# Grade 7: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 19 concepts ready. In the app: https://ai.page/roadmap/in-grade-7 Part of: [Indiana: Mathematics](https://ai.page/roadmap/in.md) Goal: Indiana academic standards: Mathematics, Grade 7 ## 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 - [Experimental probability](https://ai.page/c/experimental-probability/index.md): 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 - [The 0-to-1 Probability Scale](https://ai.page/c/the-0-to-1-probability-scale/index.md): 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 - [The Probability Scale](https://ai.page/c/the-probability-scale/index.md): 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 - [Comparing measurements](https://ai.page/c/comparing-measurements/index.md): 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) - [Angles in triangles (age 11+)](https://ai.page/c/angles-in-triangles-age-11/index.md): 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 - [Circles: Circumference & Area](https://ai.page/c/circles-circumference-and-area/index.md): 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 - [Scale and similar shapes](https://ai.page/c/scale-and-similar-shapes/index.md): 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) - [Linear Function Graphs](https://ai.page/c/linear-function-graphs/index.md): 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 - [Numbers on a number line](https://ai.page/c/numbers-on-a-number-line-maths/index.md): 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 - [Solving Linear Equations](https://ai.page/c/solving-linear-equations/index.md): 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 - [Using inverse operations](https://ai.page/c/using-inverse-operations/index.md): 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 - [Proportional Reasoning Vocabulary](https://ai.page/c/proportional-reasoning-vocabulary/index.md): 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 - [Ratio Notation](https://ai.page/c/ratio-notation/index.md): 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) - [Mixed & Improper Fractions](https://ai.page/c/mixed-and-improper-fractions/index.md): 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. - [Square and cube numbers](https://ai.page/c/square-and-cube-numbers-maths/index.md): 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. - [Factors, multiples, and primes](https://ai.page/c/factors-multiples-and-primes/index.md): 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) - [Positive and Negative Numbers](https://ai.page/c/positive-and-negative-numbers/index.md): 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) - [Sign Rules for Multiplication](https://ai.page/c/sign-rules-for-multiplication/index.md): 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. - [Numbers on a number line](https://ai.page/c/numbers-on-a-number-line-5/index.md): 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 ## Health: 0 of 100 Of its 19 own concepts: 0 have an explanation, 0 have practice, 0 have a measurement question, 0 have a checked version. Findings (each is a task for anyone's AI): - Experimental probability comes before The Probability Scale, which it needs - Experimental probability has no explanation yet - The 0-to-1 Probability Scale has no explanation yet - The Probability Scale has no explanation yet - Comparing measurements has no explanation yet - Angles in triangles (age 11+) has no explanation yet - Circles: Circumference & Area has no explanation yet - Scale and similar shapes has no explanation yet - Linear Function Graphs has no explanation yet - Numbers on a number line comes before Solving Linear Equations, which it needs - Numbers on a number line has no explanation yet - Solving Linear Equations comes before Using inverse operations, which it needs - Solving Linear Equations has no explanation yet - Using inverse operations has no explanation yet - Proportional Reasoning Vocabulary has no explanation yet - Ratio Notation comes before Factors, multiples, and primes, which it needs - Ratio Notation has no explanation yet - Mixed & Improper Fractions has no explanation yet - Square and cube numbers has no explanation yet - Factors, multiples, and primes has no explanation yet - Positive and Negative Numbers has no explanation yet - Sign Rules for Multiplication has no explanation yet - Numbers on a number line has no explanation yet Credit: The structure of Indiana academic standards: Mathematics (https://www.in.gov/doe/files/AlgebraI-Math-Content-Connectors.docx.pdf); concepts from the Marble Skill Taxonomy (v1), © Generative Spark, Inc. (withmarble.com), text CC BY-SA 4.0, database ODbL 1.0: https://github.com/withmarbleapp/os-taxonomy, mapped to its standards by Marble.