1.1 Metric Systems. Learning Target: to practice converting between different metric units. Main Ideas:

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1 1.1 Metric Systems Learning Target: to practice converting between different metric units Formula sheet Multiplying and dividing fractions Definitions Metric System The International System of Units, abbreviated SI, is the official system of measurement in Canada. It is a system of measurement using powers of 10 (10, 100, 1000, 0.1, 0.01 ). From your formula sheet: The advantage of the metric system is that it is easy to convert from one unit to another. That is because the metric system is based on the number 10. Find the missing lengths To convert between units, we will use UNIT ANALYSIS: 1) Write down what you are starting with, then a (for multiplication) 2) Find the conversion you need from the conversion table on your formula sheet 3) Write the conversion as a fraction, making sure to put the units you have at the start on the BOTTOM of the fraction, and the units you want at the TOP of the fraction (this ensures that the units you had at the start cancel out) 4) Multiply the starting amount by the fraction to get the units you want *** you may need to multiply by more than one conversion fraction to get the units you need Ex 1) Find the equivalent measurement: round decimals to nearest hundredth a) 3 km = m b) 15040cm = km

2 Adding different units together When adding units together that aren t the same, get them all in to the desired unit using unit analysis, and then add together. Round to nearest tenth Ex 2) Add: 0.2m + 47cm + 86mm mm Ex 3) Add: 4.3km m + 128cm m Word Problems Ex 4) The record for the longest long jump was set by Mike Powell of the USA, in His jump measured 8950mm. How many meters long was his jump?

3 1.2 Imperial Systems Learning Target: to estimate imperial measures of length and to convert between imperial units Anything you know about imperial measures Unit Analysis Multiplying fractions The imperial units of measure are mainly used in the United States, but in Canada they are still used for certain measurements. Lumber, plywood, and screws are examples of manufactured items that use imperial units. Common Imperial Measures of Length Warm-up: Use your formula sheet. How many inches are in a foot? How many yards are in a mile? What are the short forms for: inch foot yard mile Imperial and fractions: Ex 1) How long is this pencil (in inches)? Use the picture, not your own ruler. Conversions Ex2) Using your formula sheet and UNIT ANALYSIS, convert: a) 6 yards to feet b) 20,154 inches to miles round to nearest thousandth

4 Finding equivalent measures Ex 3) Find the equivalent measurement, and express any decimal answers to the nearest hundredth: a) 9500ft = mi b) 55 1 in = yd 4 c) 0.34mi = in Word Problem Mr. Baker set the world over 40 s discus record by achieving a throw of 23 yards, 2 feet and 9 inches. How many inches was his record setting throw?

5 1.3 Converting Metric and Imperial Systems Learning Target: to practice converting between metric and imperial units of measurement Formula sheet Unit analysis = means means If you study fields such as engineering, chemistry, and nursing, you will need to convert measurements between the two systems. To convert between metric and imperial measures, it is helpful to have equivalent values. These are listed on your formula sheet: Ex1) Ex1) A bowling lane is approximately 19 m long. What is this measurement to the nearest foot? Use unit analysis and your formula sheet: Ex2) What if you can t find the exact conversion on the formula sheet? Ex2) Convert 720cm to yards. Use unit analysis, but this time it will be a twostep conversion: round to nearest hundredth

6 Ex3) Convert the following, and round to three decimal places: a) 25.8 m = yd b) 73 in = m Ex4) Find the equivalent measurement to three decimal places: a) 7 ft 1 in = m (the height of Shaquille O Neal) b) 35 km/hr = mi/hr (the top speed of Mr. f s first car) WORD PROBLEM Using conversions to compare measurements Ex5) Two students compare their heights: Frodo is 160cm and Sam is 5'2". Who is taller, and by how much (to the nearest inch)? For all comparisons: Key In order to compare, we need Frodo: Sam:

7 1.4 Surface Area and Volume of Prisms Learning Target: to solve problems involving the surfaces areas and volumes of prisms. Pythagoras Using formulas carefully Units for area: Units for volume: Using the calculator carefully! Ex: π button (not 3.14) Definitions Surface Area the sum of the areas of all the surface faces of the shape Lateral Area the sum of the area of all the sides of a 3D object except its top and bottom bases. Refer to the 3D pictures on your formula sheet and identify the lateral area of each shape. Volume the measure of the amount of space contained in a solid. If B is the area of the base of the prism and h is the height of the prism, then: Volume = B h Step 1: Sketch and label a diagram Step 2: Write the formula you need: Ex 1) Investigate the surface area and volume formulas for a rectangular prism (on your formula sheet). Then, find the surface area and volume of a rectangular prism with a length of 4m, width of 2m and a height of 5m. Step 3: List the values you know Step 4: Substitute into the formula (use brackets!) Step 5: Evaluate and remember units! Ex2) Investigate the surface area and volume formulas of a triangular prism (on your formula sheet). Calculate the surface area and volume of the following:

8 Composite objects A composite object is an object made of two or more 3D shapes put together. To calculate and surface area, find the area of each side, and add them up. For volume, find the volume of each object individually and add them together. Ex 3) Find the surface area and the volume of the following composite object. Ex 4) Find the surface area and the volume of the following composite object.

9 1.5 Surface Areas and Volumes of Pyramids Learning Target: to solve problems involving the surface area and volumes of pyramids. Pythagoras: Area of a triangle: + other formulas on your formula sheet Using the calculator carefully! Ex: π button (not 3.14) Ex: 615 4π type 615 / (4π ) Step 1: Sketch and label a diagram Step 2: Write the formula you need: Ex 1) Find the surface area and volume of a square pyramid that has a base dimension of 7.2m, a height of 9.9m and a slant height of 10.1m (to the nearest tenth). Step 3: List the values you know Step 4: Substitute into the formula (use brackets!) Step 5: Evaluate and remember units! Missing Slant Height Ex 2) Find the surface area and volume of the following pyramid:

10 1.6 Surface Area and Volume of Cylinders, Cones and Spheres Learning Target: to solve problems involving the surface area and volume of cylinders, cones and spheres. Pythagoras Using formulas carefully Units for Surface Area: Units for volume: Definitions: Diameter a straight line passing from one edge of a circle or sphere to the other, passing through the centre. Radius a straight line extending from the centre of a circle or sphere to the edge. If you are given the diameter, divide it by 2 to get the radius. Step 1: Sketch and label a diagram Ex 1) Investigate the surface area and volume formulas for a cylinder (on your formula sheet). Then, find the surface area and volume of a cylinder with a radius of 2m and a height of 5m (to the nearest tenth). Step 2: Write the formula you need: Step 3: List the values you know Step 4: Substitute into the formula (use brackets!) Step 5: Evaluate and remember units Ex 2) Find the surface area and volume of a sphere with a diameter of 12cm.

11 What if you don t know the height? Ex3) Determine the volume of this cone to the nearest cubic inch. Working Backwards Same steps! (ALMOST) Step 1: Sketch and label a diagram Ex4) A cone has a height of 9.2m and a volume of cubic metres. Determine the radius of the base of the cone to the nearest tenth of a metre. Step 2: Write the formula you need Step 3: List the values you know Step 4: Substitute into the formula Step 5: SOLVE for what s missing and remember units.