Assignment 4

Math Lesson: Expanded Notation

Grade Level: 4

Lesson Summary: The teacher begins by making sure students can use place value to identify the value of different digits in given numbers. Students learn how to write numbers in standard notation, written form, and expanded notation. For guided practice, groups of students play a matching game. For independent practice, students write numbers in all three forms. Advanced learners will compare numbers written in different forms, and struggling learners will use a place value chart to help them with expanded notation.

Lesson Objectives:

The students will know…

· How to write numbers in standard notation, written form, and expanded notation.

The students will be able to…

· Write numbers in standard notation, written form, and expanded notation.

Learning Styles Targeted:

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Visual

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Auditory

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Kinesthetic/Tactile

Pre-Assessment: Give each student a copy of the Pre-Assessment*. Make sure students understand the directions, and allow students to work independently. When students finish, review the correct answers as a class. Reteach place value concepts, as necessary.

Whole-Class Instruction

Materials Needed: 1 piece of chart paper, writing utensils, Example Chart Paper* for teacher reference, 1 set of pre-cut and shuffled cards from the Matching Game* per group of students, 1 copy of the Independent Practice* per student, writing utensils

Procedure:

1) Tell students you want to make sure they could identify the value of different digits in numbers, because they need that skill to learn how to write numbers in a new way. Post a piece of chart paper, and divide it into three sections. See the Example Chart Paper in supplemental resources, if necessary. Tell students that they are going to learn three different ways to write numbers. Title the chart paper Three Ways to Write a Number.

2) Write standard form in the first section of the chart paper. Tell students that standard form is the most common form of writing a number, and record the definition beneath the title. Write a few examples of numbers in standard form under the definition. See the Example Chart Paper.

3) Write written form in the second section of the chart paper. Tell students that written form is when a number is written out in words, and record the definition beneath the title. Ask students to look at the first number written in the standard form section, 32. Explain that they should think of the words that they say when they read the number 32. Those words are used in the written form. Show students how to write “thirty-two” beneath the definition. See the Example Chart Paper, if necessary. Repeat this process for the other numbers that you wrote in the standard form section. Students should be able to see the same numbers written in both standard notation and written form.

4) Write expanded notation in the third section of the chart paper, and tell students that this is when it is important for them to know the value of digits in a number because expanded notation involves breaking a number down by its place value. Record the definition beneath the title. Have students look at the first number in the standard form section, 32. Point to the 3, and ask students, “What is the value of the 3 in 32?” Elicit responses until a student says, “30.” Record 30 in the blank space beneath the definition. Point to the 2, and ask students, “What is the value of the 2 in 32?” Elicit responses until a student says, “2.” Record 2 beside the 30, and add an addition symbol in between the two. Point out that if you add 30 + 2, the sum is 32. Explain that 30 + 2 is the expanded notation for 32. Repeat this process for the remaining numbers that you wrote in both the standard form and written form sections. Students should be able to see the same numbers written in all three sections.

5) Put students in groups of 2 or 3, and give each group a set of pre-cut cards from the Matching Game. Tell students to place the cards face down on the table in an array. Explain the rules of the game to students. The group should decide the order in which the students will play. Player 1 will turn over two cards. If the two cards describe the same number, player 1 gets to keep the match and play again. If the two cards do not describe the same number, player 1 should turn over the cards again, and play passes to player 2. Play continues until all matches have been made or until time is up. The player who has the most matches wins.

6) When time is up or all groups have finished, collect Matching Games from groups. Give each student a copy of the Independent Practice, explain the directions, and allow students to work independently.

Advanced Learner

Materials Needed: 1 copy of the Advanced Learner Independent Practice* per student, writing utensils

Procedure:

1) Give each student a copy of the Advanced Learner Independent Practice, and explain the directions. If necessary, do one example problem as a group. When students understand what to do, allow them to work independently.

Struggling Learner

Materials Needed: 1 copy of the Struggling Learner Activity* per student, 1 copy of the Struggling Learner Activity* to project under a document camera, a document camera connected to a projector, writing utensils

Procedure:

1) Give each student a copy of the Struggling Learner Activity, and project a copy of it under a document camera. Tell students that they will use place value charts to help them write numbers in expanded notation. Have students look at the first number, 17,238. Show students how it has been organized in a place value chart. Point to the 1 in the ten thousands place. Ask students, “How much is 1 ten thousand?” Elicit responses until a student says, “10,000.” Record 10,000 on the line beside “Expanded Notation” on the projected copy. Have students do the same. Repeat for the digits 7, 2, 3, and 8. Show students how to place addition symbols in between each number to finish the expanded notation. If students are still struggling, lead them through problem 2 as well. When students are ready, allow them to finish the remaining problems on their own.

2) After students have completed all of the questions, have students look at the first number on the page, 17,238. Tell students that you are going to help them practice saying the numbers aloud. Tell students to use a finger to cover the number behind the comma. Ask students, “What number do you see?” Students should say 17. Explain that the comma is placed after the thousands place; therefore, the comma says “thousand.” Have students say “seventeen thousand.” Have students use their finger to cover the number before the comma. Ask students, “What number do you see?” Students should say 238. Have students remove their fingers and put the whole number together by saying “seventeen thousand, two hundred thirty-eight.” Repeat this process for the remaining numbers on the page.