Elementary math, grade by grade
The big math skills from kindergarten to 5th grade, how to build fact fluency without timed-test stress, and activities and games for each strand — with AI tools that draft the practice pages for you.
Elementary math is built in layers: counting and number sense in kindergarten, addition and subtraction with place value in 1st and 2nd grade, multiplication and fractions in 3rd, and multi-digit operations, fractions and decimals in 4th and 5th. Each layer depends on the one before, so gaps in early number sense show up later as trouble with facts, fractions and word problems.
The big skills by grade
| Grade | Major work of the year |
|---|---|
| Kindergarten | Count to 100 by ones and tens, compare numbers, add and subtract within 10, fluency within 5, name 2D and 3D shapes. |
| 1st grade | Add and subtract within 20 (fluency within 10), place value with tens and ones, measure length, tell time to the half hour. |
| 2nd grade | Fluency with sums and differences within 20, add and subtract within 1,000, money, time to five minutes, foundations of multiplication. |
| 3rd grade | Multiplication and division within 100 (products of one-digit numbers from memory), unit fractions, area and perimeter, time to the minute. |
| 4th grade | Multi-digit multiplication and division, equivalent fractions, adding fractions with like denominators, decimals to hundredths, angles. |
| 5th grade | Adding and subtracting fractions with unlike denominators, multiplying fractions, decimal operations, volume, the coordinate plane. |
This summary follows the Common Core State Standards for Mathematics, which many states use as written or adapted. For the standard codes and how to read them, see our Common Core standards guide.
Concrete, representational, abstract
- 1. Concrete — Students build the idea with objects: counters, base-ten blocks, fraction strips, coins.
- 2. Representational — They draw it: ten frames, number lines, arrays, tape diagrams.
- 3. Abstract — They write it with numbers and symbols — and can explain the drawing behind the numbers.
Moving through the three stages, and back again when a student is stuck, is one of the most reliable ways to build real understanding instead of memorized steps.
Math facts and fluency
Fluency means accurate, efficient and flexible, not just fast. Teach facts through strategies (doubles, make ten, the nines trick), then practice with games. Our guide to multiplication facts strategies gives the order to teach them, and math fact fluency games has 20 low-prep ideas for addition, subtraction and multiplication.
When a student needs more
Use short, frequent checks to find the exact skill that's missing, then teach it in a small group with manipulatives. Students with a disability that affects math may have accommodations or goals decided by their IEP or 504 team; see dyscalculia accommodations and IEP goals for math.
Practice pages in minutes
The Pluma worksheet generator drafts math practice for your grade, skill and level, with an answer key and differentiated versions when you need them. Review before you print, and never enter student names or identifiable information. Free to start, no card.
Create free accountFrequently asked questions
What math should students know by the end of elementary school?
By the end of 5th grade, students are expected to add, subtract, multiply and divide whole numbers fluently, work with fractions and decimals (including adding fractions with unlike denominators), understand place value to the thousandths, and solve multi-step word problems. Exact expectations depend on your state standards.
When should students know their math facts?
Under the Common Core and most state standards, students add and subtract within 10 fluently in 1st grade, know all sums of two one-digit numbers from memory by the end of 2nd grade, and know all products of two one-digit numbers from memory by the end of 3rd grade. Check your state's standards for the exact wording.
Are timed math tests bad?
Short timed tests can cause anxiety for some students and don't show which strategies a child uses. Many teachers build fluency with games, strategy practice and untimed checks, and use brief timed practice only as a personal goal, never as a public ranking.
What is the CRA approach in math?
CRA stands for concrete, representational, abstract. Students first learn a concept with physical objects, then with drawings or models, and finally with numbers and symbols. It's useful for all students and especially helpful for those who struggle with math.
Common Core standards
Learning centers
Classroom assessment