Length and area Block 1 Student Activity Sheet


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1 Block 1 Student Activity Sheet 1. Write the area and perimeter formulas for each shape. 2. What does each of the variables in these formulas represent? 3. How is the area of a square related to the area of a rectangle? 4. How is the area of a triangle related to the area of a rectangle? 5. How can you find the perimeter of any shape? Page 1 of 2
2 Block 1 Student Activity Sheet 6. Practice your estimation skills. a. Estimate the dimensions of the smaller rectangle in centimeters. Estimate the dimensions of the larger rectangle in inches. Estimate to the nearest whole number. Label each rectangle with your estimates. b. Estimate the area and perimeter of the fried egg. Use the scale given. The area is about. The perimeter is about. Page 2 of 2
3 Block 2 Student Activity Sheet 1. Estimate the perimeter of each triangle. You can use the edge of your pencil to mark the length of the hypotenuse. Then compare it to the vertical side and the grid. Page 1 of 6
4 Block 2 Student Activity Sheet 2. How could you find the perimeters of these irregular shapes? 3. Estimate the perimeter of each irregular shape. Describe how you made your estimates. Page 2 of 6
5 Block 2 Student Activity Sheet 4. Use tiles to estimate the area of each shape. Record your estimates in the table. Shape Estimate of area in cm 2 Page 3 of 6
6 Block 2 Student Activity Sheet 5. Can you think of way to estimate the area of the two shapes shown without placing tiles on the shapes? Explain your answer. Page 4 of 6
7 Block 2 Student Activity Sheet 6. REINFORCE Estimate the perimeter of each triangle in centimeters. Each grid square represents 1 cm long by 1 cm wide. a. 1) 2) b. c. 3) 4) d. e. 5) 6) f. Page 5 of 6
8 Block 2 Student Activity Sheet 7. REINFORCE Estimate the perimeter (cm) and area (cm 2 ) of each shape. Each grid square represents 1 cm long by 1 cm wide. Page 6 of 6
9 Block 4 Student Activity Sheet 1. REINFORCE Estimate the perimeters of objects in the classroom. For each object, first estimate without a ruler, then measure with a ruler. Estimate and measure each object in both centimeters and inches. When measuring with a ruler, measure to the nearest 1 4 inch or nearest tenth of a centimeter. Record your findings in the table. An example is shown. Object Perimeter in centimeters Perimeter in inches book 25 cm + 30 cm + 25 cm + 30 cm = 110 cm 22 cm + 28 cm + 22 cm + 28 cm = 100 cm 9 in + 10 in + 9 in + 10 in = 38 in 8.75 in in in in. = 39.5 in. Page 1 of 4
10 Block 4 Student Activity Sheet 2. REINFORCE Was it easier to estimate without a ruler for inches or centimeters? Why do you think one system was more challenging than the other? 3. REINFORCE In what way(s) did your estimations without a ruler improve as you measured more objects? Page 2 of 4
11 Block 4 Student Activity Sheet 4. REINFORCE Now estimate the perimeters of objects in meters and yards. Remember to estimate without your meter or yard stick first. Object Perimeter in meters Perimeter in yards Page 3 of 4
12 Block 4 Student Activity Sheet 5. REINFORCE Pick one large object and one small object outside of the classroom. You will estimate the perimeters of these objects. Record a description of the objects and their locations. a. Small object description: b. Large object description: Estimate the perimeter of each object without using a measuring tool. Record your estimates. c. Small object perimeter estimate without using a measuring tool: d. Large object perimeter estimate without using a measuring tool: Estimate the perimeter of each object using a measuring tool. Record your estimates. e. Small object perimeter estimate using a measuring tool: f. Large object perimeter estimate using a measuring tool: Page 4 of 4
13 Block 5 Student Activity Sheet 1. Sometimes when you measure you need to convert units. For example, you might measure in feet and then convert to inches. a. How many square inches are in a square foot? Sketch a picture to help explain your answer. b. How many square inches are in 3 square feet? c. How many square centimeters are in a square meter? d. How many square millimeters are in 3 square centimeters? Page 1 of 4
14 Block 5 Student Activity Sheet 2. A table has an area of 4 square yards. How many square inches is the area of the table? 1 yard 2 = inches 2 4 yards 2 = inches 2 3. An island has an area of 12 square kilometers. How many square meters is the area of the island? 1 kilometer 2 = meters 2 12 kilometers 2 = meters 2 4. A map has an area of 8 square feet. How many square inches is the area of the map? 1 foot 2 = inches 2 8 feet 2 = inches 2 Page 2 of 4
15 Block 5 Student Activity Sheet 5. Find the area of this irregular polygon. 6. Find the area of the puzzle of the United States map. Page 3 of 4
16 Block 5 Student Activity Sheet 7. REINFORCE Find the area of each shape in square centimeters. Each grid square represents 1 cm long by 1 cm wide. a. b. c. d. Page 4 of 4
17 Block 6 Student Activity Sheet 1. Use the dimensions from the octagon to fill in the dimensions of the rectangle. Then calculate the area of the octagon. 2. Use the dimensions from the hexagon to fill in the dimensions of the rectangle. Then calculate the area of the hexagon. Page 1 of 3
18 Block 6 Student Activity Sheet 3. Use the dimensions from the pentagon to fill in the dimensions of the rectangle. Then calculate the area of the pentagon. Page 2 of 3
19 Block 6 Student Activity Sheet 4. REINFORCE Use the given coordinates to graph shapes in the coordinate plane. Then, find their areas. a. Shape 1 coordinates: A(2,7), B(6,7), C(6,0), D(5,3) b. Shape 1 area: c. Shape 2 coordinates: E(0,1), F(3,1), G(4,5), H(0,5), J(8,3) d. Shape 2 area: Page 3 of 3
20 !
21 Block 8 Student Activity Sheet 1. Consider the shapes that are used to cover the pedestal. Cut out each of the quadrilaterals. square with side lenghs of 3 inches Page 1 of 6
22 Block 8 Student Activity Sheet This page is intentionally blank so that students can cut out the pedestal shapes. Page 2 of 6
23 Block 8 Student Activity Sheet a. Make a sketch of the kite and the rectangle that can be made from it. i. What are the dimensions of the rectangle that can be made from the kite? ii. What is the area of the rectangle that can be made from the kite? Page 3 of 6
24 Block 8 Student Activity Sheet b. Make a sketch of the rhombus and the rectangle that can be made from it. i. What are the dimensions of the rectangle that can be made from the rhombus? ii. What is the area of the rectangle? c. Make a sketch of the trapezoid and the rectangle that can be made from it. i. What are the dimensions of the rectangle that can be made from the trapezoid? ii. What is the area of the rectangle? Page 4 of 6
25 Block 8 Student Activity Sheet 2. REINFORCE What are the dimensions and the area of the rectangle that can be made from the kite? 4 in. 7 in. 3 in. 3. REINFORCE What are the dimensions and the area of the rectangle that can be made from the trapezoid? 7 cm 4 cm 2 cm 2 cm Page 5 of 6
26 Block 8 Student Activity Sheet 4. REINFORCE What are the dimensions and the area of the rectangle that can be made from the rhombus? 5 2 Page 6 of 6
27 Block 9 Student Activity Sheet 1. How many trapezoids can be cut from a sheet of foam board? In other words, how many 4foot by 2foot rectangles can fit on the 8foot by 4foot sheet of foam board? Sketch at least one possible arrangement to show how you thought about the question. Copyright 2017 Agile Mind, Inc. Page 1 of 5
28 Block 9 Student Activity Sheet 2. How many kites can be cut from a sheet of foam board? In other words, how many 8foot by 1foot rectangles can fit on the 8foot by 4foot sheet of foam board? Sketch at least one possible arrangement to show how you thought about the question. Copyright 2017 Agile Mind, Inc. Page 2 of 5
29 Block 9 Student Activity Sheet 3. The pedestal is made up of 4 rhombuses, 4 trapezoids, 4 kites, and 1 square. You have filled up two complete pieces of foam board. a. How many shapes will Sean and Kyle cut from those two pieces of foam board? They will cut 4 trapezoids and 4 kites from the two pieces of foam board. b. How many shapes do they still have to cut from foam board? They still need to cut 1 square and 4 rhombuses from the foam board. Copyright 2017 Agile Mind, Inc. Page 3 of 5
30 Block 9 Student Activity Sheet 4. Sketch an efficient way to fill up a piece of foam board with the remaining pieces. The dimensions of the square part of the pedestal are 3 feet by 3 feet. If you do this efficiently, you should be able to fit all the remaining pieces into a 6foot by 4foot area. Copyright 2017 Agile Mind, Inc. Page 4 of 5
31 Block 9 Student Activity Sheet 5. Now use what you have learned about the area of the foam board and the shapes. Calculate the total surface area of the pedestal. Copyright 2017 Agile Mind, Inc. Page 5 of 5
32 !
33 Block 10 Student Activity Sheet 1. Here is the polygon representing the base of the packaging. Write the coordinates of point A as it is shown on the graph. Page 1 of 8
34 Block 10 Student Activity Sheet 2. Now consider the distance between the vertices of the polygon. Each gridline represents 1 inch. a. Points A and B both have the same ycoordinate. How far is each point from the xaxis? Page 2 of 8
35 Block 10 Student Activity Sheet b. What is the distance of each point from the yaxis? Use the absolute value of each point s xcoordinate to find out. Page 3 of 8
36 Block 10 Student Activity Sheet c. Points E and F are on the same side of the yaxis. Use absolute value to find the distances of points E and F from the yaxis. Page 4 of 8
37 Block 10 Student Activity Sheet d. What is the distance between point E and point F? Page 5 of 8
38 Block 10 Student Activity Sheet 3. Now apply what you are learning about using coordinates to find distances. a. Graph these points: A(4.2,4), B(2,1.7), C(2,3.5), D(4.2,3.5) b. Find the distance between each pair of points. i. Points A and D ii. Points C and D iii. Points B and C Page 6 of 8
39 Block 10 Student Activity Sheet 4. REINFORCE Find the length of AB. A (5,4) B (2,4) 5. REINFORCE Find the coordinates of point J, if its distance from point M is 4 units. J M (3,1) Page 7 of 8
40 Block 10 Student Activity Sheet 6. REINFORCE Practice your skills in graphing points and finding distances in the coordinate plane. a. Graph these points: E(3.7,3), F(2.4,3), G(2.4,3.5), H(3.7,2.1) b. Find the distances between each pair of points listed. i. E and F ii. F and G iii. E and H Page 8 of 8
41 Block 11 Student Activity Sheet 1. Use the coordinates in the graph to find the lengths of the polygon s remaining sides. 2. Find the total distance the machine must cut to create the polygon base. Page 1 of 5
42 Block 11 Student Activity Sheet 3. Calculate the amount of packaging material in the polygon base of the package. 4. The coordinates of a parallelogram are given. Determine whether each statement is true or false. Record your reason for each decision. a. The length of the longer side is a 4. b. The shorter side is 8 units in length. Page 2 of 5
43 Block 11 Student Activity Sheet c. d = 10 d. c > a e. a = 4 Page 3 of 5
44 Block 11 Student Activity Sheet 5. REINFORCE You plan to walk from home along the indicated route. You will start at home, go to school, to the library, to the park, and back home again. a. Fill in the missing coordinates on the graph representing your route. b. Find the distance of your route. c. Find the area of the city surrounded by your route. Show or explain your process. Page 4 of 5
45 Block 11 Student Activity Sheet 6. REINFORCE Use the coordinates given to determine the area of the polygon in square units. Show how you found your answer A (2,7) B (3,7) D (8,5) C (3,1) Page 5 of 5
46 !
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