1. Connecting Academics & Parents
Academic seminars to sharpen skills and build understanding in Understanding Perimeter & Area
Critical Point: Welcome parents to the session. This training was intended to take an hour, but can be adjusted to take more/less time as needed.
Step-by-Step Directions:
Welcome parents and introduce trainers.
Give purpose for training, which is to build the parent’s understanding of what their children are learning and strategies they will be using in the classroom, which align with the Math Florida Standards.
Explain that parents will also be leaving with “purposeful practice,” games and strategies to practice at home and will reinforce what they are learning in school.
Materials: Four different colored rectangles for each parent, 3 x 5 index cards for each parent, pentominoes sets for each group (paper or plastic – may want to purchase one set for each parent if possible), pre-cut perimeter/area sort cards, scissors, square tiles, colored pencils/crayons
Copies in packet: pentominoes, perimeter/area sort, inch graph paper (3 copies), centimeter graph paper (3 copies), geoboard paper (at least 3 copies), Design Home Challenge, Scavenger Hunt

2. Order the Shapes Covers the largest surface to the smallest surface
Allowed: cutting, folding, etc.
NOT allowed: using any type of measuring tool (rulers, tapes etc.)
Discuss the strategies you use to order the shapes.
Florida Standards for Mathematical Practice (SMP) #1:
Make Sense of Problems and Persevere in Solving Them
Critical Point: To engage parents in developing the understanding of area with a hands-on task.
Step-by-Step Directions:
Pass out the four rectangles to each parent and go over the directions to the task on the slide.
Pose the question, “How could you determine which one has the largest surface to cover without using any measuring tools?” You can only cut or fold them. Give the parents a moment to think about what they might do to get started.
Give the parents about 3 minutes to explore and solve the task by arranging the four different-colored rectangles in order from largest to smallest.
While they are exploring, monitor and pose questions. Select a few parents that used different strategies to come up and share their thinking. Some questions you may want to ask include:
“How did you determine that rectangle has a greater area?”
“What’s another way you could prove your order?”
“How does the red rectangle compare to the green rectangle?”
“How does the blue rectangle compare to the yellow rectangle?”
Click on the next slide to show examples of what they may have done.
Trainer Note – The next 2 slides show examples of what parents may have done to make sense of which rectangle takes up more space.

3. Mathematics Florida Standards Focus
Grade 3
MAFS.3.MD.3.5 Recognize area as an attribute of plane figures and understand concepts of area measurement. MAFS.3.MD.3.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). MAFS.3.MD.3.7 Relate area to the operations of multiplication and addition. MAFS.3.MD.4.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
Critical Point: Share the standards that are being learned throughout building understanding of multiplication and division.
Step-by-Step Directions:
Share the standards that will be covered.
Quickly share the standards that are involved with area and perimeter in 3rd grade. Discuss that these standards are extended upon in 4th grade, but the understanding of area and perimeter is developed in 3rd grade.
Briefly highlight some of the important parts of the standards. This is more for your background knowledge, don’t spend a lot of time on this slide, because all of the standards are covered throughout the training.
MAFS.3.MD Students learn that area is the amount of space that is covered on a figure/plane.
MAFS.3MD Discuss that it’s important to have children solve perimeter/area problems in real-world context. It is beneficial to continuously relate perimeter and area to avoid misconceptions. Finding unknown lengths is part of the process as well based on rectangle attributes. This will be applied when students find area of rectilinear figures.
Though students are not expected to use the formula for area and perimeter in 3rd grade, they develop understanding of it through exploration and connections to multiplication and addition as shown in MAFS.3MD.3.7.
If the parents want more information on the standards, encourage them to visit flstandards.org

4. MAFS Learning Progression: Perimeter & Area
Critical Point: To show where building understanding of perimeter and area standards are and how they are connected between the different grade levels.
Step-by-Step Directions:
Share the standards briefly that address perimeter/area.
Show how learning of perimeter and area progresses from earlier grades to future grades.
Copyright 2009

5. The Dog Pen
Adam is creating a dog pen for his dog Tiki. He has 12 yards of fencing to create the dog pen. What could Adam’s dog pen look like?
Insert picture of Tiki and the Misconception animation.
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.
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 12 yards relate to the perimeter?
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, formulas, addition, and a picture) If none of these strategies were used, have a “Fake participants” strategy shared that is prepared ahead of time by you.
Have parents share and make connections between the different strategies.
The purpose of this slide is for parents to get an idea of what kind of problem solving is expected in the classroom to demonstrate understanding of perimeter/area. It is essential that understanding is achieved through problem solving and connections to the real world.
Explain that by the end of the training, participants will be familiar with the type of problems involving perimeter/area and different tasks that they can implement at home with their child.
Also share that this is typically how your child’s math class is started. Students are expected to share thinking with words/pictures/or numbers to either a partner/group or the whole class.
Discuss that it’s important to think about the actions or what’s happening in the perimeter/area problems.
Trainer Note – Solving and sharing should take no longer than 5 minutes for this slide. Encourage parents to think about the way their children may solve the problem with this new learning.

6. The Dog Pen Part 2
Now Adam has decided to put square yard pieces of grass sod down in Tiki’s dog pen. Based on your design, how many square yards of grass sod does he need to buy?
Insert picture of Tiki and the Misconception animation.
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.
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 number of square pieces of grass sod compare to the 12 yards of fencing?
Do you think there will be the same number of pieces of grass sod for all models?
Select the parents that are sharing. (Consider some one that used graph paper models, square tiles, formulas, addition, multiplication, and a picture) If none of these strategies were used, have a “Fake participants” strategy shared that is prepared ahead of time by you.
Have parents share and make connections between the different strategies.
The purpose of this slide is for parents to get an idea of what kind of problem solving is expected in the classroom to demonstrate understanding of area. It is essential that understanding is achieved through problem solving and connections to the real world.
Explain that by the end of the training, participants will be familiar with the type of problems involving area and different tasks that they can implement at home with their child.
Also share that this is typically how your child’s math class is started. Students are expected to share thinking with words/pictures/or numbers to either a partner/group or the whole class.
Discuss that it’s important to think about the actions or what’s happening in the perimeter/area problems.
Trainer Note – Solving and sharing should take no longer than 5 minutes for this slide. Encourage parents to think about the way their children may solve the problem with this new learning.

7. Comparing the Problems
How do the two questions compare?
What were you determining in each problem?
Area – amount of space inside a region
Critical Point: To relate perimeter and area in real-world context and give the definitions for area/perimeter.
Step-by-Step Directions:
Pose the two questions and give the parents independent think time.
Have them discuss as a group how to the two questions compare. Hopefully they will see that the first problem dealt with perimeter because their were determining the distance around. The second problem dealt with area because the square sods being placed down to cover the dog pen dealt with covering a space with square units. If not, you want to bring that discussion out.
Click and the definition for area will appear.
Click and the definition for perimeter will appear.
Discuss that it’s important to explore these two concepts in real-world context for understanding and also continuously relate perimeter and area to avoid misconceptions. Share that we will explore perimeter and area separately and then move into relating them again and identifying area/perimeter patterns.
Perimeter – the distance around a region

8. Exploring Perimeter with Pentominoes
Choose a Pentomino shape.
Find the perimeter of the shape.
Be prepared to share your strategy for determining the perimeter.
If a child found a perimeter of 5 units for this shape, what was their misconception?
If a child found a perimeter of 7 units for this shape, what was their misconception?
Critical Point: To explore perimeter strategies with a hands-on task.
Step-by-Step Directions:
Pass out pentominoes.
Have the parents choose a pentomino piece and determine the perimeter.
Discuss strategies for finding the perimeter as a group, having a couple parents share their strategies. (May want to discuss that though many of the pentominoes have different perimeters, they all have the same area).
Click again to reveal two questions with possible misconceptions children may have and the given pentomino used. Give the parents a few minutes to discuss in their groups and then share whole group. Hopefully parents see the first child just counted the squares and found area instead of perimeter. The second child miscounted the corner parts of the pentomino piece. Discuss how these are common misconceptions children have.
If time permits, discuss how this task could be extended with children at home. Share that paper copies of pentominoes are in their packet. Discuss the two possible challenges and do if you have time:
Find the Greatest Perimeter you can by combining two pentominoes.
Find the Least Perimeter you can by combining two pentominoes.
Copyright 2009

9. Problem Solving with Perimeter
Shanna wants to frame a picture of her pet Riley. Shanna wants to put a frame around the given photo to decorate her home. What’s the perimeter of the picture? 1 2 3 4 5 16 6
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. Consider sharing strategies where parents surrounded the perimeter with square tiles, found the length and width using tiles and then doubled, used a formula, etc.
Have parents share and make connections between the different strategies.
Discuss how the formula should be developed by children after exploring multiple perimeter problems in real-world context. Also discuss connections to addition and perimeter.
Click and a misconception of how students typically find perimeter will appear. Discuss how sometimes children count the squares in this scenario rather than the sides of the square.
Click again and it will show how the correct counting can occur to find the perimeter.
Click a final time to show how using graph paper can help clear the misconception of counting the corner squares only once.
Trainer Note – If parents don’t discuss this during the sharing part, pose the question: “What way could you do it quicker than counting the squares?” 15 7 14 8 13 12 11 10 9

10. Exploring Area
Shanna decided she wants to place the photo of her pet Riley in a photo album. How much space will the photo take up in the photo album? Estimate. Then solve.
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. Consider sharing strategies where parents covered the index card with color tiles, parents that found the length and width with tiles, and parents that used a formula, etc.
Have parents share and make connections between the different strategies. Discuss the importance of using precise vocabulary and relating the model/strategy back to the original problem.
If there wasn’t a strategy shared where the parents determined the length and width and use repeated addition or multiplication to find the area pose the question: “What if you only had 10 square tiles, how could you find the area?” Then give parents time to explore and discuss the strategy for solving. If it was already discussed, skip this step.
Discuss how the formula should be developed by children after exploring multiple area problems in real-world context. Also discuss connections to multiplication arrays and area. Also discuss why the answer is in square units.
Trainer Note – If parents don’t discuss this during the sharing part, pose the question: “What way could you do it quicker than counting the squares?”

11. Complete the Square
Choose a partner, decide which color tile each partner will use to represent their squares. Decide who will go first.
Take turns making line segments on the geoboard of any length.
Whenever a player completes the fourth side of a unit square, the player places their color tile in the square.
Play continues until no more squares can be completed.
Winner is the person with the greatest area
of the geoboard covered by their color tiles.
Insert Example of game to fly in.
Critical Point: To have parents apply what they learned about area in a game they can play at home with their child.
Step-by-Step Directions:
Explain the directions to the complete the square game.
Pass out square color tiles, geoboard paper, colored pencils/crayons and give the participants some time to play the game.
Discuss how this game could be used at home to reinforce their child’s understanding of area.

12. Relating Perimeter and Area
Read the story problems.
Decide if the problem is asking you to find area or perimeter.
Place the cards into 2 piles and justify why it was an area or perimeter problem.
Use different strategies to solve the problems.
Critical Point:
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.
Trainer Notes – If time is short, skip having parents solve the problems and limit the number of problems they are sorting. The purpose of this task is for parents to realize that real-world context is essential for understanding of perimeter and area.
Copyright 2009

13. Relating Perimeter and Area
Create 2 different rectangles that have a perimeter of 24 units. Find the area.
Create 2 different rectangles that have an area of 24 square units. Find the perimeter of each shape.
What do you notice?
Critical Point: To have parents understand that identifying perimeter and area patterns in essential for a deeper understanding of perimeter/area.
Step-by-Step Directions:
Pass out graph paper and pose the first and second task for parents to explore.
Pose the question, “What do you notice?”
Discuss if it is not brought out in discussion with the above question that when the perimeters are the same, the areas will be different depending on how you arrange the square tiles. Also discuss how the more “stretched out” the square tiles are the smaller the area will be.
Discuss that when the areas are the same, the perimeters will be different depending on how the square tiles are arranged. Also, discuss when the areas are the same and the square tiles are “stretched out” the greater the perimeter will be.
Trainer Note – This task relates to the 3rd grade standard MAFS.3.MD.4.8.

14. Other Examples of Problems in 3rd Grade
Critical Point: Share the different problems children will be exposed to in 3rd grade involving area and perimeter.
Step-by-Step Directions:
Share the variety of problems your child will see. (Rectilinear will be on next slide).
Pose the question, “How would they use addition and multiplication to solve these problems?”
Also discuss on the bottom problem that children are dealing with “unknown” lengths. 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.

15. Finding Area of Rectilinear Figures
What strategies would you use to find the area of the below figure?
If a student got an area of 52 square meters, what was their misconception?
Critical Point: Explore finding area of rectilinear shapes.
Step-by-Step Directions:
Pose the two questions and give parents about 2 minutes to discuss at their groups. Discuss as a whole group what parents would do to solve the problem.
Then pose the question if it wasn’t already discussed, “How do you determine the missing sides?” Discuss how this is a struggle for many students. The student in the 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).
Discuss how hands on is still needed at this stage. Click to show the example with a grid so parents see both types of rectilinear shapes that children in 3rd grade will have to find the area of. (This helps with the hands-on visual but even before the grid shape they should use square tiles and realize that if it’s broken into two rectangles I can then add to find the whole area).
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.
Trainer Note – Don’t spend a lot of time on this slide. The purpose is just to give parents an idea on how children will use what they know about finding area of individual rectangles to find area of figures with multiple rectangles.

16. Real World Samples of Area and Perimeter
Critical Point: To share examples of real-world perimeter and area.
Step-by-Step Directions:
Share the pictures on the slide.
Discuss how perimeter and area are shown in the pictures.
Discuss how this can be done as a scavenger hunt with real world examples or pictures at home with their children.
Real World Samples of Area and Perimeter

17. 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.
Purposeful Practice:
Pentomino Perimeters
Complete the Square
Area/Perimeter Sort
Area/Perimeter Scavenger Hunt – look for objects with a given perimeter/area throughout your home.
Design Home Challenge – use the given directions to create rooms with objects and dimensions using specific perimeters and areas.
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.
Trainer Notes – If time permits, you may want to play one of the games in the training.
Copyright 2009

18. Possible Delivery Models for CAP Sessions:
School Parent night K-5
Teacher’s or grade level’s own workshop
School invites parents to a curriculum night
Break-out sessions offered by grade level and content area
Teachers who attended TTT or watched voiceover TTT video deliver sessions
Teachers who attended TTT or watched voiceover TTT video deliver sessions to their own class of parents
Grade level can organize a workshop on needed content and have own parent night
Critical Point: This slide is only shared at Train the Trainer session for delivery model options.
Step-by-Step Directions:
1. Share slide to help teachers/trainers think through implementation of this training.

19. Tips for Success in Organizing CAP sessions:
Find a team of people to help with organizing the event
Send home bright colored half-sheet flyers and use parent link calls to notify parents
Have parents rsvp
Look for sponsorships from business partners/PTA to have snacks or a full meal for the parents
Consider baby-sitting options on-site
Consider time frames that meet the needs of your parents.
Morning session, at dismissal, evenings
Critical Point: This slide is only shared at Train the Trainer session for delivery model options.
Step-by-Step Directions:
1. Share slide to help teachers/trainers think through implementation of this training.