How to learn Grade 3: Mathematics

Texas Essential Knowledge and Skills: Mathematics, Grade 3

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1. Data analysis

Pictograms and tally charts (age 6+): Read, write, and use the vocabulary of data collection and display — data, tally, tally chart, frequency, frequency table, survey, pictogram, bar chart, axis/axes, scale, label, category, discrete data, continuous data, line graph, pie chart — and apply these terms when collecting, organising, and presenting data
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

2. Geometry and measurement.

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
Measuring Perimeters: Measure the perimeter of simple 2-D shapes
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)
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
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
Area of compound shapes: Recognise area as additive; find areas of rectilinear figures by decomposing into non-overlapping rectangles and summing their areas
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
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

3. Algebraic reasoning

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)
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
Numbers on a number line: Represent whole numbers as lengths on a number line and represent sums and differences within 100 on a number line diagram

4. Number and operations

Properties of Operations: Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide
Odd or Even: Determine whether a group of objects (up to 20) has an odd or even number of members
Division as equal sharing: Understand division as sharing equally into groups or as grouping (how many groups of a given size can be made)
Fluent adding and subtracting within 100: Fluently add and subtract within 100 using strategies based on place value, properties of operations, and the relationship between addition and subtraction
Adding numbers: Add up to four two-digit numbers using strategies based on place value and properties of operations
All times tables to 12×12: Recall multiplication and division facts for multiplication tables up to 12 × 12
Rounding to 10, 100, 1000: Round any number to the nearest 10, 100, or 1000
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
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
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
Comparing fractions: Compare and order unit fractions, and fractions with the same denominator
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 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
Adding fractions (different denominators): Add and subtract fractions with denominators that are multiples of the same number by finding a common denominator
Simple Fraction Sums: Add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7)
Ordering Numbers to 1000: Compare and order numbers up to 1000 using >, =, and < symbols, based on place-value understanding
Comparing Large Numbers: Order and compare numbers beyond 1000
Place Value Problem-Solving: Solve number and practical problems involving place value with increasingly large positive numbers

5. Mathematical process standards

Precise Maths Communication: Communicate with mathematical precision: use correct vocabulary, specify units, and use symbols accurately
Choosing mathematical tools: Select and use appropriate tools and representations strategically: choose between mental, written, and diagrammatic methods; use calculators for checking; select fraction models suited to the task
Working with money: Model real-world problems involving measurement, money, and time by choosing appropriate representations and interpreting results in context