Place value understanding is the core of math. If students do not have a strong conceptual understanding of it, then they will not have the confidence or the skills to be successful in their math education. As a result, it is critical for elementary teachers to help students build a deep understanding of place value Read below to learn more!

This blog post will...

- explain why it's important for you to teach place value
- identify the essential understandings of place value in 1st, 2nd, 3rd, 4th, and 5th grade
- provide a list of common misconceptions students have about it so you can anticipate them and proactively address them

**WHY IS LEARNING ABOUT PLACE VALUE IMPORTANT?**

You should always provide your students with a purpose for learning. This can be done by explaining to them why place value is important and giving them examples of how we use place value in the real world.

Place value is the foundation of our number system. It is important because it allows us to comprehend a number’s meaning. We need place value to make sense of the order of numbers.

Relating the concept to your students’ own real-life experiences makes their work more interesting and meaningful. Real world examples of place value include how we determine the best price when shopping, how a delivery driver finds the shortest route to get a pizza to our house, or how a coach determines who swam the fastest. I encourage you to create a place value anchor chart with your students and record these examples and more.

**ESSENTIAL UNDERSTANDINGS of PLACE VALUE**

Essential understandings, also known as enduring understandings, are the big ideas we want our students to master. They help you focus your teaching on what you want your students to know, understand, and do. These “big ideas” derive from standards and serve as the foundation for designing all of your place value lessons and activities.

__FIRST GRADE__

In first grade, students should be able to...

- understand that the two digits of a two-digit number represent amounts of tens and ones.
- understand that 10 can be thought of as a bundle of ten ones — called a "ten."
- understand that the numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
- understand that 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 two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
- use place value understanding to add and subtract within 100 (including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10).
- use place value understanding to mentally find 10 more or 10 less than any given two-digit number.
- use place value understanding to subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90.

__SECOND GRADE__

In second grade, students should be able to...

- understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.
- understand that 100 can be thought of as a bundle of ten tens — called a "hundred."
- understand that the numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
- count within 1000 and skip-count by 5s, 10s, and 100s.
- read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
- compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.
- use place value understanding to fluently add and subtract within 100.
- use place value understanding to add up to four two-digit numbers.
- use place value understanding to add and subtract within 1,000.
- use place value understanding to mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.
- use place value understanding to explain why addition and subtraction strategies work.

__THIRD GRADE__

In third grade, students should be able to...

- use place value understanding to round whole numbers to the nearest 10 or 100.
- use place value understanding to fluently add and subtract within 1,000.
- use place value understanding to multiply one-digit whole numbers by multiples of 10 in the range 10-90

__FOURTH GRADE__

In fourth grade, students should be able to...

- recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
- read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.
- compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
- use place value understanding to round multi-digit whole numbers to any place.
- use place value understanding to fluently add and subtract multi-digit whole numbers.
- use place value understanding to multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers.
- use place value understanding to find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors.

__FIFTH GRADE__

In fifth grade, students should be able to...

- recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
- explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
- read, write, and compare decimals to thousandths.
- use place value understanding to round decimals to any place.
- use place value understanding to fluently multiply multi-digit whole numbers.
- use place value understanding to find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors.
- use place value understanding to add, subtract, multiply, and divide decimals to hundredths.

**COMMON STUDENT MISCONCEPTIONS ABOUT PLACE VALUE**

- In order to effectively teach your students about place value you must anticipate, identify, and correct and misconceptions or misunderstandings they have developed. To help you, I have listed some of the most common place value misconceptions your students are likely to make.
- The student does not understand the digit 0 as a placeholder. (Example: The child writes 8002 for eight hundred two.)
- The student does not understand the rule for reading numbers from left to right or reverses places within a number. (Example: The child identifies “28” as “82.”)
- The student thinks of the value of a number only in individual digits. (Example: A child thinks “38” = “3 + 8” instead of “30 + 8.”)
- The student is only able to conceive numbers as “ones.” (Example: A child thinks of 53 as 50 ones + 3 ones and is not able to move beyond and think of 53 as 5 tens and 3 ones or 53 tens and 0 ones.)
- The student is not able to “count on” and instead treats hundreds, tens and ones individually. (Example: A child who is asked to count a collection of base 34 ten blocks represented as 3 tens and 4 units counts, “10, 20, 30, 1, 2, 3, 4 instead of 10, 20, 30, 31, 32, 33, 34.)