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What is happening to the perimeter each time the tables are rearranged?

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What is happening to the perimeter each time the tables are rearranged?

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  1. Investigation #1Let’s review what has happened so far in this story…A) Thirty-two people are coming to the reunion.B) Mrs. Comfort has ordered 8 square tables for the guests. C) as the guests arrive, tables are rearranged to accommodate seating. D) With each new arrangement, Mrs. Comfort says, “But that won’t work!” until she finally gives up! Today we will be investigating perimeter and area. Each group has been given 8 Cheez-its (tables) and 32 Cheerios (guests). As I read this book, you will arrange the tables and chairs accordingly. Each time you will record the guests seated, the table arrangement, the perimeter, and area of the tables on the Seating Chart. What is happening to the perimeter each time the tables are rearranged? If shapes have the same area, do they always have the same perimeter?

  2. Investigation #2You have been given a puppy for Christmas. Your parents told you that you could have 30 square feet of the back yard to create a “play area” for your puppy, but you will have to pay for the fencing. The fencing costs $5.67 per foot. Using 30 Cheez-its, design different “play areas” for your puppy. Each time record the area, perimeter, and cost of fencing (Perimeter x $5.67). Which design should you use in order to save money on fencing?

  3. Investigation #3 Each group has been given 6 Cheez-its. You are to use these tiles to answer the following questions? • What is the perimeter of the given object? • Where would you place a tile to increase the perimeter by 0? By 1? By 2? By 3? Draw a sketch on your centimeter paper to answer each of the questions above. • What is the fewest number of tiles that can be added to increase the perimeter to 16 units? Draw a sketch of this figure. • What is the greatest number of tiles that you can add to increase the perimeter to 16 units. Draw a sketch of this figure. • Is there a way to add a tile to decrease the perimeter?

  4. Investigation #3After reading Grandfather Tang’s story, Tia and Marquez were playing with 5 of the seven-tangram pieces that Grandfather Tang used. They removed the two big triangles. Tia made a rectangle and Marquez made a square. Each group has been given 5 tangrams. Use those tangrams to create Tia’s rectangle and Marquez’s square. When you are done, trace your shapes on the grid paper, and answer the following questions: • What are the similarities in the two shapes? • What are the differences in the two shapes? • How do I measure the space surrounding each object? • What is the perimeter of each figure? Tia: ______ Marquez:______ 5. How do I measure the space each shape covers? 6. What is the area of each figure? Tia: _____ Marquez:_______ 7. How do we know the areas are the same? 8. Make a rule for finding the area of squares and rectangles.

  5. What is the difference between perimeter and area? Area is the number of square units inside of a polygon. Perimeter is the distance around a polygon. Polygons – closed plane shape with ______ sides. Quadrilateral Square- Congruent sides/ congruent angles Rhombus- parallelogram with congruent sides. Rectangle – parallelogram with 4 right angles. Trapezoid- one pair of parallel sides. Parallelogram- two sets of parallel sides.

  6. Names of Other Polygons Types of Triangles

  7. Get ready! Hold up your “A” if you need to find the AREA. Hold up your “P” if you need to find PERIMETER. A’niyah is putting grass in her backyard. The backyard is 12 yards by 12 yards. How much grass will she need for the backyard? Jabriel is putting tiles on his patio floor. The size of the patio is 8ft by 9ft. The tiles are 1ft by 1ft. How many tiles will he need to cover his patio floor? How many plants will Dakala be able to put inside of her garden? Cobi decided to put Christmas lights around the outside edge of the roof of his house. His roof was 50ft by 30ft. The lights are sold in strands of 30ft. How many strands will Cobi need to purchase?

  8. Investigation #5You and your partner have been given a half sheet of paper. You must cut the paper so that you can fit in it (it must go around your perimeter). It must remain connected. You can not cut into pieces then tape it. Investigation #6With your partner, you will use cm graph paper to create 5 figures with the perimeter of 16, 20, and 24. Each time recording the area. Investigation #7 Using hexagons, make a “hexagon train”. Create an input output table recording the number of hexagons and the perimeter. What’s the rule?

  9. How do you find the area and perimeter of complex shapes? Strategies:

  10. How do you find the missing dimension when given the area/perimeter? Investigation #8: Work with your partner to create the following: A square with a perimeter of 8 cm and an area of 4 cm A rectangle with a perimeter of 12 cm and an area of 8 cm A rectangle with a perimeter of 14 cm and an area of 12 cm A square with a perimeter of 12 cm and an area of 9 cm The perimeter of a rectangle is 30 in. The length is 12 in. What is the width? The area of a rectangle is 30 cm². The base is 6 cm. What is the height?

  11. Investigation #9Measure the length and width of each square and rectangle, and then calculate its area. 1. Using a ruler, draw a diagonal (from one corner to the opposite corner) on shapes A, B, and C.2. Along the top edge of shape D, mark a point that is not a vertex. Using a ruler, draw a line from each bottom corner to point you marked. (Three triangles should be formed.)3. Cut out the shapes. Then, divide A, B, and C into two parts by cutting along the diagonal, and divide D into three parts by cutting along the lines you drew. 4. How do the areas of the resulting shapes compare to the area of the original shape? 5. Develop a formula for finding the area of a triangle.

  12. B x H2 • Investigation # 10 • Using the Triangles labeled “1” and “2”, position each triangle on centimeter grid paper. Trace the triangle. Label the base and height of each triangle. Explain how you found the area. Include any calculations that you do. • Find a second way to place each triangle on the grid paper. Label the base and height of each triangle in its new position. Find the area of each triangle. Explain how you found the area. Include any calculations that you do. • Does changing which side you label the base change the area of the triangle? Explain. Investigation # 11: On your cm grid paper, draw 4 segments 6 cm long. Use these segments as the base for each triangle. 1) Sketch a right triangle with a height of 4 cm. 2) Sketch an isosceles triangle with a height of 4 cm. 3) Sketch a scalene triangle with a height of 4 cm. 4)Find the area of each triangle you made.

  13. Find the area of the following triangles.

  14. How do I find the area of parallelograms? Investigation #12 • You and your partner will draw a line from the lower left corner of “Rectangle A” to a point on the top edge that is three units from the upper left vertex; this line will form a 45-degree angle, with divides each of the squares through which it passes exactly in half. Cut that line. Tape the triangle that you have created to the opposite side of the remaining rectangle to create a parallelogram. • For “Rectangles B and C”, use a ruler to draw a straight line from the lower left corner diagonally to any point along the top edge where the grid lines meet. Cut out that triangle and tape it to the other end of the rectangle. One such cut is shown below. You should try to make different cuts then the other group at your table. • Find the area of each parallelogram you created. • Using shapes D and E, remove the right triangles on either the right or left side, as shown below, and move it to the other side. • What is the formula for the area of a parallelogram?

  15. Your turn! Find the area of the parallelograms.

  16. Power Point Exit Quiz. Number your paper 1 – 10. • What is the area of the above shape? • How do you find the area of a triangle? • How do you find the area of a parallelogram? • Can two shapes have the same perimeter but different areas? • Find the perimeter of this figure. • Find the area of the figure. • Find the area of the triangle. • What is the base? • What are 3 key words that indicate perimeter? • What are 3 key words that indicate area?

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