Welcome

1. Welcome K-8 Mathematics Standards Content Training Area and Perimeter

2. Facilitators Steve DePaul, Math Consultant, ESD 123

3. Purpose 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.

4. Group Norms • 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.

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

7. Adopted Washington StateK-8 Mathematics Standards

8. Balanced Standards • Conceptual Understanding • Making sense of mathematics • Procedural Proficiency • Skills, facts, and procedures • Mathematical Processes • Using mathematics to reason and think

9. Organization of the K-8 Mathematics Standards • 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

10. Standards Activity What should your students already know? What do you need to teach this year? What do they need to know for next year? 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.

11. Area and Perimeter

12. What is Area? The measure of the interior of a 2-dimensional figure.

13. Finding the Area Area is measured in square units. Count the square units in the shape below to find its area. 1 2 3 4 5 6 7 8 The area of the rectangle above is 8 square units.

14. What is Perimeter? The distance around a figure.

15. Finding the Perimeter Add the lengths of each side in the shape below to find its perimeter. 4 2 2 4 The perimeter of the rectangle above is 12 units. 4 + 2 + 4 + 2 = 12

16. Comparing Area & Perimeter A = 8 square units 4 1 2 3 4 2 2 5 6 7 8 4 P = 12 units

17. Perimeter Stays the Same 3.4.D 4.3.E

18. Perimeter Stays the Same 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?

19. Perimeter Stays the Same Wow! What other standards have we covered? Do you see any patterns here? Do you see any patterns here?

20. Break Time 30 minutes

21. Area Stays the Same 4.3.D 4.3.E

22. Area Stays the Same 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?

23. Area Stays the Same 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?

24. ExploringArea & Perimeter 4.3.B

25. Foot Area and Perimeter 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?

26. Using the String This is a great way to show that the area can change even if the perimeter doesn’t. 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?

27. Formulas for Area 4.3.C 5.3.D 5.3.E 5.3.F

28. Formula for a Rectangle 4 2 Look at the rectangle below. Can you think of a formula for determining the area?

29. Formula for a Rectangle 4 2 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?

30. Formula for a Rectangle 4 2 How about if 2 is the base?

31. Formula for a Rectangle 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.

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

33. Finding Area of a Parallelogram 4 3 You can make any parallelogram into a rectangle. The rectangle formula will now work. A = b x h

34. Finding Area of a Triangle 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?

35. Finding Area of a Triangle 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)

36. Questions

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38. Evaluation

39. Resources • About Teaching Mathematics, Marilyn Burns • www.mathsolutions.com • Elementary and Middle School Mathematics: Teaching Developmentally, 5th edition, John A. Van de Walle • www.ablongman.com