1 K-8 Mathematics Standards Content Training Area and Perimeter

 Steve DePaul, Math Consultant, ESD 123 2

 Develop participant’s conceptual understanding of area and perimeter.  Experience activities that help students develop these concepts.  Develop an understanding of the formulas used to determine them.  Discover the level of understanding for these concepts at your grade level based on the state standards. 3

 Allow ourselves and others to be seen as learners.  Monitor own airtime and sidebar conversations.  Allow for opportunities for equitable sharing.  Presume positive intentions.  Be respectful when giving and receiving opinions, ideas and approaches. 4

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For all students to learn significant mathematics, content should be taught and assessed in meaningful situations. 6

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 Conceptual Understanding ◦ Making sense of mathematics  Procedural Proficiency ◦ Skills, facts, and procedures  Mathematical Processes ◦ Using mathematics to reason and think 8

 At each grade level: ◦ 3-4 Core Content areas ◦ Additional Key Content ◦ Core Processes (reasoning, problem solving, communication)  For each of these: ◦ Overview paragraph ◦ Performance Expectation ◦ Comments/Examples 9

 Use either your Standards Document or Strands Document to find all K-8 references to area and perimeter.  Go back and carefully read the Performance Expectations and Explanatory Comments and Examples for your grade level.  Note the expectations for the grade level above and below yours. 10 What should your students already know? What do you need to teach this year? What do they need to know for next year? What should your students already know? What do you need to teach this year? What do they need to know for next year?

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12 The measure of the interior of a 2-dimensional figure.

13 Area is measured in square units. Count the square units in the shape below to find its area The area of the rectangle above is 8 square units.

14 The distance around a figure.

15 Add the lengths of each side in the shape below to find its perimeter = 12 The perimeter of the rectangle above is 12 units.

16 P = 12 units A = 8 square units

D 4.3.E 3.4.D 4.3.E

 Use the grid paper at your table to draw as many rectangles as you can with a perimeter of 24.  What is the area of each?  What do you notice? 18

Rectangle dimensions Area in square units 1 x x x x x x Do you see any patterns here? Wow! What other standards have we covered?

20 30 minutes

D 4.3.E 4.3.D 4.3.E

 Work with a partner or alone to make many different shapes with an area of 16 square units.  You must use all 16 tiles for each shape and each tile must share at least one full edge with another tile.  Find the perimeter for each shape.  Sketch the shapes on the grid paper whenever you find a perimeter that is different from previous shapes.  How many different perimeters can you find?  What do you notice? 22

 What is the smallest perimeter you found? How many different shapes had that same perimeter?  What is the largest perimeter you found? How many different shapes had that same perimeter? Do you think there are more?  Did anyone find a perimeter that was an odd number? Why or why not? 23

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 Trace your foot (with your shoe off) on the centimeter paper.  Figure the area of your foot in square centimeters.  Put some string along the outline of your foot and cut it to equal the perimeter. Measure it in centimeters.  Can you find someone with the same length perimeter? How do the areas compare? 25

 Get the string you used in the previous activity.  Tie the ends together so that you have a loop.  Use your forefingers and thumbs to hold the string apart to form a square. Note the space that represents the area.  Now slide your hands apart allowing your forefingers to move toward their respective thumbs.  What happens to the area as you do this? 26 This is a great way to show that the area can change even if the perimeter doesn’t.

C 5.3.D 5.3.E 5.3.F 4.3.C 5.3.D 5.3.E 5.3.F

 Look at the rectangle below.  Can you think of a formula for determining the area?

 Determine which side will be the base and which will be the height.  If 4 is the base, you can fit two rows of 4 square units in this rectangle. What is the area? What is the formula?

 How about if 2 is the base?

 A = b x h or  A = L x W  Base times height may be a better formula for finding the area of a rectangle because of what’s coming next. 31

 Look at the parallelogram below.  How can you find the area?  Can you think of a formula for determining the area? 32

 You can make any parallelogram into a rectangle.  The rectangle formula will now work.  A = b x h

 Look at the triangles below.  Can you think of a formula for determining the area?  Is there anything special about figuring the perimeter of a triangle? 34

 If you know the formula for a parallelogram, you can adapt it to work for any triangle.  It is crucial that students understand symmetry.  A = ½ (b x h) 35

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 About Teaching Mathematics, Marilyn Burns ◦  Elementary and Middle School Mathematics: Teaching Developmentally, 5 th edition, John A. Van de Walle ◦