Place value is a cornerstone concept in elementary math, serving as the foundation for understanding large numbers, decimals, and mathematical operations. Students’ understanding of place value in math deepens and expands as they progress through 3rd, 4th, and 5th grades.
Each year’s standards build off the previous year’s standards, which makes understanding each grade level’s place value standards essential. When we look at place value in math standards as a scope and sequence, we can set better learning targets, mastery expectations, and differentiation strategies for our students.
This blog post outlines each grade’s key place value standards and the connections between grade-level standards to help teachers build students’ confidence and mastery.
Place Value in Math Goals
3rd Grade: Use place value understanding to perform multi-digit arithmetic. The goal in 3rd grade is for students to use place value to solve problems with multi-digit numbers.
4th Grade: Students should generalize their understanding of place value for multi-digit numbers and use that understanding, along with properties of operations, to perform multi-digit arithmetic. The goal in 4th grade is for students to use place value to understand and perform operations with multi-digit whole numbers.
5th Grade: Understand the place value system and perform operations with multi-digit whole numbers and decimals to hundredths. The goal is for 5th graders to understand how the place value system works and use it to perform operations with multi-digit whole numbers and decimals to the hundredth place.
As you can see, the place value in math goals build off each other, but fully understanding how the place value system works is expected until grade 5. Remembering these goals as you look at each grade level’s place value standards is essential.
Place Value in Math Standards Language
standard algorithm and when they should be using other strategies. There are multiple times throughout 3rd, 4th, and 5th grade standards when the ways students should solve math problems are specified. The language is repetitive but can also be confusing. So below is a vocabulary you can refer back to as you navigate the standards.
Strategies are different methods or tricks for making solving problems easier. For example, you might break a problem into smaller parts or use easier numbers to help find the answer.
Algorithms: These are specific rules or steps to follow when solving a problem—for example, the steps for adding or subtracting numbers in a particular order.
Concrete models: These are real objects or tools, like blocks, counters, or cubes, that you can touch and move around to help solve problems. For example, you might use blocks to show how to add or subtract.
Drawing pictures: This means drawing shapes or images to represent numbers. For example, you might draw dots or lines to show how to add or group things together.
Use strategies and algorithms based on place value: this refers to teaching students to understand how numbers are built by looking at the value of each digit. Students should be able to solve math problems by breaking them into smaller parts according to their place value.
Example: 59 + 35 = (50 + 30) + (9 + 5)
Use strategies based on the properties of operations: This refers to students using the rules of operations (i.e., communitive, associative, and distributive properties) to solve problems.
Example: 8 × 27 = 8 × (20 +7) = (8 × 20) + (8 × 7)
Use strategies based on the relationship between addition and subtraction: this refers to students understanding that addition and subtraction are inverse operations of each other and can use their knowledge of one operation to solve problems related to the other.
Example: 340 + 210 = 550 is inverse of 550 – 340 = 210
Use strategies based on the relationship between multiplication and division: this is similar to the example above but with multiplication and division. Students understand that multiplication and division are inverse operations.
Example: 20 × 10 = 200 is inverse of 200 ÷ 20 = 10
Use the standard algorithm: solving a math problem using a step-by-step method.
Example: Line numbers up according to place value and add them column by column, starting on the right and moving left.
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Below are the place value concepts broken up by skill. This allows you to see how the skill is developed from 3rd to 5th grade. I’ve linked a grade-level standards-based activity to each standard you can use with your students to practice each specific skill.
Place Value in Math: Rounding
Rounding numbers simplifies a number while keeping it close to the original value. Look at how this skill is built through 3rd, 4th, and 5th grade.
In 3rd grade, students are expected to round numbers to the nearest 10 and 100. In 4th grade, students build upon that and round whole numbers to any place value (whole number less or equal to 1,000,000). In 5th grade, students round decimals to any place (decimals to the thousandths).
Place Value in Math: Addition and Subtraction
In 3rd grade, students add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. (See the definitions of each of these strategies above).
In 4th grade, students add and subtract multi-digit whole numbers using the standard algorithm.
It is important to note that the standard algorithm is not expected until 4th grade. In 3rd grade, the goal is for students to use various strategies and their knowledge of place value to add and subtract numbers.
In 5th grade, the standard expands beyond whole numbers and includes adding and subtracting decimal numbers to the hundredth place. Again, this standard goes back to using models, drawings, knowledge of place value, order of operations, and the connection between addition and subtraction to solve problems, not the standard algorithm.
Place Value in Math: Whole Number Multiplication
In 3rd grade, multiplication and division are explored in operations and algebraic thinking standards. However, one 3rd-grade place value standard expects students to multiply one-digit whole numbers by multiples of 10 in the range 10–90 using place value and math rules (ex. 30 × 4). This standard helps students build their knowledge of multiplying by 10.
In 4th grade, students are expected to multiply whole numbers up to four digits by one digit (e.g., 2,358 × 5) and two digits by two digits (e.g., 24 × 19). Students should solve problems using strategies based on place value and the order of operations. The standard also states that students should use illustrations such as rectangular arrays and area models to multiply numbers.
In 5th grade students are expected to multiply multi-digit whole numbers using the standard algorithm. It is important to note that the standard algorithm isn’t expected until 5th grade.
Place Value in Math: Whole Number Division
There is no 3rd-grade place value standard for division. Division concepts are explored in operations and algebraic thinking standards for 3rd graders.
In 4th grade, students find a whole number quotient with and without remainders. These division problems can have up to four-digit dividends but only one-digit divisors. Students should use place value, order of operations, and the connection between multiplication and division to solve these problems.
In 5th grade, students build upon 4th-grade division standards by finding whole number quotient with and without remainders. These division problems can have up to four-digit dividends but now have two-digit divisors. Students should use place value, order of operations, and the connection between multiplication and division to solve these problems. Using the standard algorithm for division is not expected until 6th grade.
5th grade also has a standard for multiplying and dividing decimals to the hundredth place. Students should use place value, order of operations, and the connection between multiplication and division to solve these problems. Decimals are introduced in 4th grade in fractions standards but not fully explored in place value until 5th grade.
*The following concepts do not have 3rd grade palace value standards, only 4th and/or 5th grade standards.
Place Value in Math: Place Value
In 4th grade, students work to understand the place value system by recognizing that in a multi-digit whole number, a digit in one place is 10 times more significant than what it represents in the place to its right (ex., the 5 in the number 250 is ten times greater than the 5 in the numbers 25).
Students are to begin understanding patterns in our palace value system by looking at numbers increasing.
In 5th grade, the goal is for students to understand how the place value system works by recognizing that a digit in one place is 10 times more significant than it would be in the place to its right (ex., the 5 in the number 250 is ten times greater than the 5 in the numbers 25). A digit is 1/10 of what it represents in the place to its left (ex., The 5 in the number 2.5 is 1/10 the value of the 5 in the number 25). Students are working with both whole and decimal numbers.
Place Value in Math: Read and Write Numbers
In 4th grade, students work to read and write multi-digit numbers using base-ten numerals (ex. 13), number names (ex. thirteen), and expanded form (ex. 10 + 3). The whole number should be less or equal to 1,000,000.
In 5th grade, this standard is expanded to include decimals through thousandths. So in the number 13.25, students should be able to use the base ten numeral (13.25), the number name (thirteen and twenty-five hundredths), and expanded form 1 × 10 + 3 × 1 + 2 × (.1) + 5 × (.01).
Place Value in Math: Comparing Numbers
In 4th grade, students work to compare two multi-digit numbers based on place value using the symbols <,>, and =. These numbers are limited to being less than or equal to 1,000,000.
5th-grade standards for comparing numbers build on 4th-grade standards. In 5th grade, students must compare whole and decimal numbers to the thousandth place value.
Place Value in Math: Exponents
There are no 3rd or 4th-grade standards that work with exponents. In 5th grade, students look to find and explain patterns in the number of zeros of a product when multiplying a number by powers of 10. They also need to explain patterns in placing the decimal point when a decimal is multiplied or divided by a power of 10. Students work to understand that 100 can also be written as 10². Students can practice multiplying and dividing powers of 10 with whole numbers and exponents.
Place value is the backbone of number sense and mathematical operations. By understanding the progression of place value standards and using effective teaching strategies, teachers can ensure their students build a solid foundation for future math success. Whether mastering whole numbers in 3rd grade, tackling millions in 4th grade, or diving into decimals in 5th grade, place value provides the critical building blocks for mathematical thinking.
What are your favorite strategies for teaching place value? Share your tips in the comments below! Check out this blog for more activities to practice place value in math.
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