# Grade 6: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 18 concepts ready. In the app: https://ai.page/roadmap/dodea-grade-6 Part of: [DoDEA: Mathematics](https://ai.page/roadmap/dodea.md) Goal: Department of Defense Education Activity standards: Mathematics, Grade 6 ## 1. Summarize and describe distributions. - [Understanding fractions](https://ai.page/c/understanding-fractions/index.md): Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8); use operations on fractions to solve problems involving data in line plots (e.g. redistribute total equally) ## 2. Develop understanding of statistical variability. - [Statistical Analysis Vocabulary](https://ai.page/c/statistical-analysis-vocabulary/index.md): Read, write, and use the vocabulary of statistical analysis — mean, median, mode, range, frequency, data, sample, average, chart, table, graph, pie chart, scatter graph, correlation — with understanding of what each term describes - [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 - [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. Solve real-world and mathematical problems involving area, surface area, and volume. - [Real-World Mathematical Modelling](https://ai.page/c/real-world-mathematical-modelling/index.md): Model real-world problems involving ratio, scale, volume, unit conversion, and proportional reasoning with appropriate tools, diagrams, or equations - [Estimating answers (age 10+)](https://ai.page/c/estimating-answers-age-10/index.md): 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) ## 4. Reason about and solve one-variable equations and inequalities. - [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 - [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 ## 5. Apply and extend previous understandings of arithmetic to algebraic expressions. - [Algebraic Notation](https://ai.page/c/algebraic-notation/index.md): Use and interpret algebraic notation including: ab for a × b, 3y for y + y + y, a² for a × a, a/b for a ÷ b, coefficients as fractions, and brackets for grouping; read and write algebraic expressions fluently - [Expanding Single Brackets](https://ai.page/c/expanding-single-brackets/index.md): Expand (multiply out) a single term over a bracket using the distributive property, e.g., 3(2x + 5) = 6x + 15; expand expressions involving negative multipliers ## 6. Apply and extend previous understandings of numbers to the system of rational numbers. - [Plotting points in the first quadrant](https://ai.page/c/plotting-points-in-the-first-quadrant/index.md): Plot and read ordered pairs in the first quadrant of the coordinate plane; represent real-world and mathematical problems by graphing points and interpreting coordinate values in context - [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 - [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 ## 7. Compute fluently with multi-digit numbers and find common factors and multiples. - [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 - [Fluent adding and subtracting within 1000](https://ai.page/c/fluent-adding-and-subtracting-within-1000/index.md): Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and the relationship between addition and subtraction ## 8. Apply and extend previous understandings of multiplication and division to divide fractions by fractions. - [Dividing unit fractions and whole numbers](https://ai.page/c/dividing-unit-fractions-and-whole-numbers/index.md): Solve real-world problems involving division of unit fractions by whole numbers and whole numbers by unit fractions, using visual models and equations ## 9. Understand ratio concepts and use ratio reasoning to solve problems. - [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 - [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 ## Health: 0 of 100 Of its 18 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): - Understanding fractions has no explanation yet - Statistical Analysis Vocabulary has no explanation yet - Comparing measurements has no explanation yet - The Probability Scale has no explanation yet - Real-World Mathematical Modelling has no explanation yet - Estimating answers (age 10+) has no explanation yet - Solving Linear Equations has no explanation yet - Numbers on a number line has no explanation yet - Algebraic Notation has no explanation yet - Expanding Single Brackets has no explanation yet - Plotting points in the first quadrant has no explanation yet - Positive and Negative Numbers has no explanation yet - Numbers on a number line has no explanation yet - Factors, multiples, and primes has no explanation yet - Fluent adding and subtracting within 1000 has no explanation yet - Dividing unit fractions and whole numbers has no explanation yet - Proportional Reasoning Vocabulary has no explanation yet - Ratio Notation has no explanation yet Credit: The structure of Department of Defense Education Activity standards: Mathematics (https://commonstandardsproject.com); 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.