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How to learn Grade 7: Mathematics

Minnesota academic standards: Mathematics, Grade 7

0 of 19 concepts ready to learn · Markdown, for your AI

1. Data Analysis & Probability · Calculate probabilities and reason about probabilities using proportions to solve real-world and mathematical problems.

  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. 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%

2. Data Analysis & Probability · Display and interpret data in a variety of ways, including circle graphs and histograms.

  1. 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. Data Analysis & Probability · Use mean, median and range to draw conclusions about data and make predictions.

  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

4. Geometry & Measurement · Analyze the effect of change of scale, translations and reflections on the attributes of two-dimensional figures.

  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
  2. Transformations on a grid: Represent and carry out geometric transformations on squared paper or a coordinate grid: reflections (in horizontal, vertical, and diagonal mirror lines, including the axes), translations (described as a vector or as left/right/up/down moves), and rotations (90° or 180° about a stated centre point); describe each transformation precisely using the correct language; identify which transformation maps one shape onto its image by comparing position, orientation, and size

5. Geometry & Measurement · Use reasoning with proportions and ratios to determine measurements, justify formulas and solve real-world and mathematical problems involving circles and related geometric fi

  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. 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

6. Algebra · Represent real-world and mathematical situations using equations with variables. Solve equations symbolically, using the properties of equality. Also solve equations graphically and numerica

  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
  2. 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

7. Algebra · Apply understanding of order of operations and algebraic properties to generate equivalent numerical and algebraic expressions containing positive and negative rational numbers and grouping

  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

8. Algebra · Recognize proportional relationships in real-world and mathematical situations; represent these and other relationships with tables, verbal descriptions, symbols and graphs; solve problems i

  1. 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. Algebra · Understand the concept of proportionality in real-world and mathematical situations, and distinguish between proportional and other relationships.

  1. 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

10. Number & Operation · Calculate with positive and negative rational numbers, and rational numbers with whole number exponents, to solve real-world and mathematical problems.

  1. 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
  2. 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
  3. 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
  4. 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. Number & Operation · Read, write, represent and compare positive and negative rational numbers, expressed as integers, fractions and decimals.

  1. Fractions on a number line (age 11+): Order positive and negative integers, decimals, and fractions on a number line; use the symbols =, ≠, <, >, ≤, ≥ to compare values including negative numbers and mixed representations
  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