Perimeter, Area, and Combining Like Terms

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want students to review finding the perimeter and area of a rectangle.  A common mistake is for students to confuse perimeter and area.  I walk around to monitor student progress to see if they are committing this mistake.  Some students may struggle with the idea of finding perimeter of figure b.  I encourage students to think about the length of each side.  They can also refer to their notes from the previous lesson.

I call on students to share their ideas for each problem.  Then I call on other students to share whether they agree or disagree with their classmate.  I push students to use precise language and include accurate units when sharing their answers.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others and MP6: Attend to precision. 

Note:

• When I print out the notes for students I will delete the words in parentheses.  I want students to fill in these words on their own notes.

Students complete problem 1 independently.  Then I ask students to define “coefficient” and “constant”.  If students struggle to do this, I encourage them to go back to their notes from the previous lesson.  I want students to understand that if a variable is by itself, like “a”, the coefficient is one.  Instead of writing “1a” we just write “a”.

We review the meaning of combining like terms.  Students work independently on problem 4.  When most students have finished, they participate in a Think Pair Share about their answers to problem 4.  I want students to realize that equation (a) cannot be simplified.  I want students to understand that “y” and “y squared” are not like terms so they cannot be combined.  

Notes:

• Each student needs a set of Algebra Tiles.  One type of these tiles can be seen at http://www.amazon.com/Learning-Resources-Algebra-Tile-Class/dp/B000F8R5NW/ref=sr_1_4?ie=UTF8&qid=1388415535&sr=8-4&keywords=algebra+tiles
• The set I use has blue x squared tiles, green x tiles and yellow unit tiles.
• If you do not have Algebra Tiles, you can have students cut out a set of Paper Algebra Tiles for homework the previous night.

We work together on these examples.  It is important that students write the length of each side on each shape.  I ask students what the variables inside the shape represent.  Students need to remember that the variables inside the shapes represent the area.  For the first expression we write an expression that is not simplified.  For the second expression we combine like terms and write the simplified expression.  I ask students, “Can we combine anymore like terms?  Why or why not?”  I want students to recognize that you are finished combining like terms when you are left with terms with different variables and powers and one constant.  Students are engaging in MP7: Look for and make use of structure and MP8: Look for and express regularity in repeated reasoning.

Notes:

• Before this lesson, I use the data from the previous lesson’s ticket to go to Create Homogeneous Groups.
• I use a Group Work Rubric with each group to give students feedback on their cooperation and behavior.
• I Post A Key so groups can check their work as the complete problems.

I review the task and the expectations with students.  I tell them their groups and students move.  I pass out sets of algebra tiles and group work rubrics to each group.

Students are engaging in MP1: Make sense of problems and persevere in solving them, MP5: Use appropriate tools strategically, MP6: Attend to precision, MP7: Look for and make use of structure and MP8: Look for and express regularity in repeated reasoning.

If students are struggling, I ask them one or more of the following questions:

• What is the problem asking?
• What do you know?
• What do the labels on the tiles represent here?
• Can you combine any terms?  Why or why not?
• How can you represent the same area/perimeter in a different way?

If students successfully complete the problems they can move on to the challenge question.

I have students flip to the closure section to look at figure a and figure b.  I ask them what similarities and differences they see between the figures.  Students participate in a Think Pair Share.  Students are engaging in MP1: Make sense of problems and persevere in solving them, MP3: Construct viable arguments and critique the reasoning of others, MP7: Look for and make use of structure and MP8: Look for and express regularity in repeated reasoning.

 I call on students to share their ideas.  I want students to realize that since they use the same blocks that figure a and figure b have the same area.  If students do not mention it, I ask, “Do these figures have the same perimeter?”  Students will be able to apply their knowledge to create an expression that represents the perimeter of figure a.  Students may struggle to represent the perimeter of figure b, since the unit tile is positioned underneath the x tile.  Some students may be able to figure out that the length of that side is (x – 1) + 3.  Other students may see that the side is equivalent to x + 2. Other students may not see these connections and that is okay.  I am pushing students to apply what they know to a new situation. 

I pass out the Ticket to Go and the Homework.