Mathematics Grade 6 Solve Perimeter, Area, and Volume Problems

Transcription

1 Mathematics Grade 6 Solve Perimeter, Area, and Volume Problems

2 Dear Parent or Guardian: Your son or daughter is currently learning how to find the perimeters, areas, and volumes of figures. Here is your chance to help your son or daughter practice this important skill. In this PAL Packet you will find a short activity for you and your son or daughter to do. Please do the activity and The Back Page this evening. Then sign your name on The Back Page and have your son or daughter return it tomorrow. Thanks for your help. Sincerely, Your son or daughter s teacher Grade 6 Solve Perimeter, Area, and 2004 Evans Newton Incorporated 1

3 PERIMETER, AREA, AND VOLUME Parent Pointer Using formulas or other ways of finding the perimeter, area, and volume of figures is important when you need to find specific measurements of figures. If you have moved, most likely you have used boxes to pack your belongings. So that you know how many of your belongings can fit in a box, you would want to know the volume of the box, which is the amount of space inside. Perimeter and area are measurements that are used by people in professions like construction. If construction workers are putting up a fence, they need to know the perimeter of the plot of land, or the measurement around the land. While the perimeter is the measurement around a figure, the area measures the inside of a figure. Developers need to know how to find the area of a plot of land so that they can make plans for building homes, apartment buildings, or business buildings. Math In the Home, On the Go, and For the Fun of It DIRECTIONS: Review the use of formulas to find measurements for figures with your parent or guardian by reading through the examples. Then, determine areas and perimeters of figures and compare them with other figures to see if they are larger or smaller. Last, help a fictional packing company find the volumes of packing boxes and create a comparison of your own. Talk About It After you have finished the activity, turn to The Back Page to show what you know. Now go have some fun with the activity! Grade 6 Solve Perimeter, Area, and 2004 Evans Newton Incorporated 2

4 FINDING PERIMETER, AREA, AND VOLUME Perimeter is the distance around a figure. Several formulas can be used to find the perimeter, depending upon the type of polygon. A regular polygon has sides that are all the same length and angles that are all the same measure. A polygon that does not have equal sides and angles has a different formula. 7 yd 3 yd 4 m 3 yd 4 yd 8 yd 4 m 6 yd P = 2l + 2w P = 4s P = s + s + s + s Area is the number of square units needed to cover a figure. Height Base Area of a rectangle A = l w Area of a right triangle A = 1 2 bh Volume is the number of cubic units it takes to fill a solid. Height Volume of a cube V = lwh Length Width Grade 6 Solve Perimeter, Area, and 2004 Evans Newton Incorporated 3

5 Help the following people determine if measurements are the same or if they are different. If you wish, draw diagrams on a separate piece of paper to help you. Circle the statement that is true. Ali and Robert are helping their grandmother by placing fencing around two of her rose gardens. The rectangular garden Robert is working on measures 2 feet by 3 feet. The rectangular garden in the backyard that Ali is working on measures 4 feet by 6 feet. Which statement is true about the perimeters of these gardens? The perimeter of the garden Ali is working on is twice as long as the perimeter of Robert s garden. The perimeter of the garden Robert is working on is twice as long as the perimeter of Ali s garden. The perimeter of the garden Ali is working on is one-half the length of the perimeter of Robert s garden. The perimeter of the garden Robert is working on is five feet longer than the perimeter of Ali s garden. Mr. Carpenter needs to know if one section (which forms a right triangle) of the house he is working on is larger or smaller than the other section (which also forms a right triangle). The first triangle measures 6ft for the base and 6ft for the height. The second triangle measures at 12 ft for the base and 12 ft for the height. Which statement is true? The second triangle is three times as large as the first. The second triangle is four times as large as the first. The first triangle is one-half the size of the second. The triangles are the same size. Grade 6 Solve Perimeter, Area, and 2004 Evans Newton Incorporated 4

6 Pack it Up and Move it Out! Find the volumes of the moving boxes below, and write them in the boxes marked volume. Length = 12 in Height = 12 in Width = 12 in Length = 6 in Height = 6 in Width = 6 in Volume: Volume: Draw diagrams of two boxes, write their measurements, and explain if their volumes are the same, or if one is greater than the other. Grade 6 Solve Perimeter, Area, and 2004 Evans Newton Incorporated 5

7 The Back Page Talk About It Parent Ask your child the following question: How do you find the perimeter and the area of a rectangle and a triangle? Student Answer the above question in a complete sentence on the bottom of this page. OR Do one of the following activities (use the back side of this page if needed): Show how you find the perimeter and the area of a rectangle and a triangle in a drawing. Trace objects you find around the house on grid paper, and find the perimeters and the areas of these objects. See if you can find the volume of some of these objects, like a cereal box. Student s Name Parent or Guardian s Signature Grade 6 Solve Perimeter, Area, and 2004 Evans Newton Incorporated 6