How to learn Grade 3: Mathematics

Department of Defense Education Activity standards: Mathematics, Grade 3

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1. Mathematics

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
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
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 Area: 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
Area (age 8+): Measure areas by counting unit squares (square cm, square m, square in, square ft)
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
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
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
Numbers on a number line: Solve word problems involving elapsed time by adding and subtracting time intervals in minutes, including using a number line
Telling time to the minute (age 7+): Tell and write time from analogue and digital clocks to the nearest five minutes, using a.m., p.m., and 12-hour and 24-hour notation
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
Equivalent fractions: Recognise and show, using diagrams, equivalent fractions with small denominators
Fractions on a number line (age 8+): Represent fractions on a number line: partition the interval 0 to 1 into b equal parts to locate 1/b, then mark off a lengths of 1/b from 0 to locate a/b
Equivalent fractions on a number line: 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
Comparing fractions (age 8+): Compare two fractions with the same numerator or the same denominator by reasoning about size; record comparisons with >, =, or < symbols
Fluent multiplication and division facts: Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division
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
Fluent adding and subtracting within 1000: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and the relationship between addition and subtraction
Rounding Large Numbers: Round any whole number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000, or 100,000 using place-value understanding
What Multiplication Means: Interpret products of whole numbers (e.g. 5 × 7 as the total number of objects in 5 groups of 7)
Properties of Operations: Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide
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 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)
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)
Multiplication and Division Word Problems: Use multiplication and division within 100 to solve word problems involving equal groups, arrays, and measurement quantities