# Grade 4: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 33 concepts ready. In the app: https://ai.page/roadmap/sc-grade-4 Part of: [South Carolina: Mathematics](https://ai.page/roadmap/sc.md) Goal: South Carolina academic standards: Mathematics, Grade 4 ## 1. Patterns, Algebra, and Functional Reasoning · Use reasoning to represent and solve algebraic and numerical situations. - [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 - [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 - [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 - [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 ## 2. Patterns, Algebra, and Functional Reasoning · Use multiple representations to reason and solve problems involving operational properties of fractions. - [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 - [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 - [Real-world fraction multiplication](https://ai.page/c/real-world-fraction-multiplication/index.md): Solve real-world problems involving multiplication of fractions and mixed numbers, using visual fraction models or equations - [Fractions, Decimals & Percentages](https://ai.page/c/fractions-decimals-and-percentages/index.md): Look for and use mathematical structure: exploit the relationship between fractions, decimals, and percentages; use factor pairs to simplify multiplication; apply angle facts to find unknowns; use properties of regular polygons systematically - [Fraction Addition Concepts](https://ai.page/c/fraction-addition-concepts/index.md): Understand addition and subtraction of fractions as joining and separating parts; decompose a fraction into a sum of fractions with the same denominator in more than one way - [Adding fractions (different denominators)](https://ai.page/c/adding-fractions-different-denominators/index.md): Add and subtract fractions with denominators that are multiples of the same number by finding a common denominator ## 3. Patterns, Algebra, and Functional Reasoning · Use multiple representations to reason and solve problems involving operational properties of whole numbers and decimals. - [Dividing fractions (unit fractions)](https://ai.page/c/dividing-fractions-unit-fractions/index.md): Interpret and compute division of a unit fraction by a non-zero whole number (e.g. 1/3 ÷ 4 = 1/12); use visual models and the relationship between multiplication and division to explain the result - [Long multiplication](https://ai.page/c/long-multiplication/index.md): Multiply a whole number of up to four digits by a one-digit number, and multiply two two-digit numbers, using formal written methods including long multiplication; illustrate with area models - [Multiplying by Tens](https://ai.page/c/multiplying-by-tens/index.md): Multiply one-digit whole numbers by multiples of 10 in the range 10–90 using strategies based on place value and properties of operations - [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 ## 4. Numerical Reasoning · Represent and compare fractions in multiple ways using part-whole relationships. - [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 - [Comparing fractions (age 10+)](https://ai.page/c/comparing-fractions-age-10/index.md): Compare and order fractions including fractions greater than 1, by converting to common denominators or using benchmarks - [Comparing Decimals](https://ai.page/c/comparing-decimals/index.md): Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, < - [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 ## 5. Numerical Reasoning · Represent and compare numbers using relationships within the base ten number system. - [Comparing Large Numbers](https://ai.page/c/comparing-large-numbers/index.md): Order and compare numbers beyond 1000 - [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 - [Reading and writing numbers (age 9+)](https://ai.page/c/reading-and-writing-numbers-age-9/index.md): Read, write, order, and compare whole numbers up to at least 1,000,000 using base-ten numerals, number names, expanded form, and place-value understanding ## 6. Measurement, Geometry, and Spatial Reasoning · Extend geometric reasoning to attributes of polygons and/or polyhedrons. - [Classifying shapes by properties](https://ai.page/c/classifying-shapes-by-properties/index.md): Compare and classify geometric shapes based on their properties and sizes; understand that attributes belonging to a category also belong to all subcategories; classify two-dimensional figures in a hierarchy based on properties - [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 ## 7. Measurement, Geometry, and Spatial Reasoning · Estimate and measure using units of length, liquid volume, weight, 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 - [Measuring Liquids & Masses](https://ai.page/c/measuring-liquids-and-masses/index.md): Measure and estimate liquid volumes and masses of objects using grams, kilograms, and litres; solve one-step word problems involving mass or volume - [Estimating Lengths](https://ai.page/c/estimating-lengths/index.md): Estimate lengths using units of inches, feet, centimetres, and metres - [Measuring with different units](https://ai.page/c/measuring-with-different-units/index.md): Measure the length of an object using two different length units and describe how the measurements relate to the size of the unit chosen ## 8. Measurement, Geometry, and Spatial Reasoning · Solve area and perimeter problems in real-world and mathematical situations. - [Modelling with multiplication and fractions](https://ai.page/c/modelling-with-multiplication-and-fractions/index.md): Model real-world problems involving multiplication, area, fractions, and unit conversion by choosing appropriate representations and interpreting mathematical results in context - [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) ## 9. 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 ## 10. Data, Probability, and Statistical Reasoning · Create questions, collect and analyze data, and communicate interpretations through multiple representations. - [Pictograms and tally charts (age 6+)](https://ai.page/c/pictograms-and-tally-charts-age-6/index.md): Read, write, and use the vocabulary of data collection and display — data, tally, tally chart, frequency, frequency table, survey, pictogram, bar chart, axis/axes, scale, label, category, discrete data, continuous data, line graph, pie chart — and apply these terms when collecting, organising, and presenting data - [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 33 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): - Solving Linear Equations has no explanation yet - Real-World Mathematical Modelling comes before Real-World Maths Modelling, which it needs - Real-World Mathematical Modelling has no explanation yet - Algebraic Transformations has no explanation yet - Factors, multiples, and primes has no explanation yet - Fractions on a number line has no explanation yet - Fraction Notation has no explanation yet - Real-world fraction multiplication has no explanation yet - Fractions, Decimals & Percentages has no explanation yet - Fraction Addition Concepts has no explanation yet - Adding fractions (different denominators) has no explanation yet - Dividing fractions (unit fractions) has no explanation yet - Long multiplication has no explanation yet - Multiplying by Tens has no explanation yet - Reasoning with Equivalences has no explanation yet - Comparing fractions (age 8+) has no explanation yet - Comparing fractions (age 10+) has no explanation yet - Comparing Decimals has no explanation yet - Decimal & Percent Notation has no explanation yet - Comparing Large Numbers has no explanation yet - Estimating by rounding has no explanation yet - Reading and writing numbers (age 9+) has no explanation yet - Classifying shapes by properties has no explanation yet - Types of angles has no explanation yet - Calculating with measurements has no explanation yet - Measuring Liquids & Masses has no explanation yet - Estimating Lengths has no explanation yet - Measuring with different units has no explanation yet - Modelling with multiplication and fractions has no explanation yet - Real-World Maths Modelling has no explanation yet - Perimeters of polygons has no explanation yet - Calculating Simple Probability has no explanation yet - Pictograms and tally charts (age 6+) 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.