I invite students to the carpet to begin a conversation about mechanics.
Have any of you guys ever wondered what makes a car go? Mechanics need to know a lot about the way a car works in order to make repairs. How do you suppose they learn so much about cars? They spend a lot of time breaking down various parts of the car, like the engine, to figure out just how it all works.
Well today we are going to be the mechanics of math. We are going to explore how the relationship between the value of a place of a number changes by multiplying the number by power of ten.
I begin to model and explain what my students will be expected to do. I encourage students to collaborate on effective ways to explain and solve problems. I point out the importance of using mathematical terms and models.
As I demonstrate, I ask probing questions. For instances: How do you know? Can you show me another way? Can you explain how one concepts relates to the other?
MP7- Look for and make use of structure. This allows students to make connections between other mathematical ideas and application.
Hopefully my students will see how linking different skills of mathematics can assist them in understanding and developing efficient strategies for solving problems.
In this section I want students to have plenty of time practicing building models to show the difference between the value of the place of a number by multiplying by the power of ten. Students need plenty of practice in order to understand how this pattern can be used to help them solve problems.
For struggling students I will shorten their place value chart up to the 10's place, and circle the number in the tens place to help them remember the number to be expressed.
3 x 3 compared to 3 x 30
2 x 4 compared to 2 x 40
1 x 4 compared to 1 x 40
To get students to see the relationship between the products, I ask students what is the product of 3 x 3? (9). What is the product of 3 x 30? (90) What does the nine represent in the first problem, what does the nine represent in the second problem? How does the the value of nine change? This prompts students to look for obvious patterns, and use different reasoning and strategies for those detected patterns.
Some students explain using very vague language. As students are explaining I encourage them to use math terms, so that they can begin to explain their reasoning more fluently.
Can you create a problem of your own? How would you do that? What do you think will happen?
MP8-Look for and express regularity in repeated reasoning. This skill helps students reason mathematically.
To end this part of the lesson I may ask 1-2 volunteers to share what they noticed during the activity.
In this section I want students to practice showing the different between multiplying by one digit and the power of 10 so they can begin to detect the pattern. Identifying patterns, creating equations to represent relationships between place value of a number by multiplying by the power of ten is a significant part of learning multiplication and division in the curriculum. MP8
Students work independently illustrating multiplication problems using base ten drawings, and explaining the process to help them to become better mental thinkers. As students are working I will circle the room to check for understanding. Students Practice.docx
How many ones do you need ? Why?
How many tens do you need? Why
Is there a relationship between the two given problems? If so, why? How do you know?
What happens when you multiply by ones? How does the value of the number change in the first and second problem? explain
What happens when you multiply by tens? How does the value change from the first problem?
What are some other examples of the pattern you are using? Compare your example to the given problem? What do you notice?
Students were able to see the difference between multiplying by ones and by the power of ten. Most students relied heavily on their base ten skills, while other students used the properties of operations, and illustrations to see the break-down of solving.
For struggling students I will circle the number in the tens place, so they can remember the value of the digit.
When their given time is up, I tell them to compare their work by turning and talking to their neighbor. This helps reinforce their learning through self and peer talk. After the turn and talk, I invite 1-2 students to come back together to share how they solved their problems.
In this section students will complete their exit ticket. I tell students it is time for you all to show me what you know! I encourage students to use base- tens to help them solve.
As students are working, I circle the room to check for understanding; however, I will not probe students much. Simply because, I want to see what they are thinking on their own. For instance, I ask how do you know?,. Can you explain?,. Is there another way to solve?
One student explains that it was kind of difficult for him to remember what number was in the ones/tens place. So, he had to label each number to help him identify correctly. Another student, explains she use illustrations to help her group in tens and ones. So far students are relying heavily on other mathematical concepts to help them solve. I tell them, great work you guys!
I will use students responses to determine where they are in their learning, or if this lesson needs to be re-taught in a smaller group setting.