## Placing the tiles to create "area" - Section 2: A Hands on Situation: Discovering How Factor Pairs Help

*Placing the tiles to create "area"*

# Master those Area and Perimeter Word Problems with Strategies!

Lesson 15 of 18

## Objective: SWBAT solve metric area and perimeter word problems.

## Big Idea: Language, drawing diagrams, connections to factor pairs and arrays help students solve those confusing metric word problems!

*45 minutes*

#### Starting right in!

*15 min*

Power Lesson! We got right to it!

I opened the first page of the SB file and had students take detailed notes.* We went through the file page by page and practiced each word problem together. We discussed in detail the perimeter, the importance of drawing out the problem, equations and labeling.

I emphasized the importance of really focusing on the question first. Looking for the "magic" key word that shows us if it is perimeter or area. We began solving the word problems using a familiar strategy they have been using. I told them to underline those key words and write them down in the "S" part of KWS an "A" or a "P" to remind them if they are solving for area or perimeter. Some students wondered if they could just write down the equations. I told them that it was important to note WHICH key word was listed to keep them focused on what should be solved.*My students are really weak at paying attention to what needs to be solved. As CCSS starts to take root, I predict that students will become stronger problem solvers because we are teaching them how to pay attention to details and focusing on language. In the past, my students were taught quick solutions and short cuts without much thought behind our work.*

As we continued, they discovered that a picture was the best way to solve. It told them the equations can be developed after they examine the picture carefully. You can see all the squares and how we wrote them. The last two blank pages were added for solving the equations.

When we finished, we reviewed our strategies, and noted that there were different types of area problems.** We noted that the quilt problem was not really a measurement problem per say, but used the same types of strategies and the concept of the block was not in measurements, but if it were, the blocks would each be 6400 units squared. It was a good Power Lesson!

**I copy off notes for 6 students including those who have difficulty with taking notes or are just so slow they will hold up the process. I seat these "Notemasters" in clusters of three to four people so students around them can choose to look at the notes as they copy. The Notemasters highlight everything I do and add to the notes as we add to the SB file. This little strategy works really well when the notes are detailed and the concept is rigorous. I could copy notes for everyone, but this keeps note taking skills sharp and helps those who struggle feel they have an important job keeping everyone else on task.*

****There are three types here:

1. Straight forward area and perimeter problems.

2. A problem where the area is given and you must find the side.

3. A problem where objects are spaced and placed around a perimeter.

*expand content*

Materials 18-20 square "Marlite" tiles. I* use these as student whiteboards.*

*Taking notes, discussing and solving problems whole group is rich, but I really wanted to be sure I had reached everyone. So I gave them an authentic task. I chose students and told them I wanted them to place the tiles on the floor in a rectangle to create an example of area. This is an example of us using MP4, Modeling with Mathematics, as I explained to them that it was a lot like putting down a tile floor.*

The boys I had chosen took the tiles and created their rectangle. Trying to solve the problem using the tiles shows them busily working to lay down the tile. I stood back quietly and watched curiously to see what factor pair combination would turn up, since there were 18 blocks. They did not choose 1 x18, I saw two and then three blocks laid on the end as others constructed the length. They left a gap in the center. The concept of area was not fully understood!

I was amazed to see them place the tiles down without creating an array! I talk about this in my reflections. While placing the tiles to create "area", I asked for more problem solvers to help with the situation. Collaberative work in order to solve shows how a classmate helps close the center gap and create the rectangle. We talked about how it was necessary to remember that "area" means that all the space is filled up. To connect it to past learning, I asked if they noticed that the tiles looked like an array? We discussed how arrays and area are the same concept. I connected and reviewed 'alliteration' : array, area is the same "animal!" . *I try to interweave CCSS Language Arts across the curriculum every chance I get to overarch and extend their thinking.*

The student who led them to create the rectangle correctly explained why very well. It was good to stand back and let him guide and support everyone's learning.

I invited students to come and sit around and near the tiles after we had arranged them. I told them to bring their notebooks, sketch exactly how the tiles were arranged and solve the area problem as if it were an array. Most students understood how to multiply the length times the width. They could easily see the "why" behind the area formula from looking at the tiles.

Solving for perimeter stumped most students. While we had labeled the square a square meter, the didn't understand they needed to count the edges. Since the array had been built as 3x6, it turned out that the perimeter was also 18. I was worried at that point they would think area and perimeter will always be the same, but a student saved me at that moment!

She said "There are more ways to make a rectangle with those squares." I jumped on this teachable moment and asked her to show us. She arranged the tiles in 2 x9. I asked what the perimeter would be? She walked around the outside counting and got 22 meters. I walked over to the factor pair card that hangs on my wall, pulled it off and raised it up to show all students how using factor pairs to solve for a given area, like one of the examples on our word problems, was a handy strategy and that there was more than one way to create the rectangles. I told them that the 3x6 created a perimeter of 18 just like the area and that it was not always the case because 2x9 created a 22 meter perimeter. They were fascinated.

I closed this part of the lesson by asking them to write the "Essay in 5" and went over their thoughts. We reviewed the expectations of proving how they solved word problems once more and I had them begin writing. I set the timer for 5 minutes.

*expand content*

#### Homework Practice

*10 min*

Area or Perimeter Word Problems Worksheet

I created this worksheet with some of the same type of samples that we had in the SB examples. It prepares them well for their quiz. I passed out their worksheets and we read each one together and talked about drawing pictures, labeling and trying to create equations with variables.

We discussed that the KWS chart might not be necessary anymore because we might know right away that the problem wants us to solve for area, but that paying attention to the question first helps us set our minds on what we need to do.

So, with this assignment, I am anxious to see what strategies they use and how well they understand.

*expand content*

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- UNIT 1: Place Value and Multi-Digit Addition & Subtraction
- UNIT 2: Metric Measurement
- UNIT 3: Graphing and Data
- UNIT 4: Concepts of Multiplication
- UNIT 5: Geometry
- UNIT 6: Fractions 1: Understanding Equivalence in Fractions and Decimals
- UNIT 7: Fractions 2: Addition and Subtraction Concepts/ Mini unit
- UNIT 8: Fractions 3 Mini Unit: Multiplying Fractions by Whole Numbers
- UNIT 9: Division Unit
- UNIT 10: Addition and Subtraction: Algorithms to One Million
- UNIT 11: Place Value
- UNIT 12: Addition and Subtraction Word Problems
- UNIT 13: Multiplication Unit

- LESSON 1: Pumpkin Math! Introduction to Metric Units
- LESSON 2: Metric Measurement: Playing with Non Standard Measurement & a CCSS Pre test
- LESSON 3: So What's a Meter Look Like?
- LESSON 4: Building a Meter: Comparing units.
- LESSON 5: Conversion of Centimeters to Millimeters using Yarn
- LESSON 6: Conversions: Finding a Decimeter and Conversion to Centimeters
- LESSON 7: Lewis and Clark and Kilometers
- LESSON 8: The Meter: Assessing the Skill and Conversions Part 1.
- LESSON 9: There's No Business Like Shoe Business: Part 2 Real World Applications to Assess the Standard
- LESSON 10: Finding a Gram
- LESSON 11: Building a Liter
- LESSON 12: Word Problem Language and Conversion
- LESSON 13: Designing the Perfect Floor Plan: Showing Understanding of Area and Perimeter
- LESSON 14: Conversion Quiz: This One, Not That One! Writing About Our Choices
- LESSON 15: Master those Area and Perimeter Word Problems with Strategies!
- LESSON 16: Quiz 2: Area & Perimeter Word Problems Using Metric Measurement
- LESSON 17: Centers for Reviewing Metrics!
- LESSON 18: Metric Unit Assessment