angles using angle properties and relationships.
• Solving problems involving complementary, supplementary, and vertically opposite angles.
• Applying angle knowledge to basic geometric problems and real-life situations.

• Understanding the formula for the area of a rectangle (Area = length × width).

• Knowledge of the formula for the area of a triangle (Area = ½ × base × height).
• Familiarity with the concepts of base and height in both rectangles and triangles.
• Understanding the units of area (e.g., square centimeters, square meters).

• Calculating the area of rectangles using the appropriate formula.
• Identifying the base and height in various orientations of triangles.
• Calculating the area of triangles using the correct formula.
• Solving word problems involving the area of rectangles and triangles.
• Comparing areas of different shapes and solving problems involving combined areas.

Unit Progress Criteria

• Understanding of the order of operations (BIDMAS): Brackets, Orders, Multiplication and Division (left to right), Addition and Subtraction (left to right).
• Knowledge of how to simplify expressions with multiple operations.
• Familiarity with the concept of evaluating expressions involving brackets and different operations.
• Understanding the importance of following the correct order to achieve accurate results.

• Applying the order of operations to simplify complex expressions.
• Solving problems that involve multiple operations, including brackets and indices.
• Using brackets to group operations and control the order in which they are performed.
• Evaluating expressions step-by-step according to BIDMAS rules.
• Checking and verifying results by re-evaluating expressions using the correct order of operations.

• Understanding the concept of equivalent fractions (fractions that represent the same value).
• Knowledge of how to find equivalent fractions by multiplying or dividing the numerator and denominator by the same number.
• Familiarity with simplifying fractions to their simplest form.
• Understanding the concept of fractions in different forms (e.g., 1/2 is equivalent to 2/4, 4/8, etc.).

• Generating equivalent fractions by multiplying or dividing both the numerator and the denominator by the same number.
• Simplifying fractions to their lowest terms by finding the greatest common divisor.
• Converting between fractions to compare or order them.
• Solving problems that involve identifying and creating equivalent fractions.
• Using visual aids like fraction bars or diagrams to understand and compare equivalent fractions.

• Familiarity with the use of a protractor for measuring angles and a ruler for measuring sides.
• Understanding of how to use given information (e.g., side lengths, angles) to draw specific types of triangles.

• Drawing triangles accurately using a ruler and protractor.
• Constructing triangles based on given side lengths and angle measures.
• Using geometric tools to ensure accurate measurement of sides and angles.
• Applying knowledge of triangle properties to verify the correctness of the drawn triangle.
• Solving problems involving the construction of triangles given specific criteria (e.g., angle-side-angle, side-angle-side).

• Understanding the properties of different types of triangles (e.g., equilateral, isosceles, scalene) and quadrilaterals (e.g., squares, rectangles, parallelograms, trapeziums).
• Knowledge of the sum of interior angles in triangles (180°) and quadrilaterals (360°).
• Familiarity with the properties of special triangles (e.g., right triangles, isosceles triangles) and quadrilaterals (e.g., opposite sides equal in a parallelogram, all sides equal in a square).
• Understanding the triangle inequality theorem (the sum of the lengths of any two sides must be greater than the length of the remaining side) and properties related to parallel and perpendicular lines in quadrilaterals.           

• Identifying and classifying triangles and quadrilaterals based on side lengths, angles, and symmetry.
• Calculating missing angles in triangles and quadrilaterals using their angle sum properties.
• Drawing triangles and quadrilaterals with given properties and verifying their accuracy.
• Applying the triangle inequality theorem and properties of quadrilaterals to solve geometric problems and prove relationships between different types of shapes.

• Understanding how to calculate a fraction of a given amount (e.g., ¼ of 20).
• Knowledge of simplifying fractions and converting between fractions and decimals.
• Familiarity with basic operations involving fractions (multiplying fractions by whole numbers).
• Understanding the concept of dividing an amount into equal parts based on a given fraction.         

• Calculating a fraction of a given amount by multiplying the fraction by the total amount.
• Simplifying fractions to find fractions of amounts more easily.
• Converting fractions to decimals if needed for calculation.
• Solving problems that involve finding a fraction of various amounts in real-life contexts
• Verifying calculations by checking if the result makes sense in the context of the problem.

• Understanding the concept of symmetry, including line symmetry (reflective symmetry) and rotational symmetry.
• Knowledge of how to identify lines of symmetry in various shapes and figures.
• Familiarity with the concept of tessellations (repeating patterns that cover a plane without gaps or overlaps).
• Understanding the types of shapes that can tessellate and the criteria for creating tessellations.

• Identifying lines of symmetry in different shapes and drawing lines of symmetry.
• Creating symmetrical designs by reflecting shapes across lines of symmetry.
• Recognizing and constructing tessellations using geometric shapes.
• Applying the properties of symmetry and tessellations to solve problems and create patterns.
• Analysing and describing the symmetry and tessellation properties in various real-life objects and artworks.

• Understanding the concept of a sequence and the pattern that governs its progression.
• Knowledge of common types of sequences, such as arithmetic sequences (where each term is a constant difference from the previous term) and geometric sequences (where each term is a constant multiple of the previous term).
• Familiarity with the concept of identifying the next terms in a sequence based on the pattern.

• Identifying the pattern in a given sequence (e.g., arithmetic, geometric).
• Continuing sequences by calculating and adding the next terms based on the identified pattern.
• Using given terms to determine the subsequent terms in the sequence.
• Solving problems that involve finding missing terms in sequences.
• Recognizing and describing the pattern in a sequence and explaining how the pattern continues.

• Understanding basic algebraic concepts, including variables, constants, and algebraic expressions.
• Knowledge of simple algebraic operations (addition, subtraction, multiplication, division) involving variables.
• Familiarity with the concept of substituting values into algebraic expressions.
• Understanding the use of algebraic expressions to represent mathematical relationships and solve problems.

• Identifying and using variables and constants in algebraic expressions.
• Simplifying basic algebraic expressions by combining like terms.
• Performing operations on algebraic expressions, including addition, subtraction, multiplication, and division.
• Substituting specific values for variables to evaluate algebraic expressions.
• Solving simple algebraic equations by isolating the variable and finding its value.

• Understanding the process of multiplying fractions, including multiplying the numerators and denominators.
• Knowledge of how to simplify fractions after multiplication.
• Familiarity with the process of dividing fractions, including multiplying by the reciprocal of the divisor.
• Understanding how to simplify the result of division involving fractions.

• Multiplying fractions by multiplying the numerators and denominators, and simplifying the result if needed.
• Dividing fractions by multiplying the first fraction by the reciprocal of the second fraction and simplifying the result.
• Converting improper fractions to mixed numbers and vice versa when necessary.
• Solving problems that involve multiplying and dividing fractions in various contexts.
• Checking and verifying results by ensuring calculations are simplified and correct.

• Understanding the process of expanding algebraic expressions by applying the distributive property (e.g., a(b+c)=ab+ac).
• Knowledge of the concept of factorising expressions by reversing the expansion process, including finding common factors.
• Familiarity with common algebraic identities and patterns used in expansion and factorisation.

• Expanding algebraic expressions by distributing terms and combining like terms.
• Factorising expressions by identifying and extracting the greatest common factor or using known algebraic patterns
• Simplifying expressions after expansion or factorisation.
• Solving problems involving the expansion and factorisation of algebraic expressions in various contexts.
• Verifying accuracy by checking if the expanded and factorised forms are equivalent.

• Understanding the purpose and components of a pictogram (a chart that uses pictures or symbols to represent data).
• Knowledge of how to interpret the key or legend of a pictogram, which explains what each picture or symbol represents.
• Familiarity with the concept of scaling in pictograms (e.g., one picture representing multiple units).

• Reading and interpreting data from a pictogram by understanding the symbols and their meanings.
• Creating a pictogram based on given data, using symbols to represent quantities accurately.
• Analysing and comparing data represented in pictograms to identify trends or differences.
• Solving problems that involve interpreting or creating pictograms, including using them to answer questions about data.

• Understanding the units of time (seconds, minutes, hours, days) and their conversions.
• Knowledge of how to calculate time intervals, including addition and subtraction of time.
• Familiarity with reading and interpreting time on analogue and digital clocks.
• Understanding of how to convert between different time units (e.g., minutes to hours, seconds to minutes).
• Understanding the components of a bar chart (e.g., bars, axis, labels).
• Knowledge of how to interpret the data represented by the length or height of the bars.
• Familiarity with how to read and understand the scales and labels on the axes of a bar chart.

• Performing addition and subtraction of time intervals to find the duration between two times or the end time given a start time and duration.
• Converting between different units of time (e.g., converting minutes to hours and minutes).
• Solving problems involving time, such as scheduling, calculating elapsed time, or determining time differences.
• Using clocks and calendars to accurately calculate and check time-related calculations.
• Reading and interpreting data from bar charts to extract and analyse information.
• Creating bar charts based on given data, accurately representing the values with appropriately scaled bars.
• Comparing and contrasting different sets of data represented by multiple bar charts.
• Solving problems involving bar charts, such as answering questions about the data or summarizing information.

• Understanding the concept of percentages as a way of expressing fractions out of 100.
• Knowledge of how to convert between percentages, fractions, and decimals.
• Familiarity with common percentage calculations, such as finding a percentage of an amount or percentage increase/decrease.

• Calculating percentages of given amounts (e.g., finding 25% of 80).
• Converting between percentages, fractions, and decimals for various calculations.
• Solving problems involving percentage increase and decrease (e.g., finding the new value after a 10% increase).
• Applying percentage calculations to real-life scenarios, such as discounts, interest rates, or statistical data.
• Verifying calculations by checking the accuracy of percentage results and their relevance to the problem.

• Understanding the components of a pie chart (e.g., segments, labels, and percentages).
• Knowledge of how to interpret the size of each segment in relation to the whole.
• Familiarity with how to convert data into percentages to represent in a pie chart.
• Understanding how graphs can be misleading, including issues with scale, axis manipulation, and selective data presentation.
• Knowledge of common types of misleading graphs (e.g., truncated axes, distorted scales).

• Reading and interpreting data from pie charts to understand the distribution of categories.
• Creating pie charts based on given data, accurately dividing the circle into segments that represent the correct proportions.
• Solving problems that involve comparing data from pie charts, such as determining which segment is largest or smallest.
• Converting numerical data into percentage form and using this information to accurately represent it in a pie chart.
• Identifying misleading elements in graphs, such as incorrect scales or distorted representations.
• Analysing and critiquing graphs to determine if they accurately represent the data.
• Creating accurate graphs by using proper scales and representing data fairly.
• Solving problems involving the detection of misleading information and correcting it to provide a clearer and more accurate representation.