## Examining Estimation

### Denise SimonsonBay District Schools

#### Description

Students participate in various activities which help them understand and explain the difference between an estimate and an exact amount.

#### Objectives

The student understands the relative size of whole numbers, commonly used fractions, decimals, and percents.

The student uses and justifies different estimation strategies in a real-world problem situation and determines the reasonableness of results of calculations in a given problem situation.

#### Materials

-Number Lines
-Dice
-Internet access (for online student lesson -Just About-)
-Assorted boxes and jars of miscellaneous items
-Fish Bowl with 2 sets of numbers from 0-9
-Math Practice Worksheet such as (Silver Burdett Ginn #P1-5, or a related estimation page)
-Math Paragraphs (example provided in procedures)

#### Preparations

1.Gather materials
2.Check the Internet stations to verify connectivity
3.Copy student worksheets to practice estimation
4.Write math paragraphs and related questions

#### Procedures

INTRODUCTION
1. Pair students. Each student rolls the dice and writes a two digit number. Explain to the students that their numbers will only range between 11-66.

2. Students use number lines (previously introduced) to round their numbers to the nearest 10.

3. Students compare how they rounded. (After activity, ask students to tell which rules they used to decide how to round a number.)

4. Give a definition of -estimate- and explain the difference between -estimate- and -exact.- During the discussion, have students use the words -more than,- -almost,- and -about- to describe some items in the classroom.

5. After discussion, ask questions such as: -Is \$0.23 an exact or estimated number?- (exact). -Is 34 baseball cards an exact or estimated number?- (exact).

GROUP WORK
Divide students into five groups for center work. Rotate groups every ten minutes.

Center #1 - Students work at the computers to complete the online student lesson -Just About- available from the Beacon Learning Center.

Center #2 - Students estimate the number of items contained in assorted boxes and jars.

Center #3 - Students draw numbers from a fish bowl to create two digit numbers. Using a number line, students round their numbers to the nearest 10.

Center #4 - Students complete Math Practice (P1-5) - Silver Burdett Ginn Math Series, or a related practice page. When finished, students check their answers together.

Center #5 - Students read -Math Paragraphs- and answer multiple choice questions about the paragraph. See example below:

Daniel's dad gave him almost 200 baseball cards. His mom gave him exactly 30 basketball cards and 20 baseball cards. His granddad gave him about 75 very old football cards.

1. Which word helps you know that 200 baseball cards is an estimate?
a. gave
b. baseball
c. almost

2. Which word helps you know that 75 very old football cards is an estimate?
a. gave
c. football

3. Which sentence below tells how many basketball cards Daniel received from his mom?

WRAP-UP
1. Ask students to give definitions and examples for -estimate- and -exact.- Ask this question: -Mary received \$2.00 as change from a purchase at Toys-R-Us. Is this an exact or estimated number?- (exact).

2. In their math journal, have students explain the difference between -estimate- and -exact- and list at least three ways to recognize estimated numbers.

#### Assessments

1.Observe student participation, listening for students' justifications of different estimation strategies and their understandings of the relative size of whole numbers as evidenced in their roundings.

(A checklist may be used to keep documentation of student responses, or a chart may be generated as students tell which rules they used to decide how to round a number as mentioned in step #3 of the introduction.)

2. Review students' math journal entries to see that they have a) accurately explained the difference between estimates and exact numbers, and b) listed at least 3 ways to recognize estimated numbers--ie, the presence of key words such as -more than-, -almost-, -about-.

3. Have students self-assess and self-check completed estimation practice pages (Silver Burdett Ginn #P1-5) until work is correct. Students should then pick one problem and explain how they solved it and/or explain how they can use estimation in real-world situations.