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How to learn Grade 7: Mathematics

Oklahoma academic standards: Mathematics, Grade 7

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

1. Data & Probability · Calculate and use proportional reasoning with probabilities to model and solve 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. Percentages as Fractions: Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using percentages; work with percentages greater than 100%
  3. 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

2. Data & Probability · Interpret and analyze data, creating the most appropriate display, using a variety of tools.

  1. 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
  2. Pictograms and tally charts (age 11+): Construct and interpret frequency tables, bar charts, pie charts, pictograms, and vertical line charts for both categorical and grouped numerical data, choosing appropriate representations for the data type
  3. 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 & Measurement · Analyze the effect of translations, reflections, rotations, and dilations on the attributes of two-dimensional figures on and off the coordinate plane.

  1. Coordinate Transformations: Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original

4. Geometry & Measurement · Use mathematical models and reasoning with proportions and ratios to determine measurements, justify formulas, and solve problems.

  1. 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
  2. Compound Units: Use compound units such as speed (distance ÷ time), unit pricing (cost ÷ quantity), and density (mass ÷ volume); solve problems involving compound units
  3. Real-World Mathematical Modelling: Model real-world problems involving ratio, scale, volume, unit conversion, and proportional reasoning with appropriate tools, diagrams, or equations

5. Geometry & Measurement · Develop and understand the concept of surface area and volume of rectangular prisms with rational-valued edge lengths.

  1. Estimating answers (age 10+): Find the volume of right rectangular prisms by packing with unit cubes and show it equals l × w × h (or base area × height); apply V = l × w × h and V = B × h to solve real-world problems; calculate, estimate, and compare volumes of cubes and cuboids in standard units (cm³, m³)
  2. 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

6. Algebraic Reasoning & Algebra · Use order of operations and properties of operations to generate and evaluate equivalent numerical and algebraic expressions.

  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

7. Algebraic Reasoning & Algebra · Represent mathematical situations using equations and inequalities involving variables and rational numbers.

  1. Solving Linear Equations: Use algebraic methods to solve linear equations in one variable, including equations that require rearrangement, expanding brackets, and collecting terms on both sides; solve equations with rational number coefficients

8. Algebraic Reasoning & Algebra · Identify and justify proportional relationships using mathematical models and situations; solve problems involving proportional relationships and interpret results in t

  1. Algebraic Transformations: Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs; move between word problems, algebraic representations, tables, and graphical representations
  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. 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

9. Algebraic Reasoning & Algebra · Explain the concept of proportionality in mathematical models and situations and distinguish between proportional and non-proportional relationships.

  1. Ratio Notation and Relationships: Understand that a multiplicative relationship between two quantities can be expressed as a ratio; use ratio notation; simplify ratios

10. Numbers & Operations · Calculate with rational numbers, with and without positive integer exponents, to model and solve mathematical problems.

  1. Sign Rules for Multiplication: Multiply and divide with positive and negative integers and rational numbers, understanding the rules for the sign of the product or quotient
  2. Mixed & Improper Fractions: Use the four operations with formal written methods applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

11. Numbers & Operations · Read, write, represent, and compare rational numbers, expressed as integers, fractions, and decimals. Explain and apply the concept of absolute value.

  1. Numbers on a number line: Understand the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as magnitude in real-world contexts; distinguish absolute value comparisons from ordering statements
  2. 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