The Meaning of Place Value

TEACHERS:
Jamy Myrmel / SUBJECT: Math
STANDARD:
  • 5.NBT.A.1: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.

OBJECTIVE (EXPLICIT):
  • Identify the place values from the millionths place to the hundred millions place.
  • Round numbers to each of these place values.

KEY VOCABULARY: Place Value, Decimal / MATERIALS: Blank place value chart, filled in chart
BEFORE / TEACHER WILL: Give each student a copy of ablank Place Value Chart. Tell students that you want them to complete the chart to the best of their ability. You might want to give students a hint by filling in the ones place together. Give students a few minutes to work, circulating the room as they write. Take note of which place values students already know and which ones they struggle with. During the lesson, focus mostly on the place values that students struggle with. Have students discuss their charts with their groups. / STUDENT WILL: Complete the blank place value chart to the best of their ability.
DURING / 1)TEACHER WILL: Give each student a copy of the Place Value Chart that has already been labeled. Project a copy of the same chart under a document camera. Tell students that they are going to use this chart to learn about place value.
2)Point out the decimal on the chart to students. Ask students why the decimal is a very important benchmark on the place value chart. Explain that place values to the left of the decimal grow larger; place values to the right of the decimal grow smaller. Draw an arrow starting at the decimal and moving left, and label it “getting bigger.” Have students do the same. Draw an arrow starting at the decimal and moving right, and label it “getting smaller.”
3)Explain to students that the place values that are to the left of the decimal are all larger than one and are divided into periods. Model for students how to bracket the ones, tens, and hundreds places into the units period, the thousands, ten thousands, and hundred thousands places into the thousands period, and the million, ten millions, and hundred millions into the millions period. Tell students that each period is separated by a comma.
4)Ask students what they notice about the first place value in each period. Elicit responses, leading students to see that the first place value is named the same as the period (with the exception of the units period). Ask students what they notice about the second place value in each period. Elicit responses, leading students to see that the second place value includes the word “ten” and the name of the period (with the exception of the units period). Have students underline “ten” in each of the appropriate place values. Ask students what they notice about the third place value in each period. Elicit responses, leading students to see that the third place value includes the word “hundred” and the name of the period (which the exception of the units period). Have students underline “hundred” in each of the appropriate place values.
5)After thoroughly observing and exploring the place values to the left of the decimal, have students look at the place values to the right of the decimal. Make sure students understand that the place values get smaller as they go further to the right. Have students look specifically at the endings to each of the words that name the place values, and ask them what they notice. Elicit responses until a student says that all of the place values end in “th.” Explain to students that these place values all represent fractions of one whole, so they have the fractional ending “th.” Have students underline the “th” in each of the place values as you model it on the projected copy.
6)Ask students if they notice anything else about the place values to the right of the decimal. Elicit responses, leading students to see that there is no “oneths” place value and that the place values are almost a direct mirror image of the place values to the left of the decimal. Show students how the order is the same as the place values to the left of the decimal, but reversed. Tell students that understanding all the patterns and commonalities of the place value system can help them remember the order of the place value chart.
7)Have students write in the number 586,124.79 into the appropriate places on the place value chart. Model the correct way to do it on the project copy of the place value chart. Make sure students understand how to read it aloud. If students struggle, explain to them how to use the periods to help them read the number aloud.
8)Tell students that you are going to discuss the different values of the digits in that number. Ask students, “What is the value of the 8 in this number?” Model a think aloud for students by saying, “I know the 8 is in the ten thousands place. If I change all of the smaller place values into zeroes, I can see the value is 80,000.” Ask students, “What is the value of the 5 in this number?” Remind students to use the place value to help them find the answer. Tell them to imagine that all of the smaller place values change into zeroes. Have students write the value of the 5 on their place value large enough for you to see and hold it up at your instruction. Stop and reteach, if necessary. Repeat for the other place values in the number 586,124.79.
9)If students need more practice finding the value of given digits and rounding, have them use the tissue to erase 586,124.79 and try some other numbers. Some suggested numbers are 23,446,102.389 and 1,985,388.453. / STUDENT WILL:
Think, pair, share
Copy teacher directions on their copy.
AFTER / TEACHER WILL:
Guide through the independent practice / STUDENT WILL:
When students understand how to use place value to find the value of digits, give each student an Independent Practice, explain the directions, and allow students to work independently. You may want students to use their place value charts to help them on the Independent Practice.

Name: ______Independent Practice

Place Value

  1. What is the value of the 6 in the following number? 85,311.68
  1. 0.06
  2. 0.6
  3. 6
  4. 60
  1. Which of the following numbers has a 3 in the thousandths place?
  1. 3,564.132
  2. 13,528.34
  3. 14,986.553
  4. 333,175.31
  1. Which of the following numbers has a 1 in the ten thousands place?
  1. 301,995.2
  2. 310,447.509
  3. 444,917.471
  4. 1,251,880.031
  1. What is the value of the 4 in the following number? 3,642.09
  1. 4
  2. 40
  3. 400
  4. 4,000
  1. What is the value of the 5 in the following number? 4.005

A. 0.005

B. 0.05

C. 0.5

D. 5

  1. Which of the following numbers has an 8 in the tenths place?
  1. 186.2
  2. 2,489.01
  3. 8,311.8
  4. 1,097,480
  1. What is the value of the 1 in the following number? 1,428,050.386
  1. 1
  2. 10,000
  3. 1,000,000
  4. 10,000,000
  1. Which of the following numbers has a 2 in the hundredths place?
  1. 202.25
  2. 235.14
  3. 1,762.32
  4. 45,875.2