ai.page · roadmaps

How to learn Grade 7: Mathematics

Pennsylvania academic standards: Mathematics, Grade 7

0 of 22 concepts ready to learn · Markdown, for your AI

1. Statistics and Probability · Use probability to predict outcomes.

  1. Calculating Simple Probability: Calculate the probability of a simple event with equally likely outcomes using the formula: probability = number of favourable outcomes ÷ total number of possible outcomes; express the result as a fraction in its simplest form; apply to rolling dice, drawing from bags, and other simple chance situations
  2. The Probability Scale: Understand probability as a measure on a scale from 0 (impossible) to 1 (certain); use the language of probability including likely, unlikely, certain, and impossible
  3. Experimental probability: Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability
  4. Tree diagrams: Generate theoretical sample spaces for single and combined events using listing, tables, and tree diagrams, and calculate theoretical probabilities as the number of favourable outcomes divided by the total number of equally likely outcomes
  5. Complementary events: Understand and apply the rule that probabilities of all mutually exclusive outcomes sum to one; use this to find the probability of a complementary event (P(not A) = 1 − P(A))

2. Statistics and Probability · Use statistical measures to compare two numerical data distributions.

  1. Comparing measurements: Describe, interpret, and compare distributions of a single variable using appropriate measures of central tendency (mean, median, mode) and spread (range), including the effect of outliers

3. Geometry · Determine circumference, area, surface area, and volume.

  1. Angles in triangles (age 11+): Derive and apply formulae for the area of triangles, parallelograms, and trapezia, and for the volume of cuboids and other prisms (including cylinders), connecting each formula to its geometric reasoning
  2. Circles: Circumference & Area: Calculate the circumference and area of circles using the formulae C = πd (or 2πr) and A = πr², and solve problems involving perimeters and areas of composite shapes that include circular parts

4. Geometry · Identify, use, and describe properties of angles and their measures.

  1. Understanding angles (age 11+): Apply the properties of angles at a point (360°), on a straight line (180°), and vertically opposite angles to find unknown angles in multi-step problems
  2. Angles with parallel lines: Understand and use the relationship between parallel lines cut by a transversal: corresponding angles, alternate interior angles, and co-interior (same-side interior) angles; use these to find unknown angles

5. Geometry · Describe and apply properties of geometric figures.

  1. Properties of triangles and quadrilaterals: Derive and illustrate properties of triangles, quadrilaterals, and circles using appropriate language, including interior angles, diagonals, symmetry, and relationships between side lengths

6. Expressions and Equations · Determine the reasonableness of the answer(s) in problem-solving situations.

  1. Estimation to check answers to calculations: Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy

7. Expressions and Equations · Use variables to represent quantities in a real-world or mathematical problem and construct simple equations and inequalities to solve problems.

  1. Expressions & Equations Vocabulary: Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms, and factors; distinguish between an expression (no equals sign), an equation (equals sign), and an inequality (inequality sign)
  2. Using Simple Formulae: Use simple formulae expressed in words or symbols to calculate values (e.g. perimeter = 2 × (length + width))

8. Expressions and Equations · Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers.

  1. Substituting into Formulae: Substitute numerical values into formulae and expressions including scientific formulae; evaluate expressions by replacing variables with given values and computing the result using correct order of operations

9. Expressions and Equations · Use properties of operations to generate equivalent expressions.

  1. Collecting Like Terms: Simplify algebraic expressions by collecting like terms — combine terms with the same variable and power (e.g., 3a + 2b + 5a = 8a + 2b) while maintaining equivalence

10. Ratios and Proportional Relationships · Analyze, recognize, and represent proportional relationships and use them to solve real-world and mathematical problems.

  1. Proportional Reasoning Vocabulary: Know and use advanced vocabulary of multiplicative reasoning — direct proportion, inverse proportion, ratio, rate, unit rate, compound unit, scale factor — accurately in problem-solving contexts
  2. Proportion Graphs: Represent proportional relationships using double number lines (two parallel number lines aligned at 0) and ratio tables; recognise that equivalent ratios generate straight lines through the origin when graphed
  3. Ratio Notation and Relationships: Understand that a multiplicative relationship between two quantities can be expressed as a ratio; use ratio notation; simplify ratios
  4. Proportion: Recognise and solve problems involving direct proportion (as one quantity increases, the other increases at a constant rate) and inverse proportion (as one increases, the other decreases), including graphical and algebraic representations

11. The Number System · Solve real-world and mathematical problems involving the four operations with rational numbers.

  1. Number Sets & Infinity: Appreciate the infinite nature of the sets of integers, real numbers, and rational numbers; position integers on a number line and distinguish between rational and irrational numbers
  2. Positive and Negative Numbers: Understand positive and negative numbers as describing quantities with opposite directions or values; use them in context such as temperature, floors in a building, and bank balances