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1 1 How many centimeters are in 3 meters? Multiply or Divide Using Equivalents 1 How many meters are in 500 centimeters? Use at least two different methods to solve. To convert from one unit of measurement to another, multiply or divide using equivalents. 1 meter = 100 centimeters Multiplying meters by 100 = centimeters 3 meters =? centimeters 3 meters x 100 = 300 centimeters Table Meters x 100 = Centimeters Meters Centimeters Line Model 3 meters =? centimeters Build a line model with 1 meter on one line and the equivalent 100 centimeters on the line below it. Since we need to find out how many centimeters are in 3 meters, add 2 more sections to the line model. meters 1 m 1 m 1 m centimeters 100 cm 100 cm 100 cm Then add or multiply to find out how many centimeters are in 3 meters. 1 m = 100 cm 1 m = 100 cm + 1 m = cm 3 m = 300 cm 1 m x 3 _ 3 m or 100 cm x cm 5.MD.1 Page 1 of 11 MCC@WCCUSD 02/13/15

2 2 Perimeter is measured around the outside of a 2-dimensional shape. Units are linear (line) and measure the sides. (Think about walking around the playground next to the fence.) 9 cm 2 Yazmin is building a box to hold her bookmark collection. It has a length of 9 inches, a width of 8 inches, and a height of 6 inches. What is the volume of her box? 3 cm 3 cm 9 cm The perimeter of this rectangle is P = 9cm + 3cm + 9cm + 3cm = 24 cm or Perimeter of a rectangle = 2(length) + 2(width) P = 2l + 2w P = 2 9cm ( ) + 2(3cm) = 24 cm Area measures the surface of a 2-dimensional shape and is measured in square units. (Think about covering the surface of the floor with carpet.) Parents are building a planter box for their children s classroom garden. The planter box can hold a maximum of 110 ft 3. It has a length of 11 feet and a width of 5 feet. What is the height of the planter box? 3 cm Area = bh (base x height) The area of this rectangle is A = 9cm 3cm A = 27 cm 2 9 cm The volume of a rectangular prism is 24 cm 3. If the width is 2 cm, what are all possible whole number height and length measurements? 3 cm (height) Volume measures how much it takes to fill a 3- dimensional shape with cubes and is measured in cubic units. (Think about filling a threedimensional figure like a tissue box with cubes.) 9 cm (length) 2 cm (width) The volume of a rectangular prism is 36 cm 3. If the width is 2 cm, what are all possible whole number height and length measurements? Volume = lwh (length width height) V = 9 cm 2 cm 3 cm V = 54 cm 3 5.MD.5 Page 2 of 11 MCC@WCCUSD 02/13/15

3 3 A rectangular box is filled with 36 same-sized cubes. Jamal opens the top of the box and sees 12 cubes. If he opened the right side, how many would he see? 3 A rectangular box is filled with 32 same-sized cubes. You see 8 cubes when you open the box. If you opened the front of the box, how many would you see? Right side Front When he opens the box, he sees 12 cubes, with a length of 4 and a width of 3. Use the Volume formula to find the height of 3, which is the number of layers of cubes in the box. Now that he knows the height, he can find the number of cubes that are visible from the side. It is 3 high and 3 wide, so there are 9 cubes on the side. This is what the end looks like. Three layers of 3 cubes each, which is 9 cubes. 5.MD.3 5.MD.3 Page 3 of 11 MCC@WCCUSD 02/13/15

4 4 This figure is made of cubes that are all the same size. The shaded portion is a hole that goes all the way through the figure. Find how many cubes it would take to fill the hole in the center. 4 This figure is made of cubes that are all the same size. The shaded portion is a hole that goes all the way through the figure. Find how many cubes it would take to fill the hole in the center. 1 cube width cube height To find how many cubes would fill the hole, find the length, width, and height of the hole and then multiply. Therefore, it would take 12 cubes to fill the hole. 5.MD.3 (NAEP) Page 4 of 11 MCC@WCCUSD 02/13/15

5 5 When categorizing a shape, ask yourself if the shape has the attributes of the category. (e.g. A square is a rectangle because it has 4 right angles.) (shape) (category) (attribute) Polygons are closed shapes with 3 or more line segments. Quadrilateral: A polygon with 4 sides. Quadrangle: A polygon with 4 angles. Parallelogram: A quadrilateral with 2 pairs of parallel sides. Rectangle: A parallelogram with 4 right angles. A square has 4 right angles, so it is a rectangle. Rhombus: A parallelogram with all 4 sides that are equal. This is a parallelogram. It s not a rectangle because its angles aren t right angles. It s not a rhombus because all 4 sides aren t equal. Trapezoid: A quadrilateral with exactly 1 pair of parallel sides. Trapezium: A quadrilateral with no parallel sides. Kite: A trapezium with 2 pairs of adjacent sides that are equal. 5.G.3 Page 5 of 11 MCC@WCCUSD 02/13/15

6 5 This is a. Use each of these words once to fill in the blanks: rectangle parallelogram square rhombus parallel quadrilateral This polygon is also a because it has 4 sides. This polygon is also a because it has 2 pairs of lines. This polygon is also a because it has 4 right angles. This polygon is also a because it has 4 sides that are equal. This is a. Describe this polygon s attributes: Is this polygon a quadrilateral? Why or why not? Is this polygon a parallelogram? Why or why not? Is this polygon a rectangle? Why or why not? Is this polygon a rhombus? Why or why not? Page 6 of 11 MCC@WCCUSD 02/13/15

6 Maiya is training for her first soccer season. For 5 days she ran 4 8, 6 8, 7 8, 3 8, and 4 of a 8 mile. The following week she wants to run the same amount every day.

Combine the distances and redistribute the total amount evenly to find out how far she should run if she runs the same amount every day.

They combined the fruit and then shared it equally. How much dried fruit did Robert and each of his friends receive? To make a line plot, we start with a number line marked every th.

7 6 Maiya is training for her first soccer season. For 5 days she ran 4 8, 6 8, 7 8, 3 8, and 4 of a 8 mile. The following week she wants to run the same amount every day. Make a line plot that shows the distances she ran the first week. Combine the distances and redistribute the total amount evenly to find out how far she should run if she runs the same amount every day. 6 Robert and his four friends brought different amounts of dried fruit to share after baseball practice. They brought 5 3, 5 4, 1, 5 3, and 5 4 cups. They combined the fruit and then shared it equally. How much dried fruit did Robert and each of his friends receive? To make a line plot, we start with a number line marked every th. Then we put an X above every value that Maiya ran. Example: She ran of a mile twice, so there should be two X s above. X X X X X To find the amount that Maiya should run if she wants to run the same amount every day, we should add the distances she ran and divide it by the number of days she ran (5 days). Dividing by 5 is the same as multiplying by. She should run 3/5 of a mile every day. 5.MD.2 End of Study Guide Page 7 of 11 MCC@WCCUSD 02/13/15

1 meter = 100 centimeters Dividing centimeters by 100 = meters 500 centimeters =?

8 1 You Try Solutions: How many meters are in 500 centimeters? Use at least two different methods to solve. Multiply or Divide Using Equivalents To convert from one unit of measurement to another, multiply or divide using equivalents. 1 meter = 100 centimeters Dividing centimeters by 100 = meters 500 centimeters =? meters 500 centimeters 100 = 5 meters Table Centimeters 100 = Meters Centimeters Meters Line Model 500 centimeters =? meters Build a line model with 100 centimeters on one line and the equivalent 1 meter on the line below it. Since we need to find out how many meters are in 500 centimeters, add 4 more sections to the line model. centimeters 100 cm meters 1 m Then add the meters to find out how many meters are in 500 centimeters. 100 cm = 1 m 100 cm = 1 m 100 cm = 1 m 100 cm = 1 m cm = + 1 m 500 cm = 5 m 100 cm x cm or 1 m x 5 _ 5 m 2 Yazmin is building a box to hold her bookmark collection. It has a length of 9 inches, a width of 8 inches, and a height of 6 inches. What is the volume of her box? Volume = lwh (length width height) V = 9 in 8 in 6 in V = 432 in 3 Parents are building a planter box for their children s classroom garden. The planter box can hold a maximum of 110 ft 3. It has a length of 11 feet and a width of 5 feet. What is the height of the planter box? Volume = lwh (length width height) The height is 2 ft. The volume of a rectangular prism is 24 cm 3. If the width is 2 cm, what are all possible whole number height and length measurements? Volume = lwh (length width height) So, the length and height must be multiples of 12. The possibilities are: Length (in cm) Height (in cm) CONTINUED on next page. Page 8 of 11 MCC@WCCUSD 02/13/15

If you opened the front of the box, how many would you see? Front So, the length and height must be multiples of 18.

9 2 cont d The volume of a rectangular prism is 36 cm 3. If the width is 2 cm, what are all whole number possible height and length measurements? Volume = lwh (length width height) 3 A rectangular box is filled with 32 same-sized cubes. You see 8 cubes when you open the box. If you opened the front of the box, how many would you see? Front So, the length and height must be multiples of 18. The possibilities are: Length (in cm) Height (in cm) When you open the box you see 8 cubes, with a length of 4 and a width of 2. Use the Volume formula to find the height, which is 4. The length is 4 and the height is 4, so there are 16 cubes showing in the front. Page 9 of 11 MCC@WCCUSD 02/13/15

10 4 This figure is made of cubes that are all the 5 same size. The shaded portion is a hole that goes all the way through the figure. Find how many cubes it would take to fill the hole in the center. This is a square. This polygon is also a quadrilateral because it has 4 sides. This polygon is also a parallelogram because it has 2 pairs of parallel lines. This polygon is also a rectangle because it has 4 right angles. 2 cubes wide cubes long This polygon is also a rhombus because it has 4 sides that are equal. 2 3 cubes high 3 To find how many cubes would fill the hole, find the length, width, and height of the hole and then multiply. Therefore, it would take 24 cubes to fill the hole. This is a trapezoid. Describe this polygon s attributes: A trapezoid is a polygon that has four sides and exactly 1 pair of parallel sides. Is this polygon a quadrilateral? Yes. Why or why not? It is a quadrilateral because it is a polygon with 4 sides. Is this polygon a parallelogram? No. Why or why not? It is not a parallelogram because it does not have 2 pairs of parallel sides. Is this polygon a rectangle? No. Why or why not? It is not a rectangle because it is not a parallelogram and does not have 4 right angles. Is this polygon a rhombus? No. Why or why not? It is not a rhombus because it is not a parallelogram and does not have 4 equal sides. Page 10 of 11 MCC@WCCUSD 02/13/15

6 Robert and his four friends brought different amounts of dried fruit to share after baseball 3 4 3 practice. They brought,, 1,, and 1 5 5 5 cups. They combined the fruit and then shared it equally.

11 6 Robert and his four friends brought different amounts of dried fruit to share after baseball practice. They brought,, 1,, and cups. They combined the fruit and then shared it equally. How much dried fruit did Robert and each of his friends receive? Since Robert and his friends combined the fruit and shared it equally, to find out how much fruit each person got, we must add up all the fruit and divide by the number of people sharing (5 people). Dividing by 5 is the same as multiplying by. Robert and his friends should each get 4 5 of a cup of dried fruit. Page 11 of 11 MCC@WCCUSD 02/13/15

Name Homeroom. MSMM2014

Name Homeroom. MSMM2014 1 Name Homeroom MSMM2014 8 cm area = 10 cm area = 10 cm 9 cm area = 7 cm 10 cm area = area = area = 10 cm 10 cm 10 cm MSMM2014 1 Topic: Area of Rectangles and Squares I CAN find the area of rectangles