Materials: Additional Equations.docx
In this lesson I want students to explore multiplicative comparisons. this concept helps students identify and verbalize which quantity is being multiplied and which number tells how many times.
To start I write 5 X 8 on the board. Can anyone tell me the product of these two numbers? The product is 40. So, I write 40= 5 X 8. I write 40 first so that students can see that 40 is 5 times as many as 7 and 7 times as many as five.
Now, I want to guys to really sit still while I explain a different concept! Do you have your listening ears on? Yes
5 X 8 = 40
Jane is five years old. Her sister is eight times older. How old is Jane sister? 40
I tell students, “This is a simple equations statement that represents the problem.” To make sure students understand the concept of this lesson I repeat the same strategy using a different set of numbers. I give students about 5 minutes or so to think their way through. I call on student volunteer to explain how they can represent the equation in a verbal statement. I use students’ response to determine how to assist them better through-out the lesson.
We will be focusing strongly on the following Mathematical Practices:
MP2: Reason abstractly and quantitatively.
MP3: Model with mathematics.
Materials: Group Practice Work!
In this portion of the lesson I want students to practice representing their equations with verbal statements and illustrations. I ask students to quickly move into their assigned seats. I tell them they will have about 10 minutes or so to discuss how to represents the given equations using verbal statements of multiplicative comparisons as multiplication equations.
My goal is to provide students with an opportunity to communicate their reasoning. As students are working, I circle the room to check for understanding. How do you know that the equation is represented correctly? I calculated both and got the same answer. Does your explanation make sense? Some students responded, but others had a difficult time reflecting on their learning. Did you use the appropriate mathematical language to explain your answer? Did you use the same method to solve each problem? How do you know? explain? I call on a couple of groups to share their work. Some students solved their problems correctly, but had a difficult time explaining how they solved.
As I continue to circle the room I hear students identifying and explaining patterns. I point out the difference between multiplicative and Additive comparison.
Additive comparison focuses on the difference between two quantities.
Multiplicative comparison focuses on comparing two amounts by showing that one amount is a certain number of times larger or smaller than the other.
Ryan has 7 baseball cards. Billy has 3 times as many baseball cards. How many baseball cards does Billy have?
What type of comparison is shown in the question above?
When finding the difference between multiplicative comparison and additive comparison, see that multiplicative comparisons focus on comparing two amounts by showing that one amount is a certain number of times larger or smaller than the other. It is denoted by the question, "How many times as many?"
So, the comparison shown in the question is multiplicative comparison.
What is another way to represent 35 = 5 × 7 ?
Interpret the equation given in the question.
35 = 5 × 7
One way to interpret the equation to represent the equation with words. Start by looking at each part individually.
1. The equation starts with "35", so copy "35" down.
2. When expressed in words, the "=" can be written as "is".
3. Next, copy down "5".
4. The "×" is a symbol for multiplication. It means "times as many as".
5. Last, copy down "7" to complete the equation.
When all the steps are completed and put together, the equation 35 = 5 × 7 can be represented as "35 is 5 times as many as 7".
I use students response to determine the level of understanding or if additional time should be given.
In this portion of the lesson, I invite students back to their assigned seats to work independently on a fun activity. To get them going, I demonstrate exactly what they will be doing in this activity using a different set of numbers. I circle the number 1 on the chart. I tell students that this is the starting point. What is the starting point? 1 Then, I shade in numbers 7, 8, 9. I discuss how the numbers that I shaded is 7, 8, and 9 times more than the starting number. What is the starting number? 1 Can anyone explain how 7 is 7 more than the starting number? 1 X 7 = 7. You can also add 1 + 7 = 8 to determine that if you add 7 more to 1 the total is 8. Great job guys? Can someone explain how to write a multiplicative equations to represent this equation?
Tom is 1 years old. Bill is 7 times as old as Tom. How old is Bill?
If Tom is 1 and Bill is 7 times as old as Tom I can multiply 1 X 7 to find out the age of Bill. So, Bill is seven years old.
Now! I think you guys are ready to work on your own. Are you ready? Students shout, "Yes!" I give students about 20 minutes or so to solve their problem. As students are working, I circle the room to check the level of understanding.
1. How do you know?
2. Can you explain?
I use students' responses to determine if additional practice is needed.
Materials: Journal Paper
You guys have done a great job so far! I think you are ready to Journal your learning experience or today. Are you guys ready? Students' shout, " We are ready as ready can be!"
Great! Get out your journals. I want you to create your own equation and explain how you can compare it using a multiplicative equation. Please do not forget to use illustrations. I point out the difference between multiplicative and additive comparison. I want to make sure students can explain the difference between the two on their own.
As students are working, I reinforce their learning by asking how and why questions. I use their responses to determine if additional practice time is needed.