1. Connecting Academics & Parents
Academic seminars to sharpen skills and build understanding in MATHEMATICS:
4th Grade Perimeter and Area
TRAINING MATERIALS NEEDED:
3 x 5 index cards
1 inch color tiles
Geoboards with rubberbands
Prepared area and perimeter sorting cards
Prepared “Follow Me” cards
Grid Paper for parents
RESOURCES FOR PARTICPANT PACKETS:
Powerpoint
Full page learning progression
Grid paper
Area and perimeter sorting cards
CRITICAL POINT:
The purpose of this slide is to welcome parents and share that this session is about how to help their child have a better understanding of the 4th grade standard on application of the formulas for finding the area and perimeter of rectangles.
STEP-BY-STEP DIRECTIONS:
Welcome Parents and Guardians to the training.
Share that this training is about how they can help their child better understand the 4TH grade standard on application of the formulas for finding the area and perimeter of rectangles..
Explain that they will be engaged in some activities that will help them better understand the standard and help them support their child with developing their understanding.
The training will also include some purposeful practice tasks that they can do at home.
Only spend about 2 minutes on this slide.
This presentation was made possible in part by a grant from Carnegie Corporation of New York.

2. Math may look different now.
There’s nothing better than seeing your kids SUCCEED
and there’s nothing worse than not being able to help them when they are struggling.
Share with parents that math may look different now. There’s nothing better than seeing your kids SUCCEED and there’s nothing worse than not being able to help them when they are struggling. This is research from Dr. Drew Westen, who is a professor at Emory University. Dr. Westen’s work was developed in collaboration with 100Kin 10.
Research from
Dr. Drew Westen, Emory professor,
and 100Kin10

3. Times change, technologies change, and knowledge changes about how to teach kids to apply what they know to real-life situations.
for joining in to learn more about how to help with math.
Thank you
Share that times change, technologies change, and knowledge changes too about how to teach kids to apply what they know to real-life situations. Thank parents for joining in to learn more about how to help with math.
Research from
Dr. Drew Westen, Emory professor,
and 100Kin10

4. SOLVE! A=lw P= 2l +2w or 2(l+w)
The area of Miguel’s rectangular garden is 450 square feet. The garden is 9 feet wide. How many feet of fencing will Miguel need to buy to enclose his garden on all four sides?
A=lw
P= 2l +2w or 2(l+w)
CRITICAL POINT:
Engage parents with a task in which they  solve a problem which requires them to apply their understanding of area and perimeter of a rectangle, so that they will have a reference point when analyzing student strategies for solving the same problem.
STEP-BY-STEP DIRECTIONS:
Give participants 2 minutes to solve the problem on their own. (At this point, they should not be encouraged to use manipulatives)
After 2 minutes, click to animate the formula box to fly in. Give them another minute to work. They may work with a partner for the last minute.
While parents are working, monitor their strategies and listen to their conversations.
Share with parents that now that they have had time to make sense of the problem, they will have a reference point when they look at student solutions to the same problem later in the workshop.

5. Mathematics Florida Standards Focus
Grade 4
MAFS.4.MD.1.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
CRITICAL POINT:
Expose parents to the 4th grade standard on application of the formulas for finding the area and perimeter of rectangles.
STEP-BY-STEP DIRECTIONS:
Give parents time to read the standard.
Share with parents that the problem they just solved on the previous slide was an example of a problem that is aligned with this 4th grade standard.
Explain that, while the formulas for finding area and perimeter of rectangles that they learned in school are a part of the standard, this workshop will focus on those concrete experiences that will help their child understand when and how to apply those formulas in real world problems. These experiences give meaning to the formulas and will help prevent or resolve misconceptions that their son or daughter may have.

6. Samples of Student Solutions
The child does not understand the concepts of area and perimeter.
He or she knows how to apply the formula for the area of a rectangle to find the missing dimension of 50, but does not understand how to apply that to solve for the perimeter.
The child may not understand that the question is asking them to find the perimeter of the rectangular garden.
CRITICAL POINT:
Engage parents with a task in which they analyze student misconceptions and errors with the application of the formulas for finding area and perimeter of a rectangle to give them a purpose for understanding need for solid conceptual understanding of these concepts.
STEP-BY-STEP DIRECTIONS:
1. Share with participants that this slide is a sample of work from a 4th grader.
2. Give participants 1 minute to think on their own about what the child’s misconception is.
4. Give participants another minute or so to share their thinking with a partner.
5. Have participants share out.
Click for animation to come in with an explanation of the misconception. Share this explanation with parents.
Click to animate the fly in of the formulas.
Ask follow up question, “Do you think if the student was given the formulas, it would have resolved their misconception?” Give parents one minute of think time. Have a few parents share out. Parents should see that these formulas would only be useful if the student understood that the question is an application of both perimeter and area.
A=lw
P= 2l +2w or 2(l+w)

7. Samples of Student Solutions
The child does not understand the concepts of area and perimeter.
He or she lacks the foundational understanding that area is measured in square units, and this resulted in the child using the 450 sq. ft. as a linear dimension, rather than as the area.
CRITICAL POINT:
Continue to engage parents with a task in which they analyze student misconceptions and errors with the application of the formulas for finding area and perimeter of a rectangle to give them a purpose for understanding need for solid conceptual understanding of these concepts.
STEP-BY-STEP DIRECTIONS:
1. Share with participants that this slide is another sample of work from a 4th grader.
2. Give participants 1 minute to think on their own about what the child’s misconception is.
4. Give participants another minute or so to share their thinking with a partner.
5. Have participants share out.
Click for animation to come in with an explanation of the misconception. Share this explanation with parents.
Click to animate the fly in of the formulas.
Again, ask follow up question, “Do you think if the student was given the formulas, it would have resolved their misconception?” Give parents one minute of think time. Have a few parents share out. Parents should see that these formulas would only be useful if the student understood that area is measured in square feet, and would be able to apply the formula for area to find the missing dimension of the length of the rectangle.
A=lw
P= 2l +2w or 2(l+w)

8. Samples of Student Solutions
The child understands the formula for perimeter and area, but is unable to correctly apply it to solve the problem.
He or she does not understand that the problem is requiring an application of the formulas for both area and perimeter.
CRITICAL POINT:
Continue to engage parents with a task in which they analyze student misconceptions and errors with the application of the formulas for finding area and perimeter of a rectangle to give them a purpose for understanding need for solid conceptual understanding of these concepts.
STEP-BY-STEP DIRECTIONS:
1. Share with participants that this slide is another sample of work from a 4th grader.
2. Give participants 1 minute to think on their own about what the child’s misconception is.
4. Give participants another minute or so to share their thinking with a partner.
5. Have participants share out.
Click for animation to come in with an explanation of the misconception. Share this explanation with parents.
Click to animate the fly in of the formulas.
Again, ask follow up question, “Do you think if the student was given the formulas, it would have resolved their misconception?” Give parents one minute of think time. Have a few parents share out. Parents should see that these formulas would only be useful if the student understood that they needed to also find the perimeter of the garden.
A=lw
P= 2l +2w or 2(l+w)

9. Learning Progression:
Perimeter and Area
CRITICAL POINT:
This slide shows how learning about perimeter and area progresses from earlier grades to future grades.
STEP-BY-STEP DIRECTIONS:
Give parents time to look at the learning progression. They have a full page version in their packet that might be easier to look at.
Bring parents’ attention to the 3rd, and 4th grade standards.
Ask parents what they notice about the progression from the 3rd grade standard to 4th grade and the errors that they saw in the samples of student work.
Clarify to help parents see that in order for students to be able to accurately apply the formulas for perimeter and area of a rectangle, they must have developed a solid conceptual understanding through the 3rd grade standards.
Copyright 2009

10. Why don’t we just give them the formulas??
“…do not make the mistake of bypassing formula development with your students. A conceptual development of formulas does much more than provide formulas for students. As students develop formulas, they gain conceptual understanding of the ideas and relationships involved. There is less likelihood, for example, that students will confuse area and perimeter or that they will select the incorrect formula on the test. General relationships are developed…students who understand where formulas come from do not see them as mysterious, tend to remember them, and are reinforced in the idea that mathematics makes sense. Rote use of formulas from a book offers none of these advantages.”
Teaching Student Centered Mathematics, Van De Walle
CRITICAL POINT:
Clarify for parents why application of the formulas for area and perimeter does not occur until 4th grade.
STEP-BY-STEP DIRECTIONS:
Ask parents to think about the errors that students made and the discussions that they had on the previous slides, and share why they think application of the formula for area and perimeter is not until 4th grade.
Click to animate the quote. Give parents time to read the quote and make note of any “ah-has”.
Give parents time to turn and talk to summarize the quote and share their ah-has.
If needed, clarify that we do not want to rush to that traditional algorithm. 3rd grade is really more focused on those strategies that will deepen students’ conceptual understanding to prevent common errors/misconceptions with the application of the formulas in 4th grade.
Explain to parents that, for this reason, this workshop will share with them some strategies more directly connected to the 3rd grade standards, so that parents can help support their child if he or she does not have that conceptual understanding necessary to apply the formulas.

11. Solve!
Use any of the provided tools to solve the following:
Jackie is creating an outdoor play pen for her puppy Layla. She has 24 feet of decorative fencing to create the rectangular play pen. What could the length and width of the play pen be?
CRITICAL POINT:
To engage parents in a real-world problem that is similar to what students will be doing in the classroom.
STEP-BY-STEP DIRECTIONS:
Parents should have access to a variety of tools, including grid paper, color tiles and geoboards with rubberbands.
Pose problem. Give parents 2 minutes to solve on their own using any strategy they choose.
As parents are solving, walk around and monitor different strategies being used. You will want to select 2 or 3 strategies to share. Focus on getting parents to use precise vocabulary when discussing their model/strategy. Pose questions to get parents to think deeper about their strategy and to justify their solution. Questions may include:
Is there another way you could make the play pen?
How does the 24 feet relate to the length and width?
How does your model relate to the problem?
Is there a more efficient way to find the answer?
Select the parents that are sharing. (Consider some one that used graph paper models, square tiles, and a diagram)
Ask parents the information that they were given in the problem. (The distance around the outside of the playpen). Share that this distance around the outside of a figure is the perimeter.
Also share that this is typically how a math class is started. Students are expected to share thinking with words/pictures/or numbers to either a partner/group or the whole class.

12. 5 3 Deriving the Formula for Perimeter
Jackie wants to make a lace frame for a picture of Layla. How many inches of lace will she need? 5 1 2 3 4 5 6 3
Critical Point: To explore perimeter and have parents discover a possible formula or more efficient way to find perimeter.
Step-by-Step Directions:
Pass out 3 x 5 index cards as the “photo” and square tiles to each parent.
Pose the problem and give parents 2 minutes to solve on their own.
Monitor parents, looking for parents to share different strategies. Look for a parent who put color tiles around the entire perimeter of the card and a parent who only needs to put them along the length and the width of the card.
When sharing the model that only tiled the length and the width of the card, ask the rest of the parents if they can figure out how the parent was able to use that model to find the distance around the entire card. Parents will most likely share that they either added the length and the width and doubled that sum or that they doubled the length and doubled the width and found the sum of those products.
You can click to animate and show what the tiling all the way around the picture would look, and then focus discussion just on counting the tiles for the length and width.
Discuss how they have just derived the formulas for finding the perimeter of a rectangle.
Click to animate the formulas for perimeter. If needed, clarify how these both could be used to find the perimeter of the frame. 7 8
perimeter= 2 ( length + width)
perimeter = 2length +2width

13. Solve!
Use any of the provided tools to solve the following and justify your solution:
Jackie wants to cover the ground of the playpen with Zoysia grass sod. Only the best for Layla!!
Since this sod is extremely expensive, she can only afford 24 square feet of the sod. What could the dimensions of the rectangular playpen be to protect the expensive grass from other critters?
CRITICAL POINT: To engage parents in a real-world problem that is similar to what students will be doing in the classroom.
STEP-BY-STEP DIRECTIONS:
Pose problem. Give parents 2 minutes to solve on their own using any strategy they choose. Parents should have access to a variety of tools, including grid paper, color tiles and geoboards with rubberbands.
As parents are solving, walk around and monitor different strategies being used. You will want to select 2 or 3 strategies to share. Focus on getting parents to use precise vocabulary when discussing their model/strategy. Pose questions to get parents to think deeper about their strategy and to justify their solution. Questions may include:
How does the 24 square pieces of grass sod compare to the problem when we had 24 feet of fencing?
Will your length and width be the same as the last problem?
Do you think there will be the same amount of fencing needed for everyone’s model?
Select the parents that are sharing. (Consider someone that used graph paper models, square tiles, and a diagram)
Ask parents the information that they were given in the problem. (The number of square feet that will be covered by sod). Share that this space that is covered by square feet of sod is the area of the playpen.
Point out that in the original playpen problem, the word perimeter was not in the problem, just like the word area is not in this problem. In the real world, we have to identify whether we are finding perimeter or area before we apply the formula.

14. 3 Deriving the Formula for Area
Jackie wants to put a copy of the picture of Layla in her photo album. How much of the page in the album will be covered by the photo? 1 3
Critical Point: To explore area and have parents discover a possible formula or more efficient way to find perimeter.
Step-by-Step Directions:
Pass out 3 x 5 index cards as the “photo” and square tiles to each parent.
Pose the problem and give parents 2 minutes to solve on their own.
Monitor parents, looking for parents to share different strategies. Consider sharing strategies where parents covered the index card with color tiles and parents that found the length and width with tiles.
Ask the rest of the parents to share how the covered page could be found by only using 7 color tiles (5 along length and 2 along the width). Parents will most likely share that they could skip count by 3 five times, or 5 three times, or multiply 5 x 3. Share that students will also most likely make that connection based on their understanding of arrays for multiplication.
Discuss how they have just derived the formulas for finding the area of a rectangle.
Explain that it is through experiences like this that students discover the meaning for area, understand square units, and derive the formula for area.
Click to animate the formula for area. 8
area= length x width

15. Perimeter or Area? Read the story problems.
Sort the cards into “perimeter” and “area” problems.
As you sort the cards, justify why it is a perimeter or area problem.
Critical Point: Provide parents with practice differentiating between real world problems involving perimeter and area.
Step-by-Step Directions:
Explain that now we have spent some time exploring and understanding perimeter and area separate, it’s important to bring the two concepts back together in real-world context. Many times if they are only taught in isolation, students begin having misconceptions.
Pose the directions to the parents.
Pass out the problem sort cards and give them some time to read the scenarios and place them into two piles, area or perimeter.
Discuss specific actions in the problem (not key words) that told them the problem was asking for area or perimeter.
If time permits, have them solve a few problems (maybe one of each – area and perimeter).
Discuss how this task could be implemented with their child at home.

16. Riddle me this!
I am a rectangle. My perimeter is 60 feet. My length is twice as long as my width. How much area do I cover? I am a rectangular picture frame. I am made of 24 inches of wood. I am 3 meters wide. How long am I? I am a square with a perimeter of 32 cm. What is the length of one of my sides? What is my area?
Critical Point: Share the different problems 4th graders will be expected to solve by applying their understanding of area and perimeter.
Step-by-Step Directions:
Share the variety of problems to which children will be expected to apply the formulas for area and perimeter. (Rectilinear will be on next slide).
Pose the question, “What understandings do students have to have in order to successfully solve these types of problems?” (attributes of rectangles and squares, conceptual understanding of perimeter and area, understanding of formulas for perimeter and area, understanding of relationship between multiplication and division, knowledge of facts/mult and division strategies)
Depending on time, you can have parents solve problems and strategies.
Discuss how many application problems are dealing with “unknown” dimensions. Problem solving and using the attributes of rectangles and squares will help them with this task. This is also an important strategy for when they solve area/perimeter problems with rectilinear shapes.

17. Problem Solving with Rectilinear Shapes
Joe said the entire area of the gardens is 52 sq. m. Do you agree or disagree? Why?
4m +
4 m
Critical Point: Explore finding area of rectilinear shapes.
Step-by-Step Directions:
Pose the garden question and give parents about 2 minutes to discuss at their groups. Discuss as a whole group what parents would do to solve the problem.
Pose the question “How do you determine the missing sides?” Discuss how this is a struggle for many students. Many students may get misconception got 52 because they did what most students typically do find 2 numbers and multiply without thinking about what those numbers actually represent. (The student with the misconception multiplied 8 x 3 correctly to get 24, but then multiplied 7 x 4 to get 28 – without thinking about the fact that the 7 represents the whole length and then just want part of that side to find the area of the square herb garden). Students must apply their understanding of the attributes of a rectangle to help find the missing dimensions.
Click through animations to show the opposite, equal sides of the rectangles. Now, the area of the top rectangle can be found by multiplying 8 x 3 and the bottom by multiplying 4 x 4. The sum of these two products gives the area of 40 sq. m of the rectilinear shape.
Click to show the pool problem.
Give parents time to solve.
Look for different ways that parents separated the figure into three rectangles to find their separate areas and then added to find the total. Also, look for someone who drew a large rectangle and subtracted the missing pieces.
Share these different strategies if no parent uses them.
Discuss how having a deeper understanding of the formula of area is essential to apply when decomposing a complex rectilinear shape into two rectangles to find the area. Essentially you are finding the area of both shapes and then combining the areas.

18. Take it Home and Try It! DO TRY THIS AT HOME!
Warning: Implementing this engaging activity will result in an increase in motivation and long-lasting learning.
Play games with Area and Perimeter “Follow Me” cards.
You and your child can come up with different
games to play with the cards, as well as make
additional cards for the deck.
Look around the house for items that are shaped like a rectangle or a rectilinear shape.
Ex: tv or computer screen, table top, rug, floor of a room, wall
Help your child to measure the dimensions of the item and then find the perimeter and area of the object.
You and your child can write more “Riddle me this!” problems, exchange the riddles, and solve.
Critical Point: To give parents purposeful practice and resources to use at home to reinforce understanding of perimeter and area.
Step-by-Step Directions:
When the slide appears, there are “purposeful practice” tasks. Go through the different details and encourage parents to look in their packet at the resources.
Encourage them to try it at home and use those as a guide to develop their own meaningful problems and tasks.
If time, give parents the opportunity to play with the “Area and Perimeter Follow Me” Cards. You may also want to facilitate a conversation with parents about how they would like to implement these tasks at home with their kids.

19. Online Resources
- interactive lesson and game in which player use virtual ruler to find the area and perimeter of rectangles
- player must create a virtual floorplan that meets area criteria
-player identifies rectangles that match given areas
CRITICAL POINT:
Share with parents some online games that could help reinforce this standard.
STEP-BY-STEP DIRECTIONS:
If there is time and you have internet access, visit some of these websites.
Address any additional questions parents may have.
Thank parents for coming.