# Grade 3: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 17 concepts ready. In the app: https://ai.page/roadmap/ut-grade-3 Part of: [Utah: Mathematics](https://ai.page/roadmap/ut.md) Goal: Utah academic standards: Mathematics, Grade 3 ## 1. Measurement and Data · Relate area to the operations of multiplication and addition (refer to 3.OA.5). - [Area by Tiling](https://ai.page/c/area-by-tiling/index.md): Find the area of a rectangle by tiling it with unit squares and show that the result equals the product of the side lengths - [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 - [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 - [Area and the distributive property](https://ai.page/c/area-and-the-distributive-property/index.md): Use tiling to demonstrate the distributive property: the area of a rectangle with sides a and (b+c) equals a×b + a×c; use area models to represent the distributive property ## 2. Measurement and Data · Recognize area as an attribute of plane figures and understand concepts of area measurement. - [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 ## 3. Number and Operations — Fractions · Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. - [Comparing fractions](https://ai.page/c/comparing-fractions/index.md): Compare and order unit fractions, and fractions with the same denominator - [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 - [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 - [Understanding fractions](https://ai.page/c/understanding-fractions-maths/index.md): Write simple fractions (e.g. 1/2 of 6 = 3) and recognise the equivalence of 2/4 and 1/2 - [Equivalent fractions](https://ai.page/c/equivalent-fractions/index.md): Recognise and show, using diagrams, equivalent fractions with small denominators - [Equivalent fractions on a number line](https://ai.page/c/equivalent-fractions-on-a-number-line/index.md): Understand two fractions as equivalent if they are the same size or the same point on a number line; recognise and show families of common equivalent fractions using diagrams ## 4. Number and Operations — Fractions · Understand a fraction as a number on the number line; represent fractions on a number line diagram. - [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 ## 5. Number and Operations — Fractions · Understand that a unit fraction has a numerator of one and a non-zero denominator. - [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 ## 6. Operations and Algebraic Thinking · Solve two-step word problems. - [Multi-Step Problem Solving](https://ai.page/c/multi-step-problem-solving/index.md): With teacher support, make sense of multi-step problems involving larger numbers or mixed operations by breaking them into parts, choosing strategies, and checking answers for reasonableness — children at this stage are developing the habit with guidance; independent strategy evaluation comes later - [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 - [Multi-step problems: choosing operations](https://ai.page/c/multi-step-problems-choosing-operations/index.md): Solve problems involving addition, subtraction, multiplication, and division, deciding which operations and methods to use and why; solve multi-step problems in contexts ## 7. Operations and Algebraic Thinking · Fluently multiply and divide. - [Fluent multiplication and division facts](https://ai.page/c/fluent-multiplication-and-division-facts/index.md): Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division ## Health: 0 of 100 Of its 17 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): - Area by Tiling has no explanation yet - Understanding angles (age 8+) has no explanation yet - Area of compound shapes has no explanation yet - Area and the distributive property has no explanation yet - Understanding Area has no explanation yet - Comparing fractions comes before Fractions on a number line, which it needs - Comparing fractions has no explanation yet - Comparing fractions (age 8+) comes before Fractions of a whole, which it needs - Comparing fractions (age 8+) has no explanation yet - Fraction Notation has no explanation yet - Understanding fractions has no explanation yet - Equivalent fractions has no explanation yet - Equivalent fractions on a number line comes before Fractions of a whole, which it needs - Equivalent fractions on a number line has no explanation yet - Fractions on a number line has no explanation yet - Fractions of a whole has no explanation yet - Multi-Step Problem Solving has no explanation yet - Two-Step Equations has no explanation yet - Multi-step problems: choosing operations has no explanation yet - Fluent multiplication and division facts has no explanation yet Credit: The structure of Utah academic standards: Mathematics (http://www.schools.utah.gov/CURR/mathelem/Core/ElementaryMath.aspx); 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.