Full text of ' IMP Year 1 Teacher Guide Collection Editor: Interactive Mathematics Program IMP Year 1 Teacher Guide Collection Editor: Interactive Mathematics Program Authors: Interactive Mathematics Program Christine Osborne Interactive Mathematics Program Online: CONNEXIONS Rice University, Houston, Texas This selection and arrangement of content as a collection is copyrighted by Interactive Mathematics Program. It is licensed under the Creative Commons Attribution 2.0 license (Collection structure revised: June 6, 2008 PDF generated: February 4, 2011 For copyright and attribution information for the modules contained in this collection, see p. Table of Contents 1 Year 1 Overview 2 Patterns 2.1 Unit Overview 3 2.2 Activity Notes 3 3 The Game of Pig 4 The Overland Trail 4.1 Unit Overview 29 4.2 Activity Notes 29 5 The Pit and the Pendulum 6 Shadows 6.1 Unit Overview 45 6.2 Activity Notes 45 Index 54 Attributions 57 IV Chapter 1 Year 1 Overview CHAPTER 1. YEAR 1 OVERVIEW Chapter 2 Patterns 2.1 Unit Overview 2.1.1 Overview 1 The Interactive Mathematics Program teacher materials have been moved to the Key Curriculum Press website. This link 2 will take you to the login page. After creating an account for yourself, you'll be able to access the full IMP Teacher's Guide. 2.1.2 Pacing Guides 3 The Interactive Mathematics Program teacher materials have been moved to the Key Curriculum Press website.

Long Answer with Explanation: I'm not trying to be a jerk with the previous two answers but the answer really is 'No'. Download free zz top just got paid tab pdf merge. All this means that I just don't have a lot of time to be helping random folks who contact me via this website. I also have quite a few duties in my department that keep me quite busy at times. My first priority is always to help the students who have paid to be in one of my classes here at Lamar University (that is my job after all!).

• Mathematics Course 3 Answers

From Interactive Mathematics Program Year 1 Content Area: Mathematics (Algebra). CC.A-SSE.3 Create equations and inequalities in one variable and use them to solve problems. When to approximate answers and when to be exact.

Mathematics Course 3 Answers

This link 4 will take you to the login page. After creating an account for yourself, you'll be able to access the full IMP Teacher's Guide.

2.1.3 Patterns Calculator Guide 5 The Interactive Mathematics Program teacher materials have been moved to the Key Curriculum Press website. This link 6 will take you to the login page. After creating an account for yourself, you'll be able to access the full IMP Teacher's Guide.

2.2 Activity Notes 2.2.1 The Importance of Patterns 2.2.1.1 The Importance of Patterns The Interactive Mathematics Program teacher materials have been moved to the Key Curriculum Press website. This link 8 will take you to the login page. After creating an account for yourself, you'll be able to access the full IMP Teacher's Guide. Lr This content is available online.

2 www.keypress.com/keyonline 3 This content is available online. 4 www.keypress.com/keyonline 5 This content is available online. 6 www.keypress.com/keyonline 7 This content is available online.

8 www.keypress.com/keyonline CHAPTER 2. PATTERNS 2.2.1.2 What's Next? 9 The Interactive Mathematics Program teacher materials have been moved to the Key Curriculum Press website. This link 10 will take you to the login page. After creating an account for yourself, you'll be able to access the full IMP Teacher's Guide. 2.2.1.3 Past Experiences 11 2.2.1.3.1 Intent This individual activity is best used as homework, the first assignment of the school year. Including a writing assignment like this one will establish several expectations for the course.

Purposeful homework will be assigned every day, and students' work on these assignments will be an important part of the course. Students will be asked to put their thinking — about mathematics and about themselves as learners of mathematics — to paper. All students' thoughts and ideas about the mathematics they are learning are crucial to the success of the course. Successful collaboration to do and learn mathematics is a key feature of this course. 2.2.1.3.2 Mathematics At first glance, this assignment does not look particularly mathematical. However, a growing body of research suggests that successful mathematical problem solvers are reflective thinkers.

They know mathematics, and they know about mathematics as a discipline. They are aware of themselves as mathematics learners, and they can think about their own thinking — monitoring progress, evaluating strategies, choosing among skills and tools — while doing mathematics. Psychologists call this metacognition, and it is a hallmark of the thinking of effective problem solvers. In this activity, students are asked — perhaps for the first time (and certainly not the last time in this program) — to reflect on some of their experiences as mathematics students. 2.2.1.3.3 Progression This activity is designed to be done as homework after the first class and to be discussed, in small groups and as a whole group, in the next class. 2.2.1.3.4 Approximate Time 10 minutes for introduction 20 minutes for activity (at home or in class) 10 minutes for discussion 2.2.1.3.5 Classroom Organization Whole class, then individuals, followed by small groups 9 This content is available online. 10 www.keypress.com/keyonline 11 This content is available online.

2.2.1.3.6 Doing the Activity Take the time to share your expectations for this assignment and homework in general, including what you expect from students and what students can do if they don't understand an assignment. Telling students that you want to learn more about them and their backgrounds, and that you will not be grading their essays, but just recording whether they completed the assignment, may encourage them to do the assignment and to share honestly. One important goal of the first few homework assignments is to help students establish a pattern of doing their homework regularly. Also impress upon students that they need to save their work throughout the unit, as they will be asked to include their written work on this assignment and others in the portfolios they will create at the end of this unit. For the next day's discussion, you might want students to share their essays in their groups. If you plan to follow this suggestion, let students know now that other students will be reading their written work.

2.2.1.3.7 Discussing and Debriefing the Activity Students can read the essays of the other members of their groups. You might suggest that after reading each other's thoughts and experiences, students answer the Key Questions listed below, perhaps displaying these or similar discussion questions on a transparency.

Then students can share with the class the themes their groups encountered. This is a good opportunity to reiterate that class participation — written, oral, and physical; in groups, individually, and with the whole class — is essential for success. 2.2.1.3.8 Key Questions What are some of the important mathematical ideas you have studied? How are your group's ideas about your most and least helpful learning experiences similar?

How are they different? How are your experiences, thoughts, and feelings about working with others similar? How are they different? 2.2.1.4 POW 1: The Broken Eggs 12 2.2.1.4.1 Intent As the first POW, or Problem of the Week, The Broken Eggs is students' first opportunity to work on a substantial problem over several days and communicate the results of their work in writing, using a format that will carry across the four years of the program. (See 'Problems of the Week' in the Overview to the Interactive Mathematics Program.) Link to the 'Problems of the Week' portion of the Overview.

2.2.1.4.2 Mathematics This POW is a version of a well-known problem in number theory. Here is a translation from a seventh- century text written by the Hindu mathematician Brahmagupta: An old woman goes to market, and a horse steps on her basket and crushes the eggs. The rider offers to pay for the damages and asks her how many eggs she had brought. She does not remember the exact number, but when she had taken them out two at a time, there was one egg left. The same happened when she picked them out three, four, five, and six at a time, but when she took them out seven at a time they came out even. What is the smallest number of eggs she could have had?

A similar problem was posed by the Chinese scholar Sun Tsu Suan-Ching in the third century: There are certain things whose number is unknown. Repeatedly divided by 3, the remainder is 2; by 5 the remainder is 3; and by 7 the remainder is 2.

What will be the number of things? 2 This content is available online.

PATTERNS In the activity, students search for numbers divisible by 7, but when divided by each of numbers 2 through 6 leave a remainder of 1. To find solutions to this problem, students must examine multiples of 7 and remainders when dividing by 2 through 6, and reason about patterns in these results. The Broken Eggs problem has many solutions, creating a complex task that will allow any high school student to begin to work on the question and all to pursue it as far as their interest (and time) allows (see 'About Solutions to Activities' link to About Solutions to Activities in the Overview in the Overview to the Interactive Mathematics Program). 2.2.1.4.3 Progression Students will work on this POW primarily outside of class. This unit is carefully designed to support student success, especially with this first long-term, problem-solving and writing project. The problem is posed early in The Importance of Patterns and revisited at several points over the next few class meetings.

Three students will present their solutions to the class, and all will turn in their written work.

. Provides a broad introduction of to algebra. Helps students develop strong mathematical skills and habits of mind. Improves communication and writing skills PATTERNS Students develop basic ideas about functions, integers, angles, and polygons. They learn how to work on mathematical investigations and report on their ideas both orally and in writing.

THE GAME OF PIG Students develop a mathematical analysis for a complex game based on an area model for probability. THE OVERLAND TRAIL Students look at mid-19th-century Western migration in terms of the many linear relationships involved. The PIT AND THE PENDULUM Exploring an excerpt from this Edgar Allan Poe classic, students use data from experiments and statistical ideas, such as standard deviation, to develop a formula for the period of a pendulum. SHADOWS Students use principles about similar triangles and basic trigonometry to develop formulas for finding the length of a shadow.

Covers quadratic functions and equations. Deepens students’ conceptual understanding through new contexts. Includes embedded practice DO BEES BUILD IT BEST? Students study surface area, volume, and trigonometry to answer the question, “What is the best shape for a honeycomb?” COOKIES In their work to maximize profits for a bakery, students deepen their understanding of the relationship between equations and inequalities and their graphs. IS THERE REALLY A DIFFERENCE? Students build on prior experience with statistical ideas from IMP Year 1, expanding their understanding of statistical analysis.

FIREWORKS The central problem of this unit involves sending up a rocket to create a fireworks display. This unit builds on the algebraic investigations of Year 1, with a special focus on quadratic expressions, equations, and functions. ALL ABOUT ALICE The unit starts with a model based on Lewis Carroll’s Alice’s Adventures in Wonderland, through which students develop the basic principles for working with exponents. Extends students’ understanding of material studied in preceding years of the curriculum as they learn and apply new skills. Topics include combinatorics, derivatives, and the algebra of matrices ORCHARD HIDEOUT Students study circles and coordinate geometry to determine how long it will take before the trees in a circular orchard grow so large that someone standing at the center of the orchard cannot see out. MEADOWS OR MALLS? This unit concerns making a decision about land use and builds on skills learned in Cookies about graphing systems of linear inequalities and solving systems of linear equations. SMALL WORLD, ISN'T IT? Beginning with a table of population data, students study situations involving rates of growth, develop the concept of slope, and then generalize this to the idea of the derivative.

PENNANT FEVER Students use combinatorics to develop the binomial distribution and find the probability that the team leading in the pennant race will ultimately win the pennant. HIGH DIVE Using trigonometry, polar coordinates, and the physics of falling objects, students model this problem: When should a diver on a Ferris wheel aiming for a moving tub of water be released in order to create a splash instead of a splat?. Features widely varied topics, including computer graphics, statistical sampling, and an introduction to accumulation and integrals. Builds on the strong knowledge base of IMP students THE DIVER RETURNS This unit builds upon Year 3’s High Dive problem: 'When should a diver on a Ferris wheel aiming for a moving tub of water be released in order to create a splash instead of a splat?' In Year 4, students use vectors modeling horizontal and vertical components of the diver’s initial velocity. THE WORLD OF FUNCTIONS In this unit, students explore families of functions in terms of various representations—tables, graphs, algebraic representations, and situations they can model; they also explore ways of combining functions using arithmetic operations and composition.

THE POLLSTER'S DILEMMA The central problem of this unit concerns an election poll, and students use normal distributions and standard deviations to find confidence intervals and see how concepts such as margin of error are used in polling results. HOW FAST? This unit adds integrals to the derivative concepts explored in Year 3. Students solve accumulation problems using a version of the Fundamental Theorem of Calculus.

They find that the derivative of the function that describes the amount of accumulation up to a particular time is the rate of accumulation, and that the function describing accumulation is an anti-derivative of the function describing the rate of accumulation. AS THE CUBE TURNS Students study the fundamental geometric transformations—translations, rotations, and reflections—in two and three dimensions, in order to create a display of a cube rotating around an axis in three-dimensional space.