Cologne Academy Mathematics Department Math 6 Honors Aligned Text(s): (Holt McDougal Larson Pre-Algebra Common Core Ed.) Core Knowledge Curriculum 55% Aligned Adopted: 08/2015 Board Approved: 08/28/2014 Updated: 08/16/2016
Table of Contents Math Department Lesson Plan Essentials... 2 Units and Pacing Charts Unit 1 Overview: Real Numbers & Equivalent Expressions... 4 Essential Vocabulary... 7 Pacing Chart... 8 Unit 2 Overview: Ratios and Proportional Thinking... 10 Essential Vocabulary... 12 Pacing Chart... 14 Unit 3 Overview: Volume, Areas, Similarity & Transformations... 15 Essential Vocabulary... 16 Pacing Chart... 17 Unit 4 Overview: Measures of Central Tendency, Probability & Representations... 19 Essential Vocabulary... 20 Pacing Chart... 21 Highlighted items indicate overlap of MN State Standards and the Core Knowledge Sequence. Boxed items indicate content to be introduced post-mcas. Page 2
Math Department Lesson Essentials Topic: Title of lesson. *Objective: Academic goal for students to achieve by end of lesson. *Standard: MN State Standard or Core Knowledge Sequence reference. Agenda: Sequence of instruction and activities Closure: Brief summary/overview of lesson. May include formative assessment. Homework: Continued practice of lesson. May be used as formative assessment. *Indicates required components. Note: The text has been as closely aligned with MN State Standards but additional resources may be required to include all skills (including within the Core Knowledge Sequence). Resources may be located on the s:drive under Mathematics Resources and by grade level or on the Cologne Academy intranet. Further research/exploration may be required to locate additional resources. Page 3
Overview Strand(s): Number & Operation, Algebra Unit 1: Real Numbers & Equivalent Expressions Approximate Duration of Study: 7 FULL Weeks of Instruction MNSS Knowledge Skills Rational Numbers Every rational number can be expressed as the ratio of two integers (where the denominator is not equal to 0). Show that the decimal forms of rational numbers repeat or terminate. 7.1.1.1 Every rational number can be expressed as a terminating decimal or repeating decimal. Show that the decimal forms of irrational numbers do not repeat or terminate. A number that is not rational is irrational. Write approximations of irrational or rational numbers. o π is not rational. 2 is not rational. o π can be approximated to 3.14 and 22 Equivalent Rational Numbers Decimals, fractions and percents have equivalent forms and can be converted from one form to another. Classify all real numbers. Convert between equivalent fractions, decimals and percents of negative and positive values. 7. 7.1.1.5 Number Line & the Coordinate Grid Rational numbers have a location on a number line. Between any two rational numbers is an irrational number. Pairs of rational numbers can be plotted on a coordinate grid. Graph positive and negative rational numbers on a number line. Plot pairs of positive and negative rational numbers on a coordinate grid. 7.1.1.3 7.1.1.4 7.1.2.6 Combining opposite values make zero. o Additive Inverse: a + (-a) = 0 Inequalities can be used to compare and order positive and negative rational numbers expressed as integers, fractions and decimals. Show that a value and its opposite combine to make 0. Locate opposite values on a number line. Compare and order positive and negative rational numbers, in any form, with or without a number line. Absolute Value represents a number s distance from 0 on a number line. o x = the absolute value of x. o x represents the distance from 0 to x on a number line. o x y represents the distance between x and y. Represent distance on a number line by using absolute value. Evaluate expressions such as 2x 3 + 3x. Unit 1 Page 4
Rational Numbers: Operations The Order of Operations dictates the order in which basic operations, including raising a positive rational number to whole-number exponents, should be performed. Add, subtract, multiply and divide positive and negative rational numbers that are integers, fractions, and terminating decimals. Express powers as whole numbers solutions. 7.1.2.1 7.2.3.3 7.1.2.2 Order of operations must be performed properly to simplify an expression when using a calculator or other technology. Use symbols and order of operations when using a calculator and other technology. o Recognize the conventions of using a caret. (^ raise to a power) and asterisk (* multiply); pay careful attention to the use of nested parentheses. Perform calculations, with and without the use of a calculator, with positive and negative rational numbers and positive integer exponents. Scientific Notation is a method of expressing very small or very large numbers in the form of a single digit times an integer power of 10. Convert decimal numbers to and from scientific notation. Inverse relationships between addition and subtraction can be used to explain the procedures of arithmetic with negative rational numbers. (Note: Important discussion to lead towards solving equations.) Use real world examples to make sense of arithmetic with negative rational numbers o Multiplying a distance by -1 can be thought of representing that same distance in the opposite direction. Multiplying by -1 a second time reverses directions again, giving the distance in the original direction. Rational Numbers: Interpretations 7.1.1.2 7.1.2.3 Division of two integers will always result in a rational number. Calculators and other computing technologies often truncate or round numbers. Unit 1 Interpret the decimal result of division problems when using a calculator. Express non-exact calculator results as exact answers. o 4.16666667 can be expressed as 4 1 which is the same as 6 4.16. o 4.16666666666666 is truncated and rounded to 4.16666667 Page 5
Expressions and Equations 7.2.3.1 7.2.3.2 7.2.2.4 7.2.4.1 Properties of Algebra can be used to generate equivalent expressions. o Commutative: a b = b a; a + b = b + a o Associative: (a b) c = a (b c); (a + b) + c = a + (b + c) o Distributive: ab ac = a(b c); ab + ac = a(b + c) Justify procedures used to simplify algebraic and numerical expressions. Properties of Algebra cannot be applied to all operations. Properties of algebra can be extended to variables. Show that commutative and associative properties will not work over subtraction and division. A value can be substituted into a variable for a given expression. Evaluate algebraic expressions containing rational numbers and whole number exponents at specified values of their variables. Real-world mathematical situations can be represented using mathematical terms. Translate verbal representations into mathematical representations of algebraic and numerical equations and inequalities, and vice versa. o x is at least -1 and less than 10 can be represented as: o -1 x < 10, and also on a number line. Four-fifths is three greater than the opposite of a number can be represented as 4 = -x + 3. 5 Properties of equality are used to solve for the value of a variable. o Addition, Subtraction, Multiplication, and Division Properties of Equality. o Additive Inverse: a + (-a) = 0 o Multiplicative Inverse: a 1 = 1 a Justify use of operations/properties used to solve for unknown quantities in an algebraic equation. Interpret the solution in the original context. Simplify and solve linear equations in one variable such as 3(2x 5) + 4x = 12(x + 5). Key words in word problems determine whether an algebraic equation or inequality must be constructed and solved. Properties of equality can be extended to inequalities. Addition or subtraction or the same value from both sides of an inequality maintains the inequality. Multiplying or dividing both sides of an inequality by a positive number maintains the inequality. Multiplying or dividing by a negative number reverses the inequality. Unit 1 Construct and solve one-step to multi-step equations and inequalities that represent and have real-world applications. Simplify and graph solutions to linear inequalities in one variable such as 3(2x 5) + 4x 12(x + 5). Use a number line to show why the inequality symbol is reversed when multiplying/dividing by a negative number. Create and solve word problems that require equations or inequalities. Page 6
Essential Vocabulary: Rational Number, Irrational Number, Integer, Whole Number, Natural Number, Terminating Decimal, Repeating Decimal, Equivalent, Opposites, Coordinate Grid, Quadrant, Number Line, Coordinate Pairs, Additive Inverse, Inequality, <, >, =,,, Equivalent, Truncate, Power, Base, Exponent, Order of Operations, Properties of Algebra, Associative, Commutative, Distributive, Additive Inverse, Multiplicative Inverse, Properties of Equality, Terms, Like Terms, Unlike Terms, Algebraic & Numerical Expressions and Equations, Grouping Symbols: (parenthesis ( ), brackets [ ] ), Nested Parenthesis, Variables, Evaluate, Substitute, Absolute Value, Caret. Interim 1 Unit 1 Page 7
Pacing Chart Unit 1: Real Numbers & Equivalent Expressions Time Frame Topic Suggested Activities/Assessments Resources & Text Alignment Week 1 Pre-test Week 1 Rational Numbers 5.1: Rational Numbers 9.4: Real Numbers Week 1 7.1.1.1 Equivalent Rational Numbers 7.1: Percents and Fractions 7.3: Percents and Decimals Discuss relationship between fractions, decimals and percents. 7.1.1.5 Number Line & the Coordinate Grid 5.1: Rational Numbers (Review and extend to comparing and ordering) 1.4: Comparing and Ordering Integers 1.8: The Coordinate Plane Week 2 Week 3 7.1.1.3 7.1.1.4 7.1.2.6 Week 2 Week 3 Rational Numbers: Operations 7.1.2.1 7.2.3.3 7.1.2.2 Order of Operations Bingo http://illuminations.nctm.org/lesson.aspx?id=2583 Order of Operations Lesson Tutor http://www.lessontutor.com/eesa4.html Order of Operations Worksheets http://www.mathaids.com/algebra/algebra_1/basics/order_of_operations. html 1.2: Powers and Exponents 1.3: Order of Operations 1.5: Adding Integers 1.6: Subtracting Integers 1.7: Multiplying and Dividing Integers 4.7: Scientific Notation : Using Scientific Notation pg. 211 Order of Operations: Technology Activity pg. 21 Unit 1 Page 8
Week 2 Week 3 Rational Numbers: Interpretations 1.7: Multiplying and Dividing Integers Utilize calculators to illustrate truncation and practice interpreting results. Week 4 Week 8 7.1.1.2 7.1.2.3 Expressions and Equations 7.2.3.1 7.2.3.2 7.2.2.4 7.2.4.1 HM Course 3 Text: Model Two-Step Equations pg. 100. : Technology Activity pg. 83 1.1: Expressions and Variables 2.1: Properties and Operations 2.2: The Distributive Property 2.3: Simplifying Variable Expressions 2.4: Variables and Equations 2.5: Solving Equations Using Addition or Subtraction 2.6: Solving Equations Using Multiplication or Division 2.7: Decimal Operations and Equations with Decimals 3.1: Solving Two-Step Equations 3.2: Solving Equations Having Like Terms and Parenthesis 3.3: Solving Equations with Variables on Both Sides 3.4: Solving Inequalities Using Addition or Subtraction 3.5: Solving Inequalities Using Multiplication or Division Week 9 Review Week 10 Interim 1 Unit 1 Page 9
Overview Strand(s): Number & Operation, Algebra Unit 2: Ratios and Proportional Thinking Approximate Duration of Study: 8 FULL Weeks of Instruction MNSS Knowledge Skills A ratio is a comparison between two quantities. A unit rate is the quantity per one unit. Ratios & Proportions 7.1.2.5 7.2.2.1 7.1.2.5 7.2.2.2 7.2.2.3 7.2.4.2 Identify unit rate and use it to make comparisons and predictions. o Student A reads 10 pages in 14 minutes, Student B reads 3 pages in 2 minutes, who is the faster reader? If they begin at 9 a.m., at what time will each student finish a 110 page book? Compute unit rate from simple complex fractions. o What is the average speed of someone who runs 3 4 mile in 1 3 hour? Proportions can be set up and used to solve problems involving ratios. o A proportion is two equivalent ratios. Determine if relationships are proportional. o In a table by testing for equivalent ratios. o On the coordinate plane by determining if the graph is a straight line through the origin. Solve problems resulting from proportional relationships in various contexts. o Determine the price of 12 yards of ribbon if 5 yards of ribbon cost $1.85. Choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems. Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems. o Miles per hour and feet per second, cubic inches to cubic centimeters. Proportional relationships can be represented by tables, verbal descriptions, symbols, linear equations and graphs. Identify the unit rate (constant of proportionality or slope) in tables, verbal descriptions, graphs, and equations. Translate between tables, verbal descriptions, symbols, equations and graphs given any of these representations. Unit 2 Page 10
Proportions can be used to solve multi-step ratio and percent problems. Compute distance-time (d = rt). Compute percent increase or decrease. Compute discounts, tips, unit pricing. Compute lengths in similar geometric figures (in geometry unit) Compute unit conversion when a conversion factor is given. Convert between different measurement systems. Proportions can be used to assess the reasonableness of solutions. Interpret/explain solutions of proportion problems in the context of the original problem and determine if solutions are reasonable. o Recognize that it would be unreasonable for a cashier to request $200 if you purchase a $225 item at 25% off. Slopes and Lines Extension Simple and Compound Interest 7.1.2.4 Direct and Inverse Variation 7.2.1.1 7.2.1.2 The slope of a non-vertical line is the ratio of the rise (vertical change) to the run (horizontal change) between any two points on the line. Simple interest does not use interest earned as new principal; compound interest does. A relationship between two variables, x and y, is proportional if it can be expressed in the form y = k or y = kw x A relationship between two variables, x and y, is inversely proportional if it can be expressed in the form k = y or xy = k. x Explain the concept of slope. Identify slope (m) given an equation or a line on the coordinate plane. Use slope to extend a line. Identify the y-intercept (b) given an equation or a line. Estimate values of b and m from a given linear graph. Use the y-intercept as the starting point to draw a line. Identify and write equations in slope-intercept form. Graph a line given it s equation in slope-intercept form. Compute and compare simple and compound interest. Predict future values of balances accruing simple or compound interest. Construct an equation, in slope-intercept form, to model simple interest. Construct an equation to model compound interest. Compare direct and inverse variations (equations & graphs). Rewrite direct variation in the form y = mx. Solve direct and inverse variation equations. Unit 2 Page 11
The graph of a proportional relationship is a straight line passing through the origin on the coordinate axis. The equation of the graph of direct variation is related to slopeintercept form; y = mx + b where m = constant of proportionality or slope and b = 0. Graph direct variation on the coordinate plane. Use graphing technology to examine the effects of changing the unit rate of a line. o o Simple Interest: I = P r t (interest only) Compound Interest: A = P( 1 + r n )nt Compare the graphs of simple and compound interest. Calculate and compare simple and compound interest. Essential Vocabulary: Simple Interest, Compound Interest, Principal, Constant of Proportionality, Accrue, Complex Fraction, Constant of Variation, Table of Values, Slope, Slope-Intercept Form, Y-Intercept, Coordinate Plane, Properties of Equality (addition, subtraction, multiplication, division), Inverse Operations, Proportion, Proportional, Ratio, Unit Rate, Unit Price, Direct Variation, Inverse Variation. Interim 2 Unit 2 Page 12
Pacing Chart Unit 2: Ratios & Proportional Thinking Time Frame Topic Suggested Activities/Assessments Resources & Text Alignment Week 11 Week 14 Ratios & Proportions 7.1.2.5 7.2.2.1 7.1.2.5 7.2.2.2 7.2.2.3 7.2.4.2 6.1: Ratio and Rates 6.2: Writing and Solving proportions 6.3: Solving Proportions Using Cross Products 7.2: Percents and Proportions 7.4: The Percent Equation 7.5: Percent of Change 7.6: Percent Applications Week 14 Week 16 8.2: Linear Equations in Two Variables* 8.4: The Slope of a Line* 8.5: Slope-Intercept Form* *Pre-requisites/extension to Direct and Inverse Variation Week 17 - Week 18 Simple and Compound Interest 7.1.2.4 HM Course 3 Text: Explore Compound Interest pg. 314 (Introduce Compound Interest Formula) (Also use graphing technology to explore) : Interest: Technology Activity pg. 383 (Also use graphing technology to explore) 7.7: Simple and Compound Interest Week 17 Winter Break 2016-2017 Unit 2 Page 13
Week 18 - Week 20 Direct and Inverse Variation 7.2.1.1 7.2.1.2 HM Course 3 Text Most sections of text have: Hands-On Lab; use to extend/enrich each lesson. 8.2: Linear Equations in Two Variables* 8.4: The Slope of a Line* 8.5: Slope-Intercept Form* Direct Variation and Inverse Variation pg. 290 Graphs of Direct Variations pg. 436 (Also use graphing technology to explore Direct and Inverse Variation) : Linear Equations in Two Variables* Technology Activity pg. 413 Week 21 Review Week 22 Interim 2 Page 14 Unit 2
Overview Strand(s): Algebra, Geometry & Measurement Unit 3: Volume, Areas, Similarity & Transformations Approximate Duration of Study: 7 FULL Weeks of Instruction MNSS Knowledge Skills Area and perimeter (circumference) apply to two-dimensional figures. Volume and surface area apply to three-dimensional figures. 7.3.1.1 7.3.1.2 Area, Surface Area & Volume The relationship between the diameter and circumference of a circle is proportional and that the unit rate (constant of proportionality) is π. Compute the perimeter, area, and volume of common geometric objects; use results to find measures of less common objects. Show the proportional relationship between circumference, c and diameter. o For a circle with a radius of 5 units, circumference can be written as c = π10 or c = 10π, which is in the form y = kx. Therefore the relationship is proportional. Circumference is the distance around a circle (perimeter). Area is how much space a circle covers. The formula for circumference and area of circles: o Circumference of Circle: C = 2πr or C = πd o Area of Circle: A = πr 2 Calculate the circumference and area of circles and sectors of circles to solve problems in various contexts. Solve real-world and mathematical problems involving perimeter and area of two-dimensional objects. The intersection of planes and three dimensional objects create two-dimensional shape sections. Know that the cross-section created by the intersection of a plane and a sphere is a circle. Volume is related to the capacity of an object. Surface Area is how much material is needed to cover the outside (surface) of an object. The formula for volume and surface area of a cylinder: o Volume = πr 2 h o Surface Area = 2πrh + 2 πr 2 Unit 3 Solve real-world and mathematical problems involving surface area and volume of three-dimensional objects. Justify the formula of a cylinder by decomposing the surface into two circles and a rectangle. Calculate the surface area of a sphere using the equation SA = 4πr 2. Calculate the volume of a sphere using the equation V = 4 3 πr3. Describe and construct simple right prisms, cylinders, cones, and spheres using the concepts of parallel and perpendicular lines. Calculate the surface areas and volumes of these three dimensional objects. Page 15
Similarity & Scale 7.3.2.1 7.3.2.2 7.3.2.3 7.2.4.2* 7.2.2.2* *Also Unit 2 Area and volume composite figures are found by breaking the figure in to more basic geometric objects. Similar Figures have the same shape but not necessarily the same size. o Corresponding angles in similar figures have the same measure. o Corresponding sides in similar figures are proportional. Estimate and compute the area of irregular two- and threedimensional figures. Describe properties of similarity. Compare geometric figures for similarity. Determine scale factors. Scale Factor (k) is a number that multiplies (scales) a quantity. Also called the constant of proportionality. o If k > 1, the figure will increase in size. o If 0 < k < 1, the figure will decrease in size. o When comparing two similar geometric figures, k = length ratio of corresponding sides. Apply scale factors, length ratios, and area ratios to determine side lengths and areas of similar geometric figures. o If two similar rectangles have heights of 3 and 5, and the first rectangle has a base of length 7, the base of the second rectangle has length 35. 3 A Scale Drawing depicts a real object with measurements that have been reduced or enlarged. Scale drawings are proportional to the original object. o A map is one kind of scale drawing. Scale factors can be used to convert between measurement systems. Use proportions and ratios to solve problems involving scale drawings and conversions of measurement units. Translations & Reflections 7.3.2.4 A transformation is an operation that places an original figure, the pre-image, into a new position or onto a new figure called the image. o Pre-image and image are either similar or congruent figures. Translations, rotations and reflections produce congruent figures. Describe the effect of translations and reflections of figures on a coordinate grid. Graph the image of a figure that has been translated or reflected on a coordinate grid. Determine the coordinates of the vertices of an image. Determine the image of a triangle under translations, rotations and reflections. Essential Vocabulary: Scale Factor, Scale Drawing, Similar Figure, Perimeter, Circumference, One-Dimensional Figure (line, point), Two-Dimensional Figure, Three- Dimensional Figure, Area, Surface Area, Plane, Cross Section, Cylinder, Circle Sectors, Diameter, Radius, Scale Model, Scale Drawing, Transformation, Translation, Reflection, Rotations, Pre-Image, Image, Congruent Figures, Vertex, Corresponding Angles, Corresponding Sides, Length & Side Ratios, Geometric Formulas (area/surface area), Decomposition of Geometric Figures, Perimeter, Cylinder, Coordinate Grid (Cartesian Plane, x- and y-axis), Coordinates. Interim 3 Unit 3 Page 16
Pacing Chart Unit 3: Volume, Areas, Similarity & Transformations Time Frame Topic Suggested Activities/Assessments Resources & Text Alignment Week 23 Week 25 Area, Surface Area & Volume 7.3.1.1 7.3.1.2 10.4: Circumference and Area of a Circle (Also: calculate area of circle sectors; verify proportional relationship between circumference and diameter.) 10.5: Surface Areas of Prisms and Cylinders 10.7: Volumes of Prisms and Cylinders Extend Spheres Volume and Surface Area Week 26 Week 27 Similarity & Scale 7.3.2.1 7.3.2.2 7.3.2.3 7.2.4.2* 7.2.2.2* *Also Unit 2 Also: Review conversions between systems of measurement. 6.4: Similar and Congruent Figures 12.7: Dilations 6.5: Similarity and Measurement 6.6: Scale Drawings (Also: Discuss scale models.) Also use: HM Course 3 Text Section 5-3 : Dimensional (Unit) Analysis: pg. 65, ex. 5, pg. 762 Converting Between Systems of Measurement pg. 69 Measuring Indirectly pg. 114 Week 28 Translations & Reflections 7.3.2.4 : Technology Activity pg. 715 Transformations: Concept Activity pg. 716 12.4: Translations 12.5: Reflections and Symmetry 12.6: Rotations and Symmetry* Use Rules for Rotations Week 29 Review Week 30 Interim 3 *Extension Unit 3 Page 17
Overview Strand(s): Data Analysis & Probability Unit 4: Measures of Central Tendency, Probability & Representations Approximate Duration of Study: 5 FULL Weeks of Instruction MNSS Knowledge Skills The Measures of Central Tendency: Mean, Median, Mode Calculate mean, median, mode and range for quantitative data and from Measures o Mean is the central value of a set of numbers. data represented in a display. and Range o Median is the middle number in a data set arranged in Find missing values if the mean and the remaining values are known. ascending order. o The mean of 6 scores is 72. What would the 7 th score have to be to 7.4.1.1 o Mode is the number that occurs most frequently in a data have an average of 85? 7.4.1.2 set. Draw conclusions and make predictions given data. Range is the value that gives information about the spread of the data. o o Data with a large range are more spread out. Data with a small range value are less spread out (clustered). e.g.: By looking at data from the past, Sandy calculated that the mean gas mileage for her car was 28 mpg. She expects to travel 400 miles during the next week. Predict the approximate number of gallons that she will use. Data can influence values of the measures of central tendency. Data can be summarized by a measure of central tendency. Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. o e.g. A greater outlier will increase the mean value; a lower outlier will decrease the mean. Data Display 7.4.3.1 7.4.2.1 Data can be collected and represented in a variety of displays. Random numbers can be generated using various methods. o Graphing calculator, spreadsheet, drawing numbers, rolling dice, etc. Design simple experiments and collect data. Use random number generators to simulate random situations/data. Tally data from a random number generator. A histogram is used to display data in intervals. A bar graph is used to display data by categories. Create and compare histograms and bar graphs. Display data using a spreadsheet or other graphing technology. Proportional reasoning can be used to display and interpret data in a circle graph and histogram. Create a ratio and proportion to solve for missing values. o 26 is 40% of 65 which is 144 o, or 40%, of the degrees of a circle. Create a circle graph of data collected or from a table. Create a histogram of data collected or from a table. Create a histogram of relative frequencies. Unit 4 Page 18
Box-and- Whisker & Scatter Plots Core Knowledge Probability 7.4.3.2 7.4.3.3 A box-and-whisker plot is used to display quantitative data and is plotted on a number line. Box-and-Whisker plots are split into four quartiles, each representing 25% of the data. Five data points are displayed on a box-and-whisker plot. A scatter plot shows the relationship between two variables. A scatter plot can be used to draw an informal inference about the correlation between two variables. Scatter plots can be used to make predictions concerning real world data. A sample space of an experiment is a display of the set of all possible outcomes of that experiment. The probability of an event is the chance that an event will occur; represented by a percent, decimal or fraction with a value that falls between 0 and 1. o The closer to one, the more likely the event will occur; the closer to 0, the less likely the event will occur. o Probability = Number desired events Total number of possible outcomes A simple event has a single outcome. A compound event is an event that is made up of two or more simple events. Given data, construct a box-and-whisker plot. Find the upper and lower quartiles for a data set. Interpret a box-and-whisker plot. Construct scatter plots from given data. Informally describe the relationship between two variables. o Including trends (correlation), clusters and outliers. Extension/Review: stem-and-leaf plots. Calculate probability of simple events. Express probabilities as a percent, decimal and fraction. Predict the number of outcomes of all events given the probability. o e.g. When rolling a number cube 600 times, one would predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. Explain the difference between independent and dependent events. Show that if p is the probability of an event occurring, 1 p is the probability of the event not occurring. Relative Frequency of an event is the ratio of the actual occurrences of the event to the total number of trials. Number of occurrences o Relative Frequency = Total number of trials Probability may not always match relative frequency of a data set. o The more trials, the closer relative frequency will be to probability. Find probabilities of compound events using organized lists, tables, and tree diagrams. Calculate and compare the relative frequency of an event to known probabilities. Compare data displays to known probabilities. The likelihood of an event involving geometric figures is geometric probability. Desired Area o Geometric Probability = Total Area Calculate geometric probability. o The probability of a dart striking within a circle with radius of 1 unit drawn inside a square with a side length of 5 units is approximately 13%. Essential Vocabulary: Measures of Central Tendency, Mean, Median, Mode, Range, Outlier, Cluster, Probability, Experimental Probability, Theoretical Probability, Histogram, Bar Graph, Circle Graph (Pie Chart), Stem-and-Leaf Plot, Box-and-Whisker Plot, Lower Quartile, Upper Quartile, Minimum, Maximum, Scatter Plot, Quartiles, Interquartile Range, Spreadsheet, Outcome, Event, Frequency Chart, Relative Frequency, Sample Space, Geometric Probability, Simple Event, Compound Event, Independent Event, Dependent Event, Experiment, Data, Trial, Quantity, Interim 4 Unit 4 Page 19
Pacing Chart Unit 4: Measures of Central Tendency, Probability & Representations Time Frame Topic Suggested Activities/Assessments Resources & Text Alignment Week 31 The Measures and Range 7.4.1.1 7.4.1.2 Measures of Central Tendency pg. 39 Changes in Data Values pg. 626 Also: Discuss Range; Use HM Course 3 Text Section 9-4 Use spreadsheets to display/analyze/compare data. Week 32 Data Display 7.4.3.1 7.4.2.1 Random Number Generators http://www.random.org/integers/ http://randomnumbergenerator.intemodino.com/en/ HM Course 3: Explore Variability: Technology Lab pg. 481 Create Histograms: Technology Lab pg. 495 Use Spreadsheets to Create Graphs: Technology Lab pg. 514 11.1: Stem-and-Leaf Plots and Histograms Circle Graphs pg. 618 Use Technology to Create Graphs HM Course 3 Text pg. 514 11.3: Using Data Displays Also: Discuss Random Number Generators - Manually or using technology. : Making a Histogram: Technology Activity pg. 617 Making a Box-and-Whisker Plot: Technology Activity pg. 625 Week 33 Spring Break 2016-2017 Week 34 Mathematics MCAs Unit 4 Page 20
Week 35 Week 36 Box-and- Whisker & Scatter Plots Core Knowledge HM Course 3: Create Box-and-Whisker Plots: Technology Lab pg. 487 Create a Scatter Plot: Technology Lab pg. 508 : Making Data Displays pg. 628 HM Course 3 Text 9-9: Scatter Plots 9-5: Variability (Box-and-Whisker) 11.2: Box-and-Whisker Plots Scatter Plots: s:/mathematics Resources/Grade 7 Probability 7.4.3.2 7.4.3.3 Interactive Relative Frequency: http://www.mathsisfun.com/data/relative-frequency.html Geometric Probability Tutorial http://www.virtualnerd.com/geometry/lengtharea/geometric-probability-simulations/use-area-findgeometric-probability 11.8: Counting with Venn Diagrams pg. 660 11.8: Probabilities of Disjoint and Overlapping Events 11.9: Performing a Simulation pg. 667 11.9: Independent and Dependent Events Geometric Probability: s:/mathematics Resources/Grade 7 Week 36 Week 37 HM Course 3: Use Different Models for Simulations - Hands-On Lab 10-2 Experimental and Theoretical Probabilities Hands-On Lab 10-5 : Ch. 11 Project: Conducting a Survey Week 38 Interim 4 Unit 4 Page 21