7th Grade — Math & English
Pre-algebra concepts with an eye toward UMTYMP readiness, combined with reading comprehension and grammar to sharpen analytical skills.
Math Topics MATH
Integers
Number lines, absolute value, comparing, graphingDeep understanding of integers on vertical and horizontal number lines, absolute value in real-world contexts, comparing and ordering, and graphing integer pairs.
Operations with Integers
Add, subtract, multiply, divide integersMaster all four operations with integers, understand sign rules, evaluate multi-step expressions, and solve integer word problems in context.
Decimals
All operations, estimation, word problemsFluency with decimal operations including long division with decimals, estimation strategies, and solving multi-step real-world decimal problems.
Fractions & Mixed Numbers
All operations, complex fractionsPerform all operations with fractions/mixed numbers fluently, simplify complex fractions, and solve challenging fraction word problems.
Rational Numbers
Comparing, ordering, operations, absolute valueWork with the full set of rational numbers (fractions, decimals, integers), compare and order them on number lines, and compute with mixed forms.
Exponents & Roots
Powers, square roots, scientific notationEvaluate powers including negative bases, find square roots of perfect squares, estimate non-perfect square roots, and introduce scientific notation.
Ratios, Rates & Proportions
Unit rates, proportional relationships, scale drawingsCompute unit rates, identify and use proportional relationships in tables/graphs/equations, solve proportion problems, and work with scale drawings.
Percents
Percent of change, discounts, tax, tips, interestCalculate percent increase/decrease, find sale prices after discounts, compute tax and tips, and solve simple interest problems.
Expressions & Equations
Simplifying, one- and two-step equations/inequalitiesSimplify expressions by combining like terms, solve one- and two-step equations and inequalities, and graph solution sets on number lines.
Geometry
Angles, triangles, circles, area, volume, surface areaClassify angles and triangles, use angle relationships, calculate circumference and area of circles, and find volume/surface area of 3D figures.
Probability & Statistics
Theoretical/experimental probability, sampling, dataCalculate theoretical and experimental probability, understand sampling methods, analyze data using multiple representations, and draw inferences.
English Topics ENGLISH
Reading & Literary Analysis
Point of view, figurative language, text structuresAnalyze how point of view shapes a narrative, identify figurative language (metaphor, simile, personification), and recognize common text structures.
Vocabulary Expansion
Academic vocabulary, context clues, word relationshipsBuild grade-level academic vocabulary, use multiple context clue strategies, and understand word relationships (synonyms, antonyms, analogies).
Grammar & Conventions
Phrases, clauses, modifiers, active/passive voiceIdentify and use phrases and clauses correctly, place modifiers properly, distinguish active from passive voice, and use punctuation for clarity.
Composition
Argumentative essays, research, narrative techniquesWrite structured argumentative essays with claims and counterclaims, conduct basic research with citations, and use narrative techniques in creative writing.