MATHEMATICS MAT1L Grade 9, Essentials Version A

Transcription

1 MATHEMATICS MAT1L Grade 9, Essentials Version A

2 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 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 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 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. 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 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 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 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 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. 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 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. 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. 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 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. Communicate, in writing, the solutions to proportional reasoning problems using appropriate terminology, symbols and form. Copyright 2005, Durham Continuing Education Page 9 of 41