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Lesson Plan: Expanded Notation

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Students will create, read, and decompose large numbers.

Class: 4th Grade

Duration: One or two class periods, 45 minutes each

Materials:

  • paper or large note cards numbered 0 - 10 (enough for the whole class)
  • chalkboard, whiteboard, or overhead projector

Key Vocabulary: place value, ones, tens, hundreds, thousands, ten thousands, hundred thousands, expanded notation (or expanded form)

Objectives: Students will demonstrate their understanding of place value to create and read large numbers.

Standards Met: 4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.

Lesson Introduction: Ask a few volunteer students to come to the board and write down the largest number that they can think of and read aloud. Many students will want to put endless numerals on the board, but being able to read the number aloud is a more difficult task!

Step-by Step Procedure:

  1. Give each student a sheet of paper or large note card with a numeral between 0 - 10.

  2. Call two students up to the front of the class. Any two students will work as long as they are not both holding a 0 card.

  3. Have them show their numerals to the class. For example, one student is holding a 1 and the other is holding a 7. Ask the class, “What number do they make when they stand next to each other?” Depending on where they are standing, the new number is 17 or 71. Have students tell you what the numbers mean. For example, with 17, the "7" means 7 ones, and the "1" is really 10.

  4. Repeat this process with several other students until you are confident that at least half of the class has mastered the two-digit numbers.

  5. Move on to three digit numbers by inviting three students to come to the front of the class. Let’s say that their number is 429. As in the above examples, ask the following questions:
    • What does the 9 mean?
    • What does the 2 mean?
    • What does the 4 mean?
    As students answer these questions, write the numbers down: 9 + 20 + 400 = 429. Tell them that this is called “expanded notation” or "expanded form". The term “expanded” should make sense to many students because we are taking a number and expanding it into its parts.

  6. After doing a few examples at the front of the class, have the students begin writing the expanded notation down as you invite students up to the board. With enough examples on their paper, when it comes to more complex problems, they will be able to use their notes as a reference.

  7. Continue adding students to the front of the class until you are working on four-digit numbers, then five-digit, then six. As you move into the thousands, you may want to "become" the comma that separates thousands and the hundreds, or you can assign the comma to a student. (The student that is always wanting to participate is a good one to assign this to - the comma will be called upon often!)

Homework/Assessment: You can give your students a choice of assignments - both are equally long and equally difficult, though in different ways:

  • Have students write 987,654 in expanded notation OR the largest number that they are able to.
  • Have them write 20,006 in expanded notation (Be sure to go over this one in class the next day.)

Evaluation: Write the following numbers on the board and have students write them in expanded notation:
1,786
30,551
516

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