California Mathematics — Grade 1
Comprehensive Course Syllabus
Course Overview
Our California Grade 1 Mathematics course is designed according to the California Common Core State Standards for Mathematics (CA CCSSM). The curriculum helps students build a strong mathematical foundation through number sense, addition and subtraction, place value, measurement, data, geometry, and problem-solving.
Students develop mathematical thinking by working with numbers, solving real-world problems, explaining their reasoning, recognizing patterns, measuring objects, interpreting data, and exploring shapes through engaging activities and examples.
Numbers & Place Value
Counting and Numbers to 120
Students learn to count forward from different starting numbers, read and write numbers, and represent quantities using objects, pictures, and numerals up to 120.
Understanding Tens and Ones
Students learn that two-digit numbers are made up of tens and ones and use groups of ten to understand the value of each digit.
Comparing Two-Digit Numbers
Students compare two-digit numbers by examining their tens and ones and use the symbols <, >, and = to show which numbers are greater, smaller, or equal.
Number Patterns and Counting Strategies
Students explore number patterns and practice counting by groups such as 2s, 5s, and 10s to strengthen number sense and recognize patterns in numbers.
Addition & Subtraction
Understanding Addition
Students learn addition as putting groups together or increasing a quantity and solve simple addition problems using objects, drawings, number lines, and equations.
Understanding Subtraction
Students learn subtraction as taking away, separating, comparing, or finding the difference between quantities using visual models and real-world examples.
Addition and Subtraction Within 20
Students develop strategies for adding and subtracting within 20, including counting on, making a ten, decomposing numbers, and using known facts.
Addition and Subtraction Word Problems
Students solve age-appropriate word problems involving joining, separating, comparing, and finding unknown quantities.
Fact Families and the Relationship Between Addition and Subtraction
Students understand how addition and subtraction are related and use known addition facts to help solve subtraction problems.
Addition and Subtraction Equations
Students learn the meaning of the equal sign, identify true and false equations, and find unknown numbers in simple addition and subtraction equations.
Addition, Subtraction & Place Value to 100
Adding Within 100
Students use place-value understanding, drawings, and concrete models to add two-digit numbers with one-digit numbers and multiples of 10.
Tens and Ones Strategies
Students learn to add tens to tens and ones to ones and understand when a group of ten needs to be composed during addition.
Mental Math: 10 More and 10 Less
Students practice finding 10 more or 10 less than a given two-digit number without counting one number at a time.
Subtracting Multiples of 10
Students use tens and place-value strategies to subtract multiples of 10 and explain how they arrived at their answers.
Measurement, Time & Data
Comparing and Measuring Length
Students compare objects by length and learn to measure objects using repeated units of the same size.
Measuring with Standard and Non-Standard Units
Students use simple measurement tools and units to determine the length of objects and understand why consistent units are important.
Telling Time
Students learn to read analog and digital clocks and tell time to the hour and half-hour using everyday situations.
Organizing and Representing Data
Students collect and organize information into simple categories and represent data using pictures, charts, tables, and other visual representations.
Comparing Data
Students ask and answer questions about data, including how many items are in each category and how many more or fewer items one category has than another.
Shapes & Geometry
Identifying and Describing Shapes
Students identify and describe common two-dimensional and three-dimensional shapes based on attributes such as sides, corners, faces, and other observable characteristics.
Sorting and Comparing Shapes
Students sort and classify shapes according to their attributes and explain how different shapes are alike or different.
Composing and Decomposing Shapes
Students combine simple shapes to create larger shapes and break shapes into smaller parts while exploring different ways to build and describe figures.
Equal Shares and Simple Fractions
Students explore how circles and rectangles can be divided into equal parts and learn the everyday meanings of halves, fourths, and quarters.
Mathematical Thinking & Problem Solving
Solving Real-World Problems
Students apply addition, subtraction, measurement, geometry, and data skills to solve simple problems based on everyday situations.
Using Models and Mathematical Tools
Students use objects, drawings, number lines, charts, shapes, clocks, and other appropriate tools to represent and solve mathematical problems.
Explaining Mathematical Reasoning
Students learn to explain how they found an answer, compare different strategies, and communicate their mathematical thinking using words, pictures, numbers, and equations.
Patterns, Reasoning & Mathematical Practices
Students develop habits of mathematical thinking by looking for patterns, making connections, checking their work, choosing appropriate strategies, and persevering when solving challenging problems.
Teaching Methodology
Our mathematics classes focus on conceptual understanding, problem-solving, mathematical reasoning, and hands-on learning.
Students learn through:
Learning Outcomes
By the end of Grade 1, students will be able to:
Assessment & Progress Tracking
Student progress is evaluated through: