Measurement and Geometry

Transcription

1 Name Date Class Review for Mastery: Converting Customary Units You can use the table below to convert customary units. Length 1 foot = 1 inches 1 yard = 36 inches 1 yard = 3 feet 1 mile = 5,80 feet 1 mile = 1,760 yards Weight 1 pound = 16 ounces 1 ton =,000 pounds Capacity 1 cup = 8 fluid ounces 1 pint = cups 1 quart = pints 1 quart = 4 cups 1 gallon = 4 quarts 1 gallon = 18 fluid ounces To figure out how many pounds are in 3 ounces, set up a proportion where the first ratio uses the fact that 16 ounces are in 1 pound. The second ratio should have the value you know, 3 ounces, and a variable for the value you are trying to find, x pounds. 16 ounces = 3 ounces 1 pound x pounds Then solve the proportion. 16 ounces = 3 ounces First, find the cross products. 1 pound x pounds 16x = 3 Think: 3 16 = x x = So, there are pounds in 3 ounces. Then, use a related math sentence to solve the equation. Use the table above to set up a proportion. Then find each of the values. 1. the number of pounds in 80 ounces. the number of quarts in 6 gallons 1 16 = 4 1 = 3. the number of yards in 5 miles 4. the number of cups in 0 pints

2 Name Date Class Review for Mastery: Converting Metric Units There are patterns in powers of ten = = = 1,000 The number of times 10 is a factor equals the number of zeros in the power of ten. You can use these patterns to multiply and divide by powers of ten. The number of zeros or the number of tens tells you how many places to move the decimal point. If you are dividing by a power of ten, move the decimal point left. If you are multiplying by a power of ten, move the decimal point right. 7, = = 3,400 two zeros, two places three tens, three places , Multiply or divide ,347.8 (10 10) _ , The metric system uses powers of ten. _ Each place value is 10 times as large as the place value to the right. 1, thousands hundreds tens ones tenths hundredths thousandths kilo hecto deka meters deci centi milli m = cm The centimeter unit is places to the right of the meter. m = 00 cm Move the decimal point places to the right. Use the chart to convert each measure km = mm 6. 7 dm = hm dam = m cm = dm

3 Name Date Class Review for Mastery: Area of Rectangles and Parallelograms You can use grid paper to estimate and find area of figures. The area of a figure is the amount of surface it covers. Area is measured in square units. To estimate the area of the figure below, first find the number of fully shaded squares. Next, find the number of nearly full squares. Then, find the number of half or nearly half-shaded squares. There are 6 fully shaded squares. There are nearly full squares. There are 8 half-shaded squares. (8 1 = 4) Find the estimated total number of squares shaded = 1. The area of the figure is about 1 square units. Estimate the area of each figure. 1.. _ To find the area of a rectangle, find the total number of square units. There are 3 rows of 5 squares. 3 5 = 15 So, the area of the rectangle is 15 square units. Find the area of each rectangle _

4 Name Date Class Review for Mastery: Area of Rectangles and Parallelograms (continued) To find the area of a parallelogram, first turn your parallelogram into a rectangle. Then find the area of the rectangle. Because the area of a rectangle is A = lω, the area of a parallelogram is A = bh. 4 = 8 So, the area of the parallelogram is 8 square units. Find the area of each parallelogram _ Sometimes you need to subtract a smaller area from a larger area. A rectangular yard is made up of a rectangular flower garden surrounding a rectangular vegetable garden. The yard is 9 ft by 7 ft. The vegetable garden is 3 ft by ft. What is the area of the flower garden? First find the area of the yard and the area of the vegetable garden. Area of yard: A = lw = (9 7) = 63 Area of vegetable garden: A = lw = (3 ) = 6 Then subtract the area of the vegetable garden from the area of the yard to find the area of the flower garden = 57 So the area of the flower garden is 57 square feet. Solve. 7. A rectangular yard is made up of a rectangular grass lawn surrounding a rectangular patio. The yard is 1 ft by 10 ft. The patio is 4 ft by 5 ft. What is the area of the grass lawn?

5 Name Date Class Review for Mastery: Area of Triangles and Trapezoids To find the area of a triangle, first turn your triangle into a rectangle. Next, find the area of the rectangle. 6 3 = 18 The triangle is half the area of the formed rectangle or A = 1 bh, so divide the product by. 18 = 9 So, the area of the triangle is 9 square units. Find the area of each triangle. 1.. _ To find the area of a trapezoid, first turn the trapezoid into two triangles and a rectangle. Find the area of each triangle. A = 1 bh A = 1 ( 5) = 1 10 = 5 Find the area of the rectangle. A = lw A = 4 5 = 0 Now find the sum of the areas = 30 So, the area of the trapezoid is 30 square units. Find the area of each trapezoid _

6 Name Date Class Review for Mastery: Area of Composite Figures Sometimes you can use area formulas you know to help you find the area of other figures. To find the area of the figure below, first divide the figure into figures you know. The figure is made up of a triangle, a parallelogram, and a rectangle. Next, find the area of each figure. Triangle Parallelogram Rectangle A = 1 bh A = bh A = lω = 1 (3 4) = 3 4 = 4 5 = 6 = 1 = 0 Then, find the sum of all of the areas = 38 The area of the figure is 38 square units. Find the area of each figure

7 Name Date Class Review for Mastery: Volume of Prisms Volume is the number of cubic units needed to fill a space. To find the volume of a rectangular prism, first find the area of the base. length = 3 units width = units A = l = 3 = 6 square units. The area of the base tells you how many cubic units are in the first layer of the prism. Next, multiply the result by the number of layers in the prism. The prism has 4 layers, so multiply 6 by = 4 So, the volume of the rectangular prism is 4 cubic units. Find the volume of each rectangular prism. 1.. _ To find the area of a triangular prism, first find the area of the base. A = 1 bh = 1 (5 4) = 10 square units Then multiply the result by the height of the prism = 30 The volume of the triangular prism is 30 cubic units. Find the volume of each triangular prism _

8 Name Date Class Review for Mastery: Surface Area You can use what you know about finding the area of polygon to find the surface area of a three-dimensional figure. To find the surface area of the regular triangular prism above, first find the area of each face. congruent triangular bases 3 rectangular faces A = 1 bh A = l w = 1 (4 3) = 4 6 = 6 square units = 4 square units Then, find the sum of all of the faces of the prism. SA = = 84 square units Find the surface area of each figure. 1.. _

9