Mathematics MAT1L Unit 2 Lesson 6

Transcription

1 Expenses Lesson 6

2 Mathematics MAT1L Unit 2 Lesson 6 Lesson Six Concepts Write money values, using correct units. Use estimation strategies involving addition and multiplication. Enter decimal numbers correctly on a numerical key pad. Demonstrate the effective use of a calculator in operations with decimals. Judge the reasonableness of calculations involving decimals, through estimation using mental mathematics, where appropriate. Solve problems involving estimating the totals of money values found in real contexts. Solve problems requiring estimating and calculating the cost of projects that require the purchase of multiples of the same item. Solve problems involving the cost of several items and use technology as appropriate. Identify, record, and monitor daily purchases to determine personal weekly expenditures. Explain their reasoning used in problem solving and in judging reasonableness. Communicate in writing the solutions to money problems using appropriate terminology, symbols and form. Calculating Costs Example Complete the invoice below. Copyright 2005, Durham Continuing Education Page 2 of 33

3 Mathematics MAT1L Unit 2 Lesson 6 Answer: Take the quantity of each item and multiply that number to the unit price of that same item. Repeat this step for each item. 4 x = $ SubTotal is the sum of the total of each item = $ Total is the entire bill including all service charges. Support Questions 1. Complete the invoice. Copyright 2005, Durham Continuing Education Page 3 of 33

4 Mathematics MAT1L Unit 2 Lesson 6 Expenses Expenses are anything you spend money on. For example, gas for a car or groceries. In order to budget your money properly it is important to understand how you spend your money. Keeping an expense report/invoice will help organize and budget money. Following is an example of what an expense report might look like. The values in each column are added for a total for each category Support Questions 2. Use the headings: Date, Description, Utilities, Fuel, Food, Entertainment and Other to create an expense report using the information given following: Jan. 3 Groceries $36.71 Jan. 18 Paid phone bill $71.22 Jan. 12 Gas for vehicle $35.00 Jan. 2 Groceries $18.13 Jan. 26 Food for Super Bowl party $ Jan. 21 Paid electricity bill $78.45 Jan. 31 Rent $ Jan. 17 Dinner at Pizza Hut $38.00 Copyright 2005, Durham Continuing Education Page 4 of 33

5 Mathematics MAT1L Unit 2 Lesson 6 Essential Expenses are things that must be paid for in order to live, such as housing, food, clothing, and health care. As listed about food is considered one of these essential expenses. Example a. Make a list of 5 items from the flyer below. b. Estimate the cost of these 5 items. (note: all meats are cost per pound) c. Calculate the cost of these 5 items. (note: all meats are cost per pound) Answer: Possible 5 items selected: a. o Clementine oranges o Raspberries o Dole salad o Chicken o Blade pot roast b. Estimated cost = = $20.00 c. Calculate cost = = $20.26 Copyright 2005, Durham Continuing Education Page 5 of 33

6 Mathematics MAT1L Unit 2 Lesson 6 Support Questions 3. a. Make a list of 4 items from the flyer below: b. Estimate the cost of these 4 items. (note: all meats are cost per pound) c. Calculate the cost of these 4 items. (note: all meats are cost per pound) Copyright 2005, Durham Continuing Education Page 6 of 33

7 Mathematics MAT1L Unit 2 Lesson 6 Key Question #6 1. Copy and complete the invoice below. 2. Explain in words the steps that were taken to complete the invoice in question #1. 3. Explain in detail why a person might want to keep an expense report. How might this report benefit a person or business? 4. Describe a situation where a person might use estimation when grocery shopping. Copyright 2005, Durham Continuing Education Page 7 of 33

8 Mathematics MAT1L Unit 2 Lesson 6 Key Question #6 (con t) 5. Copy the format and headings of the expense statement below then complete the expense statement. Jan. 2 Rent $ Jan. 3 Paid phone $56.21 Jan. 7 Cable bill $48.25 Jan. 10 Dinner out $35.00 Jan. 11 Electricity bill $71.69 Jan. 15 Gas for truck $41.00 Jan. 18 Groceries $28.13 Jan. 19 Movie at Theatre $22.00 Jan. 22 Groceries $74.98 Jan. 27 Gas for truck $25.00 Jan. 30 Water bill $ a. Make a list of 5 items from the flyer below: b. Estimate the cost of these 5 items. (some items are cost per pound) c. Calculate the cost of these 5 items. (some items are cost per pound) Copyright 2005, Durham Continuing Education Page 8 of 33

9 Length and the Metric System Lesson 7

10 Mathematics MAT1L Unit 2 Lesson 7 Lesson Seven Concepts Investigate, discuss and describe applications from everyday life and the workplace that would involve the measurement of length in commonly used metric units. Explain and use correctly prefixes in the metric system. Investigate, identify and used personal referents to aid in the estimation of length in everyday situations. Estimate and use measurement of length in everyday applications. Measure of Length in the Metric System Canada formally adopted the modern metric system (the Système International d'unités or SI) in How long is it? How wide is it? What is its circumference? In the metric system there are four main units of measurement that are used in answering the above question. 1. millimetres (mm) 2. centimetres (cm) 3. metres (m) 4. kilometres (km) Here are some examples of what each measurement might look like. Millimetre (mm) Centimetre (cm) Metre (m) Copyright 2005, Durham Continuing Education Page 10 of 33

11 Mathematics MAT1L Unit 2 Lesson 7 Key Conversions lengths and the metric system There are 10 mm in one cm There are 100 cm in one metre There are 1000 mm in one metre There are 1000 m in one kilometre Example a. Choose the best measure for the length of a pencil. 20 mm 20 cm 20 m Answer: A pencil is approximately 20 cm long. b. Choose the best measure for the height of a basketball rim. 1.8 m 3.1 m 5.8 m Answer: A basketball rim is approximately 3.1 m high. c. Choose the best measure for the width of a student s desk. 1.2 mm 1.2 cm 1.2 m Answer: A typical student desk is approximately 12 m wide. Copyright 2005, Durham Continuing Education Page 11 of 33

12 Mathematics MAT1L Unit 2 Lesson 7 Support Questions 1. Choose the best measure. a. Average depth of a lake 80 cm 80 m 80 km b. Length of a screw 7 mm 7 cm 7 m 2. Choose the best measure. a. Length of a Ford Explorer 3.1 m 3.1 cm 3.1 km b. Height of the CN tower 553 cm 553 m 553 km c. Width of a math textbook 20 mm 20 cm 20 m 3. Choose the best measure. a. Length of a newborn baby 30 cm 60 cm 80 cm b. Distance from Toronto to 1000 km 2000 km 4000 km Vancouver c. Thickness of a man s hand. 3.5 cm 6 cm 8 cm d. Height of a student s chair 0.6 m 1.6 m 2.0 m above the ground e. Width of a DVD movie 12 cm 18 cm 24 cm f. Average height of a National 2 m 2.25 m 2.75 m Basketball Association Player 4. Estimate each measurement using appropriate units. a. Height to the centre of a stop sign from the ground b. Width of a binder c. Length of city bus d. Distance from Oshawa to Toronto e. Thickness of an Oreo cookie f. Height of a large Tim Horton s Coffee g. Length of an NHL hockey rink Copyright 2005, Durham Continuing Education Page 12 of 33

13 Mathematics MAT1L Unit 2 Lesson 7 Key Question #7 1. Choose the best measure. a. Thickness of CD case 8 mm 8 cm 8 m b. Height of a car 2.5 m 2.5 cm 2.5 m c. Width of a butter knife 1.3 mm 1.3 cm 1.3 m 2. Choose the best measure. a. Height of a soccer net 2 m 3 m 4 m b. Distance from Oshawa to 1.8 km 60 km 460 km Peterborough c. Thickness of a muffin 5 cm 15 cm 30 cm 3. Estimate each measurement using appropriate units. a. Distance across a two lane road b. Height from the floor of a kitchen sink c. Length of a tube of toothpaste d. Thickness of a hockey puck e. Height of a bottle of Pepsi Edge f. Width of a sidewalk g. Length of kitchen broom 4. A person is usually measured in centimetres. Explain why millimetres, metres and kilometres are not typically used? Give an example to show your understanding. 5. Kilometres are typically used to measure the distance between two cities. Explain why millimetres, centimetres and metres are not used? Give an example to show your understanding. Copyright 2005, Durham Continuing Education Page 13 of 33

14 Metric System: Capacity and Mass Lesson 8

15 Mathematics MAT1L Unit 2 Lesson 8 Lesson Eight Concepts Investigate, discuss and describe applications from everyday life and the workplace that would involve the measurement of mass in commonly used metric units. Investigate, discuss and describe applications from everyday life and the workplace that would involve the measurement of mass in commonly used metric units. Explain and use correctly prefixes in the metric system. Investigate, identify and used personal referents to aid in the estimation of mass and capacity in everyday situations. Estimate and use measurement of mass and capacity in everyday applications. Measure of Mass and Capacity in the Metric System How much does it weigh? (mass) How much does it hold? (capacity) In the metric system there are three main units of measurement that are used for mass. 1. kilogram (kg) 2. gram (g) 3. milligram (mg) Here are some examples of what each measurement might look like. Kilogram (kg) Gram (g) Milligram (mg) About 1 kg About 1 g About 1 mg In the metric system there are two main units of measurement that are used for capacity. 1. litre (L) 2. millilitre (ml) Copyright 2005, Durham Continuing Education Page 15 of 33

16 Mathematics MAT1L Unit 2 Lesson 8 Here are some examples of what each measurement might look like. Litre (L) Millilitre (Ml) About 1 L About 1 ml (eyedropper) Key Conversions lengths and the metric system There are 1000 mg in one gram (g) There are 1000 g in one kilogram (kg) There are 1000 ml in one litre. (L) Example a. Choose the best measure for the mass of a truck. 6 kg 71 kg 824 kg Answer: The mass of a truck is approximately 824 kg. b. Choose the best measure for the capacity of a lawn mower gas tank. 2 L 27 L 212 L Answer: A lawn mower gas tank holds approximately 2 L. Copyright 2005, Durham Continuing Education Page 16 of 33

17 Mathematics MAT1L Unit 2 Lesson 8 Support Questions 1. Choose the best measure for capacity. a. Glass of juice 240 ml 240 L b. Jug of milk 4 ml 4 L c. Can of paint 3.1 ml 3.1 L d. Bottle of mouthwash 1.2 ml 1.2 L 2. Choose the best measure for the mass of each object. a. Bag of potatoes 5 mg 5 g 5 kg b. Chocolate Bar 200 mg 200 g 200 kg c. Weight of a newborn baby 3.6 mg 3.6 g 3.6 kg d. Can of soup 812 mg 812 g 812 kg 3. Choose the best measure for each. a. Can of soup 382 ml 83 ml 12 ml b. Plate 1.1 kg 20 kg 218 kg c. Box of cereal 9 g 52 g 326 g d. Salad dressing 8 ml 85 ml 412 ml 4. Estimate each measurement using appropriate units. a. Capacity of a cup of hot chocolate in millilitres b. Mass of a stove in kilograms c. Capacity of bath tub in litres Copyright 2005, Durham Continuing Education Page 17 of 33

18 Mathematics MAT1L Unit 2 Lesson 8 Key Question #8 1. Choose the best measure for capacity. a. Bottle of baby shampoo 400 ml 400 L b. Kitchen sink full of water 22 ml 22 L c. Container of orange juice 3.8 ml 3.8 L 2. Choose the best measure for the mass of each object. a. Pair of jeans 500 mg 500 g 500 kg b. Bar of soap 25 mg 25 g 25 kg c. teaspoon of sugar 80 mg 80 g 80 kg 3. Choose the best measure for each. a. Bottle of pop 361 ml 83 ml 12 ml b. Flintstone multi-vitamin 1 mg 20 kg 218 kg c. Apple 10 g 125 g 900 g 4. Estimate each measurement. a. Mass of CD player in grams b. Mass of a medium sized dog in kilograms c. Capacity of cereal bowl 5. Explain in your own word and with examples the difference between mass and capacity. Copyright 2005, Durham Continuing Education Page 18 of 33

19 Conversions of Metric Units Lesson 9

20 Mathematics MAT1L Unit 2 Lesson 9 Lesson Nine Concepts Explain and use correctly prefixes in the metric system. Convert between metric units commonly used in everyday applications. Converting To and From Various Metric Units Metric prefixes kilo- means thousand centi- means hundredth milli- means thousandth When Converting from a larger unit to a smaller unit multiplication is needed. kilo metre litre gram centi milli Multiply by 1000 by 100 by 10 When Converting from a smaller unit to a larger unit division is needed. milli centi metre litre gram kilo Divide by 10 by 100 by 1000 Copyright 2005, Durham Continuing Education Page 20 of 33

21 Mathematics MAT1L Unit 2 Lesson 9 Example a. Convert each measurement to the metric unit given. 6 m =? cm Answer: 6 x 100 = 600 cm Example b. Convert each measurement to the metric unit given. 527 ml =? L Answer: =.527 L Copyright 2005, Durham Continuing Education Page 21 of 33

22 Mathematics MAT1L Unit 2 Lesson 9 Support Questions 1. Convert each measurement to the metric unit given. a. 0.7 km =? m b. 9.3 cm =? mm c. m =? mm d m =? cm e. 45 kg =? g f kg =? g g. 427 mm =? m h ml =? L i g =? kg j. 250 ml =? L k. 8.2 kg =? g l. 321 m =? km m mg =? g n. kg =? mg o. 6 cm =? km p. 18 mm =? km q. 1.6 km =? cm Key Question #9 1. Convert each measurement to the metric unit given. a. 12 km =? m b. 651 m =? km c. 3.5 m =? cm d. 13 L =? ml e. 529 g =? kg f g =? mg g. 63 ml =? L h. 45 mm =? m i. 98 m =? km j. 120 cm =? mm k. 2.3 g =? mg l. 5 L =? ml m km =? m n. 45 kg =? mg o. 12 kg =? g p. 345 mg =? g q ml =? L 2. Will a 300 cm measuring tape reach along a board that is 2.75 m long? Explain with words and calculations. 3. Johnny says that 600 cm is not enough moulding for the baseboards that measure 5642 mm. Is he right in his statement? Explain. Copyright 2005, Durham Continuing Education Page 22 of 33

23 Imperial Units and Length Lesson 10

24 Mathematics MAT1L Unit 2 Lesson 10 Lesson Ten Concepts Investigate, discuss and describe applications from the everyday life and the workplace that would involve the measurement of length in feet and inches. Measure length in feet and inches, to an accuracy of ¼ inch, using a12 inch ruler. Record measurements, using commonly accepted abbreviations for the chosen units. Investigate, identify and use personal referents to aid in the estimation of length in feet and inches. Estimate and use measurements of lengths in feet and inches in everyday situations. Measure of Length in the Imperial System How long is it? How wide is it? What is its circumference? In the imperial system there are four main units of measurement that are used in answering the above question. 1. inches (in) 2. feet (ft) 3. yards(yd) 4. miles (mi) Here are some examples of what each measurement might look like. inches (in) feet (ft) yards (yds) mile (mi) Copyright 2005, Durham Continuing Education Page 24 of 33

25 Mathematics MAT1L Unit 2 Lesson 10 Key Conversions lengths and the imperial system There are 12 inches in one foot There are 3 feet in one yard There are 1760 yards in one mile Example a. Choose the best measure for the length of a pencil. 7 inches 11 inches 5 inches The symbol can also mean inches. 7 inches = 7 Answer: A pencil is approximately 7 inches long. b. Choose the best measure for the height of a basketball rim. 6 feet 10 feet 19 feet Answer: A basketball rim is 10 feet high. c. Choose the best measure for the length of a student s desk. 1 yard 2 yards 1.2 yards Answer: A typical student desk is approximately 1 yard wide. The symbol can also mean feet. 7 inches = 7 Copyright 2005, Durham Continuing Education Page 25 of 33

26 Mathematics MAT1L Unit 2 Lesson 10 Support Questions 1. Choose the best measure. a. Average depth of a lake 8 ft 200 ft 900 ft b. Length of a screw 3/ c. Wheel base of a mid-sized car 8 ft 60 ft 900 ft d. Height of a giant tree 100 inches 100 feet 100 yds e. Length of a soccer field 10 yds 110 yds 1000 yds f. Length of a peanut 1 1/8 inches 2 feet 1/2 yd g. Distance from Ajax to Oshawa 5 miles 50 miles 900 miles h. Height of an adult i. Width of a hockey rink j. Height of a toaster Using a ruler Inches are divided up into eighths (1/8ths) as shown on the diagram below. Example a. Estimate the length in inches of the object below as shown by the arrows. Copyright 2005, Durham Continuing Education Page 26 of 33

27 Mathematics MAT1L Unit 2 Lesson 10 Answer: Approximate 2 b. Using a ruler, measure the length of the object below as shown by the arrows. Round your answer to the nearest 1/8 th of an inch. Answer: Approximately 2 1/8 th Copyright 2005, Durham Continuing Education Page 27 of 33

28 Mathematics MAT1L Unit 2 Lesson 10 Support Questions 2. Estimate then calculate the length of each diagram as indicated with the arrows. (measurements should be rounded to the nearest 1/8 ) a. b. c. d. Copyright 2005, Durham Continuing Education Page 28 of 33

29 Mathematics MAT1L Unit 2 Lesson 10 Key Question #10 1. Choose the best measure. a. Width of a mid-sized car 9 ft 24 ft 120 ft b. Height of a stop sign 88 inches 84 feet 84 yds c. Width across a highway 2 yds 10 yds 50 yds d. Length of a pointer finger e. Distance from Vancouver to 100 miles 500 miles 2500 miles Montreal f. Length of a newborn child Estimate then calculate the width of a quarter in imperial units. 3. When completing a measurement, when do you think it is easier to use the imperial system and when do you think it would be easier to use the metric system. Explain with words and a numerical example for each. Copyright 2005, Durham Continuing Education Page 29 of 33

30 Mathematics MAT1L Unit 2 Lesson 10 Key Question #10 (con t) 4. Estimate then calculate the length of each diagram as indicated with the arrows. (measurements should be rounded to the nearest 1/8 ) a) b) Copyright 2005, Durham Continuing Education Page 30 of 33

31 Mathematics MAT1L Unit 2 Support Question Answers Answers to Support Questions Lesson Six Copyright 2005, Durham Continuing Education Page 31 of 33

32 Mathematics MAT1L Unit 2 Support Question Answers 3. a. Possible Answer: 1 lb of turkey, 1 ribs, 1 cheese, 1 pkg. oranges b. $1 + $ $ $5.00 = $23.00 c. $ $ $ $4.99 = $23.26 Lesson Seven 1. a. 80m b. 7 cm c. 3.1 m d. 553 m e. 20 cm 2. a. 50 cm b km c. 3.5 cm d..6 m e. 18 cm f m 3. a. 2.5 m b. 25 cm c. 8 m d. 50 km e. 1 cm f. 12 cm g. 90 m Lesson Eight 1. a. 240 ml b. 4 L c. 3.1 L d. 1.2 L 2. a. 5 kg b. 200 g c. 3.6 kg d. 812 g 3. a. 382 ml b. 1.1 kg c. 326 g d. 412 ml 4. a. 300 ml b. 100 kg c. 50 L Lesson Nine 1. a. 0.7 x 100 = 700 m b. 9.3 x 10 = 93 mm c. 2.2 x 100 = 220 cm x 10 = mm d x 100 = cm e. 45 x 1000 = g f x 1000 = 820 g g =.427 m h = L i = kg j =.25 L k. 8.2 x 1000 = 8200 g l =.321 km m = g n. 5.4 x 1000 = 5400 g x 1000 = mg o =.06 m 1000 = km p = 1.8 cm 100 =.018 m 1000 = km q. 1.6 x 1000 = 1600 m x 100 = cm Copyright 2005, Durham Continuing Education Page 32 of 33

33 Mathematics MAT1L Unit 2 Support Question Answers Lesson Ten 1. a. 200 ft b. 3/8 c. 8 ft d. 100 feet e. 110 yds f. 1 1/8 inches g. 5 miles h. 70 i. 40 j a. 1 ½ b. 1 ½ c. 4 ¼ d. 1 ¾ Copyright 2005, Durham Continuing Education Page 33 of 33