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How to learn Grade 7: Mathematics

Indiana academic standards: Mathematics, Grade 7

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

1. Data Analysis, Statistics, and Probability · Develop probability models that include the sample space and probabilities of outcomes to represent simple events with equally likely outcomes. Predict the

  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. Data Analysis, Statistics, and Probability · Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Understand that a proba

  1. The 0-to-1 Probability Scale: Understand probability as a measure expressed as a number between 0 (impossible) and 1 (certain); place events on the probability scale; express probabilities as fractions, decimals, and percentages
  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. Data Analysis, Statistics, and Probability · Make observations about the degree of visual overlap of two numerical data distributions represented in line plots or box plots. Describe how data, particu

  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 and Measurement · Solve real-world and other mathematical problems involving volume of cylinders and three-dimensional objects composed of right rectangular prisms. (E)

  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

5. Geometry and Measurement · Understand the formulas for area and circumference of a circle and use them to solve real-world and other mathematical problems; give an informal derivation of the relations

  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

6. Geometry and Measurement · Solve real-world and other mathematical problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing. Create a s

  1. Scale and similar shapes: Solve problems involving similar shapes where the scale factor is known or can be found

7. Algebra and Functions · Graph a line given its slope and a point on the line. Find the slope of a line given its graph. (E)

  1. Linear Function Graphs: Recognise that a linear function produces a straight-line graph, understand the relationship between an equation of the form y = mx + c and its graphical representation, and interpret gradient and y-intercept in context

8. Algebra and Functions · Solve inequalities of the form px + q (> or ≥) r or px + q (< or ≤) r, where p, q, and r are specific rational numbers. Represent real-world problems using inequalities of thes

  1. Numbers on a number line: Understand inequalities as statements comparing expressions, represent solutions on a number line, and solve simple linear inequalities using the same inverse-operation methods as equations

9. Algebra and Functions · Solve equations of the form px + q = r and p(x + q) = r fluently, where p, q, and r are specific rational numbers. Represent real-world problems using equations of these forms

  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

10. Algebra and Functions · Apply the properties of operations (e.g., identity, inverse, commutative, associative, distributive properties) to create equivalent linear expressions, including situations th

  1. Using inverse operations: Recognise and use relationships between operations including inverse operations; use these relationships to check answers and simplify calculations

11. Ratios and Proportional Reasoning · Represent real-world and other mathematical situations that involve proportional relationships. Write equations and draw graphs to represent these proportional rela

  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

12. Ratios and Proportional Reasoning · Use proportional relationships to solve ratio and percent problems with multiple operations (e.g., simple interest, tax, markups, markdowns, gratuities, conversions

  1. Ratio Notation: Use ratio notation to describe the relationship between two or more quantities, simplify ratios to their simplest form, and convert between ratio and fraction representations

13. Number Sense · Compute fluently with rational numbers using an algorithmic approach. (E)

  1. 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

14. Number Sense · Apply the inverse relationship between squaring and finding the square root of a perfect square whole number. Find square roots of perfect square whole numbers.

  1. Square and cube numbers: Use integer powers and associated real roots (square, cube, and higher); recognise powers of 2, 3, 4, and 5; distinguish between exact representations of roots and their decimal approximations

15. Number Sense · Find the prime factorization of whole numbers and write the results using exponents.

  1. Factors, multiples, and primes: Find all factor pairs for a whole number in the range 1–100; identify common factors and common multiples of two numbers; use these concepts to solve problems

16. Number Sense · Explain that if p and q are integers, then –(p/q) = (–p)/q = p/(–q) for all nonzero integers. (E)

  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

17. Number Sense · Use the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. (E)

  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

18. Number Sense · Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

  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