Powers of Ten Applications
Lesson 6 of 22
Objective: Students will be able to solve multiplication and division problems with using a power of ten.
Students will begin this lesson with a task question that requires them to apply their knowledge of powers of ten and spatial reasoning. Currently my class is learning about the solar system in science so I devised a story problem centered on this content. I display the question and allow the students time to discuss the question in their groups.
A satellite is orbiting the Earth at 109 meters above the surface. You bought a telescope that could magnify 1000 times. If you are on the satellite, using your telescope, would you be able to watch what people on Earth are doing? Explain your thinking.
As students are discussing this problem I want them think of the difference between 109 and 1000. Students should be able to think of 109 as 1,000,000,000 and 1000 as 103. If they are able to see both of these numbers as a power of ten they should easily be able to answer the question: No, you wouldn’t be able to see what people were doing. You would need a telescope with more magnification or your satellite would need to be orbiting closer to the earth.
In this lesson I want students to focus on the process of multiplying and dividing with a power of ten. I want them not only to solve a problem set with this process but be able to explain their thinking. I provide the students with ten problems and ask them to work on them with their neighbor. I ask them to show and explain their thinking. In previous lessons we have showed the movement of the decimal by drawing decimal jumps underneath the number.
Today you’re going to work with your neighbor to solve a set of ten problems. While you’re working on these I want you to show your thinking by using decimal jumps to show the movement of the decimal. I also want you to explain your thinking in each step of solving the problems. You can use your decimal diagram for reference if you get stuck. Once we’re done I will have some brave souls come up and share their thinking.
I allow the students about ten minutes to work on the problems. During this time I circulate the room and look for students who might need some extra help. The most common problem I find among students is their inability to determine which direction the decimal goes. I get them focused on what’s happening in the problem. Is the number getting bigger or smaller when you multiply? Then I have them compare that information to the work. Well then, does the number you're working with have to be bigger when you're done with our decimal jumps? This seems to get students back on track.
Video place holder of students explaining their answers
To wrap up this lesson I have students play a quick game with dice. The concept of the game is to have students solidify the idea that powers of ten are multiples of ten. For example, 10 x 10 x 10 x 10 = 104 = 10,000.
I explain the game to the students and model a turn on the projector. I allow them to play with a partner for about ten minutes. At the end of the game I bring students back to the whole group and ask them to tell me something they know about powers of ten. I have several students share their thoughts.
Powers of Dice Game
In this game, students roll two dice and use those two numbers to create a two-digit number. Then they roll another dice to determine the number of multiples of ten. The students multiply or divide the two-digit number by the multiples of ten.
Rules: Partnerships are given three dice. Partners take turns being the roller. The roller rolls two of the dice and determines the two-digit number they will be using and records it on their whiteboard. The roller then rolls the remaining dice to determine the number of tens they will have. The other player tells the roller if they should multiply or divide by the multiples of ten. The roller writes out the information on their whiteboard and solves the problem. They must then show the other player their work so it can be checked. The partnership switches roles and play continues.
Video place holder of students playing game.