Bulgaria NVO Grade 7 Mathematics study plan
Bulgaria NVO Grade 7 Mathematics · Give each week a clear focus.
8 weeks · About 6 hours per week
Numbers and operations (natural, integer, rational numbers; fractions and decimals; powers and roots)
Perform all four arithmetic operations with integers, including correct sign rules and order of operations.
Convert between fractions, decimals, and percents, and compare rational numbers using inequality symbols.
Simplify expressions involving powers with integer exponents and apply the relevant laws of exponents.
Compute square roots of perfect squares and simplify simple radical expressions.
Your checkpoint
A timed 20-question quiz on numbers and operations, scored at least 80%, with all errors corrected and explained in a log.
Numbers and operations (natural, integer, rational numbers; fractions and decimals; powers and roots)
Solve multi-step word problems involving fractions, decimals, and percentages, showing clear steps.
Apply the order of operations to evaluate numerical expressions containing parentheses, exponents, and roots.
Represent very large or very small numbers using scientific notation and convert between forms.
Identify and correct common computational errors, such as misapplying sign rules or exponent laws.
Your checkpoint
A set of 10 mixed word problems solved with full working, achieving at least 8 correct, and a one-page summary of error patterns.
Algebraic expressions and polynomials (monomials, polynomials, identities, simplification, factorization)
Identify monomials and polynomials, determine their degree, and write them in standard form.
Add, subtract, and multiply polynomials, including using the distributive property and FOIL method.
Apply the key algebraic identities: (a±b)^2 = a^2 ± 2ab + b^2 and (a+b)(a−b) = a^2 − b^2.
Factor common monomial factors and simple quadratic expressions using the difference of squares.
Your checkpoint
A completed worksheet of 15 polynomial operations and factorization problems, with a self-check against answer key and corrections noted.
Algebraic expressions and polynomials (monomials, polynomials, identities, simplification, factorization) & Equations and inequalities (linear equations, systems of linear equations, linear inequalities)
Simplify algebraic fractions by factoring numerators and denominators and canceling common factors.
Solve linear equations in one variable, including those with fractions and parentheses, and check solutions.
Solve systems of two linear equations using substitution and elimination methods.
Translate simple word problems into linear equations or systems and solve them.
Your checkpoint
A 30-minute test covering simplification, linear equations, and systems, scored at least 75%, with a review of mistakes.
Equations and inequalities (linear equations, systems of linear equations, linear inequalities) & Functions and coordinate geometry basics (linear function, graphs, proportional relationships)
Solve linear inequalities in one variable and represent solution sets on a number line.
Graph linear functions from equations in slope-intercept form and identify slope and intercepts.
Determine whether a point lies on a given line and find the equation of a line through two points.
Interpret proportional relationships and solve problems involving direct variation.
Your checkpoint
A set of 5 graphed linear functions with correct slope and intercept identification, plus 5 inequality problems solved and graphed on number lines.
Geometry: triangles, quadrilaterals, congruence and similarity, angle relationships
State and apply the triangle angle-sum theorem and the exterior angle theorem to find unknown angles.
Identify congruent triangles using SSS, SAS, ASA, and AAS criteria and write congruence statements.
Use properties of special quadrilaterals (parallelogram, rectangle, rhombus, square, trapezoid) to find side lengths and angles.
Apply the Pythagorean theorem to solve for missing sides in right triangles.
Your checkpoint
A geometry portfolio containing 8 solved problems (2 per goal) with diagrams and justifications, checked for accuracy.
Measurement and plane figures (perimeter, area, circles, composite figures) & Data, statistics and probability (tables, charts, averages, simple probability)
Compute perimeter and area of triangles, quadrilaterals, and circles, using appropriate formulas.
Find the area of composite figures by decomposing them into simpler shapes.
Calculate mean, median, mode, and range from a data set and interpret simple bar and line graphs.
Determine simple probabilities from equally likely outcomes and express them as fractions, decimals, or percents.
Your checkpoint
A mini-project: design a composite figure, calculate its area and perimeter, and create a table of data with mean, median, mode, and a simple probability question based on the data.
Mathematical reasoning and problem solving (word problems, modeling, justification) & Numbers and operations (natural, integer, rational numbers; fractions and decimals; powers and roots) & Algebraic expressions and polynomials (monomials, polynomials, identities, simplification, factorization) & Equations and inequalities (linear equations, systems of linear equations, linear inequalities) & Functions and coordinate geometry basics (linear function, graphs, proportional relationships) & Geometry: triangles, quadrilaterals, congruence and similarity, angle relationships & Measurement and plane figures (perimeter, area, circles, composite figures) & Data, statistics and probability (tables, charts, averages, simple probability)
Solve multi-step word problems that integrate concepts from at least two domains, clearly explaining reasoning.
Complete a full-length practice exam under timed conditions and self-score.
Review all errors from the practice exam and categorize them by domain for targeted revision.
Create a one-page summary sheet of key formulas and theorems for quick reference.
Your checkpoint
A completed full-length practice exam with a score of at least 70%, a corrected error log, and a personal formula sheet.
Milestones
Week 2: Score at least 80% on a numbers and operations quiz and correctly solve 8 out of 10 mixed word problems.
Week 4: Score at least 75% on a combined algebra and equations test, demonstrating accurate simplification and solving of linear systems.
Week 6: Complete a geometry portfolio with 8 correctly solved problems, including at least one congruence proof and one Pythagorean application.
Week 8: Achieve at least 70% on a full-length practice exam and submit a complete error log and formula sheet.