United States · Common Core State Standards
3rd Grade Mathematics
This curriculum transitions students from basic arithmetic to a deeper understanding of multiplication, division, and fractions. It emphasizes the relationship between operations and the application of mathematical properties to solve real world problems.
01The Power of Groups: Operations and Algebraic Thinking
Students explore the conceptual foundations of multiplication and division through equal groups and arrays. This unit focuses on the inverse relationship between operations and strategies for fluency.
Investigating how multiplication represents repeated addition and equal groups in real world scenarios.
Understanding division as the process of partitioning a total into equal shares or groups.
Determining the unknown whole number in a multiplication or division equation relating three whole numbers.
Applying properties of operations as strategies to multiply and divide.
Achieving fluency with multiplication and division facts within 100 using various strategies.
Applying the four operations to solve two-step word problems and assessing the reasonableness of answers.
Identifying arithmetic patterns (including patterns in the addition table or multiplication table) and explaining them using properties of operations.
02Place Value and Multi-Digit Arithmetic
Students use place value understanding and properties of operations to perform multi-digit arithmetic. This unit builds the foundation for rounding and fluently adding and subtracting within 1000.
Using place value to round whole numbers to the nearest 10 or 100.
Developing fluency with addition and subtraction within 1000 using various strategies and algorithms.
Applying place value strategies to multiply one-digit whole numbers by multiples of 10.
03Parts of a Whole: Exploring Fractions
An introduction to fractions as numbers that represent parts of a whole or points on a number line. Students focus on unit fractions and equivalent fractions.
Understanding 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts.
Representing fractions on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into equal parts.
Identifying and generating simple equivalent fractions using visual models.
Understanding whole numbers as fractions, and locating them on a number line.
Comparing two fractions with the same numerator or the same denominator by reasoning about their size.
04Measuring Our World: Time, Liquid, and Mass
Students develop skills in measuring time intervals, liquid volumes, and masses of objects. This unit emphasizes solving problems involving measurement data.
Telling time to the nearest minute and measuring elapsed time intervals in minutes.
Measuring and estimating liquid volumes and masses using standard units like grams, kilograms, and liters.
Drawing and interpreting scaled picture graphs and bar graphs to represent data sets.
Drawing and interpreting scaled picture graphs to represent data sets with several categories.
Generating measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Showing the data by making a line plot.
05Shapes and Space: Geometry and Area
Students relate area to multiplication and addition while exploring the attributes of different geometric shapes.
Understanding area as an attribute of plane figures and measuring area by counting unit squares.
Relating area to the operations of multiplication and addition through tiling and arrays.
Finding the area of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts.
Solving real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
Understanding that shapes in different categories may share attributes and that shared attributes can define a larger category.
Partitioning shapes into parts with equal areas. Expressing the area of each part as a unit fraction of the whole.
06Foundations of Problem Solving
This unit focuses on developing a systematic approach to solving mathematical problems, integrating all previously learned concepts.
Analyzing different types of word problems to identify the underlying mathematical structure.
Exploring and applying various strategies such as drawing diagrams, making tables, and working backward.
Using estimation and inverse operations to check the reasonableness of solutions to word problems.
07Advanced Operations and Algebraic Thinking
Building on foundational skills, this unit deepens understanding of multiplication and division, focusing on more complex problem structures and properties.
Using the associative and distributive properties to solve more complex multiplication and division problems.
Reinforcing the inverse relationship between multiplication and division through fact families and related equations.
Solving two-step word problems involving addition, subtraction, multiplication, and division, and representing these problems using equations with a letter standing for the unknown quantity.
08Deepening Number Sense: Fractions and Place Value
This unit extends students' understanding of fractions, including comparing and ordering, and reinforces place value concepts with larger numbers.
Using visual fraction models to compare fractions with different numerators and denominators.
Ordering a set of fractions by placing them on a number line and reasoning about their relative positions.
Reinforcing understanding of place value for whole numbers up to 1000, including reading, writing, and comparing numbers.
09Advanced Measurement and Data Analysis
This unit expands on measurement skills, focusing on problem-solving with time, liquid volume, and mass, and introduces more complex data interpretation.
Solving word problems involving addition and subtraction of time intervals in minutes.
Solving one-step word problems involving masses or liquid volumes that are given in the same units.
Interpreting information presented in scaled bar graphs to solve 'how many more' and 'how many less' problems.
Creating line plots to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).
10Geometry and Spatial Reasoning
This unit reinforces geometric understanding, focusing on attributes of shapes, area, and perimeter in more complex contexts.
Understanding that quadrilaterals include rhombuses, rectangles, and squares, and drawing examples of quadrilaterals that do not belong to any of these subcategories.
Finding the area of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems.
Exploring the relationship between perimeter and area, including finding rectangles with the same perimeter and different areas or with the same area and different perimeters.
Partitioning shapes into parts with equal areas and expressing the area of each part as a unit fraction of the whole, extending to non-unit fractions.