MATHEMATICS MAT1L Grade 9, Essentials Version A

Transcription

1 MATHEMATICS MAT1L Grade 9, Essentials Version A

2 Mathematics MAT1L Introduction Grade 9 Essentials Welcome to Grade 9 Essentials Mathematics, MAT1L. This full-credit course is part of the new Ontario Secondary School curriculum. This course emphasizes further development of mathematical knowledge and skills to prepare students for success in their everyday lives, in the workplace, in the Grade 10 LDCC course, and in the Mathematics Grade 11 and Grade 12 Workplace Preparation courses. The course is organized by three strands related money sense, measurement, and proportional reasoning. In all strands, the focus is on developing and consolidating key foundational mathematical concepts and skills by solving authentic, everyday problems. Students have opportunities to further develop their mathematical literacy and problemsolving skills and to continue developing their skills in reading, writing, and oral language through relevant and practical math activities. Material This course is self-contained and does not require a textbook. You will require lined paper, graph paper, a ruler with inches and centimetres, a calculator and a writing utensil. Expectations The overall expectations you will cover in the lesson are listed on the first page of each lesson. Lesson Description Each lesson contains one or more concepts with each being followed by support questions. At the end of the lesson the Key Questions covering all concepts in the lesson are assigned and will be submitted for evaluation. Evaluation In each lesson, there are support questions and key questions. You will be evaluated on your answers to the key questions in each lesson, the mid-term exam and the final exam. Copyright 2005, Durham Continuing Education Page 2 of 41

3 Mathematics MAT1L Introduction Support Questions These questions will help you understand the ideas and master the skills in each lesson. They will also help you improve the way you communicate your ideas. The support questions will prepare you for the key questions. Write your answers to the support questions in your notebook. Do not submit these answers for evaluation. You can check your answers against the suggested answers that are given at the end of each unit. Key Questions The key questions evaluate your achievement of the expectations for the lesson. Your answers will show how well you have understood the ideas and mastered the skills. They will also show how well you communicate your ideas. You must try all the key questions and complete most of them successfully in order to pass each unit. Write your answers to the key questions on your own paper and submit them for evaluation at the end of each unit. Make sure each lesson number and question is clearly labelled on your submitted work. What You Must Do To Get a Credit In order to be granted a credit in this course, you must Successfully complete the Key Questions for each unit and submit them for evaluation within the required time frame. Complete the mid-term exam after Unit 2. Complete and pass a final examination. Your Final Mark Each Unit has 5 lessons each worth 2% (10% per Unit x 4 Units) 40% Midterm Test 30% Term Final Examination 30% Copyright 2005, Durham Continuing Education Page 3 of 41

4 Mathematics MAT1L Introduction Unit One Lesson One Concepts Place value. Rounding money values to stated accuracies. Lesson Two Concepts Using estimation strategies involving addition, subtraction, multiplication, and division to round money values appropriately within a given context. Estimate the change for a transaction. Solve problems involving estimating the totals of money values found in real contexts. Lesson Three Concepts Entering decimals properly on a numerical keypad. 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. Lesson Four Concepts Read and interpret money values given in words and symbols, using the correct place value. Writing money values using correct units. Lesson Five Concepts Represent a given coin or bill as a combination of other coins or bills. Identify different combinations of coins and bills that would result in a given amount of money. Make the correct change for an offered amount with and without concrete materials. Communicate, orally and in writing, the solutions to money problems and the results of investigations, using appropriate terminology, symbols, and form. Copyright 2005, Durham Continuing Education Page 4 of 41

5 Mathematics MAT1L Introduction Unit Two 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. 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 references to aid in the estimation of length in everyday situations. Estimate and use measurement of length in everyday applications. 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 references to aid in the estimation of mass and capacity in everyday situations. Estimate and use measurement of mass and capacity in everyday applications. Copyright 2005, Durham Continuing Education Page 5 of 41

6 Mathematics MAT1L Introduction Lesson Nine Concepts Explain and use correctly prefixes in the metric system. Convert between metric units commonly used in everyday applications. 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 references to aid in the estimation of length in feet and inches. Estimate and use measurements of lengths in feet and inches in everyday situations. Unit Three Lesson Eleven Concepts Investigate, discuss and describe applications from the everyday life and the workplace that would involve the measurement of mass and capacity. Record measurements, using commonly accepted abbreviations for the chosen units. Investigate, identify and use personal references to aid in the estimation of mass and capacity. Estimate and use measurements of mass and capacity in everyday situations. Lesson Twelve Concepts Explain and use correctly prefixes in the imperial system. Convert between imperial units commonly used in everyday applications. Lesson Thirteen Concepts Explain and use correctly prefixes in the imperial and metric system. Convert between imperial and metric units commonly used in everyday applications. Lesson Fourteen Concepts Explore and describe situations from everyday life and the workplace that require calculation or measurement of perimeter. Estimate, measure, and calculate perimeters drawn from applications in everyday life and the workplace. Copyright 2005, Durham Continuing Education Page 6 of 41

7 Mathematics MAT1L Introduction Explain and illustrate how to determine the perimeter of any figure bounded by straight line segments. Select the most appropriate standard unit to measure perimeter. Solve problems involving perimeter in applications drawn from everyday situations. Organize measurement information, using a simple framework Explain their reasoning used in problem solving and in judging reasonableness. Communicate, in writing, the solutions to measurement problems and the results of investigations, using appropriate terminology, symbols and form. Lesson Fifteen Concepts Explore and describe situations from everyday life and the workplace that require calculating and measuring area. Investigate the areas of a variety of rectangles, using concrete materials. Estimate, measure, and record rectangular areas found in everyday life and the workplace, using uniform non-standard units. Predict and explain, from experiences involving concrete materials that the area of any rectangle can be found by multiplying its length by its width. Estimate and calculate the areas of rectangles, drawn from applications in everyday life and the workplace. Estimate and calculate the areas of regions that can be broken into rectangles. Organize measurement information, using a simple framework Explain their reasoning used in problem solving and in judging reasonableness. Communicate, in writing, the solutions to measurement problems and the results of investigations, using appropriate terminology, symbols and form. Unit Four Lesson Sixteen Concepts Explore and describe situations from everyday life and the workplace that require calculating or measurement of volume. Investigate the volume of a variety of prisms whose bases involve rectangular regions. Predict and explain, from investigations involving the building of prisms, that the volume of a prism is given by multiplying the area of its base by its height. Estimate and calculate the volumes of rectangular prisms drawn from applications in everyday life and the workplace. Select the most appropriate standard unit to measure volume of a figure. Solve problems involving volume in applications drawn from everyday situations. Organize measurement information, using a simple framework. Explain their reasoning used in problem solving and in judging reasonableness. Communicate, in writing, the solutions to measurement problems and the results of investigations, using appropriate terminology, symbols and form. Copyright 2005, Durham Continuing Education Page 7 of 41

8 Mathematics MAT1L Introduction Lesson Seventeen Concepts Represent the magnitudes of the fractions 1, 1, 1, 2, and 3 using manipulatives and by constructing diagrams and models. Represent the addition and subtraction of 1, 1, 3, and 1, in the context of fractional parts of an hour, a cup, a dollar, and an inch by constructing diagrams and using models. Estimate and add pairs of simple fractions with the support of an appropriate model. Interpret simple fractions of a dollar in decimal form. Read, interpret and explain, in writing, data displayed in simple tables and graphs. Lesson Eighteen Concepts Explore the relationship between fractions 1, 1, 1, 2, and 3 and decimals using a calculator, concrete materials and diagrams. Round decimal values appropriately within a given context. Represent and explain the meaning of percent as part of 100, by constructing diagrams, using concrete materials. Explore the relationship between fractions, decimals and percentages using a calculator, concrete materials and diagrams. Identify and use common equivalences or approximations between fractions and percentages. Solve problems involving fractions and percentages in practical situations. Read, interpret and explain, in writing, data displayed in simple tables and graphs. Explain their reasoning used in problem solving and in judging reasonableness. Communicate, in writing, the solutions to proportional reasoning problems using appropriate terminology, symbols and form. Lesson Nineteen Concepts Identify and use ratios, including equivalent ratios, to express the relationship among quantities represented by models and diagrams. Explore and describe the use of ratios from their personal experiences. Solve simple problems using equivalent ratios. Explain their reasoning used in problem solving and in judging reasonableness. Communicate, in writing, the solutions to proportional reasoning problems using appropriate terminology, symbols and form. Copyright 2005, Durham Continuing Education Page 8 of 41

9 Mathematics MAT1L Introduction Lesson Twenty Concepts Explore and identify rates drawn from their experiences, and the units used in them. Calculate rates in activities drawn from their experiences. Solve problems involving rates. Calculate and compare the unit costs of items found in everyday situations. Explain their reasoning used in problem solving and in judging reasonableness. Communicate, in writing, the solutions to proportional reasoning problems using appropriate terminology, symbols and form. Copyright 2005, Durham Continuing Education Page 9 of 41

10 Rounding Numbers Lesson 1

11 Mathematics MAT1L Unit 1 Lesson 1 Lesson One Concepts Place value Rounding money values to stated accuracies Place Value Place Value is the value given to the place in which a digit appears in a numeral. Example a. What place value is the zero (0) in? Answer: ten thousands b. What place value in the four (4) in? Answer: hundredths Copyright 2005, Durham Continuing Education Page 11 of 41

12 Mathematics MAT1L Unit 1 Lesson 1 Support Questions 1. For each number give the place value of the bolded digit. a b c d e f Rounding Rounding is when a number is expressed to the nearest digit. Steps to consider when rounding to a given digit. Step #1 Step #2 Step #3 Find the value of the digit you are rounding to. Look at the value of the digit immediately to the right of the digit found in step #1. If the value of the digit from step #2 is 5 or more then round the value of the digit from step #1 up one value. If the value of the digit from step #2 is 4 or less then keep the value of the digit from step #1 the same. Step #4 All digits to the right of the rounded value now become zero. No zeros are needed once you have reached the decimal. Example a. Round to the nearest thousands. Answer: Step #1 Find the value of the digit you are rounding to Copyright 2005, Durham Continuing Education Page 12 of 41

13 Mathematics MAT1L Unit 1 Lesson 1 Step #2 Look at the value of the digit immediately to the right of the digit found in step # Step #3 If the value of the digit from step #2 is 4 or less then keep the value of the digit from step #1 the same Step #4 All digits to the right of the rounded value now become zero. No zeros are needed once you have reached the decimal Example b. Round to the nearest million. Since this value (7) is more than or equal to 5 then the 8 in the millions place value becomes a 9. Answer: rounds to c. Round to the nearest tens. Since this value (6) is more than or equal to 5 then the 9 in the tens place value rounds up one value. This makes the 9 a 10 which is not possible. Therefore, the 3 in front of the 9 rounds to a 4. Answer: rounds to d. Round to the nearest hundredth. Answer: rounds to Since this value (5) is more than or equal to 5 then the 6 in the hundredths place value becomes a 7. Since this rounding happens in the decimals then no zeros are needed after the rounded number. Copyright 2005, Durham Continuing Education Page 13 of 41

14 Mathematics MAT1L Unit 1 Lesson 1 Support Questions 2. Round each of the following numbers to the bolded place value indicated in brackets. a (tens) b (hundredths) c (ten thousands) d (ones) e (hundreds) f (tenths) g (hundreds) h (tenths) i (thousands) j (hundreds) Rounding and Money It is important to remember that when calculating numbers that represent money you must always round to the nearest cent (penny). This means you must round to the nearest hundredth. Example a. Round to the nearest cent. Answer: rounds to $ b. Round to the nearest cent. Since this value (3) is less than 5 then the 9 in the hundredths place value stays the same. Since this value (6) is more than or equal to 5 then the 9 in the hundredths place value rounds up to the next value. Since the 9 cannot become the 2 in the tenths place value now becomes a 3 and the 9 is replaced with a zero. Answer: rounds to $ With money we always include the zeros up to and including the hundredths place value. $ not as $ Copyright 2005, Durham Continuing Education Page 14 of 41

15 Mathematics MAT1L Unit 1 Lesson 1 Support Questions 3. Round each of the following numbers to the indicated bolded money value in brackets. a (hundred dollars) b (cent) c (ten dollars) d (dollar) e (cent) f (cent) g (thousand dollars) Key Question #1 1. For each number give the place value of the bolded digit. a b c d e f Round each of the following numbers to the bolded place value indicated in brackets. a (tenths) b (ones) c (millions) d (thousands) 3. Round each of the following numbers to the indicated bolded money value in brackets. a (ten cents) b (ten thousand dollars) c (cent) d (dollar) e (cent) f (cent) Copyright 2005, Durham Continuing Education Page 15 of 41

16 Estimation Lesson 2

17 Mathematics MAT1L Unit 1 Lesson 2 Lesson Two Concepts Using estimation strategies involving addition, subtraction, multiplication, and division to round money values appropriately within a given context. Estimate the change for a transaction. Solve problems involving estimating the totals of money values found in real contexts. Estimation Estimation is a reasonable guess of a measurement; also, an approximation that results from using rounded numbers in a calculation. When using estimation, rounding numbers in your head is key. Use whole numbers in your calculations to make the mental math as easy as possible. Example a. Estimate the cost of two items selling for $ and $ Answer: 197 can be rounded to 200 and can be rounded to 75. Therefore the estimated cost is = $ b. Estimate the perimeter of an object that has sides 11cm, 18.3 cm and 9 cm. Answer: = 40 cm Round to easy working numbers. c. Estimate the cost of purchasing one of each item given on the flyer following: Copyright 2005, Durham Continuing Education Page 17 of 41

18 Mathematics MAT1L Unit 1 Lesson 2 Answer: = $38 Estimation can be a helpful technique when shopping with only cash on you. Estimate how much you would have left from $50 after purchasing a meal that cost $ Answer: = $30.00 Always remember to include the dollar sign ($) when answering questions involving money. Remember to include the cents in your answer when answering money questions even if the cents are zero. Copyright 2005, Durham Continuing Education Page 18 of 41

19 Mathematics MAT1L Unit 1 Lesson 2 Support Questions 1. Estimate the cost of two items selling for $ and $ Estimate the cost of three items selling for $19.50, $3.50 and $ Estimate the cost of two items selling for $22.50 and $ Estimate the cost of three items selling for $7.49, $1.29 and $ Estimate the perimeter of an object that has sides 8 cm, 11.3 cm and 19.2 cm. 6. Estimate the perimeter of an object that has sides 7.4 m, 22.8 m, 18.1 m and m. 7. Estimate the cost of purchasing one of each item with the circled price on the flyer. Copyright 2005, Durham Continuing Education Page 19 of 41

20 Mathematics MAT1L Unit 1 Lesson 2 8. Estimate the distance from Toronto to Oshawa given the route shown on the map following: 9. Estimate the total cost of all the items given on the invoice following: Copyright 2005, Durham Continuing Education Page 20 of 41

21 Mathematics MAT1L Unit 1 Lesson 2 Key Question #2 1. Estimate the cost of two items selling for $73.00 and $ Estimate the cost of three items selling for $10.50, $1.50 and $ Estimate the cost of two items selling for $71.50 and $ Estimate the cost of three items selling for $4.99, $6.79 and $ Estimate the perimeter of an object that has sides m, 77.8 m and 12.9 m. 6. Estimate the perimeter of an object that has sides 3.6 cm, 27.8 cm, 98.1 cm and cm. 7. Estimate the cost of purchasing one of each item given on the flyer following: 8. Estimate the distance from Oshawa to Peterborough given the route shown on the map following: Copyright 2005, Durham Continuing Education Page 21 of 41

22 Mathematics MAT1L Unit 1 Lesson 2 Key Question #2 (con t) 9. Estimate the total cost of all the items given on the invoice following: Copyright 2005, Durham Continuing Education Page 22 of 41

23 Working with Decimals Lesson 3

24 Mathematics MAT1L Unit 1 Lesson 3 Lesson Three Concepts Entering decimals properly on a numerical keypad. 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. Decimals It is important to understand what the value in a decimal actually represents. For example, 5 means 0.05 not.5 as often written. Example a. Write 4.5 in dollar form. Answer: 4.5 means $4.50 Be careful that 4.5 is not written as $4.05 which means 4 dollars and 5 cents. Operations involving the calculator and decimals. Key terms: Sum: the answer to an addition question Difference: the answer to a subtraction question Product: the answer to a multiplication question Quotient: the answer to a division question b. Find the sum of 4.7 and Answer: = Using estimation to check the answer: = is close to therefore the calculation seems reasonable. Estimation can be helpful as a quick check of your answer. Estimation can help detect whether the value was entered into the calculator correctly. c. Find the difference of 9.72 from Answer: = Using estimation to check the answer: = is close to therefore the calculation seems reasonable. Copyright 2005, Durham Continuing Education Page 24 of 41

25 Mathematics MAT1L Unit 1 Lesson 3 d. Find the product of and Answer: x 4.16 = Using estimation to check the answer: 15 x 4 = is close to therefore the calculation seems reasonable. e. Find the quotient Answer: Using estimation to check the answer: 12 x 3 = 4. 4 is close to 3.99 therefore the calculation seems reasonable. This symbol means that the answer is approximately equal to a certain value is not the exact answer but with rounding is very close. f. Find the answer CAREFUL: = 6.11 This answer is incorrect. The numerator (top of the fraction) must be done first before dividing. Answer: = This is the correct answer. g. Find the answer Answer: = 1.8 Using estimation to check the answer: = 2. 2 is close to 1.8 therefore the calculation seems reasonable. Calculator Steps Needed: Type in 4.6 first then press this +/- button. Your display will now show 4.6. Next add 6.4 to 4.6 and you will get the answer 1.8. Copyright 2005, Durham Continuing Education Page 25 of 41

26 Mathematics MAT1L Unit 1 Lesson 3 Support Questions 1. Write each in dollar form. a. 5 b. 81 c Use estimation to find the sum of the following numbers. a b c Use your calculator to find the sum of the following numbers. a b c Use estimation to find the difference of the following numbers. a b c Use your calculator to find the difference of the following numbers. a b c Use estimation to find the product of the following numbers. a. 3.5 x 6.7 b x 6.78 c x 9.61 d x 2.13 e x 3.98 f x Use your calculator to find the product of the following numbers. a. 3.5 x 6.7 b x 6.78 c x 9.61 d x 2.13 e x 3.98 f x Use estimation to find the quotient of the following numbers. a b c d e f Use your calculator to find the quotient of the following numbers. a b c d e f Copyright 2005, Durham Continuing Education Page 26 of 41

27 Mathematics MAT1L Unit 1 Lesson 3 Support Questions (con t) 10. Use estimation to find the answers to the following questions. a b c Use your calculator to find the answers to the following questions. a b c Calculate the total cost of all the items on the invoice shown following: Copyright 2005, Durham Continuing Education Page 27 of 41

28 Mathematics MAT1L Unit 1 Lesson 3 Key Question #3 1. Write each in dollar form. a. 12 b. 4 c Use estimation to find the sum of the following numbers. a b c Use your calculator to find the sum of the following numbers. a b c Use estimation to find the difference of the following numbers. a b c Use your calculator to find the difference of the following numbers. a b c Use estimation to find the product of the following numbers. a. 4.5 x 6.1 b x 5.28 c x 2.10 d x 1.97 e x 2.98 f x Use your calculator to find the product of the following numbers. a. 4.5 x 6.1 b x 5.28 c x 2.10 d x 1.97 e x 2.98 f x Use estimation to find the quotient of the following numbers. a b c d e f Use your calculator to find the quotient of the following numbers. a b c d e f Copyright 2005, Durham Continuing Education Page 28 of 41

29 Mathematics MAT1L Unit 1 Lesson 3 Key Question #3 (con t) 10. Use estimation to find the answers to the following questions. a b Use your calculator to find the answers to the following questions. a b Calculate the total cost of all the items on the invoice shown below: Copyright 2005, Durham Continuing Education Page 29 of 41

30 Interpreting Money Lesson 4

31 Mathematics MAT1L Unit 1 Lesson 4 Lesson Four Concepts Read and interpret money values given in words and symbols, using the correct place value. Writing money values using correct units. Money talk Money can be written in many different forms. For example, $34K means thirty four thousand $ and $8 Mil means eight million $ Example a. Write eight thousand twenty seven dollars as a dollar amount. Answer: $8 027 This is dollars so the dollar sign must be in the answer. A comma is no longer accepted as proper number notation. The comma is replace now with a space. 8,027 becomes b. Write 450 thousand as a number. Answer: c. Write 45 cents as a dollar amount. Answer: $0.45 Support Questions 1. Write each in dollar form. a. 65 cents. b. 23 thousand c million d. 212 thousand e. 7 thousand f. 8 hundred g. forty one thousand three hundred twelve h. seven million four hundred thirty eight thousand six hundred Copyright 2005, Durham Continuing Education Page 31 of 41

32 Mathematics MAT1L Unit 1 Lesson 4 Support Questions 2. Write each dollar amount in words. a. $ b. $813 c. $ d. $ e. $ f. $ g. $ h. $0.05 i. $0.91 j. $23.12 Key Question #4 1. Write each in dollar form. a. 18 cents. b. 34 thousand c. 1.5 million d. 2 hundred e. 7 cents f. 8 thousand g. eighteen thousand seven hundred sixty four h. ten million seventy two thousand six hundred twenty nine 2. Write each dollar amount in words. a. $0. 05 b. $3.45 c. $79.12 d. $ e. $1.02 f. $ Copyright 2005, Durham Continuing Education Page 32 of 41

33 Mathematics MAT1L Unit 1 Lesson 4 Key Question #4 (con t) 3. Write the value of the money shown below in words and as a dollar value. a. b. 4. Explain why it would be important to understand how to write values of money from words into dollars amounts. Copyright 2005, Durham Continuing Education Page 33 of 41

34 Making Change Lesson 5

35 Mathematics MAT1L Unit 1 Lesson 5 Lesson Five Concepts Represent a given coin or bill as a combination of other coins or bills. Identify different combinations of coins and bills that would result in a given amount of money. Make the correct change for an offered amount with and without concrete materials. Communicate, orally and in writing, the solutions to money problems and the results of investigations, using appropriate terminology, symbols, and form. Represent money in different denominations. Denomination: the value of a certain unit of money. Example a. Represent in two different ways a $5.00 bill as a combination of other coins or bills. Answer: #1 2 $2 coins and 1 $1 coin. #2 5 $1 coins b. Identify 2 different combinations of coins and bills that would result $ Answer: #1 1 $20 dollar bill, 1 $2 coin, 1 $1 coin, 2 quarters, 2 dimes and 3 pennies. #2 2 $10 dollar bills, 3 $1 coins, 7 dimes, and 3 pennies. Support Questions 1. Represent in two different ways a $10.00 bill as a combination of at least 4 different coins or bills. 2. Represent in two different ways a $ bill as a combination of at least 5 different coins or bills. 3. Represent in two different ways a $2.00 coin as a combination of at least 3 different coins. 4. Represent in two different ways a $1.00 coin as a combination of at least 3 different coins. 5. Identify 2 different combinations of coins and bills that would result $ Copyright 2005, Durham Continuing Education Page 35 of 41

36 Mathematics MAT1L Unit 1 Lesson 5 6. Identify 2 different combinations of coins and bills that would result $ Identify 2 different combinations of coins and bills that would result $ Making Change Example a. What change should be given when $25.00 is tendered for a purchase of $21.34? Answer: = $3.64 Tendered means how much did money was given to the cashier to pay a purchase. b. What is the minimum number of coins/bills and how many of each denomination should be given back by a cashier when $20.00 is tendered for a purchase of 17.24? Answer: 5 coins/bills; 1 $2 coins, 3 quarters and 1 penny. Support Questions 8. What change should be given when $ is tendered for a purchase of $105.61? 9. What change should be given when $22.00 is tendered for a purchase of $20.91? 10. What change should be given when $ is tendered for a purchase $171.55? 11. What is the minimum number of coins/bills and how many of each denomination should be given back by a cashier when $50.00 is tendered for a purchase of $38.73? 12. What is the minimum number of coins/bills and how many of each denomination should be given back by a cashier when $ is tendered for a purchase of $66.79? Copyright 2005, Durham Continuing Education Page 36 of 41

37 Mathematics MAT1L Unit 1 Lesson 5 Key Question #5 1. Represent in two different ways a $20.00 bill as a combination of at least 4 different coins or bills. 2. Represent in two different ways a $50.00 bill as a combination of at least 5 different coins or bills. 3. Represent in two different ways a $5.00 bill as a combination of at least 3 different coins. 4. Represent in two different ways a $10.00 coin as a combination of at least 4 different coins. 5. Identify 2 different combinations of coins and bills that would result $ Identify 2 different combinations of coins and bills that would result $ Identify 2 different combinations of coins and bills that would result $ What change should be given when $75.00 is tendered for a purchase of $70.43? 9. What change should be given when $50.00 is tendered for a purchase of $18.34? 10. What change should be given when $ is tendered for a purchase $109.67? 11. What is the minimum number of coins/bills and how many of each nomination should be given back by a cashier when $60.00 is tendered for a purchase of $43.18? 12. What is the minimum number of coins/bills and how many of each nomination should be given back by a cashier when $ is tendered for a purchase of $82.65.? Copyright 2005, Durham Continuing Education Page 37 of 41

38 Mathematics MAT1L Unit 1 Lesson 5 Key Question #5 (con t) 13. You have the following money available for each purchase: What would you offer to get rid of the most coins/bills from each purchase? a. $6.32 b. $24.73 c. $44.27 d. $ Kristen has to pay for a purchase that is $9.28. Why might Kristen pay with just a $10 bill and why might Kristen pay with a $10 bill, 1 quarter and 1 nickel? Copyright 2005, Durham Continuing Education Page 38 of 41

39 Mathematics MAT1LA Unit 1 Support Question Answers Answers to Support Questions Lesson One 1. a. tens b. millions c. ten thousands d. tenths e. ones f. thousands 2. a b c d e f g h i j a. $ b. $ c. $ d. $ e. $ f. $35.00 g. $ Lesson Two 1. $ $80.00 = $ $ $ $1.00 = $ $ $20.00 = $ $ $ $10.00 = $ cm + 10 cm + 20 cm = 40 cm m + 20 m + 20 m + 40 m = 90 m 7. $ $ $ $ $ $ $ = $ km + 5 km + 10 km + 5 km + 5 km +3 km = 33 km 9. $ $ $ $ $ $ $ $50.00 = $ Lesson Three 1. a. $0.05 b. $0.81 c. $ a = 11 b = 14 c = a b c a. 4 7 = 3 b. 7 7 = 0 c = a. 3.2 b c Copyright 2005, Durham Continuing Education Page 39 of 41

40 Mathematics MAT1LA Unit 1 Support Question Answers 6. a. 4 x 7 = 28 b. 7 x 7 = 49 c. 4 x 10 = 40 d. 70 x 2 = 140 e. 16 x 4 = 64 f. 100 x 5 = a b c d e f a. 8 1 = 8 b = 4 c = 2.5 d = 7 e = 2 f = 5 9. a b c d e f a = = 8 8 = 1 b = = 6 2 = c = 50 = 50 5 = a = = b = 5.84 = c = = $ $ $ $ $ $46.13 = $ Lesson Four 1. a. $0.65 b. $ c. $ d. $ e. $7 000 f. $800 g. $ h. $ a. twenty six thousand one hundred dollars b. eight hundred thirteen dollars c. six hundred twenty three thousand dollars d. one million dollars e. eight million five hundred thousand dollars f. seventeen million two hundred thirty seven thousand ninety dollars g. two hundred eighteen million three hundred six dollars h. 5 cents i. ninety one cents j. twenty three dollars and twelve cents. Copyright 2005, Durham Continuing Education Page 40 of 41

41 Mathematics MAT1LA Unit 1 Support Question Answers Lesson Five 1. Possible answers: 1 five, 2 twos, 3 quarters, 2 dimes, 1 nickel 1 five, 1 two, 1 one, 4 quarters, 10 dimes 2. Possible answers: 3 twenties, 2 tens, 3 fives, 2 twos, 1 one 1 fifty, 1 twenty, 2 tens, 1 five, 2 twos, 1 one 3. Possible answers: 1 one, 2 quarters, 5 dimes 4 quarters, 8 dimes, 4 nickels 4. Possible answers: 2 quarters, 4 dimes, 2 nickels 3 quarters, 2 dimes, 1 nickel 5. Possible answers: 7 tens, 1 one, 1 quarter 1 fifty, 1 twenty, 1 one, 1 quarter 6. Possible answers: 1 ten, 1 five, 3 ones, 2 quarters, 1 dime, 4 pennies 3 fives, 1 two, 1 one, 2 quarters, 2 nickels, 4 pennies 7. Possible answers: 2 hundreds, 1 twenty, 1 ten, 2 twos, 9 dimes, 8 pennies 11 twenties, 1 ten, 2 twos, 3 quarters, 2 dimes, 3 pennies 8. $ $ = $ $ $20.91 = $ $ $ = $ different denominations: 1 ten, 1 one, 1 quarter, 2 pennies different denominations: 1 twenty, 1 ten, 1 two, 1one, 2 dimes, 1 penny Copyright 2005, Durham Continuing Education Page 41 of 41