Texas Mathematics — Grade 1
Comprehensive Course Syllabus
Course Overview
Our Texas Grade 1 Mathematics course is designed according to the Texas Essential Knowledge and Skills (TEKS) standards. The curriculum develops strong mathematical foundations through interactive learning, real-life applications, hands-on activities, and problem-solving exercises.
Students build confidence in counting, addition, subtraction, place value, measurement, geometry, time, money, and data interpretation while developing logical thinking and analytical skills.
Number Sense & Place Value
Counting and Number Recognition
Students learn to read, write, count, and recognize numbers up to 120. They practice counting forward, backward, and identifying missing numbers through interactive games and number activities.
Place Value (Tens & Ones)
Students understand how numbers are made using tens and ones. They use place value blocks, charts, and grouping activities to build a strong foundation for future arithmetic.
Comparing and Ordering Numbers
Students compare numbers using greater than (>), less than (<), and equal to (=). They also arrange numbers in ascending and descending order while developing number sense.
Skip Counting
Students practice skip counting by 2s, 5s, and 10s. This topic prepares students for multiplication concepts introduced in later grades.
Number Patterns
Students recognize simple number patterns and predict the next number in a sequence, strengthening logical thinking and observation skills.
Ordinal Numbers
Students use ordinal words such as first, second, and third to describe position in a line or sequence. They practice with classroom races, story events, and everyday routines.
Addition & Subtraction
Addition Within 20
Students learn different strategies to add numbers within 20 using pictures, objects, number lines, and mental math techniques.
Subtraction Within 20
Students develop subtraction skills by understanding “taking away,” “finding the difference,” and solving everyday subtraction problems.
Fact Families
Students explore the relationship between addition and subtraction by learning fact families, helping them solve equations more efficiently.
Word Problems
Students solve simple real-life addition and subtraction word problems by identifying important information and selecting the correct mathematical operation.
Doubles & Near Doubles
Students learn doubles facts such as 4 + 4 and use them to solve near doubles like 4 + 5. This strategy builds quick and confident addition within 20.
Adding Three Numbers
Students add three small numbers by grouping two of them first. They discover that numbers can be added in any order and the total stays the same.
Measurement
Measuring Length
Students compare and measure objects using both standard and non-standard units such as paper clips, blocks, inches, and centimeters.
Comparing Objects
Students compare objects based on length, height, weight, and capacity using terms like longer, shorter, heavier, lighter, more, and less.
Time
Students learn to read analog and digital clocks to the hour and half-hour while understanding daily schedules and routines.
Money
Students identify and count U.S. coins including pennies, nickels, dimes, and quarters. They solve simple money problems using real-life shopping examples.
Measuring Weight & Capacity
Students explore how heavy objects are and how much containers hold using balance scales, cups, and everyday items. They record and discuss their measurement results.
Calendar Skills
Students name the days of the week and months of the year and locate dates on a calendar. They connect calendar time to schedules, birthdays, and school events.
Geometry
Two-Dimensional Shapes
Students identify and describe common 2D shapes such as circles, squares, rectangles, triangles, hexagons, and trapezoids based on their sides and corners.
Three-Dimensional Shapes
Students recognize 3D objects including cubes, spheres, cones, cylinders, and rectangular prisms by observing objects used in everyday life.
Composing & Decomposing Shapes
Students combine and separate shapes to create new figures, improving spatial reasoning and visualization skills.
Attributes of Shapes
Students describe shapes using math language such as sides, vertices, and curves. They sort shapes by their attributes and explain how the groups are alike and different.
Shapes in the Real World
Students find 2D and 3D shapes in buildings, signs, toys, and nature. This helps them connect geometry vocabulary to the world around them.
Building & Drawing Shapes
Students draw shapes and build them with sticks, clay, and pattern blocks. Creating shapes by hand strengthens their understanding of each shape's attributes.
Data Analysis
Sorting & Classifying Objects
Students group objects by color, size, shape, or other characteristics and explain their reasoning.
Picture Graphs
Students collect simple data and represent it using picture graphs. They answer questions by interpreting the information shown.
Bar Graphs
Students create and read simple bar graphs to compare quantities and understand basic data analysis.
Tally Marks & T-Charts
Students record counts using tally marks and organize them in simple T-charts. They practice counting tallies in groups of five.
Collecting Data with Surveys
Students ask simple survey questions such as favorite fruit or pet and gather answers from classmates. They organize the responses before graphing them.
Drawing Conclusions from Data
Students answer questions about graphs using words like most, fewest, more, and less. They explain what a graph shows in their own words.
Fractions (Introduction)
Equal Parts
Students understand that objects can be divided into equal parts and recognize halves and fourths using pictures and real-world objects.
Everyday Fractions
Students identify fractions in familiar situations such as sharing pizza, sandwiches, fruits, and chocolate bars.
Fair Shares
Students divide sets of objects equally among two or four friends. They discuss what makes a share fair and what to do with leftovers.
Fraction Vocabulary
Students use words and phrases such as half of, fourth of, and quarter of to describe parts of a whole. Clear vocabulary prepares them for fraction symbols in later grades.
Comparing Halves & Fourths
Students discover that cutting a whole into more equal parts makes each part smaller. They compare halves and fourths of the same object using models.
Paper Folding & Fraction Art
Students fold and cut paper shapes to create halves and fourths. Hands-on fraction art makes equal parts easy to see and remember.
Mathematical Thinking & Problem Solving
Patterns & Logic
Students solve puzzles, identify patterns, and complete logical reasoning activities to strengthen analytical thinking.
Mental Mathematics
Students improve speed and accuracy through daily mental math exercises involving counting, addition, subtraction, and estimation.
Real-Life Mathematics
Students apply mathematics in everyday situations such as shopping, measuring, telling time, organizing objects, and solving simple practical problems.
Two-Step Thinking
Students solve simple problems that need two steps, such as adding first and then comparing. They learn to plan before they solve.
Explaining Your Reasoning
Students explain how they solved a problem using words, pictures, and numbers. Talking about math builds confidence and deeper understanding.
Choosing Tools & Strategies
Students decide which tool fits a task, such as counters, a number line, or a hundred chart. Choosing wisely helps them work accurately and independently.
Personal Financial Literacy
Earning Income
Students learn that money earned from work is called income. They talk about jobs people do at home and in the community.
Income Buys Goods & Services
Students identify income as a way to obtain goods and services. They sort examples such as toys and haircuts into goods or services.
Spending & Saving
Students distinguish between spending money right away and saving it for later. They discuss saving for something special using simple examples.
Wants & Needs
Students tell the difference between things people need, such as food and shelter, and things people want. They practice making thoughtful choices with limited money.
Charitable Giving
Students consider how people share money and goods to help others. They discuss simple ways families give in their communities.
Classroom Store Activities
Students role-play buying and selling in a pretend classroom store. They count coins, make choices, and practice polite money exchanges.
Keeping Money Safe
Students discuss safe places to keep money, such as a piggy bank or a bank. They learn why keeping track of money matters.
Algebraic Reasoning & Number Sentences
Understanding the Equal Sign
Students learn that the equal sign means both sides have the same value. They test number sentences such as 5 + 2 = 3 + 4 with counters.
Missing Addends
Students find the unknown number in sentences like 6 + ? = 10. They use ten frames and counting on to solve for the missing part.
True or False Equations
Students decide whether number sentences are true or false and explain their reasoning. This sharpens careful checking and number sense.
Balancing Both Sides
Students use a pan balance model to make both sides of an equation equal. Balancing builds early algebra thinking in a hands-on way.
Part-Part-Whole Models
Students break numbers into parts and put parts together using part-part-whole diagrams. This model connects addition and subtraction clearly.
Growing & Repeating Patterns
Students extend repeating patterns and simple growing patterns with shapes and numbers. They describe the rule that makes each pattern work.
Input-Output Machines
Students play with simple function machines that add or subtract the same number every time. They predict outputs and discover the machine's rule.
Fluency & Mental Math Strategies
Counting On & Counting Back
Students start from a number and count on to add or count back to subtract. This strategy makes small sums and differences fast and accurate.
Ten Frames
Students use ten frames to see numbers as groups of ten and extras. Ten frames make teen numbers and sums easy to picture.
Making a Ten
Students break apart numbers to make a ten first, such as turning 8 + 5 into 10 + 3. Making ten is a powerful shortcut for addition within 20.
Number Bonds
Students build number bonds that show how a number splits into two parts. Knowing bonds for numbers up to 10 speeds up all later arithmetic.
Hundred Chart Work
Students find numbers, count by tens, and spot patterns on a hundred chart. Moving up, down, and across the chart deepens place value sense.
Estimating Quantities
Students make reasonable guesses about how many objects are in a group and then check by counting. Estimation builds practical number judgment.
Fact Fluency Games
Students play quick, friendly games that practice addition and subtraction facts. Regular game-based practice makes facts automatic without stress.
Spatial Sense & Position
Position Words
Students describe where objects are using words such as above, below, beside, between, and behind. They follow and give simple position directions.
Left & Right
Students practice telling left from right in movement games and drawing tasks. Clear direction sense supports geometry, reading, and daily life.
Simple Maps & Grids
Students find objects on simple picture maps and classroom grids. They describe paths from one place to another using position words.
Introduction to Symmetry
Students fold shapes and pictures to discover lines of symmetry. They find symmetry in letters, butterflies, and everyday objects.
Slides, Flips & Turns
Students move shapes by sliding, flipping, and turning them. They notice that a shape stays the same shape no matter how it moves.
Tangrams & Shape Puzzles
Students fill puzzle outlines using tangram pieces and pattern blocks. Puzzle play strengthens visualization and perseverance.
Building with Blocks
Students copy and create structures from blocks and cubes. They describe their buildings using shape and position vocabulary.
Review, Projects & Grade 2 Readiness
Cumulative Review
Students revisit numbers, operations, measurement, geometry, and data through mixed practice. Spaced review keeps every skill fresh.
Math Journals
Students draw and write about how they solve problems in a simple math journal. Journals help teachers see each child's thinking.
Hands-On Math Projects
Students complete small projects such as a class graph, a shape collage, or a pretend store. Projects combine several skills in one fun task.
Math Vocabulary Review
Students review key words such as sum, difference, digit, and equal. Strong vocabulary helps them understand directions and word problems.
Skills Check-Ins
Students complete short, low-pressure check-ins on core skills. Results guide extra practice so no gaps carry into 2nd grade.
Family Math Activities
Students take home simple games and tasks to play with family members. Practicing together connects classroom math to home life.
Looking Ahead to Grade 2
Students preview 2nd grade ideas such as numbers to 1,200 and adding two-digit numbers. A confident preview makes the next school year feel familiar.
Teaching Methodology
Our teaching approach emphasizes conceptual understanding rather than memorization. Students learn through:
Learning Outcomes
By the end of Grade 1, students will be able to:
Assessment & Progress Tracking
Student progress is evaluated through: