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How to learn Grade 7: Mathematics

Tennessee academic standards: Mathematics, Grade 7

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1. Grade 7 · Summarize a numerical data set in relation to its context.

  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

2. Grade 7 · Develop a probability model and use it to find experimental or theoretical probabilities of events.

  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. 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

3. Grade 7 · Calculate theoretical and experimental probability of simple events.

  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

4. Grade 7 · Use variables to represent quantities in a real-world and mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

  1. Estimating answers (age 13+): Use graphs of linear and quadratic functions to estimate output values for given inputs, find approximate solutions to equations, and interpret graphical information in real-world contexts
  2. 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

5. Grade 7 · Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers presented in any form (whole numbers, fractions, and decimals).

  1. Advanced Multi-Step Problems: Make sense of complex multi-step problems involving ratio, proportion, algebra, negative numbers, and all four operations with fractions and decimals by analysing given and unknown quantities, planning solution strategies, and evaluating reasonableness using estimation and inverse operations

6. Grade 7 · Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

  1. Decimals and fractions (age 11+): Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8); convert fluently between the two forms
  2. Multiplying fractions (age 11+): Interpret fractions and percentages as operators — find a fraction or percentage of an amount by multiplying, understanding that 'of' means multiply (e.g., 3/4 of 200 = 3/4 × 200 = 150)
  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

7. Grade 7 · Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

  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

8. Grade 7 · Recognize and represent proportional relationships between quantities.

  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
  2. 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