How to learn Grade 3: Mathematics

Pennsylvania academic standards: Mathematics, Grade 3

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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: 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)

Understanding angles (age 8+): Multiply side lengths to find areas of rectangles and represent whole-number products as rectangular areas
Area (age 8+): Measure areas by counting unit squares (square cm, square m, square in, square ft)

Pictograms and tally charts: Interpret and construct simple pictograms, tally charts, block diagrams, and simple tables
Measuring & Plotting Lengths: Generate measurement data by measuring lengths to the nearest whole unit and display the data on a line plot
Picture & Bar Graphs: 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+): 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

Halves and quarters (age 7+): Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately

Telling time to the minute (age 8+): Tell and write time to the nearest minute using analogue and digital clocks

Choosing measurement units: 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: Measure, compare, add, and subtract lengths (m/cm/mm), mass (kg/g), and volume/capacity (l/ml) using standard units
Measuring Liquids & Masses: Measure and estimate liquid volumes and masses of objects using grams, kilograms, and litres; solve one-step word problems involving mass or volume

Fractions as parts of shapes: Partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole

Understanding angles (age 8+): 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: 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

Understanding fractions: 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: Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations
Multi-Step Problem Solving: 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: 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: 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: Solve problems involving addition, subtraction, multiplication, and division, deciding which operations and methods to use and why; solve multi-step problems in contexts

Division as Unknown Factor: 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: Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide

Unknown in Multiplication & Division: Determine the unknown whole number in a multiplication or division equation relating three whole numbers (e.g. 8 × ? = 48, ? × 6 = 42)
What Multiplication Means: Interpret products of whole numbers (e.g. 5 × 7 as the total number of objects in 5 groups of 7)
What Division Means: 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: Use multiplication and division within 100 to solve word problems involving equal groups, arrays, and measurement quantities

Fraction Notation: 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: 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+): 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+): 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): Add and subtract fractions with denominators that are multiples of the same number by finding a common denominator
Fractions on a number line: Recognise and use fractions as numbers: place unit fractions and non-unit fractions with small denominators on a number line

Ordering Numbers to 1000: Compare and order numbers up to 1000 using >, =, and < symbols, based on place-value understanding
Multiplying by Tens: 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: Add up to four two-digit numbers using strategies based on place value and properties of operations