# 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/mn-grade-7 Part of: [Minnesota: Mathematics](https://ai.page/roadmap/mn.md) Goal: Minnesota academic standards: Mathematics, Grade 7 ## 1. Data Analysis & Probability · Calculate probabilities and reason about probabilities using proportions to solve real-world and mathematical problems. - [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 - [Percentages as Fractions](https://ai.page/c/percentages-as-fractions/index.md): Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using percentages; work with percentages greater than 100% ## 2. Data Analysis & Probability · Display and interpret data in a variety of ways, including circle graphs and histograms. - [Pictograms and tally charts (age 11+)](https://ai.page/c/pictograms-and-tally-charts-age-11/index.md): Construct and interpret frequency tables, bar charts, pie charts, pictograms, and vertical line charts for both categorical and grouped numerical data, choosing appropriate representations for the data type ## 3. Data Analysis & Probability · Use mean, median and range to draw conclusions about data and make predictions. - [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 & Measurement · Analyze the effect of change of scale, translations and reflections on the attributes of two-dimensional figures. - [Coordinate Transformations](https://ai.page/c/coordinate-transformations/index.md): Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original - [Transformations on a grid](https://ai.page/c/transformations-on-a-grid/index.md): Represent and carry out geometric transformations on squared paper or a coordinate grid: reflections (in horizontal, vertical, and diagonal mirror lines, including the axes), translations (described as a vector or as left/right/up/down moves), and rotations (90° or 180° about a stated centre point); describe each transformation precisely using the correct language; identify which transformation maps one shape onto its image by comparing position, orientation, and size ## 5. Geometry & Measurement · Use reasoning with proportions and ratios to determine measurements, justify formulas and solve real-world and mathematical problems involving circles and related geometric fi - [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 - [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 ## 6. Algebra · Represent real-world and mathematical situations using equations with variables. Solve equations symbolically, using the properties of equality. Also solve equations graphically and numerica - [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 - [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 ## 7. Algebra · Apply understanding of order of operations and algebraic properties to generate equivalent numerical and algebraic expressions containing positive and negative rational numbers and grouping - [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 ## 8. Algebra · Recognize proportional relationships in real-world and mathematical situations; represent these and other relationships with tables, verbal descriptions, symbols and graphs; solve problems i - [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 ## 9. Algebra · Understand the concept of proportionality in real-world and mathematical situations, and distinguish between proportional and other relationships. - [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 ## 10. Number & Operation · Calculate with positive and negative rational numbers, and rational numbers with whole number exponents, to solve real-world and mathematical problems. - [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 - [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 - [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 ## 11. Number & Operation · Read, write, represent and compare positive and negative rational numbers, expressed as integers, fractions and decimals. - [Fractions on a number line (age 11+)](https://ai.page/c/fractions-on-a-number-line-age-11/index.md): Order positive and negative integers, decimals, and fractions on a number line; use the symbols =, ≠, <, >, ≤, ≥ to compare values including negative numbers and mixed representations - [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 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 has no explanation yet - Percentages as Fractions has no explanation yet - Pictograms and tally charts (age 11+) has no explanation yet - Comparing measurements has no explanation yet - Coordinate Transformations has no explanation yet - Transformations on a grid has no explanation yet - Circles: Circumference & Area has no explanation yet - Proportional Reasoning Vocabulary has no explanation yet - Solving Linear Equations comes before Substituting into Formulae, which it needs - Solving Linear Equations has no explanation yet - Algebraic Transformations has no explanation yet - Substituting into Formulae has no explanation yet - Proportion comes before Proportion Graphs, which it needs - Proportion has no explanation yet - Proportion Graphs has no explanation yet - Positive and Negative Numbers has no explanation yet - Numbers on a number line has no explanation yet - Sign Rules for Multiplication has no explanation yet - Mixed & Improper Fractions has no explanation yet - Fractions on a number line (age 11+) has no explanation yet - Number Sets & Infinity has no explanation yet Credit: The structure of Minnesota academic standards: Mathematics (http://education.state.mn.us/MDE/EdExc/StanCurri/K-12AcademicStandards/Math/index.html); 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.