Warm-up: True or False: Decimals (10 minutes)
The purpose of this warm-up is for students to compare different ways of representing a decimal number. It will be important in this and future lessons to write a given decimal in a different form. For example, it is convenient to write 7.3 as 7.300 in order to compare it to 7.299.
- Display one statement.
- “Give me a signal when you know whether the statement is true and can explain how you know.”
- 1 minute: quiet think time
- Share and record answers and strategy.
- Repeat with each statement.
Decide if each statement is true or false. Be prepared to explain your reasoning.
- \(7.06 = 7.006\)
- \(7.06 = 7.060\)
- \(7.06 = 7.600\)
- “How did you decide if the second equation is true?” (I looked at the value of the digits in each place. They are all the same except for an extra 0. But 0 thousandths does not change the value of the number.)
Activity 1: Farther and Faster (10 minutes)
The purpose of this activity is for students to compare decimals using the context of distance. Students should have access to hundredths grids, if they choose to use them. Monitor for students who compare the decimals using
- place value reasoning to compare the 1 tenth for Diego's throw with the 1 hundredth for Jada's throw
- hundredths grids for the decimal part of the throws
- number lines, recalling work from a previous course
When students decide to compare the decimals using number lines or hundredths grids, they are using appropriate tools strategically (MP5).
Advances: Conversing, Speaking
Materials to Copy
- Small Grids
- Groups of 2
- Display the image in student workbook.
- “Have you ever thrown a frisbee?”
- Poll the class.
- “A frisbee is a disc. In the Olympics, there is an event called the discus throw. Participants try to throw a metal disc as far as they can.”
- 2 minutes: independent work time
- 5 minutes: partner work time
- Monitor for students who use reasoning named in the activity narrative.
- Diego and Jada were competing to see who could throw the frisbee further. Diego threw the frisbee 5.10 meters. Jada threw the frisbee 5.01 meters.
Who threw the frisbee further?
Be prepared to explain your thinking.
- Tyler and Han were competing to see who could swim the length of the pool faster. Tyler swam the length of the pool in 35.15 seconds. Han swam the length of the pool in 35.30 seconds. Who swam the length of the pool faster? Be prepared to explain your thinking.
- Ask previously selected students to share their solutions.
- “Both problems are about comparing decimals. How are the problems different?” (The units are different in the two problems. One is meters and the other is seconds. In one problem, the winner has the greater number and in the other problem, the winner has the lesser number.)
Activity 2: Farthest Frisbee Flight (20 minutes)
- using hundredths grids or other diagrams
- using expanded form and comparing the value in each place
Make hundredths grids available for students.
When students use strategies that are based on place value they are looking for and making use of place value structure (MP7).
Supports accessibility for: Memory, Conceptual Processing
Materials to Copy
- Small Grids
- Groups of 2
- Display: 0.01, 0.001
- “Which is greater? How do you know?” (0.01 because it’s a hundredth and that’s more than a thousandth or 0.001.)
- 6–8 minutes: partner work time
- “Get together with a different pair of students and list all of your distances for Tyler and for Priya in increasing order.” (Answers vary.)
- 4–5 minutes: group work time
- Han threw the frisbee farther than Diego. How far might Han have thrown the frisbee?
- Tyler threw the frisbee farther than Diego but less than 6 meters. How far might Tyler have thrown the frisbee?
- Mai threw the frisbee a shorter distance than Jada. How far might Mai have thrown the frisbee?
- Priya threw the frisbee a shorter distance than Jada, but more than 5 meters. How far might Priya have thrown the frisbee?
- Invite students to share their distances for Mai and Priya.
- “How did you find some possible distances for Mai?” (I could pick any number that was 5 or less so there were lots of choices, 5, 4, 4.7, 4.8)
- “How was finding a distance for Priya different than finding a distance for Mai?” (I had to pick a number that was bigger than 5 but Priya had just 1 hundredth. I could not find a number using just hundredths. I had to use thousandths because they’re smaller than hundredths.)
- “What strategies did you use to put the numbers in your group in order?” (We had some duplicate numbers so we needed to find those. We looked at the whole number and then the tenths, hundredths, and thousandths to find which number was the greatest.)
“Today we used place value understanding to compare decimals.”
\(0.51 = 0.510\)
\(0.52 = 0.520\)
“How is this helpful for determining numbers that come between these two numbers?” (We can name all the thousandths. There aren’t any hundredths between 0.51 and 0.52.)
“What is a number that is between 0.51 and 0.52? How do you know?” (0.513 because it has 3 more thousandths than 0.51 but it is still smaller than 0.52 which has an extra hundredth.)