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Unit Title #1: Number Systems and Number Operations Grade Level/Course: 6th Grade Math Common Core State Standard: The Number System Domain 1 6.NS.2, 6.NS.5, 6.NS.6c, 6.NS.7.c, 6.NS.7.a, 6.NS.7.b, 6.NS.7.b, 6.NS.3 New York State Standards 6.N.1 , 6.N.2, 6.N.3, 6.N.4, 6.N.5, 6.N.20,6.N.21, 6.N.22, 6.N.23, 6.N.24, 6.N.25, 6.N.27 Essential Questions: What is the importance of place value in ordering numbers? What are the distinguishing characteristics between rational and irrational numbers? What would our society be like without decimals? What are the patterns that are found in our number system? What is the importance of place value when ordering numbers? Do operations work the same with decimals as they do whole numbers? Where/How do we use rounding and estimation in everyday life? What are the properties of mathematics? Is there a proper order of operations? If we neglect to follow the order of operations, is our calculation correct? Content: Decimals enable us to be more precise and exact in our calculations and measurements. Recognizing math properties enables us to apply the relationships that are found in operations to solve math problems. Following the order of operations yields accurate calculations. Skills: Compute single digit division Mastery of Place Value (Whole numbers & Decimals) Recognize decimal place value Add, subtract, multiply and divide decimals Identify and define Math properties Order of Operations Use of exponents Prime Factorization Assessments(s): Unit#1 exam Quizzes Portfolio Pieces Teacher Observations Self Reflections Cooperative Learning Projects Activities: Create your own Restaurant menu Decimal Operations Project (budget) Materials and Resources: Impact Math Course 1 Chapter 3 Lesson 3.1, 3.2 and 3.4 Chapter 2, Lesson 2.1 and 2.3 Red Hot Topics www.glencoe.com http://illuminations.nctm.org/ www.mathalicious.com www.brainpop.com www.makeitreallearning.com Vocabulary/Specialized terms: Place value, dividend, divisor, quotient, remainder, rational numbers, compare and ordering, Estimate, Round, exponent, base, terminating and repeating decimals, order of operations Unit Title 2: Fraction Operations Grade Level/Course: 6th Grade Math Common Core State Standard: The Number System Domain 1 6.NS.1, 6.NS.4 New York State Standards 6.N.16, 6.N17, 6.N.18, 6.N.19 Essential Questions: What is different about fractions with unlike denominators? How are dividing fractions similar to multiplying fractions? What steps are necessary in order to divide mixed numbers? How are finding the GCF and LCM related? What is the relationship between the four different operations when using them with fractions? Content: Following the order of operations yields accurate calculations. Finding like denominators enables us to easily order, compare, add, and subtract decimals. There is a relationship between fractions and decimals. There are specific methods used to solve fractions involving the operations. Skills: Prime factorization. GCF LCM Use LCM to find the LCD Use LCD to find like denominators. Reducing fractions using GCF. Conversion of improper fractions and mixed numbers Assessments(s): Unit#2 exam Quizzes Portfolio Pieces Teacher Observations Cooperative Learning Projects Activities: Foldable activity (differences between GCF and LCM) Recipe Project Materials and Resources: Impact Math Course 1 Chapter 4, Lesson 4.1-4.3 www.glencoe.com Red Hot Topics Math Advantage http://illuminations.nctm.org/ www.mathalicious.com www.brainpop.com Vocabulary/Specialized terms: Factors, multiples, LCM (least common multiple), GCF (greatest common factor), divisibility, prime factorization, reciprocal, mixed numbers Add/Subtract fractions with like and unlike denominators Convert between mixed number and improper fractions Reciprocal, rename Unit Title # 3: Ratios, Rates, Proportions and Percents Grade Level/Course: 6th Grade Math Common Core State Standard: Ratios and Proportional Relationships Domain 2 6.RP.1, 6.RP.3.a, 6.RP.2, 6.RP.3.b, 6.RP.3.c, 6.RP.3.d New York State Standards 6.N.6, 6.N.7,6.N.8, 6.N.9, 6.N.10, 6.N.11, 6.N.12, 6.N.21, 6.A.5 Essential Questions: How are rates, ratios, proportion and percents related? How/Where do we use rates, ratios, proportions and percents in everyday life? Content: Numbers are inventions that represent quantities, rates, sequence and characteristics of familiar things and experiences. Skills: Writes ratios as fractions. Write equivalent ratios as proportions. Using cross products to verify the proportionality of two fractions. Distinguishing between rate and ratio. Writing percents as fractions and decimals. Use proportions to solve percentage problems. Assessments(s): Unit#3 exam Quizzes Portfolio Pieces Teacher Observations Cooperative Learning Projects Activities: Liliana’s Gift Percent Project Biggest Loser (Percent of Change) Materials and Resources: Impact Math Course#1 Chapter 6 Lesson 6.2 Chapter 5 Lesson 5.1, 5.2, 5.3 Red Hot Topics www.glencoe.com http://illuminations.nctm.org/ www.mathalicious.com Big Foot Conspiracy www.brainpop.com www.makeitreallearning.com Vocabulary/Specialized terms: Ratio, Unit rate, percent, proportions, means and extremes, equivalent ratios, ratio chart, benchmark fractions, percent of a quantity Unit Title# 4: Geometry and Coordinate Plane Grade Level/Course: 6th Grade Math Common Core State Standard: Geometry Domain 4 6.G.1, 6.G.2, 6.G.3, 6.G.4 New York State Standards 6.N.13, 6.N.14, 6.N.15, 6.G.2, 6.G.3, 6.G.4, 6.A.2, 6.A.6, 6.M.1, 6.M.7, 6.M.8 6.G.10,6.G.11 Essential Questions: What is perimeter, area, circumference, and how are they related? How is geometry used in our world? How is space measured? Content: There are specific formulas that are used to compute the area, perimeter volume, and circumference of various geometric shapes. Standard units of measure are used to understand our calculated data. Both the real and man-made world is formed out of geometric shapes. Skills: Calculate the area and perimeter of squares, rectangles, parallelograms, trapezoids and triangles. Calculate the volume of a rectangular prism. Determine the perimeter and area of irregular polygons. Translate two-step verbal expressions into algebra. Use substitution to evaluate expressions. Solve word problems using geometric relationships and formulas. Assessments(s): Unit#4 exam Quizzes Portfolio Pieces Teacher Observations Cooperative Learning Projects Activities: Create your own Dreamhouse Materials and Resources: Impact Math Chapter 7 Lessons 7.1, 7.2,7.3 Chapter 8 Lessons 8.2 and 8.3 Chapter 1 Lessons 1.3 Red Hot Topics Math Advantage www.glencoe.com http://illuminations.nctm.org/ www.mathalicious.com www.brainpop.com Vocabulary/Specialized terms: Area, square unit, quadrilateral, formulas-parallelogram, rectangle, square, rhombus, trapezoid, composite polygon, solid figures-three dimensional figures, face, vertex, edge, net, prism, surface area, volume, cubic units, coordinate plane, x- axis, y-axis, quadrants, ordered pair, counterclockwise, origin, x-coordinate, y- coordinate Unit Title#5: Circles and Circle Relationships Grade Level/Course: 6th Grade Math Common Core State Standard: Ratios and Proportional Relationships: Domain 2 Under CCSS this will be a 7th grade concept 7.G.4, 7.G.6 New York State Standards 6.G.5, 6.G.6, 6.G.7, 6.G.8, 6.G.9, 6.M.7, 6.M.8, 6.A.2, 6.A.6 Essential Questions: Why do formulas exist? What is area, circumference, and perimeter and how are they related? How is geometry used in our world? Content: There are specific formulas to help us precisely calculate area and perimeter of various spaces that are different sizes/shapes. There are standard units of measure to enable a uniform understanding of data and measurements. Skills: Derive and apply the formulas for the area and circumference of a circle. Calculate the Sector of a circle Assessments(s): Unit#5 exam Quizzes Portfolio Pieces Teacher Observations Cooperative Learning Projects Activities: Foldable activity Materials and Resources: Impact Math Course 1 Chapter 1 Lessons 1.3 Chapter 7 Lessons 7.2 Red Hot Topics www.glencoe.com http://illuminations.nctm.org/ www.mathalicious.com www.brainpop.com Vocabulary/Specialized terms: Identify parts of a circle-diameter, radius, chord, center of circle Sector of circle Radii Circumference Area perimeter Unit Title# 6: Patterns and Intro to Algebra Grade Level/Course: 6th Grade Math Common Core State Standard: Expressions and Equations Domain 3 6.EE.1, 6.EE2.a., 6.EE.2.b, 6.EE.6, 6.EE.2.c, 6.EE.3, 6.EE.4 New York State Standards 6.A.1, 6.A.2, 6.A.6 Essential Questions: When are equations used? How are one and two step equations solved? How do the mathematical properties allow you to simplify an equation? Content: A pattern of change can be described through a function. A variable represents an unknown that will change in different settings. We can use variables and operations to represent real life scenarios. Skills: Write and solve two- step equations for verbal sentences. Solve problems using equations and inverse operations. Identify expressions Evaluate and write expressions Assessments(s): Unit#6 exam Quizzes Portfolio Pieces Teacher Observations Cooperative Learning Projects Activities: Foldable activity Cell Phone Plan (investigating linear relationships) Materials and Resources: Impact Math Chapter 3.3, Chapter 5 and Chapter 6 Red Hot Topics Math Advantage www.glencoe.com http://illuminations.nctm.org/ www.mathalicious.com www.brainpop.com Vocabulary/Specialized terms: Expression, order of operations (review), equivalent expressions, equation, independent and dependent variables. Unit Title# 7: Data Analysis and Probability Grade Level/Course: 6th Grade Math Common Core State Standard: Statistics and Probability Domain 5 6.SP.1, 6.SP2, 6.SP.3, 6.SP.5.c 6.SP.4, 6.SP.5.a, 6.SP.5.b, 6.SP.5.c, 6.SP.5.d New York State Standards 6.S.5, 6.S.6, 6.S.7, 6.S.8 Essential Questions: What are the mean, median, mode and range? What are the best ways to predict the outcomes of an experiment? Can data be manipulated to show what you want? What kind of conclusions can be made from a set of data? Content: Calculating central tendencies enables us to draw conclusions about a set of data. Outcomes of an experiment can be written in fraction form. Predictions of future events can be made from a set of data. Skills: Determine mean, median, mode and range for given sets of data. Read, interpret, draw conclusions and make predictions on graphs for various information and statistics. Determine the probability of a single event. Write probabilities as a fraction in lowest terms Assessments(s): Unit#7 exam Quizzes Portfolio Pieces Teacher Observations Cooperative Learning Project Activities: Foldable activity Materials and Resources: Impact Math Course 1 Chapter 4 Lesson 4.4 Chapter 10 Lessons 10.1 -10.3 Math Advantage Red Hot Topics www.glencoe.com http://illuminations.nctm.org/ www.mathalicious.com www.brainpop.com Vocabulary/Specialized terms: Mean, median, Mode and range of data Measures of central tendency Probability Sample space Tree diagrams Unit Title# 8: Measurement Grade Level/Course: 6th Grade Math Common Core State Standard: Ratios and Proportional Relationship: Domain 5 6.RP.3.d New York State Standards 6.M.2, 6.M.3, 6.M.4, 6.M.5, 6.M.6, 6.M.7, 6.M.8, 6.M.9 Essential Questions: Why are unit labels important? How are proportions related to converting units? Content: Capacity measures the amount of liquid a container can hold. Mass is the amount of matter in an object. Proportions compare equivalent measurements. Skills: Convert units using proportions. Identify customary and metric units of mass or capacity. Assessments(s): Unit#8 exam Quizzes Portfolio Pieces Teacher Observations Cooperative Learning Projects Activities: Foldable activity Materials and Resources: Impact Math Chapter 7 Lesson 7.4 Red Hot Topics www.glencoe.com http://illuminations.nctm.org/ www.mathalicious.com www.brainpop.com Vocabulary/Specialized terms: Customary unit of capacity, metric unit of capacity, liter, milliliter, gallon man chart, pints, cups, quarts, gallons Unit Title# 9: Advanced Statisitics and Probability Grade Level/Course: 6th Grade Math Common Core State Standard: Statistics and Probability Domain 5 6.SP.4, 6.SP.5.a, 6.SP. 5.b, 6.SP.5.c, 6.SP.5.d, New York State Standards 6.S.1, 6.S.2, 6.S.3, 6.S.4, 6.S.9, 6.S.10, 6.S.11 Essential Questions: How should data be collected and analyzed? Is the way that you display data dependent on the specific investigation/question or set of data collected? How do you support conclusions that you want to make from a set of data? Content: Conducting an investigation begins with asking proper questions. Data can be collected and displayed in various formats. There are many interpretations that can be drawn from a collected set of data. Skills: Analyze sets of data to determine appropriate graphing options. List possible outcomes for compound events. Assessments(s): Unit#9 exam Quizzes Portfolio Pieces Teacher Observations Cooperative Learning Projects Activities: Foldable activity Materials and Resources: Math Advantage Chapter 18 Lessons 18.1 and 18.2 Red Hot Topics www.glencoe.com http://illuminations.nctm.org/ www.mathalicious.com www.brainpop.com Vocabulary/Specialized terms: Data, graph, pictograph, bar graph, line graph, histogram, circle graph, sample space, compound events, probability, dependent events, event, tree diagram, frequency table, tally marks