# Grade 3: 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/ar-grade-3 Part of: [Arkansas: Mathematics](https://ai.page/roadmap/ar.md) Goal: Arkansas academic standards: Mathematics, Grade 3 ## 1. Grade 3 · Organize and analyze 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 - [Sorting Data into Categories](https://ai.page/c/sorting-data-into-categories/index.md): Organise and represent data with up to three categories by counting objects in each category and sorting categories by quantity ## 2. Grade 3 · Tell time and solve problems about elapsed time. - [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 - [Telling time to the minute (age 8+)](https://ai.page/c/telling-time-to-the-minute-age-8/index.md): Tell and write time to the nearest minute using analogue and digital clocks ## 3. Grade 3 · Calculate the area of rectangles and liquid volume. - [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 - [Understanding angles (age 8+)](https://ai.page/c/understanding-angles-age-8-maths/index.md): Multiply side lengths to find areas of rectangles and represent whole-number products as rectangular areas - [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 ## 4. Grade 3 · Investigate measurement using rulers. - [Measuring length (age 7+)](https://ai.page/c/measuring-length-age-7/index.md): Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, metre sticks, and measuring tapes ## 5. Grade 3 · Analyze attributes of shapes to develop generalizations about their properties. - [Understanding angles (age 8+)](https://ai.page/c/understanding-angles-age-8/index.md): Understand that shapes in different categories may share attributes defining a larger category; classify quadrilaterals (rhombuses, rectangles, squares) and draw examples of quadrilaterals not in those subcategories - [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 ## 6. Grade 3 · Develop and apply an understanding of foundational algebraic concepts. - [Division as Unknown Factor](https://ai.page/c/division-as-unknown-factor/index.md): Understand division as an unknown-factor problem (e.g. find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8) - [Unknown in Multiplication & Division](https://ai.page/c/unknown-in-multiplication-and-division/index.md): Determine the unknown whole number in a multiplication or division equation relating three whole numbers (e.g. 8 × ? = 48, ? × 6 = 42) ## 7. Grade 3 · Solve real-world 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 - [Multiplication and Division Word Problems](https://ai.page/c/multiplication-and-division-word-problems/index.md): Use multiplication and division within 100 to solve word problems involving equal groups, arrays, and measurement quantities ## 8. Grade 3 · Perform operations using place value understanding and properties of operations. - [Shape patterns (age 7+)](https://ai.page/c/shape-patterns-age-7/index.md): Look for and use mathematical structure: apply place-value patterns to three-digit operations, use multiplication/division relationships, and exploit shape properties to classify - [Mental multiplication and division](https://ai.page/c/mental-multiplication-and-division/index.md): Use place value, known and derived facts to multiply and divide mentally, including multiplying by 0 and 1, dividing by 1, and multiplying together three numbers - [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 - [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 - [Fluent adding and subtracting within 1000](https://ai.page/c/fluent-adding-and-subtracting-within-1000/index.md): Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and the relationship between addition and subtraction ## 9. Grade 3 · Develop and apply equivalent fraction understanding. - [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 ## 10. Grade 3 · Build a conceptual understanding of fractions. - [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 - [Fractions on a number line](https://ai.page/c/fractions-on-a-number-line/index.md): Recognise and use fractions as numbers: place unit fractions and non-unit fractions with small denominators on a number line - [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 - [Fractions as parts of shapes](https://ai.page/c/fractions-as-parts-of-shapes/index.md): Partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole - [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 ## 11. Grade 3 · Use place value understanding to compare numbers. - [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 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 >, =, < - [Ordering Numbers to 1000](https://ai.page/c/ordering-numbers-to-1000/index.md): Compare and order numbers up to 1000 using >, =, and < symbols, based on place-value understanding - [Comparing Large Numbers](https://ai.page/c/comparing-large-numbers/index.md): Order and compare numbers beyond 1000 ## 12. Grade 3 · Understand the base ten place value system. - [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 - [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) - [Decimal place value (age 9+)](https://ai.page/c/decimal-place-value-age-9/index.md): Round decimals with two decimal places to the nearest whole number and to one decimal place ## 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): - Representing numbers with objects (age 8+) has no explanation yet - Sorting Data into Categories has no explanation yet - Estimating answers (age 7+) has no explanation yet - Telling time to the minute (age 8+) has no explanation yet - Measuring Liquids & Masses has no explanation yet - Understanding angles (age 8+) has no explanation yet - Understanding Area has no explanation yet - Measuring length (age 7+) has no explanation yet - Understanding angles (age 8+) has no explanation yet - Classifying shapes by line properties has no explanation yet - Division as Unknown Factor has no explanation yet - Unknown in Multiplication & Division has no explanation yet - Two-Step Equations has no explanation yet - Multiplication and Division Word Problems has no explanation yet - Shape patterns (age 7+) has no explanation yet - Mental multiplication and division has no explanation yet - Properties of Operations has no explanation yet - Understanding fractions (age 9+) has no explanation yet - Fluent adding and subtracting within 1000 has no explanation yet - Equivalent fractions (age 9+) has no explanation yet - Fraction Addition Concepts has no explanation yet - Fractions on a number line has no explanation yet - Fractions of a whole has no explanation yet - Fractions as parts of shapes has no explanation yet - Unit fractions has no explanation yet - Comparing fractions (age 8+) has no explanation yet - Comparing Decimals has no explanation yet - Ordering Numbers to 1000 has no explanation yet - Comparing Large Numbers comes before Place value of each digit, which it needs - Comparing Large Numbers has no explanation yet - Reading and writing numbers (age 9+) has no explanation yet - Place value of each digit has no explanation yet - Decimal place value (age 9+) has no explanation yet Credit: The structure of Arkansas academic standards: Mathematics (https://dese.ade.arkansas.gov/admin/Files/AR_2023_K-8,_Alg,_Geo_Math_Standards_LS_6.21.23_LS.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.