# Grade 7: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 22 concepts ready. In the app: https://ai.page/roadmap/ar-grade-7 Part of: [Arkansas: Mathematics](https://ai.page/roadmap/ar.md) Goal: Arkansas academic standards: Mathematics, Grade 7 ## 1. Grade 7 · Understand theoretical and experimental probability for simple experiments. - [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 - [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. Grade 7 · Interpret and organize data. - [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 ## 3. Grade 7 · Understand and use scale factor. - [Scale and similar shapes (age 11+)](https://ai.page/c/scale-and-similar-shapes-age-11/index.md): Use scale factors to interpret and create scale diagrams and maps, calculating real-life distances from map measurements and vice versa ## 4. Grade 7 · Solve problems using various angle properties of lines. - [Understanding angles (age 11+)](https://ai.page/c/understanding-angles-age-11/index.md): Apply the properties of angles at a point (360°), on a straight line (180°), and vertically opposite angles to find unknown angles in multi-step problems ## 5. Grade 7 · Describe cross sections of three-dimensional figures. - [3-D shapes (age 11+)](https://ai.page/c/3-d-shapes-age-11/index.md): Use the properties of faces, surfaces, edges, and vertices of 3-D shapes (cubes, cuboids, prisms, cylinders, pyramids, cones, and spheres) to solve problems, including visualising cross-sections ## 6. Grade 7 · Solve problems involving area, volume, and surface area. - [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 - [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 ## 7. Grade 7 · Use understanding of algebraic expressions and equations to represent relationships between two quantities. - [Algebraic Transformations](https://ai.page/c/algebraic-transformations/index.md): Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs; move between word problems, algebraic representations, tables, and graphical representations ## 8. Grade 7 · Apply properties of operations to create equivalent expressions. - [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. Grade 7 · Analyze proportional relationships and solve multi-step ration and percent problems. - [Proportion Graphs](https://ai.page/c/proportion-graphs/index.md): 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 - [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 ## 10. Grade 7 · Analyze and use unit rates to solve problems. - [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 - [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 - [Compound Units](https://ai.page/c/compound-units/index.md): Use compound units such as speed (distance ÷ time), unit pricing (cost ÷ quantity), and density (mass ÷ volume); solve problems involving compound units ## 11. Grade 7 · Apply all properties and operations to all rational numbers. - [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 - [Multi-step problems: choosing operations](https://ai.page/c/multi-step-problems-choosing-operations/index.md): Solve problems involving addition, subtraction, multiplication, and division, deciding which operations and methods to use and why; solve multi-step problems in contexts - [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 ## 12. Grade 7 · Model and compute with rational numbers. - [Decimals and fractions (age 11+)](https://ai.page/c/decimals-and-fractions-age-11/index.md): 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 - [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 - [Number Sets & Infinity](https://ai.page/c/number-sets-and-infinity/index.md): Appreciate the infinite nature of the sets of integers, real numbers, and rational numbers; position integers on a number line and distinguish between rational and irrational numbers ## Health: 0 of 100 Of its 22 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 - Experimental probability has no explanation yet - Comparing measurements has no explanation yet - Scale and similar shapes (age 11+) comes before Proportional Reasoning Vocabulary, which it needs - Scale and similar shapes (age 11+) has no explanation yet - Understanding angles (age 11+) has no explanation yet - 3-D shapes (age 11+) has no explanation yet - Angles in triangles (age 11+) has no explanation yet - Circles: Circumference & Area has no explanation yet - Algebraic Transformations has no explanation yet - Numbers on a number line has no explanation yet - Proportion Graphs has no explanation yet - Proportion comes before Proportional Reasoning Vocabulary, which it needs - Proportion has no explanation yet - Advanced Multi-Step Problems has no explanation yet - Proportional Reasoning Vocabulary has no explanation yet - Compound Units has no explanation yet - Sign Rules for Multiplication comes before Positive and Negative Numbers, which it needs - Sign Rules for Multiplication has no explanation yet - Multi-step problems: choosing operations has no explanation yet - Mixed & Improper Fractions has no explanation yet - Decimals and fractions (age 11+) has no explanation yet - Positive and Negative Numbers has no explanation yet - Numbers on a number line has no explanation yet - Number Sets & Infinity has no explanation yet Credit: The structure of Arkansas academic standards: Mathematics (https://dese.ade.arkansas.gov/admin/Files/AR_2023_K-8,_Alg,_Geo_Math_Standards_LS_6.21.23_LS.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.