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PISCATAWAY TOWNSHIP SCHOOLS Quibbletown Middle School Gail Cunningham ~ Email:gcunningham@pway.org ~ Phone: 732-752-0444 Ext. 5342 6th Grade Mathematics Course Title: Math 6 Textbook: McDougal Littell: Middle School Math, Course 1 Pearson: Connected Mathematics 2 – Grade 6 Prime Time Filling and Wrapping Bits & Pieces II How Likely Is It? Bits & Pieces III Course Description: Sixth grade Math is a discovery and application of number sense, numerical operations, algebraic thinking, geometry, measurement, probability/statistics, and data analysis. The goal for students in this course, through the New Jersey Core Curriculum Standards, is to use appropriate operations involving whole numbers, fractions, decimals, and percents in problem solving situations. Students will regularly represent ideas graphically and in written form. The use of technology (calculators, computer software, etc.) will be used to enable students to focus on the problem solving process. As students are immersed in hands-on activities and real-life applications, lessons will contain a variety of experiences in order to address the range of learning styles. Students’ progress will be monitored through benchmarks, standardized tests, and assessments in order to promote understanding and proficiency. Approximate Topic Time Frame Fraction, Decimal, Percent Review Marking Measuring Geometric Objects Develop and apply strategies and formulas for finding perimeter and area. Period Triangle, square, rectangle, parallelogram, and trapezoid. Recognize that shapes with the same perimeter do not necessarily have the 1 same area and vice versa. Recognize the decimal nature of United States currency and compute with money. Develop informal ways of approximating the measures of familiar objects (e.g., use a grid to approximate the area of the bottom of one’s foot). Number Sense Develop and apply number theory concepts in problem solving situations. Primes, factors, multiples, common multiples, common factors. Find squares and cubes of whole numbers. Understand and use the various relationships among operations and properties of operations. Understand and apply the standard algebraic order of operations for the four basic operations, including appropriate use of parentheses. Units of Measurement Convert measurement units within a system (e.g. 3 feet = ____ inches). Use measurement and estimates to describe and compare phenomena. 1 PISCATAWAY TOWNSHIP SCHOOLS Quibbletown Middle School Gail Cunningham ~ Email:gcunningham@pway.org ~ Phone: 732-752-0444 Ext. 5342 6th Grade Mathematics Approximate Topic Time Frame Fractions Use real-life experiences, physical materials, and technology to construct Marking meanings for numbers: All integers; All fractions as part of a whole, as Period subset of a set, as a location on a number line, and as divisions of whole numbers; All decimals. 2 Compare and order numbers. Recognize the appropriate use of each arithmetic operation in problem situations. Determine the reasonableness of an answer by estimating the result of operations. Construct, use, and explain procedures for performing calculations with fractions and decimals with: Pencil-and paper; Mental math; Calculator. Decimals & Percents Understand and use whole-number percents between 1 and 100 in a variety of situations. Use whole numbers, fractions, and decimals to represent equivalent forms of the same number. Use a variety of estimation strategies for both number and computation. Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer. Determine whether a given estimate is an overestimate or an underestimate. 2 PISCATAWAY TOWNSHIP SCHOOLS Quibbletown Middle School Gail Cunningham ~ Email:gcunningham@pway.org ~ Phone: 732-752-0444 Ext. 5342 6th Grade Mathematics Approximate Topic Time Frame Ratios & Proportions Explore the use of ratios and proportions in a variety of situations. Marking Use a scale to find a distance on a map or a length on a scale drawing. Period Probability 3 Determine probabilities of events: Event, complementary event, probability of an event; Multiplication rule for probabilities; Probability of certain event is 1 and of impossible event is 0; Probabilities of event and complementary event add up to 1. Determine probability using intuitive, experimental, and theoretical methods (e.g., using model of picking items of different colors from a bag): Given numbers of various types in a bag, what is the probability that an item of one type will be picked; Given data obtained experimentally, what is the likely distribution of items in the bag? Geometric Properties & Measuring Geometric Objects Understand and apply concepts involving lines and angles: Notation for line, ray, angle, line, segment; Properties of parallel, perpendicular, and intersecting lines; Sum of the measures of the interior angles of a triangle is 180˚. Identify, describe, compare, and classify polygons and circles: Triangles by angles and sides; Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi; Polygons by number of sides; Equilateral, equiangular, regular; All points equidistant from a given point form a circle. Compare properties of cylinders, prisms, cones, pyramids, and spheres. Select and use appropriate units to measure angles, area, surface area, and volume. Develop and apply strategies and formulas for finding…Circumference and area of a circle. 3 PISCATAWAY TOWNSHIP SCHOOLS Quibbletown Middle School Gail Cunningham ~ Email:gcunningham@pway.org ~ Phone: 732-752-0444 Ext. 5342 6th Grade Mathematics Approximate Topic Time Frame Geometric Properties & Measuring Geometric Objects Identify, describe, and draw the faces or shadows (projections) of three- Marking dimensional geometric objects from different perspectives. Identify a three-dimensional shape with given projections (top, front, and side Period views). Identify a three-dimensional shape with a given net (i.e., a flat pattern that folds 4 into a 3D shape). Select and use appropriate units to measure angles, area, surface area, and volume. Develop and apply strategies and formulas for finding the surface area and volume of rectangular prisms and cylinders. Transforming Shapes & Coordinate Geometry Use a translation, a reflection, or a rotation to map one figure onto another congruent figure. Create geometric shapes with specified properties in the first quadrant on a coordinate grid. Patterns, Functions, and Relationships Use patterns, relations, and linear functions to model situations: Using variables to represent unknown quantities; Using concrete materials, tables, graphs, verbal rules, algebraic expressions/equations/inequalities. Recognize, describe, extend, and create patterns involving whole numbers and rational numbers: Descriptions using tables, verbal rules, simple equations, and graphs; Formal iterative formulas (e.g., NEXT = NOW * 3); Recursive patterns, including Pascal’s Triangle and the Fibonacci Sequence. Describe the general behavior of functions given by formulas or verbal rules (e.g., graph to determine whether increasing or decreasing, linear or not). Solve simple linear equations with manipulatives and informally: Whole- number coefficients only, answers also whole numbers; Variables on one or both sides of the equation. Understand and apply the properties of operations and numbers: Distributive property; The product of a number and its reciprocal is 1. Evaluate numerical expressions. Data Analysis Draw freehand sketches of graphs that model real phenomena and use such graphs to predict and interpret events: Changes over time; Relations between quantities; Rates of change (e.g., when is plant growing slowly/rapidly, when is temperature dropping most rapidly/slowly). Read, interpret, select, construct, analyze, generate questions about, and draw inferences from displays of data: Bar graph, line graph, circle graph, table, 4 PISCATAWAY TOWNSHIP SCHOOLS Quibbletown Middle School Gail Cunningham ~ Email:gcunningham@pway.org ~ Phone: 732-752-0444 Ext. 5342 6th Grade Mathematics histogram: Range, median, and mean; Calculators and computers used to record and process information. Analyze vertex-edge graphs and tree diagrams: Can a picture or a vertex-edge graph be drawn with a single line? (degree of vertex); Can you get from any vertex to any other vertex? (connectedness) Use vertex-edge graphs to find solutions to practical problems: Delivery route that stops at specified sites but involves least travel; Shortest route from one site on a map to another. Discrete Mathematics Apply the multiplication principle of counting: Simple situations (e.g., you can make 3 × 4 = 12 outfits using 3 shirts and 4 skirts); Number of ways a specified number of items can be arranged in order (concept of permutation); Number of ways of selecting a slate of officers from a class (e.g., if there are 23 students and 3 officers, the number is 23 × 22 × 21). List the possible combination of two elements chosen from a given set (e.g., forming a committee of two from a group of 12 students; finding how may handshakes there will be among ten people if everyone shakes each other person’s hand once). Solve counting problems and justify that all possibilities have been enumerated without duplication: Organized lists, charts, tree diagrams, tables; Venn diagrams. Grading Criteria: Quarterly Cumulative Assessments 10% Projects 25% Tests/Quizzes 30% Class work 25% Homework 10% *Above percentages are subject to a five percent adjustment based on the teacher’s discretion. 5 PISCATAWAY TOWNSHIP SCHOOLS Quibbletown Middle School Gail Cunningham ~ Email:gcunningham@pway.org ~ Phone: 732-752-0444 Ext. 5342 6th Grade Mathematics Supplies Needed: Pencils, Pencils and more Pencils (Students will need to maintain a daily supply of pencils in class) Pencil Sharpner (No battery operated) Agenda book (for recording homework) – [1st copy to be provided by school] Loose Leaf Notebook (to be divided into sections) OR Pocket Folders for handouts White-lined paper (hole-punched and college ruled) Classroom Rules & Expectations: ► On Time - Students are expected to be on time for class with needed supplies. : If a student is late to class without a pass, the lateness is considered unexcused. ► Class Participation – Students are expected to participate in class activities (group work, answering questions, asking questions, board work, individual assignments, etc.) ► Homework/Projects - All assignments are due at the beginning of class on their due date. Late assignments will not be accepted. ► Locker Use - Students may go to their lockers before homeroom, before lunch, after lunch, and during dismissal. Students may not go to lockers during class. It is the student’s responsibility to remember to bring all needed items to class (before class begins). ► Absences – if a student misses class, it is his or her responsibility to get all class notes and find out what work needs to be made up. He or she may contact a classmate to find out what was missed. Classmate 1 __________________________________Phone ___________________________________ Classmate 2 __________________________________Phone ___________________________________ Classmate 2 __________________________________Phone ___________________________________ If a student was absent when an assignment was given, the assignment should be handed in at the beginning of class on the first day the student returns to school. All make-up assignments should be completed within the amount of days that the student was absent (i.e. if a student was absent 3 days, they have 3 days to make up the assignments.). School rules will be enforced in all classroom settings (See Student Code of Conduct) 6 PISCATAWAY TOWNSHIP SCHOOLS Quibbletown Middle School Gail Cunningham ~ Email:gcunningham@pway.org ~ Phone: 732-752-0444 Ext. 5342 6th Grade Mathematics 6th Grade Mathematics – Notebook Organization Section Category What to Include In this section, keep classroom rules and procedures and notebook 1 Forms organization sheet. You can print the course syllabus from my website if needed. Class Notes/Reflections This section should include: 2 Any and all work you do for in-class problems; this includes your Hints: work on Connected Math investigations and/or textbook problems Date each entry. and any handouts. Include words, charts, pictures, or anything else Identify problems with the to show your thinking. problem number and unit name. Any notes you take; write anything that will help you remember Always revise what you what you were thinking. These notes are for your reference as you have written by crossing it solve in-class problems, answer homework questions, work on out, rather than by erasing. This helps you and your quizzes, and prepare for tests. teacher to follow your thinking. It does not count Your Mathematical Reflections from each Investigation. against you to cross out your old work. This section will include: 3 All homework assignments. Your homework should be written on lined loose-leaf notebook paper or graph paper and be clearly identified with the following information: Name Date Homework Assignments Homework Assignment Description and Assessments Show all work DO NOT write your homework on the same page as class notes! All check-ups, quizzes, tests, projects, and self assessments. DO NOT WRITE IN YOUR CONNECTED MATH BOOK 4 Your Connected Mathematics (only worksheets) All work should be written in your Class Notes section. Binder/Investigations 7 PISCATAWAY TOWNSHIP SCHOOLS Quibbletown Middle School Gail Cunningham ~ Email:gcunningham@pway.org ~ Phone: 732-752-0444 Ext. 5342 6th Grade Mathematics Please read and sign the section below. This page should be DETACHED and RETURNED to Ms. Cunningham by: ___________________________________________________ I have read the syllabus (on my teacher’s website) and class policy/procedures for Ms. Cunningham’s math class. I understand the contents of this document and will contact the teacher by phone, email or in person to clarify any questions or concerns. I agree to abide by the above expectations and procedures. Student Name (print):__________________________________________________________________ Student Signature:_____________________________________________Date:__________________ Parent’s Name (print): _________________________________________________________________ Parent/Guardian Signature:____________________________________Date:___________________ _____________________________________________________________________________________ Parent email: (print) – also indicate who this email belongs to (i.e. Mary Smith – M.Smith991@yahoo.com) _____________________________________________________________________________________ Additional email: (print) – also indicate who this email belongs to. Parent Phone Number’s (Please provide all contact numbers where you can be reached.) Name:_________________________________________ Phone:_______________________________ Name:_________________________________________ Phone:_______________________________ If additional space is needed, please continue on the back of this page. Menger Sponge 8

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