Finding the Area of a Rectangle

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SWBAT use the area formula for rectangles to solve real world and mathematical problems.

Big Idea

Understanding area and using formulas is a skill used in Algebra and Geometry.


10 minutes

This problem has the students working with perimeter.  I’m using this to get a clear picture if students understand that this is a perimeter problem.  I will be looking to see how students solve this .  Do they know how to start the problem? (MP1:Sense-making).  Are they using a drawing to help them understand the problem? (MP4:models)  I want students to have a good understanding of perimeter before we begin finding the area.  6th grade common core does not cover perimeter so I was going to use this problem as a quick reminder on how to do it.  I will be asking students how they knew they were to find the perimeter?  What makes this a perimeter problem?  I’m looking for students to tell me that they knew because they had to find the total distance between the three cities. Students should be able to do this problem independently.  If they struggle, allow them time to work with a tablemate.

Tools:  Do NOW problem

Finding the Area Using Squares

25 minutes

During this section, I will be having the students “act out” how to find the area of rectangles and squares.  Each student or pair of students needs to have some square measuring tool.  You can use the hundredths from the base 10 blocks or square pattern blocks.  The size of the manipulative really doesn’t matter as I will be using units for each measurement. We will get into specific units of measure when we use the formula.

For each problem, I’m asking the students to find out how many squares will cover a rectangle with certain side lengths. Students will represent the rectangle on their desk with the squares given. By asking the students to transform the side lengths, create the rectangle, and find its area, we are using MP2.  Students may struggle with creating the whole rectangle.  Remind students that when we find the area of a figure, we are finding how many squares will cover the whole figure.  Ask students how many sides a rectangle has?  What do they know about the side lengths of a rectangle.  This will help them when creating the rectangle for the first time using the squares.  After students create the rectangle, ask them what the area of the rectangle is?    In the power point, I’ve shown both ways the rectangle can be created.  Ask students if this matters when trying to find the area?  Then ask them what property supports their answer?

I will be using the squares for three of the five problems. The last two problems have the rectangle and square on the grid.  I want students to find the area and explain how they got their solution.  Students should say they either counted all the squares or multiplied the side lengths together to get the area. 

Using squares also helps students make a connection with the label for area: u².  You can also ask them what happens when you multiply units by units?  Students should see that you get u².  Using the correct label falls under MP 6:  using precision

Tools:  Practicing area with squares problems, square manipulatives

Using the Area Formula

20 minutes

Before showing students the area formula, I’m going to give them some time to think about the connection between counting the squares and how they can do the math to save them some time.  Ask students if they have found a short cut to finding area.  Give them time to look back over their notes.  Students should see that they can just multiply the side lengths together to get the area.  Have students write the formulas in their notes.  Explain to students that a formula is an expression that can be used to find the solution and it works every time. 

Students will then work on two problems where they will use the formula for a rectangle and a square.  Students may struggle when all four side lengths are given.  Remind students that the formula is l x w.  Ask them how many terms are in the formula?  They should see that only two terms are in the formula which means only two numbers are multiplied together. 


20 minutes

The students will be working with their tablemates on a roundtable. Each problem has them finding the area of a rectangle or a square.  The first 4 problems are straight forward questions.  The problem students may have will be finding the area when there is a fraction involved and finding the area when given the area and a side length.  If students have trouble finding the area while using fractions, remind them they can always change the fraction into a decimal.  If students have trouble finding the side length when given the area, encourage students to draw a picture.  Then have them substitute into the formula.  At this time, they should see that it has become an equation.  They can then solve the multiplication equation.

Question 8 has the students finding possible dimensions for a 30yd² family room.  Students can come  up with the factors of 30, however, I’m looking for students to say that the only logical dimensions for the family room would be 6 yds x 5 yds.  All other dimensions wouldn’t make sense.

The roundtable activity supports MP3 by asking students to check the work of others and offer support if needed.

Tools:  Roundtable


10 minutes

The students will be completing a Comprehension Menu.  Students should complete all 4 boxes and place a mark in the box that was easiest for them to solve. This should be collected as evidence of student learning.

The comprehension menu supports mathematical practices:

MP1: Students make sense of problems and look for an entry point

MP2: Students make sense of the different mathematical relationships

MP5: Students use the tool strategically

Tools:  Comprehension Menu