# Grade 6: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 23 concepts ready. In the app: https://ai.page/roadmap/ne-grade-6 Part of: [Nebraska: Mathematics](https://ai.page/roadmap/ne.md) Goal: Nebraska academic standards: Mathematics, Grade 6 ## 1. Grade 6 · Probability: Students will interpret and apply concepts of probability. - [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 ## 2. Grade 6 · Analyze Data and Interpret Results: Students will represent and analyze the data and interpret the results. - [Calculating the Mean](https://ai.page/c/calculating-the-mean/index.md): Calculate and interpret the mean as an average of a data set - [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 - [Line graphs (age 10+)](https://ai.page/c/line-graphs-age-10/index.md): Interpret and construct pie charts and line graphs; use these to solve problems ## 3. Grade 6 · Measurement: Students identify geometric attributes that create two- and three-dimensional shapes in order to perform measurements and apply formulas to find area and volume. - [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 - [Properties of triangles and quadrilaterals](https://ai.page/c/properties-of-triangles-and-quadrilaterals/index.md): Derive and illustrate properties of triangles, quadrilaterals, and circles using appropriate language, including interior angles, diagonals, symmetry, and relationships between side lengths ## 4. Grade 6 · Attributes: Students will identify and describe geometric attributes of two- dimensional shapes. - [3-D shapes (age 10+)](https://ai.page/c/3-d-shapes-age-10/index.md): Recognise, describe, and build simple 3-D shapes, including making nets ## 5. Grade 6 · Applications: Students will solve authentic problems with algebraic expressions, equations, and inequalities. - [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 - [Expressions & Equations Vocabulary](https://ai.page/c/expressions-and-equations-vocabulary/index.md): Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms, and factors; distinguish between an expression (no equals sign), an equation (equals sign), and an inequality (inequality sign) ## 6. Grade 6 · Algebraic Processes: Students will apply the operational properties when evaluating expressions and solving equations and inequalities. - [Advanced Multi-Step Problems](https://ai.page/c/advanced-multi-step-problems/index.md): 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 - [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 - [Substituting into Formulae](https://ai.page/c/substituting-into-formulae/index.md): 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 ## 7. Grade 6 · Represent: Students will represent ratios and rates on the coordinate plane. - [Proportion](https://ai.page/c/proportion/index.md): 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 - [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 - [Understanding fractions (age 10+)](https://ai.page/c/understanding-fractions-age-10/index.md): Move fluently between real-world situations, diagrams, coordinate grids, algebraic expressions, tables, and symbolic equations involving fractions, ratio, and algebra, explaining connections between representations ## 8. Grade 6 · Ratios and Rates: Students will understand the concept of ratios and unit rates, use language to describe the relationship between two quantities, and use ratios and unit rates to solve auth - [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 - [Percentages (age 9+)](https://ai.page/c/percentages-age-9/index.md): Know and use the vocabulary of ratio and proportion — ratio, proportion, percentage, scale, equivalent, unequal, relative size, part-to-part, part-to-whole, and out of — and understand the difference between ratio (comparing parts to parts) and proportion (comparing a part to the whole) ## 9. Grade 6 · Operations: Students will compute with fractions and decimals accurately. - [Ratio (age 11+)](https://ai.page/c/ratio-age-11/index.md): Use conventional notation for the priority of operations including brackets, powers, roots, and reciprocals; apply BIDMAS/BODMAS consistently to evaluate complex numerical expressions - [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 - [Division with remainders (age 10+)](https://ai.page/c/division-with-remainders-age-10/index.md): Divide numbers up to 4 digits by a two-digit divisor using formal written long division, interpreting remainders as whole numbers, fractions, or by rounding as appropriate ## 10. Grade 6 · Numeric Relationships: Students will demonstrate, represent, and show relationships among fractions, decimals, percents, and integers within the base-ten number system. - [Fractions on a number line](https://ai.page/c/fractions-on-a-number-line-3/index.md): Understand and use place value for decimals, measures, and integers of any size; extend the number system to include all positive and negative integers, decimals, and fractions on a single number line - [Decimal & Percent Notation](https://ai.page/c/decimal-and-percent-notation/index.md): Read, write, and use decimal and percentage notation correctly — decimal, decimal point, tenths, hundredths, thousandths, percentage, per cent, % symbol, convert, terminating decimal — and understand the relationships between fractions, decimals, and percentages as three ways of expressing the same value - [Number Pattern Relationships](https://ai.page/c/number-pattern-relationships/index.md): Generate two numerical patterns using two given rules; identify relationships between corresponding terms; form ordered pairs and graph them on a coordinate plane ## Health: 0 of 100 Of its 23 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): - The Probability Scale has no explanation yet - Calculating the Mean has no explanation yet - Comparing measurements has no explanation yet - Line graphs (age 10+) has no explanation yet - Angles in triangles (age 11+) has no explanation yet - Properties of triangles and quadrilaterals has no explanation yet - 3-D shapes (age 10+) has no explanation yet - Numbers on a number line has no explanation yet - Expressions & Equations Vocabulary comes before Algebraic Notation, which it needs - Expressions & Equations Vocabulary has no explanation yet - Advanced Multi-Step Problems has no explanation yet - Algebraic Notation has no explanation yet - Substituting into Formulae has no explanation yet - Proportion has no explanation yet - Plotting points in the first quadrant has no explanation yet - Understanding fractions (age 10+) has no explanation yet - Ratio Notation has no explanation yet - Percentages (age 9+) has no explanation yet - Ratio (age 11+) has no explanation yet - Mixed & Improper Fractions has no explanation yet - Division with remainders (age 10+) has no explanation yet - Fractions on a number line has no explanation yet - Decimal & Percent Notation has no explanation yet - Number Pattern Relationships has no explanation yet Credit: The structure of Nebraska academic standards: Mathematics (https://www.education.ne.gov/wp-content/uploads/2022/10/Nebraskas-College-and-Career-Ready-Standards-for-Mathematics-Final-10.20.22.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.