# Grade 3: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 27 concepts ready. In the app: https://ai.page/roadmap/sc-grade-3 Part of: [South Carolina: Mathematics](https://ai.page/roadmap/sc.md) Goal: South Carolina academic standards: Mathematics, Grade 3 ## 1. Patterns, Algebra, and Functional Reasoning · Use reasoning to represent and solve algebraic and numerical situations. - [Justifying mathematical reasoning](https://ai.page/c/justifying-mathematical-reasoning/index.md): Construct and follow multi-step mathematical arguments; identify errors in reasoning and explain why a method works or does not work - [Extending Table Patterns](https://ai.page/c/extending-table-patterns/index.md): Recognise and use repeated reasoning to generalise: extend multiplication table patterns, derive unknown facts from known ones, and describe rules for sequences ## 2. Patterns, Algebra, and Functional Reasoning · Use multiple representations to reason and solve problems involving operational properties of whole numbers. - [Reasoning with Equivalences](https://ai.page/c/reasoning-with-equivalences/index.md): Recognise and use repeated reasoning to generalise: extend patterns in equivalent fractions and percentage conversions, derive unknown facts from known facts, describe general rules for sequences and predict terms ## 3. Numerical Reasoning · Represent and compare fractions in multiple ways using part-whole relationships. - [Comparing fractions](https://ai.page/c/comparing-fractions/index.md): Compare and order unit fractions, and fractions with the same denominator - [Fraction Notation](https://ai.page/c/fraction-notation/index.md): Read, write, and use fraction notation correctly — fraction, numerator, denominator, unit fraction, non-unit fraction, proper fraction, improper fraction, mixed number, equivalent fraction, simplest form — and understand what each term describes, including the roles of the numerator and denominator in expressing parts of a whole - [Fractions of a whole](https://ai.page/c/fractions-of-a-whole/index.md): Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a/b as a parts of size 1/b - [Comparing fractions (age 8+)](https://ai.page/c/comparing-fractions-age-8/index.md): Compare two fractions with the same numerator or the same denominator by reasoning about size; record comparisons with >, =, or < symbols - [Equivalent fractions](https://ai.page/c/equivalent-fractions/index.md): Recognise and show, using diagrams, equivalent fractions with small denominators - [Fractions of a whole (age 8+)](https://ai.page/c/fractions-of-a-whole-age-8/index.md): Express whole numbers as fractions (e.g. 3 = 3/1) and recognise fractions equivalent to whole numbers (e.g. 4/4 = 1, 6/1 = 6) - [Understanding fractions](https://ai.page/c/understanding-fractions-2/index.md): Move fluently between real-world situations, diagrams, and symbolic equations involving three-digit numbers and fractions, explaining what each part represents - [Fractions on a number line](https://ai.page/c/fractions-on-a-number-line-maths/index.md): Move fluently between real-world situations, diagrams, number lines, and symbolic equations involving multiplication, fractions, and decimals, explaining what each representation shows - [Unit fractions](https://ai.page/c/unit-fractions/index.md): Recognise, find, and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators ## 4. Numerical Reasoning · Represent and compare numbers using relationships within the base ten number system. - [Estimating by rounding](https://ai.page/c/estimating-by-rounding/index.md): Estimate the answer to a calculation and use inverse operations to check answers; apply to increasingly large numbers using rounding and inverse reasoning - [Representing Numbers](https://ai.page/c/representing-numbers/index.md): Identify, represent, and estimate numbers using different representations including the number line - [Numbers to 10,000](https://ai.page/c/numbers-to-10-000/index.md): Identify, represent, and estimate numbers up to 10,000 using different representations - [Comparing Large Numbers](https://ai.page/c/comparing-large-numbers/index.md): Order and compare numbers beyond 1000 ## 5. Measurement, Geometry, and Spatial Reasoning · Extend geometric reasoning to attributes of polygons and/or polyhedrons. - [Types of angles](https://ai.page/c/types-of-angles/index.md): Identify acute and obtuse angles; compare and order angles up to two right angles by size - [Lines, Rays & Angles](https://ai.page/c/lines-rays-and-angles/index.md): Draw and identify points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines; identify these in two-dimensional figures ## 6. Measurement, Geometry, and Spatial Reasoning · Estimate and measure using units of length, liquid volume, currency, and intervals of time. - [Calculating with measurements](https://ai.page/c/calculating-with-measurements/index.md): Measure, compare, add, and subtract lengths (m/cm/mm), mass (kg/g), and volume/capacity (l/ml) using standard units - [Estimating Lengths](https://ai.page/c/estimating-lengths/index.md): Estimate lengths using units of inches, feet, centimetres, and metres - [Estimating answers (age 7+)](https://ai.page/c/estimating-answers-age-7/index.md): Estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes, and hours ## 7. Measurement, Geometry, and Spatial Reasoning · Solve area and perimeter problems in real-world and mathematical situations. - [Real-World Maths Modelling](https://ai.page/c/real-world-maths-modelling/index.md): Model real-world problems involving scaling, unit conversion, area/perimeter, and percentage by selecting appropriate mathematical representations and interpreting results in context - [Perimeters of polygons](https://ai.page/c/perimeters-of-polygons/index.md): Solve problems involving perimeters of polygons: find perimeter from side lengths, find an unknown side length, and explore rectangles with same perimeter but different areas (or vice versa) - [Understanding Area](https://ai.page/c/understanding-area/index.md): Understand that a unit square has one square unit of area and that the area of a plane figure is the number of unit squares that cover it without gaps or overlaps ## 8. Data, Probability, and Statistical Reasoning · Represent the probability of simple events and determine possible outcomes. - [Calculating Simple Probability](https://ai.page/c/calculating-simple-probability/index.md): Calculate the probability of a simple event with equally likely outcomes using the formula: probability = number of favourable outcomes ÷ total number of possible outcomes; express the result as a fraction in its simplest form; apply to rolling dice, drawing from bags, and other simple chance situations ## 9. Data, Probability, and Statistical Reasoning · Collect and analyze data and communicate through multiple representations. - [Picture & Bar Graphs](https://ai.page/c/picture-and-bar-graphs/index.md): Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories; solve put-together, take-apart, and compare problems using information presented in a bar graph - [Representing numbers with objects (age 8+)](https://ai.page/c/representing-numbers-with-objects-age-8/index.md): Draw a scaled picture graph and a scaled bar graph to represent a data set; solve one- and two-step comparison, sum, and difference problems using bar charts, pictograms, and tables ## Health: 0 of 100 Of its 27 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): - Justifying mathematical reasoning has no explanation yet - Extending Table Patterns has no explanation yet - Reasoning with Equivalences has no explanation yet - Comparing fractions has no explanation yet - Fraction Notation has no explanation yet - Fractions of a whole has no explanation yet - Comparing fractions (age 8+) has no explanation yet - Equivalent fractions has no explanation yet - Fractions of a whole (age 8+) has no explanation yet - Understanding fractions has no explanation yet - Fractions on a number line has no explanation yet - Unit fractions has no explanation yet - Estimating by rounding has no explanation yet - Representing Numbers has no explanation yet - Numbers to 10,000 has no explanation yet - Comparing Large Numbers has no explanation yet - Types of angles has no explanation yet - Lines, Rays & Angles has no explanation yet - Calculating with measurements has no explanation yet - Estimating Lengths has no explanation yet - Estimating answers (age 7+) has no explanation yet - Real-World Maths Modelling has no explanation yet - Perimeters of polygons has no explanation yet - Understanding Area has no explanation yet - Calculating Simple Probability has no explanation yet - Picture & Bar Graphs has no explanation yet - Representing numbers with objects (age 8+) has no explanation yet Credit: The structure of South Carolina academic standards: Mathematics (https://ed.sc.gov/instruction/standards/mathematics/standards/2025-south-carolina-college-and-career-ready-mathematics-standards/); 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.