# Grade 3: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 36 concepts ready. In the app: https://ai.page/roadmap/pa-grade-3 Part of: [Pennsylvania: Mathematics](https://ai.page/roadmap/pa.md) Goal: Pennsylvania academic standards: Mathematics, Grade 3 ## 1. M03.D-M.1 Measurement, Data, and Probability · M03.D-M.4.1 Solve problems involving perimeters of polygons and distinguish between linear and area measures. - [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) ## 2. M03.D-M.1 Measurement, Data, and Probability · M03.D-M.3.1 Determine the area of a rectangle and apply the concept to multiplication and to addition. - [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 (age 8+)](https://ai.page/c/area-age-8/index.md): Measure areas by counting unit squares (square cm, square m, square in, square ft) ## 3. M03.D-M.1 Measurement, Data, and Probability - [Pictograms and tally charts](https://ai.page/c/pictograms-and-tally-charts/index.md): Interpret and construct simple pictograms, tally charts, block diagrams, and simple tables - [Measuring & Plotting Lengths](https://ai.page/c/measuring-and-plotting-lengths/index.md): Generate measurement data by measuring lengths to the nearest whole unit and display the data on a line plot - [Picture & Bar Graphs](https://ai.page/c/picture-and-bar-graphs/index.md): Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories; solve put-together, take-apart, and compare problems using information presented in a bar graph - [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 ## 4. M03.D-M.1 Measurement, Data, and Probability · M03.D-M.1.3 Solve problems and make change involving money using a combination of coins and bills. - [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 ## 5. M03.D-M.1 Measurement, Data, and Probability · M03.D-M.1.1 Tell and write time to the nearest minute and solve problems by calculating time intervals. - [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 ## 6. M03.D-M.1 Measurement, Data, and Probability · M03.D-M.1.2 Solve problems involving measurement and estimation of temperature, liquid volume, mass, and length - [Choosing measurement units](https://ai.page/c/choosing-measurement-units/index.md): Choose and use appropriate standard units to measure length (m/cm), mass (kg/g), temperature (°C), and capacity (litres/ml) to the nearest appropriate unit - [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 ## 7. M03.C-G.1 Geometry - [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 ## 8. M03.C-G.1 Geometry · M03.C-G.1.1 Identify, compare, and classify shapes and their attributes. - [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 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 ## 9. M03.A-F.1 Algebraic Concepts · M03.B-O.3.1 Solve problems involving the four operations, and identify and explain patterns in arithmetic. - [Understanding fractions](https://ai.page/c/understanding-fractions-2/index.md): Move fluently between real-world situations, diagrams, and symbolic equations involving three-digit numbers and fractions, explaining what each part represents - [Patterns in Times Tables](https://ai.page/c/patterns-in-times-tables/index.md): Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations - [Multi-Step Problem Solving](https://ai.page/c/multi-step-problem-solving-maths/index.md): Make sense of multi-step problems involving four operations, fractions, and area/volume by identifying sub-steps, choosing a strategy, and monitoring progress - [Advanced Multi-Step Problems](https://ai.page/c/advanced-multi-step-problems/index.md): Make sense of complex multi-step problems involving ratio, proportion, algebra, negative numbers, and all four operations with fractions and decimals by analysing given and unknown quantities, planning solution strategies, and evaluating reasonableness using estimation and inverse operations - [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 ## 10. M03.A-F.1 Algebraic Concepts · M03.B-O.2.1 Understand properties of multiplication and the relationship between multiplication and division. - [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) - [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 ## 11. M03.A-F.1 Algebraic Concepts · M03.B-O.1.1 Represent and solve problems involving multiplication and division. - [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) - [What Multiplication Means](https://ai.page/c/what-multiplication-means/index.md): Interpret products of whole numbers (e.g. 5 × 7 as the total number of objects in 5 groups of 7) - [What Division Means](https://ai.page/c/what-division-means/index.md): Interpret whole-number quotients (e.g. 56 ÷ 8 as the number of objects in each share or the number of equal groups) - [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 ## 12. M03.A-F.1 Algebraic Concepts · M03.A-F.1.1 Explore and develop an understanding of fractions as numbers. - [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 - [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 - [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 - [Fractions of a whole (age 8+)](https://ai.page/c/fractions-of-a-whole-age-8/index.md): Express whole numbers as fractions (e.g. 3 = 3/1) and recognise fractions equivalent to whole numbers (e.g. 4/4 = 1, 6/1 = 6) - [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 - [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 ## 13. M03.A-T.1 Numbers and Operations · M03.A-T.1.1 Apply place-value understanding and properties of operations to perform multi-digit arithmetic. - [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 - [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 - [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 ## Health: 0 of 100 Of its 36 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): - Perimeters of polygons has no explanation yet - Understanding angles (age 8+) has no explanation yet - Area (age 8+) has no explanation yet - Pictograms and tally charts has no explanation yet - Measuring & Plotting Lengths has no explanation yet - Picture & Bar Graphs has no explanation yet - Representing numbers with objects (age 8+) has no explanation yet - Halves and quarters (age 7+) has no explanation yet - Telling time to the minute (age 8+) has no explanation yet - Choosing measurement units has no explanation yet - Calculating with measurements has no explanation yet - Measuring Liquids & Masses has no explanation yet - Fractions as parts of shapes comes before Fractions of a whole, which it needs - Fractions as parts of shapes has no explanation yet - Understanding angles (age 8+) has no explanation yet - Classifying shapes by properties has no explanation yet - Understanding fractions has no explanation yet - Patterns in Times Tables comes before Properties of Operations, which it needs - Patterns in Times Tables has no explanation yet - Multi-Step Problem Solving has no explanation yet - Advanced Multi-Step Problems has no explanation yet - Two-Step Equations has no explanation yet - Multi-step problems: choosing operations has no explanation yet - Division as Unknown Factor comes before What Multiplication Means, which it needs - Division as Unknown Factor comes before What Division Means, which it needs - Division as Unknown Factor has no explanation yet - Properties of Operations comes before What Multiplication Means, which it needs - Properties of Operations has no explanation yet - Unknown in Multiplication & Division has no explanation yet - What Multiplication Means has no explanation yet - What Division Means has no explanation yet - Multiplication and Division Word Problems has no explanation yet - Fraction Notation has no explanation yet - Fractions of a whole has no explanation yet - Comparing fractions (age 8+) has no explanation yet - Fractions of a whole (age 8+) has no explanation yet - Adding fractions (different denominators) has no explanation yet - Fractions on a number line has no explanation yet - Ordering Numbers to 1000 has no explanation yet - Multiplying by Tens has no explanation yet - Adding numbers has no explanation yet Credit: The structure of Pennsylvania academic standards: Mathematics (https://www.pdesas.org/Page/Viewer/ViewPage/12/); 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.