Grade 7 Maths Worksheets

Learning Objectives

• Recognise proportional relationships by checking whether corresponding values form equivalent ratios
• Use constant multiplicative change (a single scale factor) to find missing values in proportional situations
• Identify the constant of proportionality k in models of the form y = kx

Learning Objectives

• Translate a real-world situation into an equation by defining variables and writing equivalent modeled expressions
• Solve equations to find the variable value that satisfies the modeled relationship
• Interpret the solution in context and check that it makes sense

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

• Define relative frequency as the fraction of times an event occurs in repeated trials
• Calculate relative frequency from a set of observed counts (and simplify the fraction)
• Use relative frequency to estimate probability and interpret it as long-run behavior

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

• 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

• 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

• Translate word statements into linear equations of the form px + q = r
• Identify the variable, coefficient(s), and constant when rewriting a situation as an equation
• Solve linear equations after rewriting from words

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

• 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

• 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

• Apply sequential percent changes using multiplicative factors (e.g., discount then tax).
• Represent percent change using parts of a 100% tape diagram model.
• Translate percent situations into equations and solve for the unknown original amount.+ Show more

Learning Objectives

• Use the distributive property with rational coefficients (fractions and negatives) to expand expressions with parentheses
• Rewrite equivalent expressions by distributing the same rational factor to every term inside parentheses
• Combine like terms after distribution to simplify correctly+ Show more

Learning Objectives

• Solve equations of the form px + q = r by using equivalent transformations to isolate the variable.
• Handle fractions and negative numbers correctly when subtracting q and dividing by p.
• Check that a proposed value makes the original equation true.

Learning Objectives

• Interpret solution sets for equations and inequalities in the context of a problem statement
• Use equivalent algebraic forms to keep the same meaning when modelling and interpreting results
• Match inequality solution direction to words like “at least” and “no more than”

Learning Objectives

• Translate “at least” and “no more than” situations into linear inequalities
• Solve linear inequalities and interpret the solution as a range of allowed values
• Match inequality signs to open/closed boundaries when representing solution sets on number lines

Learning Objectives

• Extract a greatest common factor (GCF) to rewrite a linear expression as a product
• Use factoring as the reverse of distribution to connect factored and expanded forms
• Solve linear equations by factoring out a common factor

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

• 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

• Use a common nonzero denominator to clear fractions from both sides of an equation.
• Solve the resulting equation with integer coefficients and keep the same solution set.
• Connect clearing denominators to checking solutions in the original fractional equation.

Learning Objectives

• Apply the distributive property to expand expressions with parentheses.
• Combine like terms after expansion to write an equivalent linear expression in simplest form.
• Handle negative and fractional coefficients correctly during distributive expansion.

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

• Use vertical angle relationships to set up equations that show two angles are equal
• Use linear pair (supplementary) relationships to set up equations that add to 180°
• Solve equations to find unknown angle measures and explain why the equation matches the diagram

Learning Objectives

• Interpret lengths on a scale drawing and identify corresponding drawing and actual lengths
• Find a scale factor as a ratio (actual ÷ drawing) and use it consistently
• Use the scale factor to calculate missing drawing or actual lengths+ 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

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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• Multiply rational numbers and apply predictable sign rules for products and quotients.
• Divide rational numbers by rewriting division as multiplication by the reciprocal.
• Simplify products and quotients of fractions and check reasonableness using magnitude.+ Show more

Learning Objectives

• Interpret |x| as the distance of a rational number x from 0
• Compare rational numbers using their absolute values (distances from 0)
• Solve simple absolute value equations+ Show more

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

• Interpret absolute value |x| as the distance of x from 0 on a number line.
• Explain why absolute values are always nonnegative and why opposite signs can give the same absolute value.
• Compute absolute values using distance from 0 and absolute value properties.

Learning Objectives

• Use the distributive property to expand expressions of the form p(x+q)
• Convert factored/parenthetical equations into equivalent linear equations
• Combine like terms correctly after expanding, then solve for the variable

Learning Objectives

• Understand the concept of sequences and patterns in mathematics.
• Apply rules and formulas to generate and analyze sequences.
• Use sequences to model real-world situations and introduce basic coding concepts.+ Show more

Learning Objectives

• Understand and properly apply the order of operations in evaluating expressions.
• Solve multi-step problems involving parentheses, exponents, multiplication, division, addition, and subtraction.
• Analyze how different arrangements of operations affect the results of expressions.+ Show more

Learning Objectives

• Understand and interpret proportional relationships using visual tools like tables and double number lines.
• Apply proportional reasoning to solve real-world problems involving ratios, rates, and percentages.
• Analyze and verify the consistency of solutions derived from proportional models.+ Show more

Learning Objectives

• Understand and interpret proportional relationships in different contexts.
• Solve real-world problems involving ratios, rates, and proportions.
• Compare and evaluate different expressions of proportionality.+ Show more

Learning Objectives

• Understand and interpret ratios and rates in real-world contexts.
• Apply proportional reasoning to solve problems involving measurements, money, and data.
• Model and compare different scenarios using ratios and rates to evaluate solutions.+ Show more

Learning Objectives

• Understand the properties of exponents, including product and power of a power laws.
• Apply exponent rules to simplify expressions in mathematical and real-world contexts.
• Interpret exponential expressions in practical situations such as population growth or decay.+ Show more

Learning Objectives

• Apply percentage calculations to real-world problems involving discounts, taxes, and interest.
• Interpret the meaning of percent ratios and analyze how changing bases or rates affects outcomes.
• Develop problem-solving strategies for verifying the reasonableness of percentage calculations.+ Show more

Learning Objectives

• Identify and describe key properties of two-dimensional shapes such as angles, parallel lines, and symmetry.
• Apply geometric concepts to interpret real-world shapes and scenarios.
• Calculate angles and measures within polygons and circles.+ Show more

Learning Objectives

• Understand and apply formulas for calculating the surface area of cylinders, cones, and pyramids.
• Interpret real-world problems involving surface area in contexts like packaging and construction.
• Decompose three-dimensional objects into nets and interpret cross-sections for surface area calculations.+ Show more