Maths Worksheets

Learning Objectives

• Convert a ratio into a unit rate by dividing so the second quantity is 1
• Interpret unit rates in real-world contexts such as speed and price per item
• Solve problems using unit rates to scale to different quantities

Learning Objectives

• Classify real numbers as rational or irrational
• Use the rule for sums to predict whether a sum is rational or irrational without full evaluation
• Reason about rationality patterns when adding rational and irrational numbers+ Show more

Learning Objectives

• Interpret unit rates as ratios divided to a per-1 quantity, even when amounts are fractions
• Compute unit rates by dividing by a fractional quantity (using equivalent fractions or reciprocals)
• Use tape diagrams and ratio reasoning to support unit rate calculations with fractional parts+ Show more

Learning Objectives

• Interpret what each variable in a formula represents by using unit reasoning
• Use a formula to calculate an output while checking that units are consistent
• Rewrite formulas and apply unit-based thinking to confirm constants and conversion factors

Learning Objectives

• Summarize a distribution of relative frequency estimates using its center (typical value).
• Describe variability using measures such as the interquartile range (IQR) or range.
• Compare distributions from different chance processes by comparing their center and spread.

Learning Objectives

• Describe how a dilation scales distances from a fixed center using a scale factor
• Find the image of points under a dilation using coordinates and the scale factor
• Use dilation properties to reason about proportional segments, preserved angles, and parallel lines

Learning Objectives

• Use the distance formula to find the length of a segment between two points on a coordinate plane
• Compute horizontal and vertical changes (Δx and Δy) and substitute them into the distance formula
• Interpret squared differences to handle negative coordinates correctly

Learning Objectives

• Use the Inscribed Angle Theorem: an inscribed angle equals half the measure of the corresponding central angle that intercepts the same arc.
• Use the same-arc property: inscribed angles that intercept the same arc are congruent.
• Set up and solve simple equations to find unknown angle measures in circle diagrams.

Learning Objectives

• Use relative frequency (number of successes ÷ number of trials) to estimate a probability.
• Describe how relative frequency tends to stabilize as the number of trials increases.
• Compare experimental estimates to a probability model using closeness (error).+ Show more

Learning Objectives

• Represent probability using numbers between 0 and 1 and interpret 0 and 1
• Match probability statements to inequalities and interval notation
• Convert probability values between decimal and fraction forms when outcomes are equally likely

Learning Objectives

• Understand basic probability concepts through experiments such as spinning a spinner and rolling dice.
• Apply probability calculations to interpret experimental results and compare them with theoretical predictions.
• Evaluate the assumptions and limitations of probability models in real-world contexts.+ Show more

Learning Objectives

• Identify when two algebraic expressions are equivalent by rewriting them using distributive property and combining like terms
• Expand expressions with brackets (e.g., a(b+c)) to show equivalent forms clearly
• Explain how the structure of an expression shows what each coefficient contributes+ Show more

Learning Objectives

• Evaluate combined functions such as (f+g)(x), (f-g)(x), (fg)(x), and (f/g)(x) at a given x-value.
• Write combined function rules in terms of f(x) and g(x), including simplifying when possible.
• Identify restrictions on x for (f/g)(x) when the denominator function equals 0.

Learning Objectives

• Use the Remainder Theorem to connect dividing by x-a to the value p(a).
• Use p(a)=0 to decide when x-a is a factor of p(x).
• Use non-zero remainders to rule out incorrect factors/roots.

Learning Objectives

• Understand and calculate theoretical probabilities using fractions and percentages.
• Apply probability concepts to real-world scenarios and interpret experimental results.
• Develop mathematical reasoning through multi-step probability problems.+ Show more

Learning Objectives

• Interpret income and expenses to assess financial health.
• Apply mathematical calculations to solving budgeting scenarios.
• Differentiate between fixed and variable costs in personal finance.+ Show more

Learning Objectives

• Understand that converting a decimal to a percent means multiplying by 100
• Convert decimals (including decimals greater than 1) into percents
• Relate the size of a decimal to the size of its percent value

Learning Objectives

• Understand the structure and components of linear algebraic expressions.
• Apply algebraic expressions to solve real-world problems involving costs, distances, and measurements.
• Interpret tables and graphs representing linear relationships to analyze data.+ Show more

Learning Objectives

• Recognise when two figures are similar using corresponding angles and a constant scale factor.
• Calculate a corresponding length using multiplication (or division) with the scale factor from one figure to the similar figure.
• Interpret scale factor directions (from original to image, and image back to original) correctly.

Learning Objectives

• Understand how quadratic relations can model real-world situations.
• Formulate quadratic expressions from contextual problems.
• Apply vocabulary and concepts related to quadratic functions in practical scenarios.+ Show more

Learning Objectives

• Identify different representations of rational numbers in real-world contexts.
• Convert between fractions, decimals, and percentages accurately.
• Apply rational number concepts to solve practical problems involving shopping, budgeting, and data analysis.+ Show more

Learning Objectives

• Identify the gradient (rate of change) and y-intercept (starting value) from points on a line
• Write a linear equation in the form y = mx + b that matches a graph
• Use y = mx + b to predict y-values for given x-values

Learning Objectives

• Understand the relationship between angle measures and trigonometric values on the unit circle.
• Apply geometric interpretations of sine, cosine, and tangent in various quadrants.
• Analyze symmetry properties and periodicity of trigonometric functions.+ Show more

Learning Objectives

• Use unit conversion factors written as ratios to cancel unwanted units
• Convert quantities that include derived units (e.g., speed, density, area, volume per time)
• Apply a multi-step conversion chain while keeping units consistent throughout

Learning Objectives

• Apply geometric principles to solve real-world measurement problems involving composite figures.
• Decompose complex figures to simplify calculations of area and volume.
• Use formulas accurately to find measurements in applied contexts.+ Show more

Learning Objectives

• Understand and interpret ratios in practical contexts such as medication dosages and recipes.
• Apply proportional reasoning to solve multi-step problems involving real-world data.
• Analyze and compare ratios and rates to make informed decisions in everyday situations.+ Show more

Learning Objectives

• Identify and describe numeric patterns using a rule (addition, multiplication, or algebraic expression).
• Generate terms of a pattern and extend it to find the next term.
• Solve simple equations that come from pattern rules to find the pattern position or missing values.+ Show more

Learning Objectives

• Identify and interpret zeros of polynomial functions and their multiplicities.
• Apply algebraic techniques such as synthetic division and factorization to find roots.
• Analyze how roots influence the shape and behavior of polynomial graphs in real-world contexts.+ Show more

Learning Objectives

• Represent geometric objects using algebraic equations on the coordinate plane (lines, circles, and absolute value graphs).
• Justify coordinate geometry statements by reasoning algebraically about relationships, not by checking only a few cases.
• Use algebraic transformations (expanding, rearranging, substituting) to prove two conditions describe the same set of points.

Learning Objectives

• Understand different methods of collecting data systematically.
• Apply sampling techniques to gather representative data.
• Interpret data presented in tables and graphs.+ Show more

Learning Objectives

• Interpret key features of quadratic graphs, including vertex, axis of symmetry, and intercepts.
• Apply algebraic methods to identify features of parabolas from equations and graphs.
• Analyze real-world situations modeled by quadratic functions, focusing on graph features and parameters.+ Show more

Learning Objectives

• Understand the concepts of simple and compound interest.
• Apply formulas to calculate interest over different periods and rates.
• Interpret real-world scenarios involving savings, loans, and investment growth.+ Show more

Learning Objectives

• Understand how quadratic relations arise from real-world scenarios such as projectile motion and economic models.
• Identify key features of quadratic graphs and link these features to algebraic expressions.
• Interpret the practical significance of quadratic functions and their graphical representations.+ Show more

Learning Objectives

• Understand how translations, reflections, stretches, and compressions affect the graphs of linear, quadratic, and exponential functions.
• Apply algebraic transformations to modify and interpret the equations of functions in real-world contexts.
• Analyze the effect of graphical transformations on key features such as intercepts, vertices, and symmetry.+ Show more

Learning Objectives

• Apply formulas to calculate the area of composite shapes.
• Determine the surface area of three-dimensional objects.
• Decompose complex figures into simpler shapes for measurement.+ Show more

Learning Objectives

• Understand the basic criteria for triangle congruence, including side-angle-side and angle-side-angle.
• Apply the congruence criteria to determine whether two triangles are congruent in real-world contexts.
• Use logical reasoning and calculations to verify congruence of geometric figures.+ Show more

Learning Objectives

• Factorise quadratic trinomials using integer factor pairs
• Use the factored form to solve quadratic equations
• Identify the zeros (solution values) from factored products

Learning Objectives

• Understand different methods for representing data visually, such as bar graphs, pie charts, and line graphs.
• Interpret and analyze various graphical data displays to recognize patterns, trends, and insights.
• Apply mathematical reasoning to construct and compare data visualizations accurately and effectively.+ Show more

Learning Objectives

• Understand and apply formulas for calculating the perimeter of rectangles, triangles, and irregular shapes.
• Calculate and interpret the area of various plane figures in real-world scenarios.
• Solve multi-step problems involving perimeter and area, combining reasoning and calculation skills.+ Show more

Learning Objectives

• Understand how to analyze ratios and proportions in real-world contexts.
• Apply proportional reasoning to solve problems involving scale models, rates, and comparisons.
• Assess the reasonableness of solutions using contextual clues and patterns.+ Show more

Learning Objectives

• Solve linear equations algebraically using different methods.
• Interpret solutions within real-world contexts such as budgeting and resource allocation.
• Validate reasonableness of solutions in practical scenarios.+ Show more

Learning Objectives

• Factor rational expressions to reveal common numerator and denominator factors.
• Simplify rational expressions by canceling matching factors while tracking excluded values.
• Explain why a simplified rational expression is equivalent only for allowed input values.

Learning Objectives

• Understand how to calculate interest on loans and investments.
• Interpret and analyze financial documents including fees and interest rates.
• Apply percentage calculations to real-world financial scenarios.+ Show more

Learning Objectives

• Understand how to add, subtract, multiply, and divide fractions and decimals.
• Apply strategies such as common denominators and cross-multiplication to simplify calculations.
• Estimate results to assess reasonableness and validate solutions in real-world contexts.+ Show more

Learning Objectives

• Understand how to convert between fractions, decimals, and percentages.
• Apply percentage calculations to real-world scenarios such as discounts and markups.
• Develop problem-solving skills involving multi-step percentage calculations.+ Show more

Learning Objectives

• Calculate sine, cosine, and tangent of an acute angle in a right triangle using side ratios.
• Use the Pythagorean theorem to find missing sides before applying trigonometric ratios.
• Explain why trigonometric ratios depend only on the acute angle for similar right triangles.

Learning Objectives

• Apply trigonometric ratios to find missing sides and angles in right triangles.
• Use inverse trigonometric functions to determine angles from side lengths.
• Solve multi-step problems involving real-world contexts such as construction and mapping.+ Show more

Learning Objectives

• Apply fractional reasoning to interpret ratios and proportions in real-world scenarios.
• Solve practical problems involving division of resources, discounts, and data interpretation using fractions.
• Develop strategies for multi-step calculations involving fractions in everyday contexts.+ Show more