# Grade 4: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 32 concepts ready. In the app: https://ai.page/roadmap/in-grade-4 Part of: [Indiana: Mathematics](https://ai.page/roadmap/in.md) Goal: Indiana academic standards: Mathematics, Grade 4 ## 1. Data Analysis · Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using data displayed in - [Understanding fractions](https://ai.page/c/understanding-fractions/index.md): Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8); use operations on fractions to solve problems involving data in line plots (e.g. redistribute total equally) ## 2. Data Analysis · Formulate questions that can be addressed with data. Collect, organize, and graph data from observations, surveys, and experiments using line plots with whole number intervals, single- - [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 ## 3. Measurement · Apply the area and perimeter formulas for rectangles to solve real-world and other mathematical problems. Investigate the area of complex shapes composed of rectangles by decomposing the - [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) - [Area of compound shapes](https://ai.page/c/area-of-compound-shapes/index.md): Recognise area as additive; find areas of rectilinear figures by decomposing into non-overlapping rectangles and summing their areas ## 4. Measurement · Use the four operations to solve real-world problems involving distances, intervals of time, volumes, masses of objects, and money. Include addition and subtraction problems involving si - [Measurement Conversions](https://ai.page/c/measurement-conversions/index.md): Solve problems involving the calculation and conversion of units of measure, using decimal notation and multi-step reasoning in real-world contexts ## 5. Measurement · Within given measurement systems, convert larger units to smaller units, including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec., and use these conversions to solve real-world problems. - [Converting measurement units](https://ai.page/c/converting-measurement-units/index.md): Convert between different units of measure (e.g. kilometre to metre, hour to minute, minute to second, year to month, week to day) - [Converting measurement units (age 9+)](https://ai.page/c/converting-measurement-units-age-9/index.md): Know relative sizes of measurement units within one system (km/m/cm/mm, kg/g, l/ml, hr/min/sec); convert between different metric units and express measurements in terms of a smaller unit; record equivalents in conversion tables ## 6. Measurement · Measure length to the nearest quarter-inch, eighth-inch, and millimeter. (E) - [Halves and quarters (age 8+)](https://ai.page/c/halves-and-quarters-age-8/index.md): Generate measurement data by measuring lengths to the nearest half and quarter inch; display the data on a line plot with a scale marked in whole numbers, halves, and quarters ## 7. Geometry · Classify triangles and quadrilaterals based on the presence or absence of parallel or perpendicular lines, or right, acute, or obtuse angles. - [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 ## 8. Geometry · Identify, describe, and draw rays, angles (right, acute, obtuse), and perpendicular and parallel lines using appropriate tools (e.g., ruler, straightedge, and technology). Identify these in - [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 ## 9. Computation and Algebraic Thinking · Describe the relationship between two terms and use it to find a second number when a first number is given. Generate a number pattern that follows a given rule. - [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 ## 10. Computation and Algebraic Thinking · Solve real-world problems involving addition and subtraction of fractions referring to the same whole and having common denominators (e.g., by using visual fractio - [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 ## 11. Computation and Algebraic Thinking · Add and subtract mixed numbers with common denominators (e.g., by replacing each mixed number with an equivalent fraction and/or by using properties of operations - [Adding and subtracting mixed numbers](https://ai.page/c/adding-and-subtracting-mixed-numbers/index.md): Add and subtract mixed numbers with like denominators, including by converting to improper fractions or using properties of operations ## 12. Computation and Algebraic Thinking · Add and subtract fractions with common denominators using visual fraction models. Decompose non-unit fractions to represent them as iterations of unit fractions. ( - [Adding Fractions (Unlike Denominators)](https://ai.page/c/adding-fractions-unlike-denominators/index.md): Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions to produce a common denominator ## 13. Computation and Algebraic Thinking · Solve real-world problems with whole numbers involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to rep - [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 ## 14. Computation and Algebraic Thinking · Investigate the mathematical relationship between factors and multiples for whole numbers from 1-100, including the set of factors and multiples for given numbers. - [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 ## 15. Computation and Algebraic Thinking · Show how the order in which two numbers are multiplied (commutative property) and how numbers are grouped in multiplication (associative property) will not change - [Properties of Operations](https://ai.page/c/properties-of-operations/index.md): Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide ## 16. Computation and Algebraic Thinking · Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors using strategies based on place value, the properties of operatio - [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 ## 17. Computation and Algebraic Thinking · Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properti - [Adding numbers](https://ai.page/c/adding-numbers/index.md): Add up to four two-digit numbers using strategies based on place value and properties of operations - [Decimal place value](https://ai.page/c/decimal-place-value-2/index.md): Multiply one-digit numbers with up to two decimal places by whole numbers (e.g. 3.47 × 6) - [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 ## 18. Number Sense · Use place value understanding to round multi-digit whole numbers to any given place value. - [Decimal place value](https://ai.page/c/decimal-place-value-3/index.md): Round decimals to any place using place-value understanding; round any whole number to a required degree of accuracy - [Place Value Problem-Solving](https://ai.page/c/place-value-problem-solving/index.md): Solve number and practical problems involving place value with increasingly large positive numbers ## 19. Number Sense · Compare two decimals to hundredths by reasoning about their size based on the same whole. Record the results of comparisons with the symbols > , = , or < , and justify the conclusions ( - [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 >, =, < ## 20. Number Sense · Write tenths and hundredths in decimal and fraction notations. Use words, models, standard form, and expanded form to represent decimal numbers to hundredths. Mentally calculate fractio - [Decimal equivalents of tenths and hundredths](https://ai.page/c/decimal-equivalents-of-tenths-and-hundredths/index.md): Recognise and write decimal equivalents of any number of tenths or hundredths (e.g. 3/10 = 0.3, 27/100 = 0.27) - [Decimals for Tenths & Hundredths](https://ai.page/c/decimals-for-tenths-and-hundredths/index.md): Use decimal notation for fractions with denominators 10 or 100; read and write decimal numbers as fractions (e.g. 0.62 = 62/100, 0.71 = 71/100) ## 21. Number Sense · Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark, such as 0, 1/2, and 1). - [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 ## 22. Number Sense · Use fraction models to represent two equivalent fractions with attention to how the number and size of the parts differ even though the fractions themselves are the same size. Use this - [Equivalent fractions](https://ai.page/c/equivalent-fractions/index.md): Recognise and show, using diagrams, equivalent fractions with small denominators ## 23. Number Sense · Model mixed numbers and improper fractions using visual fraction models such as number lines and area models. Use a visual fraction model to show the equivalency between whole numbers a - [Multiplying fractions](https://ai.page/c/multiplying-fractions/index.md): Understand a/b as a multiple of 1/b; multiply proper fractions and mixed numbers by whole numbers, supported by visual models (e.g. 3 × 2/5 = 6/5 = 1 1/5) - [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 ## 24. Number Sense · Read and write whole numbers up to 1,000,000. Use words, models, standard form, and expanded form to represent and show equivalent forms of whole numbers up to 1,000,000. - [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 - [Reading and writing numbers to 1000](https://ai.page/c/reading-and-writing-numbers-to-1000/index.md): Read and write numbers to 1000 in numerals, number names, and expanded form ## Health: 0 of 100 Of its 32 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): - Understanding fractions comes before Adding Fractions (Unlike Denominators), which it needs - Understanding fractions has no explanation yet - Pictograms and tally charts (age 6+) has no explanation yet - Perimeters of polygons has no explanation yet - Area of compound shapes has no explanation yet - Measurement Conversions has no explanation yet - Converting measurement units has no explanation yet - Converting measurement units (age 9+) has no explanation yet - Halves and quarters (age 8+) has no explanation yet - Types of angles has no explanation yet - Lines, Rays & Angles has no explanation yet - Number Pattern Relationships has no explanation yet - Real-world fraction multiplication has no explanation yet - Adding and subtracting mixed numbers has no explanation yet - Adding Fractions (Unlike Denominators) has no explanation yet - Real-World Mathematical Modelling has no explanation yet - Factors, multiples, and primes has no explanation yet - Properties of Operations has no explanation yet - Division with remainders (age 10+) has no explanation yet - Adding numbers has no explanation yet - Decimal place value has no explanation yet - Long multiplication has no explanation yet - Decimal place value has no explanation yet - Place Value Problem-Solving has no explanation yet - Comparing Decimals has no explanation yet - Decimal equivalents of tenths and hundredths has no explanation yet - Decimals for Tenths & Hundredths has no explanation yet - Comparing fractions (age 8+) has no explanation yet - Equivalent fractions has no explanation yet - Multiplying fractions has no explanation yet - Dividing fractions (unit fractions) has no explanation yet - Reading and writing numbers (age 9+) has no explanation yet - Reading and writing numbers to 1000 has no explanation yet Credit: The structure of Indiana academic standards: Mathematics (https://www.in.gov/doe/files/AlgebraI-Math-Content-Connectors.docx.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.