California Mathematics — Grade 2
Comprehensive Course Syllabus
Course Overview
Our California Grade 2 Mathematics course is designed according to the California Common Core State Standards for Mathematics (CA CCSSM) and the 2023 California Mathematics Framework. The curriculum develops strong foundations in place value, addition and subtraction, problem-solving, measurement, time, money, data, geometry, and mathematical reasoning.
Students strengthen their mathematical thinking by working with numbers up to 1,000, solving one- and two-step problems, using standard measurement units, working with money and time, interpreting data, and reasoning about shapes and their attributes.
Numbers & Place Value
Numbers to 1,000
Students learn to read, write, represent, and compare numbers up to 1,000 using numerals, number names, models, and expanded form.
Hundreds, Tens & Ones
Students understand that three-digit numbers are composed of hundreds, tens, and ones and learn the value represented by each digit.
Counting and Skip-Counting
Students count within 1,000 and practice skip-counting by 2s, 5s, 10s, and 100s to recognize numerical patterns and build number sense.
Comparing Three-Digit Numbers
Students compare three-digit numbers using their hundreds, tens, and ones values and use <, >, and = to record comparisons.
Number Forms and Representations
Students represent numbers using standard form, word form, expanded form, base-ten models, number lines, and other visual representations.
Addition & Subtraction
Addition and Subtraction Within 20
Students develop fluency with addition and subtraction within 20 using mental strategies and understand relationships between addition and subtraction facts.
Adding Within 100
Students use place-value understanding and properties of operations to add two-digit numbers accurately and efficiently.
Subtracting Within 100
Students use place-value strategies, models, and the relationship between addition and subtraction to subtract two-digit numbers.
Adding and Subtracting Within 1,000
Students build understanding of addition and subtraction with three-digit numbers and use place-value strategies to solve increasingly complex calculations.
Mental Math with 10 and 100
Students mentally add or subtract 10 or 100 from numbers within the appropriate range and recognize how the hundreds and tens digits change.
Estimation and Reasonableness
Students use estimation strategies to determine whether an answer is reasonable and develop habits of checking mathematical solutions.
Mathematical Problem Solving
One-Step Word Problems
Students solve addition and subtraction word problems involving joining, separating, combining, taking apart, and comparing quantities.
Two-Step Word Problems
Students solve problems that require two operations and learn to organize information and complete the required steps in the correct order.
Unknown Numbers in Equations
Students solve equations where the unknown number may appear in different positions and use drawings, objects, and equations to represent problems.
Choosing Problem-Solving Strategies
Students learn to select appropriate strategies such as drawing models, using number lines, making a table, decomposing numbers, or working with objects.
Explaining Mathematical Thinking
Students explain why their addition and subtraction strategies work and communicate their reasoning using numbers, words, drawings, and mathematical models.
Equal Groups & Foundations of Multiplication
Equal Groups
Students explore situations involving equal groups of objects and recognize how repeated groups can be represented mathematically.
Repeated Addition
Students use repeated addition to represent equal groups and begin connecting repeated addition with early multiplication concepts.
Arrays
Students arrange objects into rows and columns to create simple arrays and use them to represent equal groups.
Odd and Even Numbers
Students determine whether a group of objects or a number is odd or even and explain their reasoning using pairs and equal groups.
Measurement, Time & Money
Measuring Length
Students measure and estimate the lengths of objects using standard units such as inches, feet, centimeters, and meters.
Using Measurement Tools
Students learn to select and use appropriate measurement tools, such as rulers, yardsticks, meter sticks, and measuring tapes.
Comparing and Solving Length Problems
Students compare measurements and solve addition and subtraction problems involving lengths represented in the same unit.
Telling Time to the Nearest Five Minutes
Students read analog and digital clocks and tell and write time to the nearest five minutes using a.m. and p.m.
Understanding Money
Students identify common coins and bills, understand their values, and represent monetary amounts using dollars and cents.
Solving Money Problems
Students solve simple real-world problems involving money, including combining amounts and determining reasonable amounts in everyday situations.
Data & Graphs
Collecting and Organizing Data
Students collect information and organize it into categories so that it can be represented and analyzed.
Picture Graphs
Students create and interpret picture graphs where each picture represents a specified number of objects or data points.
Bar Graphs
Students create and interpret simple bar graphs and use the information to answer questions about quantities.
Line Plots
Students represent measurement data on line plots using a consistent measurement scale and interpret the information shown.
Comparing Data
Students use graphs and data displays to answer questions, compare quantities, and determine how many more or fewer items are in different categories.
Geometry & Shapes
Identifying Shape Attributes
Students identify and describe shapes using attributes such as the number of sides, vertices, angles, and equal or unequal lengths.
Recognizing Triangles and Quadrilaterals
Students identify and classify triangles and quadrilaterals based on their defining attributes.
Partitioning Shapes
Students divide circles and rectangles into equal shares and describe the parts using words such as halves, thirds, and fourths.
Equal Shares and Fractions
Students understand that equal shares of the same whole have equal size and begin using fractional language to describe these parts.
Reasoning About Shapes
Students compare, classify, and describe shapes based on their attributes and recognize that different shapes can share common characteristics.
Teaching Methodology
Our mathematics classes focus on conceptual understanding, problem-solving, mathematical reasoning, and real-world application.
Students learn through:
Learning Outcomes
By the end of Grade 2, students will be able to:
Assessment & Progress Tracking
Student progress is evaluated through: