# Grade 4: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 40 concepts ready. In the app: https://ai.page/roadmap/nd-grade-4 Part of: [North Dakota: Mathematics](https://ai.page/roadmap/nd.md) Goal: North Dakota academic standards: Mathematics, Grade 4 ## 1. Fourth Grade - [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 - [Fractions on a number line](https://ai.page/c/fractions-on-a-number-line-2/index.md): Solve word problems involving distances, time intervals, liquid volumes, masses, and money using the four operations with fractions or decimals; represent with diagrams including number lines - [Measurement Line Plots](https://ai.page/c/measurement-line-plots/index.md): Make a line plot to display measurement data in fractions of a unit (1/2, 1/4, 1/8); solve problems involving addition and subtraction of fractions using line plot data - [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) - [Understanding fractions (age 9+)](https://ai.page/c/understanding-fractions-age-9-maths/index.md): Construct and present logical mathematical arguments involving multiple steps; critique others' reasoning about fractions, angles, or calculations and clearly explain errors or alternative methods - [Measuring angles](https://ai.page/c/measuring-angles/index.md): Measure angles in whole-number degrees using a protractor; draw given angles and sketch angles of specified measure - [Measuring angles (age 9+)](https://ai.page/c/measuring-angles-age-9/index.md): Recognise angle measure as additive; find unknown angles by adding or subtracting on a diagram using equations with a symbol for the unknown - [Using Simple Formulae](https://ai.page/c/using-simple-formulae/index.md): Use simple formulae expressed in words or symbols to calculate values (e.g. perimeter = 2 × (length + width)) - [Halves and quarters (age 7+)](https://ai.page/c/halves-and-quarters-age-7/index.md): Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately - [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 - [2-D shapes (age 8+)](https://ai.page/c/2-d-shapes-age-8/index.md): Identify lines of symmetry in 2-D shapes presented in different orientations; recognise line-symmetric figures and draw lines of symmetry - [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 - [Classifying shapes by line properties](https://ai.page/c/classifying-shapes-by-line-properties/index.md): Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or angles of a specified size; recognise right triangles as a category - [Shape patterns](https://ai.page/c/shape-patterns-maths/index.md): Generate a number or shape pattern that follows a given rule; identify apparent features of the pattern not explicit in the rule and explain informally why they occur - [Multiplicative Comparison](https://ai.page/c/multiplicative-comparison-maths/index.md): Interpret a multiplication equation as a comparison (e.g. 35 = 5 × 7 means 35 is 5 times as many as 7); represent verbal statements of multiplicative comparisons as equations - [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 - [Two-Step Equations](https://ai.page/c/two-step-equations/index.md): Solve two-step word problems using the four operations; represent problems using equations with a letter standing for the unknown quantity - [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 - [Division with remainders](https://ai.page/c/division-with-remainders/index.md): Solve multi-step word problems using the four operations with whole numbers, including interpreting remainders in context; represent with equations using a letter for the unknown; check with estimation - [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 - [Multiplying and dividing (age 10+)](https://ai.page/c/multiplying-and-dividing-age-10/index.md): Multiply and divide numbers by 10, 100, and 1000 giving answers up to three decimal places, understanding that digits shift position in the place-value chart - [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) - [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 of a whole (age 10+)](https://ai.page/c/fractions-of-a-whole-age-10/index.md): Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b); solve word problems involving division of whole numbers leading to fractional or mixed-number answers - [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 - [Addition and subtraction word problems](https://ai.page/c/addition-and-subtraction-word-problems-maths/index.md): Solve word problems involving addition and subtraction of fractions with like denominators, using visual models and equations - [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 - [Equivalent fractions (age 9+)](https://ai.page/c/equivalent-fractions-age-9/index.md): Explain why a fraction a/b is equivalent to (n×a)/(n×b) using visual models; use this principle to recognise and generate equivalent fractions, including tenths and hundredths - [Converting tenths to hundredths](https://ai.page/c/converting-tenths-to-hundredths/index.md): Express a fraction with denominator 10 as an equivalent fraction with denominator 100 and use this to add fractions with denominators 10 and 100 (e.g. 3/10 + 4/100 = 34/100) - [Place value of each digit](https://ai.page/c/place-value-of-each-digit/index.md): Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones) - [Long multiplication (age 10+)](https://ai.page/c/long-multiplication-age-10/index.md): Fluently multiply multi-digit whole numbers (up to 4 digits by 2 digits) using the formal written method of long multiplication - [Adding and subtracting (age 8+)](https://ai.page/c/adding-and-subtracting-age-8/index.md): Add and subtract numbers with up to four digits using formal written methods of columnar addition and subtraction - [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 - [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 >, =, < - [Comparing Large Numbers](https://ai.page/c/comparing-large-numbers/index.md): Order and compare numbers beyond 1000 - [Place Value × 10 Pattern](https://ai.page/c/place-value-10-pattern/index.md): Recognise that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g. 700 ÷ 70 = 10) - [Place Value × 10 and ÷ 10](https://ai.page/c/place-value-10-and-10/index.md): Recognise that in a multi-digit number, a digit in one place represents 10 times as much as in the place to its right and 1/10 of what it represents in the place to its left - [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 - [Constructing mathematical arguments](https://ai.page/c/constructing-mathematical-arguments/index.md): Construct and present logical mathematical arguments involving multiple steps and formal reasoning; critique others' reasoning about fractions, algebra, ratio, or geometry and clearly explain errors or alternative approaches ## Health: 0 of 100 Of its 40 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): - Converting measurement units (age 9+) has no explanation yet - Fractions on a number line has no explanation yet - Measurement Line Plots has no explanation yet - Understanding fractions has no explanation yet - Understanding fractions (age 9+) has no explanation yet - Measuring angles has no explanation yet - Measuring angles (age 9+) has no explanation yet - Using Simple Formulae has no explanation yet - Halves and quarters (age 7+) has no explanation yet - Measurement Conversions has no explanation yet - 2-D shapes (age 8+) has no explanation yet - Lines, Rays & Angles has no explanation yet - Classifying shapes by line properties has no explanation yet - Shape patterns has no explanation yet - Multiplicative Comparison has no explanation yet - Factors, multiples, and primes has no explanation yet - Two-Step Equations has no explanation yet - Long multiplication has no explanation yet - Division with remainders has no explanation yet - Properties of Operations has no explanation yet - Multiplying and dividing (age 10+) has no explanation yet - Multiplying fractions has no explanation yet - Real-world fraction multiplication has no explanation yet - Fractions of a whole (age 10+) has no explanation yet - Dividing fractions (unit fractions) has no explanation yet - Addition and subtraction word problems has no explanation yet - Comparing fractions (age 8+) has no explanation yet - Comparing fractions (age 10+) has no explanation yet - Equivalent fractions (age 9+) has no explanation yet - Converting tenths to hundredths has no explanation yet - Place value of each digit has no explanation yet - Long multiplication (age 10+) has no explanation yet - Adding and subtracting (age 8+) has no explanation yet - Decimal place value has no explanation yet - Comparing Decimals has no explanation yet - Comparing Large Numbers has no explanation yet - Place Value × 10 Pattern has no explanation yet - Place Value × 10 and ÷ 10 has no explanation yet - Reading and writing numbers (age 9+) has no explanation yet - Constructing mathematical arguments has no explanation yet Credit: The structure of North Dakota academic standards: Mathematics (https://www.nd.gov/dpi/sites/www/files/documents/Academic%20Support/ND%20Mathematics%20K-12%20Standards.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.