Grade 7 Mathematics study plan

Write and evaluate numerical expressions involving whole-number exponents and the order of operations, scoring at least 18 of 20 on a self-made drill set.

Translate verbal phrases such as 'five less than twice a number' into algebraic expressions and back again, correctly handling subtraction and division order reversals.

Identify and combine like terms and apply the distributive property to expand and factor linear expressions with integer coefficients.

Explain in writing why 2(x + 3) and 2x + 6 are equivalent, using a numeric substitution check as evidence.

Solve two-step equations of the form px + q = r and p(x + q) = r, showing each inverse operation in sequence.

Solve word problems by first defining a variable with units, then writing and solving the equation, then checking the answer against the original context.

Solve and graph one-variable inequalities on a number line, including cases where multiplying or dividing by a negative reverses the inequality symbol.

Distinguish equations with one solution, no solution, and infinitely many solutions by simplifying both sides first.

Derive and use the constant of proportionality to write equations of the form y = kx from tables, verbal descriptions, and coordinate pairs.

Set up and solve multi-step percent problems (tax, tip, markup, markdown, simple interest) using equations rather than guess-and-check.

Convert a proportional relationship between two representations (table to equation, graph to equation) and verify the constant is identical.

Solve scale-drawing problems by writing a proportion and interpreting the scale factor in context.

Compute unit rates associated with ratios of fractions, including rates like meters per half-hour and dollars per three-quarter pound.

Decide whether two quantities are in a proportional relationship by testing for a constant ratio across a table and by checking whether the graph passes through the origin.

Identify the constant of proportionality from a graph, table, equation, and verbal description, and state its meaning with units.

Represent proportional relationships with equations and use them to predict unknown values, then interpret points on the graph as ordered pairs in context.

Add, subtract, multiply, and divide positive and negative integers and rational numbers, applying the rules for signs without a calculator.

Convert between fractions, decimals, and percents for terminating and repeating decimals, and identify which rational numbers have repeating expansions.

Apply the properties of operations (commutative, associative, distributive, additive inverse) to simplify expressions with rational coefficients.

Solve real-world problems involving signed quantities such as elevation, temperature change, and account balances, and justify the sign of the answer.

Use random sampling to draw inferences about a population, and explain why a sample must be representative rather than convenient.

Compare two populations using measures of center and variability (mean, median, mean absolute deviation, range) and state which measure best supports a claim.

Generate and analyze a sample space for simple and compound events using lists, tables, and tree diagrams.

Compute experimental and theoretical probabilities for compound events and explain discrepancies between them in terms of sample size.

Solve problems involving the circumference and area of circles, using both an exact pi form and a decimal approximation, and label answers with correct square or linear units.

Find the area of triangles, quadrilaterals, and composite figures by decomposing shapes and identifying the needed dimensions.

Solve real-world volume and surface area problems for prisms and pyramids, including figures with fractional edge lengths.

Build and interpret box plots and dot plots, and use them to compare two data sets by median, interquartile range, and overall shape.

Complete two full-length mixed-domain practice tests under timed conditions and score each by domain to find remaining weak areas.

Re-teach your two lowest-scoring subskills from scratch using worked examples, then re-test only those subskills.

Assemble a single condensed review sheet covering every formula and rule you needed during the eight weeks.

Practice showing work and writing final answers with units, since unexplained answers are the most common avoidable point loss.