Standards Met: CCSS.Math.Content.4.NBT.A.2; 5.NBT.A.3
Objective: Use knowledge of place value to order numbers from least to greatest
What You Need: Class set of the following: sheet of paper with blanks for a nine-digit number, list of nine icebreaker questions that have one-digit numeric answers (e.g., “What is the first digit in your address?” “What is your shoe size?”)
What to Do: This is a great icebreaker to get your students moving and talking about place value at the start of the new school year.
Begin by passing out the following to each student: a sheet of paper with blanks for a nine-digit number and a list of nine icebreaker questions that have one-digit numeric answers. Then, tell students they will ask one another the nine questions (one classmate per question). If an answer is not a whole number (such as a shoe size of 7½), they should round up to the nearest whole number before writing it in one of the blanks on their paper.
Once students have filled in all nine blanks, have them add commas or a decimal point between some of the blanks to make the numbers easier to read. If you want to do whole numbers only, as you might at the beginning of fourth grade, you’ll add only commas (e.g., 234,521,578). For fifth graders, or advanced fourth graders, you can add commas and a decimal point and make the number something like this: 2,345,215.78. (Or simply use four or five questions and digits to make it easier.) Finally, have students line themselves up from least to greatest number.
Live Number Line
Standards Met: CCSS.Math.Content.4.NBT.A.2; 5.NBT.A.3
Objective: Apply knowledge of place value to order and compare numbers
What You Need: Colored electrical tape to create a number line divided into segments (tenths and/or hundredths), note cards with numbers expressed in decimal format, camera, projector
What to Do: Chris Latham, a former math instructional coach at Groveton Elementary School in Alexandria, Virginia, says the biggest block to understanding place value is lack of number sense. “Kids need to know that our base-10 number system is the most efficient way to represent numbers. Once they understand how numbers really work in this system, they’ll be able to internalize the ideas behind place value.” To help students build this understanding, Latham suggests having them become numerical values on a giant number line.
Start by giving each student a note card with a different numeral between 0 and 1 expressed in decimal form. Without using the number line yet, ask students to stand in order from least to greatest. “Having students talk about their thinking gives you a good indication of how well (or not) they understand place value,” says Latham. (Some students, for example, may think that .39 is larger than .7, because 39 is greater than 7.) Once students are lined up holding their numerals in the order they think is correct, take a photo of the line to record their positions.
Next, label each end of the number line with a 0 and a 1, and ask students how the smaller lines in between should be labeled. If they need help, direct them to count how many segments make up the distance between 0 and 1. Using sticky notes, pairs or teams of students can label tenths expressed in decimal form (and hundredths, when ready). When the entire number line is labeled, have students once more stand in order on the line from least to greatest, and take another photo. Project both photos together and let students compare the results.
Standards Met: CCSS.Math.Content.4.NBT.A.2; 5.NBT.A.3.A
Objective: Compare four different forms of the same number and understand that all represent the same quantity
What You Need: Signs marked A, B, C, and D to label each corner of the classroom; a projector to show various sets of numbers written in standard form, word form, expanded form, and expanded notation; writing paper
What to Do: Shametria Routt Banks, a former fourth- and fifth-grade teacher at Cactus Ranch Elementary School in Round Rock, Texas, puts a twist on the traditional Four Corners game. “The beauty of this strategy is that students must use what they know about place value to determine which representation is not like the others; however, there is more than one way to discriminate between the representations, so justification is key!” says Routt Banks, who blogs at The Routty Math Teacher.
First, review place value by showing an example of a number written in four different forms, with each form labeled as A, B, C, or D. Example: A. 156,347 (standard form); B. one hundred fifty-six thousand, three hundred forty-seven (word form); C. 100,000 + 50,000 + 6,000 + 300 + 40 + 7 (expanded form); and D. 1 × 100,000 + 5 × 10,000 + 6 × 1,000 + 3 × 100 + 4 x 10 + 7 × 1 (expanded notation).
Then, project a new number written in four different forms, labeled A, B, C, and D, with one form being incorrect. Have students work in pairs or small groups to determine which representation is incorrect, and jot down their justifications. (Give them a limited time to work, say, one to two minutes.) Ask students to go to the corner of the room labeled with the letter that represents the response they chose. Give each corner group an opportunity to discuss why they believe their choice is incorrect, and then have students take turns sharing their reasoning with the whole group.
To extend, read a number out loud and challenge students to write it in a form other than standard.
The Race to One
Standards Met: CCSS.Math.Content.4.NBT.A.1; 4.NBT.B.4
Objective: Apply understanding of tenths, hundredths, and thousandths to build one whole
What You Need: One sheet of drawing paper and one mini-whiteboard and marker per student, colored pencils, ruler, calculator, set of two dice per pair of students—one standard die and one with two sides each showing the following: 1/10, 1/100, and 1/1000
What to Do: Sharon Hooper, the gifted teacher at Milford Elementary School in Marietta, Georgia, recommends using a game called The Race to One to teach place value.
Put students into pairs. Hand out paper and have kids divide their sheet into two rows of five equal rectangles. Explain that all 10 rectangles together represent the number 1, and the first student in each pair to color in the whole sheet will win “the race to one.”
Have students take turns rolling the dice and multiplying the two numbers rolled (for example, 6 × 1/100 = 6/100). They should convert their fractions to decimals, which in this case would be .06, and record their answers on their whiteboards. Next, they should color in the corresponding number of parts on their rectangle sheets. So, for example, if they roll a 1 and a 1/10 (.1), they color in one of their 10 rectangles. If hundredths are rolled, the student may use a pencil and ruler to divide one of the tenths boxes into 10 equal parts and color in the number of hundredths rolled. If thousandths are rolled, the student may divide one of the hundredths boxes into 10 parts and color in the numbers of thousandths rolled.
When the last number needed to complete one whole is rolled, the entire piece of drawing paper should be colored in. To check their work, students will add the decimals recorded on their whiteboards to make sure that the answer equals 1.
Photo: Mike Kemp/Blend Images/Getty Images