Area of Rectangles
Lesson 1 of 14
Objective: SWBAT apply the area formula for rectangles to solve mathematical and real world problems.
Think About It
Students work in pairs on the Think About It problem. After 3 minutes of work time we discuss strategies for finding the total number of square units in the bottom, larger rectangle.
Some students will count up all of the squares, while others will determine the total by multiplying the number of rows by the number of columns. Students did learn about area of rectangles in 5th grade at our school, so some students will say that they multiplied length by width to find the area. I also expect students to use the first rectangle, with an area of 6 square units, to calculate the area of the larger rectangle by decomposing it into smaller into rectangles with 6 square units. Both strategies are valid, since each promotes conceptual understanding of the use of multiplication to count regions to measure area. A good conversation to have with students at this point is: (a) How are these two strategies the same? (b) How are these two strategies different?
After hearing all of the various strategies students used, we discuss the efficiency of multiplying the length by the width.
Intro to New Material
The purpose of this lesson is to review the concept of area of a rectangle, before diving deeper into the concept of area measurement. In this unit, students will learn about the area of several types of polygons. In the process they'll derive the formulas for the area of parallelograms, triangles, and trapezoids using rectangles as a reference.
I start the Intro to New Material by having students discuss Example 1. I stress the importance of precision in our work, and make sure students label their answers with square feet (MP6). Throughout this unit, if students forget the proper units, I ask them if they mean pickles (so, if a students said the answer was 21 for this problem, I'd respond with '21 pickles?'). Because the area of rectangles is not new material for my students, I can focus on precision and organization in this lesson. I expect my students to write down the formula they are using, substitute in the known values, and then solve using appropriate units.
Example 2 gives us the opportunity to discuss alternative versions of the formula for finding the area of a square. In addition to A = l x w, I show students A = s x s and A = s2. We talk about why all three versions are acceptable. It's important that my students are comfortable with these alternate versions at this point in our curriculum.
Part B of Example 2 requires students to find the area of a small tile, and the determine how many of the small tiles will fit in a larger area. I have students lead this conversation, and we follow whatever strategy is shared with the class - even if it initially leads us in the wrong direction. I want students to experiment with different paths to the solution.
Students work in pairs on the Partner Practice problem set. As they work, I circulate around the room and check in with each group. I am looking for:
- Are students explaining how an array can be used to determine area?
- Are students applying the correct formula to determine the area of rectangles?
- Is student work organized, including all of the steps to solving using the formula and substitution?
- Are students drawing an appropriate representation, if needed?
- Are students justifying their use of area formulas to solve real world problems?
- Are students using the correct units?
I am asking:
- How did you use an array to determine the area of the shape?
- How did you know to find the area of the shape given the context of the problem?
- What does the area of this shape represent?
- What units should you use?
For problems that do not provide a picture of the figure, it is not my expectation that every student draws one. Pictures are an appropriate representation, as are formulas and equations. I want my students to show that they understand the problems, using whatever method works the best for their thinking. If a pair is struggling with a problem, I will suggest that they try drawing the figure and representing the given information. I won't, though, force a group to draw the rectangles if they're able to use formulas to represent the problem.
Students work on the Independent Practice problem set. There are many application problems in this set, and I make sure that I circulate around the classroom and check in with each student multiple times while they're working.
I do allow students access to calculators during this lesson. I want students practicing as many different application problems as time allows, and I don't want them to be slowed by calculations. Most of my students will not touch the calculators until they get to the decimal and fraction problems.
Question 4 is a nice preview of the next lesson in this unit.
I really like Question 8. It requires students to use many of the skills we've learned this year. They need to apply the area formula, and then substitute in the known values. They'll need to simplify the width, using the order of operations. They might use the distributive property to simply further (although this step isn't necessary). They have to substitute in a value for y. Many great things happening in this one simple problem!
Closing and Exit Ticket
After independent work time, I have students spend 4-5 minutes talking with their partners about Problem 9. They share strategies and compare answers, and ask clarifying questions of one another. I'm available as a resource to pairs who need extra support during this time.