How to learn Grade 3: Mathematics

South Carolina academic standards: Mathematics, Grade 3

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1. Patterns, Algebra, and Functional Reasoning · Use reasoning to represent and solve algebraic and numerical situations.

Justifying mathematical reasoning: Construct and follow multi-step mathematical arguments; identify errors in reasoning and explain why a method works or does not work
Extending Table Patterns: Recognise and use repeated reasoning to generalise: extend multiplication table patterns, derive unknown facts from known ones, and describe rules for sequences

2. Patterns, Algebra, and Functional Reasoning · Use multiple representations to reason and solve problems involving operational properties of whole numbers.

Reasoning with Equivalences: Recognise and use repeated reasoning to generalise: extend patterns in equivalent fractions and percentage conversions, derive unknown facts from known facts, describe general rules for sequences and predict terms

3. Numerical Reasoning · Represent and compare fractions in multiple ways using part-whole relationships.

Comparing fractions: Compare and order unit fractions, and fractions with the same denominator
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 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)
Understanding fractions: Move fluently between real-world situations, diagrams, and symbolic equations involving three-digit numbers and fractions, explaining what each part represents
Fractions on a number line: Move fluently between real-world situations, diagrams, number lines, and symbolic equations involving multiplication, fractions, and decimals, explaining what each representation shows
Unit fractions: Recognise, find, and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators

4. Numerical Reasoning · Represent and compare numbers using relationships within the base ten number system.

Estimating by rounding: Estimate the answer to a calculation and use inverse operations to check answers; apply to increasingly large numbers using rounding and inverse reasoning
Representing Numbers: Identify, represent, and estimate numbers using different representations including the number line
Numbers to 10,000: Identify, represent, and estimate numbers up to 10,000 using different representations
Comparing Large Numbers: Order and compare numbers beyond 1000

5. Measurement, Geometry, and Spatial Reasoning · Extend geometric reasoning to attributes of polygons and/or polyhedrons.

Types of angles: Identify acute and obtuse angles; compare and order angles up to two right angles by size
Lines, Rays & Angles: Draw and identify points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines; identify these in two-dimensional figures

6. Measurement, Geometry, and Spatial Reasoning · Estimate and measure using units of length, liquid volume, currency, and intervals of time.

Calculating with measurements: Measure, compare, add, and subtract lengths (m/cm/mm), mass (kg/g), and volume/capacity (l/ml) using standard units
Estimating Lengths: Estimate lengths using units of inches, feet, centimetres, and metres
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

7. Measurement, Geometry, and Spatial Reasoning · Solve area and perimeter problems in real-world and mathematical situations.

Real-World Maths Modelling: Model real-world problems involving scaling, unit conversion, area/perimeter, and percentage by selecting appropriate mathematical representations and interpreting results in context
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

8. Data, Probability, and Statistical Reasoning · Represent the probability of simple events and determine possible outcomes.

Calculating Simple Probability: Calculate the probability of a simple event with equally likely outcomes using the formula: probability = number of favourable outcomes ÷ total number of possible outcomes; express the result as a fraction in its simplest form; apply to rolling dice, drawing from bags, and other simple chance situations

9. Data, Probability, and Statistical Reasoning · Collect and analyze data and communicate through multiple representations.

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