How to learn Grade 3: Mathematics

North Carolina academic standards: Mathematics, Grade 3

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1. Geometry

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 line properties: 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
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

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
Equivalent fractions: Recognise and show, using diagrams, equivalent fractions with small denominators
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
Unit fractions: Recognise, find, and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators

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)
Area by Tiling: Find the area of a rectangle by tiling it with unit squares and show that the result equals the product of the side lengths
Calculating with measurements: Measure, compare, add, and subtract lengths (m/cm/mm), mass (kg/g), and volume/capacity (l/ml) using standard units
Estimating answers (age 7+): 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+): Tell and write time to the nearest minute using analogue and digital clocks
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

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
Addition and subtraction within 1000: Add and subtract within 1000 using concrete models, drawings, and strategies based on place value; understand composing and decomposing tens and hundreds
Adding numbers: Add up to four two-digit numbers using strategies based on place value and properties of operations

Fluent multiplication and division facts: Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division
Patterns in Times Tables: Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of 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
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)
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)
Multiplicative Comparison: 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
Multiplication and Division Word Problems: Use multiplication and division within 100 to solve word problems involving equal groups, arrays, and measurement quantities