What math should a 1st grader know?

What Math Concepts Are Taught in First Grade?

Article Summary: They learn to use estimations skills to explain measurement. This is also connected with geometry as they learn how to measure the length, area, volume, and mass of different objects. They learn how to measure all aspects of circles, prisms, and pyramids. They learn to use different traditional measuring tools for taking measurements of objects.

Why Do We Study Math?

Math teaches us how to develop logical thoughts which is to say that we clearly identify with problems and devise solutions to satisfy the conditions that they put in play. Over the course of a student’s math career, they will learn the importance of planning the correct steps to reach a conclusion. We often neglect to see how often we use math in our daily lives. A recent Ivy League study attempted to quantify the number of instances that a typical person uses math in their daily lives. It became near impossible to quantify that number because it was too frequent. The study had to be stopped because subjects could carry on with their normal daily activities because they had to report every time, they used math. It occurred so frequently, that they were distracted to heavily from their daily routines.

First grade math concepts cover a range of mathematics topics. These are the math concepts that students should understand by the end of the first grade based on the National Mathematics Standards.

Numbers and Operations concepts taught in the first grade include the use whole numbers in a variety of arithmetic and real world situations. Students apply addition, subtraction, division, and multiplication to problems and differentiate between the four operations. They use various strategies for using whole numbers to solve real and simulated situations. First grade students additionally study basic fractions such as 1/2, 1/4, etc. They use calculators, along with traditional tools to solve arithmetic operations.

Geometry concepts are taught by developing an understanding of two and three dimensional objects, such as: squares, rectangles, triangles, circles, cubes, rectangles, etc. They also study the objects to compare their parts related to two and three dimensional shapes. Additional areas of geometry and shapes focus on how close objects are to other objects in relation to how near or how far away they are to each other. Students apply the concept of distance in relation to maps and globes. In addition, they relate the ideas of geometry to other concept areas of mathematics. They learn to recognize geometric shapes in common everyday objects.

Algebra concepts concentrate on the study of patterns for repeating and growing patterns in the properties of objects. They develop an understanding of patterns in sounds, shapes, and numbers. They use changes in patterns to quantify and qualify descriptions.

Measurement concepts focus on the using standard and non-standard units of measurement to determine the relationships between different objects. For example: using their bodies, cubes, their feet, and other objects to find the length of an object. They learn to use estimations skills to explain measurement. This is also connected with geometry as they learn how to measure the length, area, volume, and mass of different objects. They learn how to measure all aspects of circles, prisms, and pyramids. They learn to use different traditional measuring tools for taking measurements of objects.

Data Analysis and Probability concepts are designed to have students use appropriate language to ask questions regarding data they collected. They sort and classify objects to make predictions of outcomes. They learn how to develop questions that will help them find the differences between two samples in a population. Describe predictions as likely or unlikely to happen based on their data. Represent data in using concrete objects, pictures, and graphs.

Problem Solving for first grade students focuses the development of problem solving strategies to help them develop a fundamental understanding of mathematics. Students use word problems and other real world simulations in problems solving situations.

Representation concepts focus on students learning to collect and organize data, then using the data to solve problems. Answers are presented as models that are numerical, written, physical, and social. They are able to draw graphs, charts, tables, and other forms to explain how they solved a problem.

Connection concepts are designed for first grade students to demonstrate how to make connections to real world applications and other subject content areas. This includes making connections with other concepts in mathematics.

Communicate their mathematics ideas in the form of sentences, drawings, posters, and multimedia applications is another concept that students need to master. This is used to ascertain their level of understanding as they explain mathematical concepts to other students and teachers.

Reasoning and Proof concepts are used to explain mathematical findings and problem solving techniques. This is necessary so that they develop skills on how to present logical arguments to math situations.

All of these mathematical concepts are used to develop a well rounded base knowledge of mathematical ideas and language as students’ progress to higher levels of mathematics.

Parents please read this!

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Seven Math Skills Your Child Will Learn in 1st Grade

Your child is heading to first grade! After the year in kindergarten, your first grader will be ready for some amazing growth. For many children, first grade is the year that they bloom as readers and mathematicians. Get ready to support your child’s mathematical growth by learning about first grade math skills.

In first grade, you can expect your child to learn about:

1. Addition and subtraction facts to 20

Now that your child has mastered the idea of adding and subtracting, they’re ready to practice math facts. This means getting faster when answering addition and subtraction problems to 20.

Help your child develop fluency by asking basic addition and subtraction problems — we find that using treats can help keep kids interested! If your first grader needs support, encourage the use of physical objects or fingers as problem-solving tools.

2. Addition and subtraction as inverse operations

Your child probably understands the concept of addition as “putting together” and subtraction as “taking apart.” In first grade, children are encouraged to see the connections between addition and subtraction. Your child will learn how addition and subtraction are inverse operations, or that one is the opposite of the other, and create “fact families” of related addition and subtraction problems.

When working with addition and subtraction, ask your child to see connections. For example, if your child has four dolls and three cars, ask how many toys there are in all. Then ask how many toys there would be if the four dolls are taken away.

3. Count and write within 120

Your child has probably mastered counting to 20. But in first grade kids will learn to count all the way up to 120! That’s not all. Kids will be expected to not only count, but write, the numbers. This is great practice for understanding multi-digit numbers.

At home: Encourage your child to write numbers whenever possible. Talk about how two-digit numbers are made up of tens and ones and how three-digit numbers are made up of hundreds, tens, and ones. Just looking closely at multi-digit numbers together can be a great learning opportunity.

4. Add within 100

Now that your child has an understanding of numbers past 100 as well as basic addition and subtraction facts, it’s time to practice adding within 100. Children will practice adding one-digit numbers to two-digit numbers using strategies like counting on and number charts. Children can practice adding larger numbers with the help of a 1-100 chart.

First graders are also ready to practice adding and subtracting 10s to and from two digit numbers.

At home: Help your child see patterns when adding and subtracting 10s. For example, after solving a problem like 59 — 10 = 49, point out to your child that 49 has one less 10 than 59. This is another great way to learn about place value.

5. Measure objects

In first grade, kids learn how to measure using rulers and more unusual things like paper clips. After taking measurements, children compare and order objects by length.

At home: Kids love measuring things around the house, so keep a couple of rulers handy. Pay attention to how your child is using a ruler and taking measurements. Sometimes kids don’t quite measure from end to end, so they might need a bit of help.

6. Tell time to hour and half hour

One of the trickiest concepts first graders will learn is to tell time. Using analog clocks is confusing, especially when kids are more used to seeing digital clocks. In first grade, your child will learn about the big and little hands of a clock and will practice telling time to the hour and half hour.

At home: Get hold of an analog clock for your home (either a real one or one made just for learning). Talk with your child about the time and how the hands move around the clock. Remember to just focus on telling time to the hour and half hour to start!

7. Understand basic fractions

First graders also get an introduction to fractions as equal shares. They will learn how to divide into equal groups and learn basic fractions like ½, ⅓, and ¼. First graders usually have a good understanding of fairness, so practicing making equal shares should be a relatively easy task for them!

At home: Help your child to divide pizzas, pies, and sandwiches into equal shares. As you do, talk about the fractions of the whole that you created.

First graders are ready to dive deep into mathematical concepts. Find time to connect with your child about classroom learning and get ready to have some fun!

Written by Lily Jones, Lily loves all things learning. She has been a kindergarten & first grade teacher, instructional coach, curriculum developer, and teacher trainer. She loves to look at the world with curiosity and inspire people of all ages to love learning. She lives in California with her husband, two kids, and a little dog.

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Typical First Grade Math Curriculum

Carol Bainbridge has provided advice to parents of gifted children for decades, and was a member of the Indiana Association for the Gifted.

Updated on June 13, 2020

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In kindergarten, children are introduced to numbers and math concepts. In first grade, the math skills they learn to build on the concepts they should have learned by the end of kindergarten. They will gain a better understanding of number concepts and will expand their math abilities. The specific goals for a first-grade class can vary a bit from state to state and from school to school, but there are some general expectations.

Math Skills a First Grader Is Expected to Learn

In general, your child will be expected to perform the tasks on this list by the end of first grade.  

Numbers and Counting

• Count by 1s, 2s, 5s, 10s, and 25s past 100
• Read, write, and understand numbers to 999
• Identify numbers in the ones and then tens place in a two-digit number
• Demonstrate an understanding of the parts-to-whole relationship by modeling simple fractions (1/2, 1/4, and whole) using manipulatives and pictures

Classifying and Estimating

• Classify familiar two- and three-dimensional objects by common attributes (color, position, shape, size, roundness, number of corners) and explain which attributes are being used to classify the objects
• Estimate answers to addition or subtraction problems and then solve the problem and compare the answer to the estimation (Ex: How many quarters do you need to buy an ice cream bar that costs $1.25?)
• Estimate number of objects in a collection (i.e. number of circles on a page, number of marshmallows in a bag, etc.)

Shapes, Graphs and Data Analysis

• Identify and describe one- and two-dimensional objects (circles, triangles, squares, rectangles, spheres, cylinders, rectangular prisms, pyramids, cones, and cubes)
• Identify, describe, and extend simple repeating patterns (i.e. 1, 3, 5 — next number is 7
• Collect and organize data and record it in tally charts, tables, bar graph, and line graphs

Measuring and Comparing

• Measuring in standard and non-standard units
• Compare volume of liquids in containers of different sizes
• Compare the length, weight, and volume of two or more objects by using direct comparison or a nonstandard unit
• Demonstrate an understanding of the concepts of less than, equal to, or greater than by comparing and ordering whole numbers to 100 using the symbols for those concepts ()
• Identify one more than, one less than, 10 more than, and 10 less than some other number
• Order objects by weight from lightest to heaviest

Time and Money

• Count combination of quarters, dimes, nickels, and pennies to at least $1.00
• Tell time to the nearest quarter-hour on both a digital and analog clock
• Relate time to events (longer, shorter, before, after)
• Read a calendar and identify the month, date, and days of the week

Adding and Subtracting

• Add and subtract to and from 30
• Add three one-digit numbers
• Solve addition and subtraction problems with one- and two-digit numbers
• Demonstrate an understanding of mathematical symbols (+, -, =)
• Create and solve problems with a known answer (i.e. 3 + __ = 5)
• Solve simple story problems

What Should You Do If Your Child Can Perform These Tasks Before First Grade?

Some mathematically gifted children may be able to perform some of the tasks on this list before the end of first grade. For instance, they may be able to add and subtract single-digit numbers in their heads. Some may even be able to add and subtract double-digit numbers in their heads. And a few are even able to do some of it before they enter kindergarten.

If your child is one of those kids who can perform these tasks (and possibly more) and is not yet in first grade, you have a few options. One is to keep your child where he is in school and provide enrichment at home. If your child is happy where he is and is not complaining about or frustrated by any lack of challenge, this could be a good option.

You can provide enrichment with supplemental materials at home, in community programs, or online sites like the Khan Academy.

However, if your child needs the challenge at school, you have a couple of other options to try, depending on what the school has to offer and is willing to do for your child, as well as what your child’s overall strengths are. If your child is advanced in math, but not in other areas, you can see if the teacher can provide some differentiated instruction in math. Your child’s school might also have a pullout program that provides kids with enrichment and challenge in specific areas, such as math.

If your child is globally gifted, you might try to explore the possibility of a grade skip. Keep in mind that your child should be socially and emotionally prepared to be with older children (most are) for this option to work.

Chances are that you won’t have much of a choice. Not all teachers differentiate and not all schools have pullout programs. And most schools seem to resist grade skipping. That means that you may be looking at supplementing your child’s learning at home. However, your chances are better if you can document what your child is able to do in math and show it to the school officials.

1 Source

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1. Common Core Standards Initiative. Grade 1: Introduction.

By Carol Bainbridge
Carol Bainbridge has provided advice to parents of gifted children for decades, and was a member of the Indiana Association for the Gifted.