What Math Do 1st Graders Learn

First grade marks a significant step in a child's mathematical journey, laying the foundation for more complex concepts they will encounter in later grades. The curriculum focuses on building a strong understanding of numbers, basic operations, measurement, geometry, and data analysis, all while fostering a positive attitude towards math.

Building a Solid Foundation: Math Concepts for First Graders

First grade math is all about creating a strong base. Children learn to understand numbers, how they work, and how they relate to each other. This understanding is crucial for future math success. The key areas covered in first-grade math include:

• Number Sense: Understanding the meaning of numbers and their relationships.
• Addition and Subtraction: Mastering basic addition and subtraction facts.
• Measurement: Learning to measure length, weight, and time.
• Geometry: Identifying and describing basic shapes.
• Data Analysis: Interpreting and creating simple graphs.

Let's explore each of these areas in detail.

Diving into Number Sense

Number sense is the bedrock of mathematical understanding. In first grade, children develop a strong grasp of what numbers represent and how they behave. This includes:

• Counting: Counting to 120, starting from any number less than 120. This involves recognizing the sequence of numbers and understanding the one-more-than relationship.
• Place Value: Understanding that a two-digit number is composed of tens and ones. For example, 34 is understood as 3 tens and 4 ones.
• Comparing Numbers: Using terms like greater than, less than, and equal to to compare numbers up to 100. They learn to use symbols like >, <, and = to represent these comparisons.
• Number Patterns: Identifying and extending simple number patterns. For instance, recognizing the pattern in 2, 4, 6, 8... and continuing it.
• Ordinal Numbers: Understanding ordinal numbers like first, second, third, etc., to describe position in a sequence.

Why is Number Sense Important?

A strong number sense allows children to:

• Estimate quantities.
• Solve problems flexibly.
• Detect errors in calculations.
• Develop a deeper understanding of mathematical concepts.

Without a solid foundation in number sense, children may struggle with more advanced math topics later on.

Mastering Addition and Subtraction

First grade is a critical time for developing fluency in addition and subtraction. Children learn to:

• Addition Facts: Memorizing addition facts up to 10 + 10. This includes understanding the commutative property of addition (e.g., 3 + 5 = 5 + 3).
• Subtraction Facts: Mastering subtraction facts related to addition facts. For example, if they know 7 + 3 = 10, they should also know 10 - 3 = 7 and 10 - 7 = 3.
• Adding and Subtracting within 20: Solving addition and subtraction problems within 20 using strategies like counting on, counting back, using number lines, and making tens.
• Word Problems: Solving one-step word problems involving addition and subtraction. This requires them to understand the context of the problem and identify the appropriate operation to use.
• Properties of Operations: Understanding properties of addition such as the identity property (adding zero doesn't change the number) and the commutative property (order doesn't matter when adding).

Strategies for Teaching Addition and Subtraction:

• Using Manipulatives: Using concrete objects like counters, blocks, or beads to represent numbers and perform operations.
• Number Lines: Using number lines to visualize addition and subtraction as movements along the line.
• Ten Frames: Using ten frames to help children visualize numbers and understand the relationship to ten.
• Games: Playing games that involve addition and subtraction facts to make learning fun and engaging.

Exploring Measurement

First graders begin their journey into the world of measurement by learning to describe and compare the attributes of objects. Key concepts include:

• Length: Measuring the length of objects using non-standard units like paper clips or cubes, and then transitioning to standard units like inches and centimeters.
• Weight: Comparing the weight of objects using terms like heavier than, lighter than, and the same as.
• Time: Telling time to the hour and half-hour using analog and digital clocks. Understanding the concepts of before and after in relation to time.
• Comparing and Ordering: Comparing and ordering objects based on their length, weight, or capacity.

Hands-on Activities for Measurement:

• Measuring the Classroom: Have students measure the length of the classroom using their feet or using rulers.
• Weighing Objects: Use a balance scale to compare the weight of different objects in the classroom.
• Telling Time Games: Play games that involve matching times on analog and digital clocks.

Discovering Geometry

Geometry in first grade focuses on identifying and describing basic shapes. Children learn to:

• Identify Shapes: Recognizing and naming two-dimensional shapes like circles, squares, triangles, and rectangles, and three-dimensional shapes like cubes, cones, cylinders, and spheres.
• Describe Attributes: Describing the attributes of shapes, such as the number of sides, corners, and faces.
• Compose Shapes: Combining simple shapes to create more complex shapes. For example, putting two triangles together to make a square.
• Spatial Reasoning: Understanding spatial relationships such as above, below, beside, in front of, and behind.

Activities to Enhance Geometric Understanding:

• Shape Sorting: Sort shapes based on their attributes.
• Shape Hunts: Go on a shape hunt in the classroom or at home, identifying objects that resemble different shapes.
• Building with Blocks: Use blocks to build structures and explore spatial relationships.

Understanding Data Analysis

First graders are introduced to the basics of data analysis. They learn to:

• Collect Data: Collecting data by asking questions and recording the responses.
• Organize Data: Organizing data using tally marks, tables, and simple graphs.
• Interpret Data: Interpreting data from graphs and tables to answer questions about the data. For example, identifying the most popular item in a survey.
• Create Graphs: Creating simple bar graphs and picture graphs to represent data.

Engaging Activities for Data Analysis:

• Class Surveys: Conduct class surveys on topics like favorite colors, foods, or animals.
• Graphing Activities: Create graphs to represent the data collected from the surveys.
• Interpreting Graphs: Ask questions about the data represented in the graphs.

The Curriculum in Detail: A Closer Look

To understand what first graders learn in math, let's break down the curriculum further. The specific standards may vary slightly depending on the state or district, but the core concepts remain consistent.

Number and Operations in Base Ten

This area focuses on place value and using that understanding to perform operations. First graders will:

• Understand Place Value: Recognize that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
  • 10 can be thought of as a bundle of ten ones — called a "ten."
  • The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
  • The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
• Compare Two-Digit Numbers: Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
• Add within 100: Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
• Given a Two-Digit Number, Mentally Find 10 More or 10 Less: Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
• Subtract Multiples of 10: Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Operations and Algebraic Thinking

This area focuses on understanding the meaning of addition and subtraction and using that understanding to solve problems. First graders will:

• Represent and Solve Problems Involving Addition and Subtraction:
  • Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
  • Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
• Understand and Apply Properties of Operations and the Relationship Between Addition and Subtraction:
  • Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
  • Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8.
• Add and Subtract within 20:
  • Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
  • Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
• Work with Addition and Subtraction Equations:
  • Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 0.
  • Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ? – 3, 6 + 6 = ?.

Measurement and Data

This area focuses on measuring lengths and telling time. First graders will:

• Measure Lengths Indirectly and by Iterating Length Units:
  • Order three objects by length; compare the lengths of two objects indirectly by using a third object.
  • Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.
• Tell and Write Time: Tell and write time in hours and half-hours using analog and digital clocks.
• Represent and Interpret Data:
  • Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

Geometry

This area focuses on reasoning with shapes and their attributes. First graders will:

• Reason with Shapes and Their Attributes:
  • Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
  • Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.
  • Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

Tips for Supporting First Graders in Math

Parents and educators can play a significant role in supporting first graders' math learning. Here are some tips:

• Make Math Fun: Use games, activities, and real-life situations to make math engaging and enjoyable.
• Use Manipulatives: Provide concrete objects like counters, blocks, and beads to help children visualize math concepts.
• Connect Math to Real Life: Show children how math is used in everyday situations, such as cooking, shopping, or telling time.
• Encourage Problem Solving: Encourage children to try different strategies to solve problems and explain their thinking.
• Provide Positive Feedback: Offer praise and encouragement to build children's confidence in their math abilities.
• Read Math-Related Books: Read books that incorporate math concepts to make learning more interactive.
• Practice Regularly: Consistent practice is key to mastering math skills. Set aside time each day for math activities.
• Communicate with Teachers: Stay in touch with your child's teacher to understand their progress and identify areas where they may need extra support.
• Be Patient: Learning takes time, so be patient and supportive as children develop their math skills.
• Embrace Mistakes: Teach children that mistakes are a natural part of learning and an opportunity to grow.

Common Challenges in First Grade Math

While first grade math lays a critical foundation, some children may face challenges. Here are some common difficulties:

• Number Sense Deficits: Difficulty understanding the meaning of numbers and their relationships.
• Memorizing Math Facts: Struggle to memorize addition and subtraction facts.
• Word Problems: Difficulty understanding and solving word problems.
• Place Value Confusion: Misunderstanding the concept of place value.
• Telling Time: Difficulty telling time using analog clocks.
• Spatial Reasoning: Challenges with spatial reasoning and understanding geometric concepts.

How to Address These Challenges:

• Targeted Interventions: Provide individualized instruction to address specific areas of difficulty.
• Multisensory Learning: Use a variety of sensory experiences to help children understand concepts.
• Repetition and Practice: Provide ample opportunities for repetition and practice.
• Visual Aids: Use visual aids like number lines, ten frames, and charts to support learning.
• Break Down Concepts: Break down complex concepts into smaller, more manageable steps.
• Positive Reinforcement: Offer positive reinforcement and encouragement to build confidence.

The Importance of First Grade Math

First grade math is not just about learning numbers and shapes; it's about developing critical thinking skills and problem-solving abilities that will benefit children throughout their lives. A strong foundation in math can:

• Improve Cognitive Skills: Enhance cognitive skills like logical reasoning, critical thinking, and problem-solving.
• Boost Academic Performance: Lead to improved academic performance in other subjects, particularly science and technology.
• Enhance Career Opportunities: Open doors to a wider range of career opportunities in fields like engineering, finance, and computer science.
• Promote Financial Literacy: Equip individuals with the skills needed to manage their finances effectively.
• Foster Confidence: Build confidence and a positive attitude towards math.

Conclusion

First grade math is a crucial stepping stone in a child's mathematical journey. By focusing on number sense, addition and subtraction, measurement, geometry, and data analysis, first graders develop a strong foundation for future success in math. Parents and educators can support children's learning by making math fun, using manipulatives, connecting math to real life, and providing positive feedback. With a solid foundation in first grade math, children can develop the skills and confidence they need to excel in math and beyond. Remember that every child learns at their own pace, and patience and encouragement are key to fostering a love of math.