Worksheet Worksheets

Learning Objectives

• Convert numbers between standard form and scientific notation
• Use exponent rules to multiply and divide numbers written in scientific notation
• Compare numbers in scientific notation using their powers of 10

Learning Objectives

• Understand proportional relationships can be written in the form y = kx.
• Identify and interpret the constant of proportionality k as the unit rate.
• Solve simple equations of the form kx = y to find x or k.+ Show more

Learning Objectives

• Solve linear equations in one variable using the properties of equality while keeping both sides balanced.
• Use inverse operations to isolate the variable, including when the equation has fractions or like terms.
• Check solutions by substituting the value back into the original equation.

Learning Objectives

• Identify proportional relationships on a coordinate grid by checking that the line passes through the origin.
• Use plotted points on a proportional graph to find the constant of proportionality k and the equation y = kx.
• Interpret proportional graphs using rate reasoning: compute and compare y/x values for nonzero points.+ Show more

Learning Objectives

• Recognise that proportional relationships form straight lines that pass through the origin.
• Find the unit rate (slope) k from plotted points on a line through the origin.
• Use y = kx to predict y-values for new x-values and check whether a point fits the relationship.

Learning Objectives

• Represent a percent increase or decrease as a multiplicative factor (e.g., +15% → ×1.15, −25% → ×0.75).
• Use proportional reasoning to find a new amount from a base amount after a percent change.
• Interpret percent models and conversion tables to move between fraction, decimal, and percent forms.

Learning Objectives

• Identify x-intercepts and y-intercepts from a coordinate grid by reading where a graph crosses the axes.
• Interpret x-intercepts as input values where the output equals 0 (zeros).
• Interpret the y-intercept as the output value when the input is 0.+ Show more

Learning Objectives

• Use function composition (f∘g)(x)=f(g(x)) to build a new function
• Evaluate composed functions for given inputs while respecting domain constraints
• Solve equations involving composed functions

Learning Objectives

• Identify relative maxima and relative minima (turning points) from a function graph.
• Connect turning points to meaningful peaks and dips in the modeled quantity.
• Describe end behavior using output values as inputs become very large in magnitude or approach domain boundaries.

Learning Objectives

• Complete proportional tables by finding missing values using a constant ratio y/x
• Use the constant of proportionality y/x to extend patterns in tables
• Check whether a table represents a proportional relationship by comparing y/x across rows+ Show more

Learning Objectives

• Use tape diagrams to interpret ratios and ratios that stay equivalent when quantities are scaled.
• Solve multi-step ratio scaling problems by applying proportional scale factors consistently across steps.
• Check that intermediate and final quantities keep the same ratio.

Learning Objectives

• Identify typical values (centre) such as the median and mode from line plots and box plots.
• Interpret spread (range and IQR) to describe variability and how it affects reliability or risk in real contexts.
• Use shape features (skewness, clustering, and gaps) and outliers to explain differences between data sets.

Learning Objectives

• Use box plots to compare the center (median) and spread (IQR) of two groups.
• Use line plots to compare typical values and variability between groups by describing where most data cluster.
• Make informal comparative inferences about populations using sample summaries, including uncertainty and the effect of outliers.

Learning Objectives

• Read a box plot to identify the five-number summary: minimum, Q1, median, Q3, and maximum.
• Calculate and interpret the interquartile range (IQR) from Q1 and Q3, including what it says about the middle 50% of the data.
• Use the 1.5 × IQR rule to identify outliers on a box plot.+ Show more

Learning Objectives

• Interpret key features of a graph (points, slope/shape, vertex) to determine a function rule.
• Use coordinate pairs on a graph to find an explicit equation and describe how outputs change as inputs change.
• Use the domain shown by the graph when applying the model beyond the plotted points.

Learning Objectives

• Identify the input and output variables from a table of reliable data pairs.
• Construct an explicit functional rule that matches the pattern in a table.
• Use the rule to predict output values for new inputs.

Learning Objectives

• Identify what coefficients, factors, and exponents represent in an algebraic expression.
• Interpret how changing parts of an expression changes the quantity described in a context.
• Translate between worded descriptions and algebraic expressions using correct structure.+ Show more

Learning Objectives

• Clear denominators in rational equations to form equivalent polynomial (often quadratic) equations
• Identify excluded values (values that make denominators zero) when solving rational equations
• Solve the resulting quadratic and check candidate solutions against excluded values

Learning Objectives

• Determine slope using rise and run from two points on a coordinate grid
• Compare slopes from different pairs of points on the same line to confirm slope is constant
• Use sign (positive/negative/zero) to interpret slope direction from points

Learning Objectives

• Describe congruence using transformations such as translations, reflections, and rotations.
• Use coordinates to find the image of points after a transformation.
• Verify congruence by comparing corresponding lengths in transformed figures.

Learning Objectives

• Use volume formulas to find the volume of cylinders, cones, and spheres.
• Substitute values for radius and height into the correct formula and simplify accurately.
• Solve for an unknown radius or height using volume relationships.+ Show more

Learning Objectives

• Use surface area formulas to calculate total outside area of 3D shapes.
• Combine base area and lateral area to find the total surface area for composite shapes.
• Solve equations that come from surface area formulas involving π.+ Show more

Learning Objectives

• Compare rational numbers by using their positions relative to 0 on the number line.
• Order rational numbers with different signs and with the same sign.
• Use absolute value (distance from 0) to justify comparisons.

Learning Objectives

• Identify when two figures are similar using equal corresponding angles and proportional corresponding side lengths
• Use the scale factor between similar figures to find unknown side lengths
• Solve similarity problems involving proportional relationships and apply angle equality to find missing angles+ Show more

Learning Objectives

• Use the rules for products involving rational numbers and irrational numbers
• Apply the “nonzero” condition when multiplying a rational number by an irrational number
• Classify expressions as rational or irrational without fully evaluating them

Learning Objectives

• Use rational approximations to locate the value of an irrational number (like √2) between nearby decimals on a number line
• Compare irrational numbers by comparing their rational decimal approximations
• Translate number-line order information into inequality statements

Learning Objectives

• Understand that solving x^3 = p gives x = ∛p
• Use cube root notation correctly for positive and negative values of p
• Evaluate cube roots by checking that cubing the result gives p

Learning Objectives

• Explain why dividing by a nonzero rational number q is the same as multiplying by its reciprocal 1/q.
• Rewrite quotients of rational numbers as multiplication problems using multiplicative inverses.
• Evaluate and simplify rational-number divisions and interpret the reciprocal/cancellation patterns.

Learning Objectives

• Solve equations of the form x² = a and x³ = a using exact radical solutions
• Express solutions symbolically using square roots and cube roots (not decimals)
• Relate radical solutions to their positions on the number line

Learning Objectives

• Add and subtract integers and rational numbers using sign-sensitive calculations.
• Solve linear equations involving rational coefficients by performing balanced inverse operations.
• Use equivalent forms (like factoring/distributing) to simplify rational-number expressions.

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

• Combine successive rational changes (rises and drops) to find a net change in context
• Use rational multipliers and fractions to scale quantities and interpret the meaning of the result
• Check whether a rational answer makes sense by interpreting its direction and magnitude in the scenario

Learning Objectives

• Recognize that similarity transformations keep angle measures the same while changing side lengths by a common scale factor.
• Use transformation sequences (dilations, rotations, reflections, translations) to map one figure to a similar figure on a coordinate grid.
• Find scale factors and corresponding lengths using ratios and proportional reasoning.

Learning Objectives

• Translate real-world situations into rational-number expressions using addition, subtraction, multiplication, and division.
• Interpret the meaning of positive and negative values (gain vs. loss, up vs. down) in the context of the situation.
• Simplify and evaluate rational expressions to find interpretable results.

Learning Objectives

• Classify numbers as rational or irrational based on their decimal expansions
• Convert between fractions and terminating or repeating decimals to identify rational numbers
• Recognize common irrational numbers such as √2 and π and justify why they are irrational

Learning Objectives

• Use a scale factor to convert a drawing length to an actual length in a scale drawing.
• Set up and use a consistent correspondence between matching segments to find missing lengths.
• Solve simple equations that model proportional relationships in scale drawings.

Learning Objectives

• Use a line of best fit to model the overall trend in a scatter plot
• Calculate the slope and intercept of a best-fit line and interpret what they mean
• Use a best-fit line to make reasonable predictions within the domain of the data+ Show more

Learning Objectives

• Explain why corresponding angle measures stay the same when making a scale drawing.
• Use angle preservation to find the actual angle from the angle shown on the drawing.
• Justify that scaling changes lengths but not the opening between intersecting rays.

Learning Objectives

• Add and subtract radicals by combining only like radicals (same radicand).
• Simplify radical expressions using perfect squares and exponent/root rules.
• Simplify products and quotients of radicals by combining factors under one radical when appropriate.

Learning Objectives

• Track units through multiplication and division to determine the unit of a derived quantity
• Identify the correct derived unit from a given formula and unit assignments
• Use unit checking to confirm whether an answer matches the situation

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

• Identify whether a data display shows a positive, negative, or no association between two variables
• Explain why correlation (association) does not prove causation
• Use numerical features of graphs (center/spread/outliers) to describe relationships without making causal claims

Learning Objectives

• Describe how translations, rotations, and reflections move points on a 2D coordinate grid.
• Calculate the image of a point under a specified rigid motion.
• Use properties of rigid motions to verify that distances and angles are preserved.

Learning Objectives

• Use the Remainder Theorem to find the remainder when a polynomial is divided by a linear factor
• Convert remainder information into an equation involving p(a) and solve for unknown coefficients
• Check understanding by distinguishing correct and incorrect statements about remainders

Learning Objectives

• Use the Remainder Theorem to find the remainder when dividing a polynomial by (x − a)
• Evaluate p(a) quickly by substitution, without performing long division
• Use remainders to solve for unknown parameters inside a polynomial

Learning Objectives

• Use vertical angles to find unknown angle measures in intersecting lines.
• Use linear pair relationships to solve for unknown angles on a straight line.
• Recognise and apply the idea of supplementary angles formed by adjacent angles.

Learning Objectives

• Use the triangle area formula A = (1/2)bh to find the area of a geometric component on a scale drawing.
• Apply a uniform scale factor to relate drawing areas to actual areas.
• Use additive area relationships to combine areas of parts to get a total actual area.+ Show more

Learning Objectives

• Determine the area scale factor when all lengths in a scale drawing are multiplied by the same scale factor
• Use the rule area scale factor = (length scale factor)² to find missing areas
• Interpret how changing linear dimensions affects surface coverage on a scale drawing