Grade 7 ACCELERATED Mathematics CURRICULUM GUIDE … grade Accelerated Math Curriculum... ·...

TBOE Board Approved Revised 6/2015

TRENTON PUBLIC SCHOOLS Department of Curriculum and Instruction

108 NORTH CLINTON AVENUE TRENTON, NEW JERSEY 08609

Grade 7 ACCELERATED Mathematics

CURRICULUM GUIDE AND INSTRUCTIONAL ALIGNMENT


Grade7/8UnitsataGlance(FromNJDOEModelCurriculum-eachunitisdesignedtotakeapproximately30days.)

Overview Theunitdesignwascreatedinlinewiththeareasoffocusforgrade7and8MathematicsasidentifiedbytheCommonCoreStateStandardsandthePARCCModelContentFrameworks. Grade7AcceleratedMathematicswillmovethestudentsfromtheconceptsdevelopedingrades6and7,modelingrelationshipswithvariablesandequationsandratioandproportionalreasoning,tomakingconnectionsbetweenproportionalrelationships,lines,andlinearequations.Theideaofafunctionintroducedingrade8isaprecursortoconceptsaboutfunctionsthatareincludedinthehighschoolstandards.Eachunitiscomprisedofstandardsthatareconsideredmajorcontentalongwithstandardsthatincludesupportingand/oradditionalcontent.Thereare2unitthatcompletetheworkdoneinGrade6Acceleratedcompletinggrade7CCSS.AdditionallyallCCSSfor8thgradearecompletedduringthisyeartoensurestudentscompleteAlgebra1in8thgrade.


Unit1:Geometry(7th)SLO Pre-

requisite Standard Standard Description

Draw,construct,anddescribegeometricalfiguresanddescribetherelationshipsbetweenthem.

6.NS.8 7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

7.G.3 Describethetwo-dimensionalfiguresthatresultfromslicingthree-dimensionalfigures,asinplanesectionsofrightrectangularprismsandrightrectangularpyramids.

7.G.5 Usefactsaboutsupplementary,complementary,vertical,andadjacentanglesinamulti-stepproblemtowriteandsolvesimpleequationsforanunknownangleinafigure.

Solvereal-lifeandmathematicalproblemsinvolvinganglemeasure,area,surfacearea,andvolume.

6.G.46.G.2

7.G.4 Understandthatattributesbelongingtoacategoryoftwo-dimensionalfiguresalsobelongtoallsubcategoriesofthatcategory.Forexample,allrectangleshavefourrightanglesandsquaresarerectangles,soallsquareshavefourrightangles.

7.G.6 Solvereal-worldandmathematicalproblemsinvolvingarea,volumeandsurfaceareaoftwo-andthree-dimensionalobjectscomposedoftriangles,quadrilaterals,polygons,cubes,andrightprisms.


Unit2:Geometry(8th)

SLO Pre-Requisite

Standards Description/SLO’s

Understandcongruenceandsimilarityusingmodels,transparencies,orgeometrysoftware.

8.G.1 Verify experimentally the properties of rotations, reflections, and translations. a) Lines are taken to lines, and line segments to line segments of the same length. b) Angles are taken to angles of the same measure. c) Parallel lines are taken to parallel.

8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

7.RPA.2A

8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-

dimensional figures using coordinates.

8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two dimensional figures, describe a sequence that exhibits the similarity between them.

7.6.B.5 8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.


Unit3:TheNumberSystem

Know that there are numbers that are not rational and approximate them by rational numbers.

8.NS.1

Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

8.NS.2 Use rational approximations of irrational numbers to compare he size irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., 02). For example, by truncating the decimal expansion of 02, show that 02 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Work with radicals and integer exponents.

8.EE.1

Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27

8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger.

8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.


Unit4:EquationsUnderstand the connections between proportional relationships, lines, and linear equations.

.

8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Analyze and solve

linear equations and pairs of simultaneous linear equations

7.EE.4A

8.EE.7 Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

8.EE.8

Analyze and solve pairs of simultaneous linear equations. a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.


Use functions to model relationships between quantities

8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g.,

where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Unit 5: Functions and Geometry

Define, evaluate, and compare functions.

8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change

8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

Understand and apply the Pythagorean Theorem.

8.G.6 8.G.6 Explain a proof of the Pythagorean Theorem and its converse.

8.G.7 8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. 8.G.8 8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate

system.


Unit6:StatisticsandProbabilitySLO Pre-

requisite Standard Standard Description

Use random sampling to draw inferences about a population

6.SP.1 7.SP.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

6.SP.2 6.SP.4

7.SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

Draw informal comparative inferences about two populations.

6.SP.4 6.SP.5c

7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

6.SP.3 6.SP.4

7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

Investigate chance processes and develop, use, and evaluate probability models

7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

7.SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.


7.SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event. c. Design and use a simulation to generate frequencies for compound events. . For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?


Unit7:StatisticsandProbabilityInvestigate patterns of association in bivariate data.

8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

8.SP.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. 8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.


UNIT NAME: Geometry

Grade Level: 7th Accelerated District-Approved Text: Glencoe Math Course 2 and 3 Unit 1:

Stage 1 – Desired Results

Enduring Understandings/Goals: Understand the properties of transformations and how to apply a composition of transformations. Understand the properties of parallel lines and transversals and the angles created by them. Justify the internal angle sum of triangles. Justify the external angle measure of triangles. Essential Questions: How can algebra concepts be applied to geometry? How can we best show or describe the change in position of a figure? How can you determine congruence and similarity? Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

Standard: M= Major Content

A = Additional S= Supporting

Student Learning Objectives

Suggested Instructional Strategies

Suggested Assessments

Suggested Resources

IQL = Inquiry Lab PSI= Problem Solving

Investigation 21CC= 21st Century Careers


• 7.G.1. [A]

• Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Can use scale drawing to determine the actual dimensions and area of a geometric figure Can use a different scale to reproduce a similar scale drawing

• Use the online Virtual Box Activity via http://phschool.com, Geometer's SketchPad, or geometric shape models to help students construct geometric shapes

• Using a two-band sketcher (two rubber bands tied together), a copy of an image, and a blank graph paper; have students enlarge or reduce the image based on a predetermined scale

Skill: Suppose the area of one triangle is 16sq units and the scale factor between this triangle and a new triangle is 2.5. What is the area of the new triangle? Task: If a 4 by 4.5 cm rectangle is enlarged by a scale of 3, what is the new perimeter? What is the new area?

Standards Content Key- (Identified by PARCC Model Content Frameworks). [M] Major Content [S] Supporting Content [A] Additional Content

McGraw Hill Glencoe Math Course 2

[A] 7.G.1: Ch. 7 PSI, IQL 7-4, 7-4 • Pg. 567-569, 571-574, 575-

582, 583-584 • www.illuminations.nctm.org • www.quantile.com • phschool.com

• 7.G.2. [A]

• Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Can draw a geometric shape with specific conditions Can construct a triangle when given three measurements: 3 side lengths, 3 angle measurements, or a combination of side and angle measurements Can determine when three specific measurements will result in one unique triangle, more than on possible triangle, or no possible triangles


• Provide opportunities for students to physically construct triangles with straws, sticks, or geometry apps prior to using rulers and protractors to discover and justify the side and angle conditions that will form triangles

Skill: Elian likes even numbers and wants to use them as measurements for his flag. He is trying to decide which of these three sets of measurements he should use: ü side lengths of 2 in., 4 in., and

6 in. ü angle measures of 20°, 40°,

and 60° ü side length of 2 in., and angle

measures of 40° and 60° On a separate piece of paper, try to draw each triangle that Elian is considering. Task: Elian likes even numbers and wants to use them as measurements for his flag. He is trying to decide which of these three sets of

[A] 7.G.2: IQL 7-3, 7-3 • 551-554, 555-562, 563-566 • www.illuminations.nctm.org • www.quantile.com • CCSS Investigation 4:

Geometry Topics


measurements he should use: ü side lengths of 2 in., 4 in., and

6 in. ü angle measures of 20°, 40°,

and 60° ü side length of 2 in., and angle

measures of 40° and 60° Which triangle should Elian choose for his flag? Explain how you decided.

7.G.3. [A] Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids

Can name the two-dimensional figure that represents a

particular slice of a three dimensional

figure

• Students should have the opportunity to physically create some of the three-dimensional figures, slice them in different ways, and describe in pictures and words what has been found. For example, use clay to form a cube, then pull string through it in different angles and record the shape of the slices found.


Skill:

Marcus is serving cheese and crackers at a party. He has one rectangular block of cheese and one cylindrical block of cheese. He wants to slice the cheese into different shapes. Marcus has a box of rectangular crackers. 1. How should Marcus slice each block of cheese? Draw a picture of one slice from each block. Task:

Marcus is serving cheese and crackers at a party. He has one rectangular block of cheese and one cylindrical block of cheese. He wants to slice the cheese into different shapes.

[A] 7.G.3: 7-6 • Pg. 593-600 • www.illuminations.nctm.org • www.quantile.com • CCSS Investigation 4:

Geometry Topics


Would the size or shape of the slices of cheese change as he slices through

each block? If so, explain how they would change

7.G.4. [A] Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Can state the formula for finding the area and circumference of a circle Use formulas to compute the area and circumference of a circle Can determine the diameter or radius of a circle when the circumference is given Can use a ratio and algebraic reasoning to compare the area and circumference of

a circle

• In pairs, to understand the relationships between radius, diameter, circumference, pi and area, students can observe this by folding a paper plate several times, finding the center at the intersection, then measuring the lengths between the center and several points on the circle

Think-pair-share: Problem solving cards

Skill: An engine has two wheels that are joined by a belt. The belt makes the wheels turn at the same rate.

Write a ratio of the area of the larger wheel to the area of the smaller wheel. Task: An engine has two wheels that are joined by a belt. The belt makes the wheels turn at the same rate.

Is the symbol π needed for the ratio? Explain why or why not.

[A] 7.G.4: IQL 8-1, 8-1, IQL 8-2, 8-2, 8-3 Ch. 8 PSI • Pg. 611-612, 613-620, 621-

622, 623-630, 631-638, 647-649

• www.illuminations.nctm.org • www.quantile.com CCSS Investigation 4: Geometry

Topics

• 7.G.5 [A]

• Use facts about supplementary, complementary,

Can state the relationship between supplementary, complementary, and vertical angles

• Provide students the opportunities to explore angle relationships first through measuring and finding the patterns

Skill: The diagram shows how Elian will use 3 straight cuts of a piece of rectangular poster board to make 2 isosceles triangles and 4 smaller right

[A] 7.G.5: Ch. 7 PSI, IQL 7-4, 7-4 • Pg. 535-542, 543-550 • www.illuminations.nctm.org • www.quantile.com


vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Can use angle relationships to write algebraic equations for unknown angles Can use algebraic reasoning and angle relations to solve multi-step problems

among the angles of intersecting lines or within polygons, then utilize the relationships to write and solve equations for multi-step problems

• In pairs, allow students

to use a protractor to measure the two angles that are formed on either side of the added line, and add the measurements of the two angles

triangles for new flags.

The measure of ∠ is 38°. Elian knows that the sum of the measures of the angles of a triangle is 180°. Elian writes the equation j + k = 90. Explain why this equation is true. Task: The diagram shows how Elian will use 3 straight cuts of a piece of rectangular poster board to make 2 isosceles triangles and 4 smaller right triangles for new flags.

The third angle of the triangle containing angles ∠ c and ∠ k is a right angle. Write and solve an equation to find the measure of ∠ c. Explain your work.

• CCSS Investigation 4: Geometry Topics


7.G.6 [A] Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Determine that area of two-dimensional figures

Determine the surface area and volume of three-dimensional figures

Solve real-world-

problems involving area, surface area,

and volume


Think-pair-share: Problem solving cards

Skill: Icey’s Ice Cream Parlor purchased ice cream in 2.5 gallon cylindrical containers. Each container is

inches high and 9 inches in diameter. A jumbo scoop of ice cream comes in the shape of a sphere that is approximately 4 inches in diameter. How many jumbo scoops can Icey’s serve from on 2.5 gallon container of ice cream? Task:

The edges of a cube measure 10 centimeters. Describe the dimensions

of a cylinder and a cone with the same volume as the cube. Explain.

[A] 7.G.6: 8-3, 8-4, CH. 8 PSI, IQL 8-5, IQL 8-6, 8-6, 8-7, IQL 8-8, 8-8 • Pg. 631-638, 639-646, 647-

649, 651-652, 653-660, 661-664, 665-672, 673-676, 677-684, 685-688, 689-696

• www.illuminations.nctm.org • www.quantile.com


UNIT NAME: Geometry (8th)

Grade level: 7th Accelerated District-Approved Text: Glencoe Math Course 2 and 3 Unit 2:


Enduring Understandings/Goals: Understand the properties of transformations and how to apply a composition of transformations. Understand the properties of parallel lines and transversals and the angles created by them. Justify the internal angle sum of triangles. Justify the external angle measure of triangles. Essential Questions: How can algebra concepts be applied to geometry? How can we best show or describe the change in position of a figure? How can you determine congruence and similarity? Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

Standard: M= Major

A= Additional S= Supporting


• Suggested Instructional Strategies


Suggested Resources

IQL = Inquiry Lab

PSI = Problem Solving Investigation

21cc= 21st Century Careers 8.G.1 [M] Verify experimentally the properties of rotations, reflections, and translations:

S.L.O. 1 Utilize the properties of rotation, reflection or translation to model

• Problem Based Learning

• Teacher Directed (I do, we do, you do)

Skill Based Task: • Translating a Figure on

the coordinate plane a specified number of

Glencoe Math Course 3 Chapter 6

• IQL pp. 445-452 • Lesson 1 pp. 453-460


a. Lines are taken to lines, and line segment to line segments of the same length.

b. Angles are taken to angles of the same measure.

c. Parallel lines are taken to parallel lines.

Pre-Requisite Skills: Are described above

and relate pre-images of lines, line segments, and angles to their resultant image through physical representations and/or geometry software.

• Study Groups/Small Groups/flexible groups Instruction

• Center based learning • Technology • Demonstration • Cooperative Groups • Participation &

Discussion • Projects • Flip model Academic Strategies and/or Resources in text and website: • Math in the Real

World • Chapter Foldables for

Notes • Note Taking within

the text • Graphic Novel • Quick Review • RTI & Differentiated

Instruction • Standardized Test

Practice • Real World Link • Rate Yourself • Online Tutor • Watch out (error or

misconception correction)

• Chapter Review • Inquiry Labs • Problem Solving

Investigations • 21st Century Careers

units to the left and down. Record the new coordinates. Translate the figure again.

• Reflecting a few figures on the coordinate plane, recording the coordinates before and after.

• Rotate a few figures on the coordinate plane, recording the coordinates before

Problem Based Task: Students use compasses, protractors and rulers or technology to explore figures created from translations, reflections and rotations. Characteristics of figures, such as lengths of line segments, angle measures and parallel lines, are explored before the transformation (pre-image) and after the transformation (image). Students can explain that these transformations produce images of exactly the same size and shape as the pre-image and are known as rigid transformations. Assessments from text: • Quick Check

• Lesson 2 pp. 461-468 • IQL pp. 473-474 • Lesson 3 pp. 475-482

• Supplemental textbooks • Technology Software • SMARTBOARD • Graphic Organizers • Manipulatives • Grid/Graph Paper • Pattern Blocks/Shapes • Geoboards • Multiplication Tables • Reflection mirrors • Tracing paper • See web resources below


• Editable assessments online

• Mid-Chapter Check • Chapter tests Built in Checks for understanding: • Stop and Reflect • What’s the math? • Ticket out the Door

8.G.2 [M] Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

S.L.O. 2 Apply an effective sequence of rotations, reflections and translations to prove that two dimensional figures are congruent.










Skill Based Task: • Translating a Figure on

the coordinate plane a specified number of units to the left and down. Record the new coordinates. Translate the figure again.

• Reflecting a few figures on the coordinate plane, recording the coordinates before and after.

• Rotate a few figures on the coordinate plane, recording the coordinates before and after.

Problem Based Task: • Given two figures: Is

figure A congruent to figure A’? Explain how you know.

• Given two figures: Describe the sequence of transformations that resulted in the transformation of Figure A to Figure A’

Assessments from text:


• IQL pp. 501-508 • Lesson 1 pp. 509-516 • IQL pp. 517-520 • Lesson 2 pp. 521-528 • IQL 529-530 (need access to

Geometer’s Sketch pad)

• Supplemental textbooks • Technology Software • SMARTBOARD • Graphic Organizers • Manipulatives • Grid/Graph Paper • Pattern Blocks/Shapes • Geoboards • Multiplication Tables • Tracing Paper • Ruler • See web resources below






• Quick Check • Editable assessments

online • Mid-Chapter Check • Chapter tests Built in Checks for understanding: • Stop and Reflect • What’s the math? • Ticket out the Door

8.G.3 [M] Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates

S.L.O. 3 Use the coordinate plane to locate pre-images of two dimensional figures and determine the coordinates of a resultant image after applying dilations, rotations, reflections and translations. S.L.O. 4 Recognize dilation as a reduction or enlargement of a figure and determine the scale factor.





Discussion • Projects • Flip model Academic Strategies and/or Resources in text and Website: • Math in the Real



the text • Graphic Novel • Quick Review

Skill Based Task: • Translating, reflecting,

rotating or dilating a given Figure A on a coordinate plane to create Figure A’. Record the coordinates. Describe the transformation.

Problem Based Task: Students identify the transformation based on the coordinates of the image and the pre-image. Example: identifying a transformation as a dilation and giving the scale factors. Students perform a transformation given a pre-image. Example: Given a pre-image students perform a 270 degree rotation counter-clockwise about the origin.

S.L.O. 3 Glencoe Math Course 3 Chapter 6

• Lesson 1 pp. 453-460 • Lesson 2 pp. 461-468 • PSI pp. 469-471 • Lesson 3 pp. 475-482

S.L.O 4 Glencoe Math Course 3 Chapter 6

• IQL pp. 483-486 • Lesson 4 pp. 487-494

• Supplemental textbooks • Technology Software • SMARTBOARD • Graphic Organizers • Manipulatives • Grid/Graph Paper • Pattern Blocks/Shapes • Geoboards • Multiplication Tables • Geoboards • See web resources below


• RTI & Differentiated Instruction

• Standardized Test Practice

• Real World Link • Rate Yourself • Online Tutor • Watch out (error or




Assessments from text: • Quick Check • Editable assessments


8.G.4 [M] Understand that a two dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

S.L.O. 5 Apply an effective sequence of transformations to determine that figures are similar when corresponding angles are congruent and corresponding sides are proportional. Write similarity statements based on such transformations.







Notes

Skill Based Task: Students enlarge and reduce figures based upon scale factor. Students determine similarity of given figures by performing a series of transformations. Students describe similarity using similarity statements. Problem Based Task: Example: Given two figures: Is Figure A similar to Figure A’? Explain how you know or justify your answer. Example: Describe the sequence of transformations that results in a given Figure A’ from Figure A.


• IQL pp.483-486 • 21CC pp. 495-496

Chapter 7 • IQL pp. 535-536 • Lesson 3 pp. 537-544 • Lesson 4 pp. 545-552 •

• Supplemental textbooks • Technology Software • SMARTBOARD • Graphic Organizers • Manipulatives • Grid/Graph Paper • Pattern Blocks/Shapes • Geoboards • Multiplication Tables • Tracing paper • Ruler • See web resources below


• Note Taking within the text

• Graphic Novel • Quick Review • RTI & Differentiated






Assessments from text: • Quick Check • Editable assessments


8.G.5 [M] Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

S.L.O 6 Justify facts about angles created when parallel lines are cut by a transversal. S.L.O 7 Justify facts about the exterior angles of a triangle, the sum of the measures of the interior angles of a triangle and the angle relationship used to identify similar triangles.






Skill Based Task: Students construct various triangles and find the measures of the interior and exterior angles. Students make conjectures about the relationship between the measure of an exterior angle and the other two angles of a triangle. (the measure of an exterior angle of a triangle is equal to the sum of the measures of the other two interior angles) and the sum of the exterior angles (360º). Using these relationships, students use deductive reasoning to find the

Glencoe Math Course 3 S.L.O 6 Chapter 5

• IQL pp. 365-370 • Lesson 1 pp. 371-378 • Lesson 2 pp. 379-386

S.L.O. 7 Chapter 5

• IQL pp. 387-388 • Lesson 3 pp. 389-396

Chapter 7 • IQL pp. 535-536 • PSI pp. 531-533 • Lesson 5 pp. 553-560

• Supplemental textbooks • Technology Software • SMARTBOARD • Graphic Organizers • Manipulatives










measure of missing angles. Students construct parallel lines and a transversal to examine the relationships between the created angles. Students recognize vertical angles, adjacent angles and supplementary angles from 7th grade and build on these relationships to identify other pairs of congruent angles. Using these relationships, students use deductive reasoning to find the measure of missing angles. Problem Based Task: Example 1: You are building a bench for a picnic table. The top of the bench will be parallel to the ground. If m 1 = 148˚, find m 2 and m 3. Explain your answer. Solution: Angle 1 and angle 2 are alternate interior angles, giving angle 2 a measure of 148º. Angle 2 and angle 3 are supplementary. Angle 3 will have a measure of 32º so the m 2 + m 3 = 180º Assessments from text: • Quick Check • Editable assessments

online • Mid-Chapter Check

• Grid/Graph Paper • Pattern Blocks/Shapes • Geoboards • Multiplication Tables • See web resources below


• Chapter tests Built in CFU’s: • Stop and Reflect • What’s the math? • Ticket out the Door

Stage 2 – Assessment Evidence

Suggested Performance Tasks: • Exemplars • Extended projects • Math Webquests • Writing in Math/Journal • Inquiry Labs • Problem Solving Investigations • 21st Century Careers

Other Evidence: • Classwork • Exit Slips • Homework • Individual and group tests • Open-ended questions • Portfolio • Quizzes • Checks for Understanding

Stage 3 – Learning Plan Lesson Plan Template

with suggested pacing for required 80 minute math block Lesson

Objective

Opening/Do Now

10-15 minutes

Homework Review

5-10 minutes

Instructional Components

Mini Lesson I DO/ WE DO

15-20 minutes

Independent/Partner/Group Work

YOU DO 20-30 minutes

Summary and Exit Slip

10 minutes

Using 3-part, student-friendly language. Ex. With 80% proficiency, I will solve 10 addition word problems.

Do Now could include: • Spiral review of

prerequisite skills for today’s lesson,

• Pretest skills to see where students are regarding today’s objective, or

• Contain writing in math type of

May choose to review a few specific problems from previous night’s homework to review for understanding. Students may also have a few they struggled with and need re-teaching.

Whole group mini-lesson with a check for understanding afterwards.

Lesson activity including at least one check for understanding. Math centers should be implemented during this time. Suggestions:

• Technology • Problem-based/Skill-based

Task • Vocabulary Work • Writing in Math • Art/Music Connections

As a class, teacher should facilitate a summary of today’s targeted objective then provide an exit question (last check for understanding) that allows students to individually prove their understanding of the objective.


prompt/question for students to explain their thinking, etc.

•

On-Line Resources http://connected.mcgraw-hill.com http://illuminations.nctm.org/

http://nlvm.usu.edu/ https://www.khanacademy.org/ http://www.brightstorm.com/math/ http://www.cast.org/

http://www.parcconline.org/ http://www.state.nj.us/education/modelcurriculum/ http://www.corestandards.org/about-the-standards http://www.scholastic.com/commoncore/common-core-free-

resources.htm http://ocw.mit.edu/high-school/more/for-teachers/


UNIT NAME: The Number System

Grade level: 7th grade Accelerated District-Approved Text: Glencoe Math Course 2 and 3 Unit 3


Enduring Understandings/Goals: Rational numbers can be represented in multiple ways and are useful when examining situations involving numbers that are not whole.

Essential Questions: How can mathematical Ideas be represented? Why is helpful to write numbers in different ways?

Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

Standard: M= Major

A= Additional S= Supporting


Suggested Instructional Strategies Suggested Assessments

Suggested Resources

IQL = Inquiry Lab

PSI = Problem Solving Investigation

21cc= 21st Century Careers

8.NS.1 [S] Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers

S.L.O. 1 Compare rational and irrational numbers to demonstrate that the decimal expansion of irrational numbers do not repeat; so that

• Problem Based Learning • Teacher Directed (I do, we do, you

do) • Study Groups/Small

Groups/flexible groups Instruction • Center based learning • Technology

Skill Task: Given a number, tell if it is rational or irrational and why. Define rational and irrational numbers. Differentiate between terminating, repeating & non-terminating, non-repeating decimals

Glencoe Math Course 3 Chapter 1 • Lesson 1 pp. 5-14 • Lesson 10 pp. 89-86 • Unit Project 1 pp.

103-104


show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

every rational number has a decimal expansion which eventually repeats and converts such decimals into rational numbers.

• Demonstration • Cooperative Groups • Participation & Discussion • Projects • Flip model Academic Strategies and/or Resources in text and website: • Math in the Real World • Chapter Foldables for Notes • Note Taking within the text • Graphic Novel • Quick Review • RTI & Differentiated Instruction • Standardized Test Practice • Real World Link • Rate Yourself • Online Tutor • Watch out (error or misconception

correction) • Chapter Review • Inquiry Labs • Problem Solving Investigations • 21st Century Careers

Problem-Based Task:

• Example 1: Change .4444… into a fraction.

• Example 2: Investigate repeating patterns that occur when fractions have denominators of 9, 99 or 11

Assessments from text: • Quick Check • Editable assessments online • Mid-Chapter Check • Chapter tests Built in Checks for understanding: • Stop and Reflect • What’s the math? Ticket out the Door

• Supplemental

textbooks • Technology Software • SMARTBOARD • Graphic Organizers • Manipulatives • Grid/Graph Paper • Pattern Blocks/Shapes • Geoboards • Multiplication Tables • See web resources

below

8.NS.2 [S] Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1

S.L.O. 2 Use rational numbers to approximate and locate irrational nu8mbers on a number line and estimate the value of expressions involving irrational numbers.



Groups/flexible groups Instruction • Center based learning • Technology • Demonstration • Cooperative Groups • Participation & Discussion • Projects • Flip model Academic Strategies and/or Resources in text and website:

Skill Task: Students locate rational and irrational numbers on the number line. Problem-Based Task: Example 1: Find an approximation for the square root of 28 Example 2: Compare the square roots of 2 and 3 Assessments from text:

Glencoe Math Course 3 Chapter 1 • Lesson 8 pp. 71-78 • IQL pp. 79-80 • Lesson 9 pp. 81-88 • Lesson 10 pp. 89-96 • Unit Project pp. 103-

104 • Supplemental

textbooks • Technology Software • SMARTBOARD • Graphic Organizers • Manipulatives


and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

• Math in the Real World • Chapter Foldables for Notes • Note Taking within the text • Graphic Novel • Quick Review • RTI & Differentiated Instruction • Standardized Test Practice • Real World Link • Rate Yourself • Online Tutor • Watch out (error or misconception


• Quick Check • Editable assessments online • Mid-Chapter Check • Chapter tests Built in Checks for understanding: • Stop and Reflect • What’s the math? • Ticket out the Door

• Grid/Graph Paper • Multiplication Tables • See web resources

below

8.EE.1 [M] Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–

3 = 1/33 = 1/27.

S.L.O. 3 Apply the properties of integer exponents to simplify and write equivalent numerical expressions.



Groups/flexible groups Instruction • Center based learning • Technology • Demonstration • Cooperative Groups • Participation & Discussion • Projects • Flip model Academic Strategies and/or Resources in text and website: • Math in the Real World • Chapter Foldables for Notes • Note Taking within the text • Graphic Novel • Quick Review • RTI & Differentiated Instruction • Standardized Test Practice

Skill Task: Students can generate equivalent expressions fluently. Given 3�, they generate 3x3x3x3 NOT 3x4; Give 5x5, they generate 5² Problem-Based Task: Students solve problems to demonstrate their understanding that: � Bases must be the same before exponents can be added, subtracted or multiplied. � Exponents are subtracted when like bases are being divided � A number raised to the zero (0) power is equal to one. � Negative exponents occur when there are more factors in the denominator. These exponents can be expressed as a positive if left in the denominator. � Exponents are added when like bases are being multiplied � Exponents are multiplied when an

Glencoe Math Course 3 Chapter 1 • Lesson 2 pp. 15-22 • Lesson 3 pp. 23-30 • Lesson 4 pp. 31-38 • PSI pp. 39-41 • Lesson 5 pp. 43-59 • Supplemental

textbooks • Technology Software • SMARTBOARD • Graphic Organizers • Manipulatives • Grid/Graph Paper • Multiplication Tables • See web resources

below


• Real World Link • Rate Yourself • Online Tutor • Watch out (error or misconception


exponents is raised to an exponent � Several properties may be used to simplify an expression Assessments from text: • Quick Check • Editable assessments online • Mid-Chapter Check • Chapter tests Built in Checks for understanding: • Stop and Reflect • What’s the math? • Ticket out the Door

8.EE.3 [M] Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger.

S.L.O. 4 Use scientific notation to estimate and express the values of very large or very small numbers and compare their values. (How many times larger/smaller is one than the other?)



Groups/flexible groups Instruction • Center based learning • Technology • Demonstration • Cooperative Groups • Participation & Discussion • Projects • Flip model Academic Strategies and/or Resources in text and website: • Math in the Real World • Chapter Foldables for Notes • Note Taking within the text • Graphic Novel • Quick Review • RTI & Differentiated Instruction • Standardized Test Practice • Real World Link • Rate Yourself • Online Tutor

Skill Task: Students use scientific notation to express large and small numbers recognizing that an increase of 1 in the exponent, increases value 10 times and a decrease of 1 in the exponent, decreases the value 10 times. Problem-Based Task: Example 1: How much larger is 6 x 105 compared to 2 x 103 Solution: 300 times larger since 6 is 3 times larger than 2 and 105 is 100 times larger than 103. Example 2: Which is the larger value: 2 x 106 or 9 x 105?

Solution: 2 x 106 because the exponent is larger

Example 3: Express 2.45 x 105 in standard form.

Glencoe Math Course 3 Chapter 1 • Lesson 6 pp. 51-58 • Lesson 7 pp. 59-66 • IQL pp. 67-70

Overlapping Lessons with 8.EE.4 • Supplemental


below


• Watch out (error or misconception correction)

• Chapter Review • Inquiry Labs • Problem Solving Investigations • 21st Century Careers

Solution: 245,000 Assessments from text: • Quick Check • Editable assessments online • Mid-Chapter Check • Chapter tests Built in Checks for understanding: • Stop and Reflect • What’s the math?

• Ticket out the Door

8.EE.4 [M] Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

S.L.O. 5 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. (Interpret scientific notation generated when technology has been used for calculations.) S.L.O. 6 In real world problem solving situations choose units of appropriate size for measurement of very small and very large quantities.



Groups/flexible groups Instruction • Center based learning • Technology • Demonstration • Cooperative Groups • Participation & Discussion • Projects • Flip model Academic Strategies and/or Resources in text and Website • Math in the Real World • Chapter Foldables for Notes • Note Taking within the text • Graphic Novel • Quick Review • RTI & Differentiated Instruction • Standardized Test Practice • Real World Link • Rate Yourself • Online Tutor • Watch out (error or misconception

correction)

Skill Task: Students understand scientific notation as generated on various calculators or other technology. Students enter scientific notation using E or EE (scientific notation), * (multiplication), and ^ (exponent) symbols. Example 1: 2.45E+23 is 2.45 x 1023 and 3.5E-4 is 3.5 x 10-4 (NOTE: There are other notations for scientific notation depending on the calculator being used) Problem-Based Task: Example 1: (6.45 x 1011)(3.2 x 104) = (6.45 x 3.2)(1011 x 104) Rearrange factors = 20.64 x 1015 Add exponents when multiplying powers of 10

= 2.064 x 1016 Write in scientific notation

Example 2:

Glencoe Math Course 3 Chapter 1 • Lesson 6 pp. 51-58 • Lesson 7 pp. 59-66 • IQL pp. 67-70 Some overlapping lessons with 8.EE.3 • Supplemental


below


• Chapter Review • Inquiry Labs • Problem Solving Investigations • 21st Century Careers

3.45 x 105 6.3 105 – (-2) Subtract exponents when dividing powers of 10 6.7 x 10-2 1.6 = 0.515 x 107 Write in scientific notation = 5.15 x 106

Example 3:

(0.0025)(5.2 x 104) = (2.5 x 10-3)(5.2 x 105) Write factors in scientific notation

= (2.5 x 5.2)(10-3 x 105) Rearrange factors = 13 x 10 2 Add exponents when multiplying powers of 10

= 1.3 x 103 Write in scientific notation

Assessments from text: • Quick Check • Editable assessments online • Mid-Chapter Check • Chapter tests Built in Checks for understanding: • Stop and Reflect • What’s the math? • Ticket out the Door


Stage 2 – Assessment Evidence Suggested Performance Tasks:

• Exemplars • Extended projects • Math Webquests • Writing in Math/Journal • Inquiry Labs • Problem Solving Investigations • 21st Century Careers


Stage 3 – Learning Plan


Lesson Plan Template with suggested pacing for required 80 minute math block

Lesson Objective

Opening/Do Now

10-15 minutes

Homework Review

5-10 minutes



15-20 minutes




10 minutes





• Contain writing in math type of prompt/question for students to explain their thinking, etc.









http://www.parcconline.org/ http://www.state.nj.us/education/modelcurriculum/ http://www.corestandards.org/about-the-standards http://www.scholastic.com/commoncore/common-core-free-resources.htm http://ocw.mit.edu/high-school/more/for-teachers/


UNIT NAME: EXPRESSIONS AND EQUATIONS

Grade level: 7th grade Accelerated District-Approved Text: Glencoe Math Course 2 and 3 Unit 4:


Enduring Understandings/Goals: Algebraic expressions and equations are used to model real-life problems and represent quantitative relationships and predict results. Essential Questions: What is equivalence? How can we model relationships between quantities? Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

Standard: M = Major

S= Supporting A= Additional




Suggested Resources

IQL = Inquiry Lab

PSI = Problem Solving Investigation 21cc= 21st Century

Careers 8.EE.5 [M] Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different

S.L.O. 1 Graph and analyze the different representations of proportional relationships and interpret the unit rate as the slope of the graph which

• Problem Based Learning • Teacher Directed (I do, we do,

you do) • Study Groups/Small

Groups/flexible groups Instruction

• Center based learning • Technology • Demonstration

Skill task: Students identify the unit rate (or slope) in graphs, tables and equations to compare two proportional relationships represented in different ways. Problem Based Task: Compare two scenarios, represented differently (graph and equation) to determine

Glencoe Math Course 3 Chapter 3 • Lesson 1 pp. 169-

178 • IQL pp. 179-180 • Lesson 2 pp. 181-

188 • Lesson 3 pp. 189-


ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

indicates the rate of change.

• Cooperative Groups • Participation & Discussion • Projects • Flip model Academic Strategies and/or Resources in text &website: • Math in the Real World • Chapter Foldables for Notes • Note Taking within the text • Graphic Novel • Quick Review • RTI & Differentiated

Instruction • Standardized Test Practice • Real World Link • Rate Yourself • Online Tutor • Watch out (error or

misconception correction) • Chapter Review • Inquiry Labs • Problem Solving Investigations • 21st Century Careers

which represents a greater speed. Explain your choice including a written description of each scenario. Be sure to include the unit rates in your explanation. Assessments from text: • Quick Check • Editable assessments online • Mid-Chapter Check • Chapter tests Built in Checks for understanding: • Stop and Reflect • What’s the math? • Ticket out the Door


textbooks • Technology

Software • SMARTBOARD • Graphic Organizers • Manipulatives • Grid/Graph Paper • Rulers • Multiplication

Tables • See below for

websites

8.EE.6 [M] Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

S.L.O. 2 Derive the equation of a line (y = mx for a line through the origin and the equation y = mx +b for a line intercepting the vertical axis at b) and use similar triangles to explain why the slope (m) is the same between any two points on a non-vertical line in




• Center based learning • Technology • Demonstration • Cooperative Groups • Participation & Discussion • Projects • Flip model Academic Strategies and/or Resources in text & website:

Skill Task: Students write equations in the form y = mx + b for lines not passing through the origin, recognizing that m represents the slope and b represents the y-intercept. Problem Based task: A triangle between A and B has a vertical height of 2 and a horizontal length of 3. A triangle between B and C has a vertical height of 4 and a horizontal length of 6. The simplified ratio of the vertical height to the horizontal length of both triangles is 2 to 3, which also represents a slope of 2/3


206 • IQL pp. 207-208 Chapter 7 • Lesson 6 pp. 561-



Software • SMARTBOARD • Graphic Organizers


the coordinate plane.

• Math in the Real World • Chapter Foldables for Notes • Note Taking within the text • Graphic Novel • Quick Review • RTI & Differentiated



for the line, indicating that the triangles are similar. Given an equation in slope-intercept form, students graph the line represented. Students write equations in the form y = mx for lines going through the origin, recognizing that m represents the slope of the line. Assessments from text: • Quick Check • Editable assessments online • Mid-Chapter Check • Chapter tests Built in Checks for understanding: • Stop and Reflect • What’s the math? • Ticket out the Door

• Manipulatives • Grid/Graph Paper • Rulers • Multiplication

Tables • See below for

websites

8.EE.7 [M] Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). b. Solve linear

S.L.O. 3 Solve linear equations in one variable with rational number coefficients that might require expanding expressions using the distributive property and/or combining like terms, including examples with one solution, infinite solutions, or no solution.




• Center based learning • Technology • Demonstration • Cooperative Groups • Participation & Discussion • Projects • Flip model Academic Strategies and/or Resources in text and website: • Math in the Real World • Chapter Foldables for Notes • Note Taking within the text

Skill Task: Students solve one-variable equations including those with the variables being on both sides of the equals sign. Students recognize that the solution to the equation is the value(s) of the variable, which make a true equality when substituted back into the equation. Equations shall include rational numbers, distributive property and combining like terms. Problem-Based Task: Students write equations from verbal descriptions and solve. Example 4: Two more than a certain number is 15 less than twice the number. Find the number. Solution: n + 2 = 2n – 15 17 = n

Glencoe math Course 3 Chapter 2 • Lesson 1 pp. 108-

118 • IQL pp. 119-120 • Lesson 2 pp. 121-

128 • Lesson 3 pp. 129-

136 • PSI pp. 137-139 • IQL pp. 141-144 • Lesson 4 pp. 145-

152 • Lesson 5 pp. 153-

160 • 21CC pp. 161-



equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Pre-requisite 7.EE.4A

• Graphic Novel • Quick Review • RTI & Differentiated






Tables

8.EE.8 [M] Analyze and solve pairs of simultaneous linear equations. a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have

S.L.O. 4 Solve systems of linear equations in two variables by inspection, algebraically, and/or graphically (estimate solutions) to demonstrate solutions correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.




• Center based learning • Technology • Demonstration • Cooperative Groups • Participation & Discussion • Projects • Flip model Academic Strategies and/or Resources in text and website: • Math in the Real World • Chapter Foldables for Notes • Note Taking within the text • Graphic Novel • Quick Review • RTI & Differentiated

Skill Task: Students graph a system of two linear equations, recognizing that the ordered pair for the point of intersection is the x-value that will generate the given y-value for both equations. Students recognize that graphed lines with one point of intersection (different slopes) will have one solution, parallel lines (same slope, different y-intercepts) have no solutions, and lines that are the same (same slope, same y-intercept) will have infinitely many solutions. Problem-Based Task: Plant A and Plant B are on different watering schedules. This affects their rate of growth. Compare the growth of the two plants to determine when their heights will be the same.

From data, write an equation, graph the data, and respond to: At which week will both

Glencoe Math Course 3 Chapter 3 • PSI pp. 217-219 • IQL pp. 229-230

(graphing calculator required)

• IQL pp. 231-232 • Lesson 7 pp. 233-

242 • Lesson 8 pp. 243-

250 • IQL pp. 251-252 • 21CC pp. 253-

254

• Supplemental


Software


no solution because 3x + 2y cannot simultaneously be 5 and 6. c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.



plants be the same height?


• SMARTBOARD • Graphic Organizers • Manipulatives • Grid/Graph Paper • Rulers • Multiplication

Tables

8.F. 4 [S] Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

S.L.O. 5 Construct a function to model the linear relationship between two variables and determine the rate of change and initial value of the real world data it represents from either graphs or tabulated values.




• Center based learning • Technology • Demonstration • Cooperative Groups • Participation & Discussion • Projects • Flip model Academic Strategies and/or Resources in text & website: • Math in the Real World • Chapter Foldables for Notes • Note Taking within the text • Graphic Novel • Quick Review • RTI & Differentiated

Instruction

Skills Task: Students identify the rate of change (slope) and initial value (y-intercept) from tables, graphs, equations or

verbal descriptions to write a function (linear equation). Students

Problem Based Task:

Example 1:

Write an equation that models a linear relationship from a table.

Example 2: A line has a zero slope and passes through the point (-5, 4). What is the equation of the line? Solution: y = 4 Example 3: Write an equation for the line that has a slope of 1/2 and passes though the point (-2, 5)


276 • Lesson 3 pp. 287-

294 • Lesson 4 pp. 295-

304 • PSI pp. 305-307 • Lesson 5 pp. 309-

318 • Lesson 6 pp. 319-

326 Lessons Overlap with Function Unit • Supplemental


Software • SMARTBOARD • Graphic Organizers • Manipulatives


• Standardized Test Practice • Real World Link • Rate Yourself • Online Tutor • Watch out (error or


Solution: y = 1/2 x + 6 Assessments from text: • Quick Check • Editable assessments online • Mid-Chapter Check • Chapter tests Built in Checks for understanding: • Stop and Reflect • What’s the math? • Ticket out the Door

• Grid/Graph Paper • Rulers • Multiplication

Tables

8.F.5 [S] Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g. where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

S.L.O. 6 Sketch a graph of a function from a qualitative description and give a qualitative description of a graph of a function.




• Center based learning • Technology • Demonstration • Cooperative Groups • Participation & Discussion • Projects • Flip model Academic Strategies and/or Resources in text and website: • Math in the Real World • Chapter Foldables for Notes • Note Taking within the text • Graphic Novel • Quick Review • RTI & Differentiated

Instruction • Standardized Test Practice • Real World Link • Rate Yourself

Skills Task:

Given a verbal description of a situation, students sketch a graph to model that situation. Given a graph of a situation, students provide a verbal description of the situation.

Problem Based task:

Describe a given graph of a function between x = 2 and x = 5? Draw a graph based on a given narrative. Assessments from text: • Quick Check • Editable assessments online • Mid-Chapter Check • Chapter tests Built in Checks for understanding: • Stop and Reflect • What’s the math? • Ticket out the Door


334 • Lesson 8 pp. 335-

342 • IQL pp. 343-346 • Lesson 9 pp. 347-

354 Lessons overlap from functions unit and extend • Supplemental



Tables


• Online Tutor • Watch out (error or




Lesson Objective

Opening/Do Now

10-15 minutes

Homework Review

5-10 minutes



15-20 minutes




10 minutes









• Technology • Problem-based/Skill-

based Task • Vocabulary Work • Writing in Math • Art/Music Connections










UNIT NAME: FUNCTIONS



Enduring Understandings/Goals: The characteristics of functions and their representations are useful in making sense of patterns and solving problems involving quantitative relationships. Essential Questions: How can you find and use patterns to model real –world situations? How can we model relationships between quantities? How are patterns used when comparing two quantities?


Standard:

M=major S=Supporting A=Additional




Suggested Resources

IQL= Inquiry Lab

PSI= Problem Solving Investigation

21CC=21st Century Careers

8.F.1 [M] Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and

S.L.O. 1 Define linear functions as a rule that assigns one output to each input and determine if data



Groups/flexible groups Instruction • Center based learning • Technology • Demonstration

Skill Task: Students understand rules that take x as input and gives y as output is a function. Functions occur when there is exactly one y-value is associated with any x-value. Using y to represent the output we can represent this function


• IQL pp. 285-286 • Lesson 2 pp. 277-284 • Lesson 3 pp. 287-294 • Lesson 4 pp. 295-304 (Lessons 1 is under


the corresponding output. (Function notation is not required in Grade 8.)

represented as a graph or in a table is a function.

• Cooperative Groups • Participation & Discussion • Projects • Flip model Academic Strategies and/or Resources in text and website • Math in the Real World • Chapter Foldables for Notes • Note Taking within the text • Graphic Novel • Quick Review • RTI & Differentiated Instruction • Standardized Test Practice • Real World Link • Rate Yourself • Online Tutor • Watch out (error or misconception


with the equations y = x2 + 5x + 4. Students are not expected to use the function notation f(x) at this level. Students identify functions from equations, graphs, tables, and ordered pairs. Problem-Based Task: Given tables of data or a relation students determine whether they are functions or not functions. Justify their answers. Assessments from text: • Quick Check • Editable assessments online • Mid-Chapter Check • Chapter tests Built in Checks for understanding: • Stop and Reflect • What’s the math? Ticket out the Door

standard 8.F.4 but supports learning for 8.F.1)

• Supplemental textbooks

• Technology Software • SMARTBOARD • Graphic Organizers • Manipulatives • Grid/Graph Paper • Rulers • Multiplication Tables • See web resources

below

8.F.2 [M] Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression,

S.L.O. 2 Compare two functions each represented in a different way (numerically, verbally, graphically, and algebraically) and draw conclusions about their properties (rate of change and intercepts).



Groups/flexible groups Instruction • Center based learning • Technology • Demonstration • Cooperative Groups • Participation & Discussion • Projects • Flip model Academic Strategies and/or Resources in text and website

Skill Task: Students compare two functions from different representations. Problem-Based Task: Compare the two linear functions listed below and determine which has a negative slope: Problem 1 Function 1: Gift Card Samantha starts with $20 on a gift card for the bookstore. She spends $3.50 per week to buy a magazine. Let

Glencoe Math Course 3 Chapter 4 • PSI pp. 305-307 • Lesson 5 pp. 309-318

• Supplemental

textbooks • Technology Software • SMARTBOARD • Graphic Organizers • Manipulatives • Grid/Graph Paper • Rulers • Multiplication Tables


determine which function has the greater rate of change.

• Math in the Real World • Chapter Foldables for Notes • Note Taking within the text • Graphic Novel • Quick Review • RTI & Differentiated Instruction • Standardized Test Practice • Real World Link • Rate Yourself • Online Tutor • Watch out (error or misconception


y be the amount remaining as a function of the number of weeks, x. Problem 2: The school bookstore rents graphing calculators for $5 per month. It also collects a non-refundable fee of $10.00 for the school year. Write the rule for the total cost (c) of renting a calculator as a function of the number of months (m). c = 10 + 5m Assessments from text: • Quick Check • Editable assessments online • Mid-Chapter Check • Chapter tests Built in Checks for understanding: • Stop and Reflect • What’s the math? Ticket out the Door

• See web resources below

8.F.3 [M] Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

S.L.0. 3 Utilize equations, graphs, and tables to classify functions as linear or non-linear, recognizing that y = mx + b is linear with a constant rate of change.



Groups/flexible groups Instruction • Center based learning • Technology • Demonstration • Cooperative Groups • Participation & Discussion • Projects • Flip model Academic Strategies and/or Resources in text:\ and website • Math in the Real World

Skill Task: Graph y = x + 3 Problem-Based Task: Determine if the functions listed below are linear or non-linear. Explain your reasoning. 1. y = -2x2 + 3 2. y = 0.25 + 0.5(x – 2) 3. A = Πr2 4. Data in a table 5. Data in a graph Assessments from text:

Glencoe Math Course 3 Chapter 4 • Lesson 4 pp. 295-304 • Lesson 7 pp. 327-334 • Lesson 8 pp. 335-342 • IQL pp. 343-346

(needs graphing calculator)

Chapter 3 pp. 199 – 206 supports this standard but will be done again in Equations unit.

• Supplemental

textbooks


• Chapter Foldables for Notes • Note Taking within the text • Graphic Novel • Quick Review • RTI & Differentiated Instruction • Standardized Test Practice • Real World Link • Rate Yourself • Online Tutor • Watch out (error or misconception


• Quick Check • Editable assessments online • Mid-Chapter Check • Chapter tests Built in Checks for understanding: • Stop and Reflect • What’s the math? Ticket out the Door


below

8.EE.2 [M] Work with radical and integer exponents.

Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

S.L.O. 1 Evaluate square roots and cubic roots of small perfect squares and cubes respectively and use square and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p where p is a positive rational number.



Groups/flexible groups Instruction • Center based learning • Technology • Demonstration • Cooperative Groups • Participation & Discussion • Projects • Flip model Academic Strategies and/or Resources in text and website: • Math in the Real World • Chapter Foldables for Notes • Note Taking within the text • Graphic Novel • Quick Review • RTI & Differentiated Instruction • Standardized Test Practice • Real World Link • Rate Yourself

Skill-Based Task: Students recognize perfect squares and cubes, understanding that non-perfect squares and non-perfect cubes are irrational. Students recognize that squaring a number and taking the square root √ of a number are inverse operations; likewise, cubing a number and taking the cube root are inverse operations. NOTE: (-4)2 = 16 while -42 = -16 since the negative is not being squared. This difference is often problematic for students, especially with calculator use Students understand that when taking the square root of 8 it ends in the calculator but it is not terminating, it is irrational. Students identify roots as rational or irrational. Problem-Based Task:

Glencoe Math Course 3 Chapter 1 • Lesson 8 pp. 71 – 78 • IQL pp. 79-80 • Lesson 9 pp. 81-88 • Lesson 10 pp. 89-96

(covered already in Unit #2)


• Technology Software • SMARTBOARD • Graphic Organizers • Manipulatives • Grid/Graph Paper • Rulers • Multiplication Tables • Square tiles and cubes

to develop understanding of squared and cubed numbers


S.L.O. 2 Identify √2 as irrational

• Online Tutor • Watch out (error or misconception


• Approximating Square Roots Geometrically using grid paper, a straight edge, and compass.

• Work with a partner to gather ratios of a the human body like Leonardo da Vinci and approximate the Golden Ratio


• Calculators to verify and explore patterns

• Place value charts to connect the digit value to the exponent (negative and positive)

• Student created square and square root charts


8.G.6 [M] Understand and apply the Pythagorean Theorem. Explain a proof of the Pythagorean Theorem and its converse.

S.L.O. 3 Explain a proof of the Pythagorean Theorem and its converse.



Groups/flexible groups Instruction • Center based learning • Technology • Demonstration • Cooperative Groups • Participation & Discussion • Projects • Flip model Academic Strategies and/or Resources in text and website: • Math in the Real World • Chapter Foldables for Notes • Note Taking within the text • Graphic Novel • Quick Review

Skill-Based Task: Determine whether or not triangles are in fact right triangles using the Pythagorean Theorem and its Converse. Problem-Based Task: Construct an informal proof of the Pythagorean theorem using grid paper squares. (IQL pp. 409-410) Assessments from text: • Quick Check • Editable assessments online • Mid-Chapter Check • Chapter tests Built in Checks for understanding:

• Glencoe Math Course 3 • Chapter 5 • IQL pp. 409-410 • Lesson 5 pp. 411-418 • IQL pp. 419 – 422


• Technology Software • SMARTBOARD • Graphic Organizers • Manipulatives • Grid/Graph Paper • Rulers • Multiplication Tables • Square tiles and cubes

to develop understanding of squared and cubed


• RTI & Differentiated Instruction • Standardized Test Practice • Real World Link • Rate Yourself • Online Tutor • Watch out (error or misconception


• Stop and Reflect • What’s the math? • Ticket out the Door

numbers • From the National

Library of Virtual Manipulatives

• Pythagorean Theorem – Solve two puzzles that illustrate the proof of the Pythagorean Theorem.

• Right Triangle Solver – Practice using the Pythagorean theorem and the definitions of the trigonometric functions to solve for unknown sides and angles of a right triangle.

• City street grid maps for students to find straight line distance between two points using the Pythagorean Theorem


8.G.7 [M] Understand and apply the Pythagorean Theorem. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

S.L.O. 4 Utilize the Pythagorean Theorem to determine unknown side lengths of right triangles in two and three dimensions



Groups/flexible groups Instruction • Center based learning • Technology • Demonstration • Cooperative Groups • Participation & Discussion • Projects • Flip model Academic Strategies and/or Resources

Skill-Based Task: The Irrational Club wants to build a tree house. They have a 9-foot ladder that must be propped diagonally against the tree. If the base of the ladder is 5 feet from the bottom of the tree, how high will the tree house be off the ground? Problem-Based Task: Given:

Glencoe Math Course 3 Chapter 5 • Lesson 5 pp. 411 -

418 • Lesson 6 pp. 423-430 Lessons overlap from 8.G.6

• Supplemental

textbooks • Technology Software • SMARTBOARD


to solve real-world and mathematical problems

in text and website: • Math in the Real World • Chapter Foldables for Notes • Note Taking within the text • Graphic Novel • Quick Review • RTI & Differentiated Instruction • Standardized Test Practice • Real World Link • Rate Yourself • Online Tutor • Watch out (error or misconception


Find the length of d in the figure above if a = 8 in., b = 3 in. and c = 4in.


Ticket out the Door

• Graphic Organizers • Manipulatives • Grid/Graph Paper • Rulers • Multiplication Tables • Square tiles and cubes

to develop understanding of squared and cubed numbers

• From the National Library of Virtual Manipulatives

• Pythagorean Theorem – Solve two puzzles that illustrate the proof of the Pythagorean Theorem.

• Right Triangle Solver – Practice using the Pythagorean theorem and the definitions of the trigonometric functions to solve for unknown sides and angles of a right triangle.

8.G.8 [M] Understand and apply the Pythagorean Theorem. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

S.L.O. 5 Use the Pythagorean Theorem to determine the distance between two points in the coordinate plane



Groups/flexible groups Instruction • Center based learning • Technology • Demonstration • Cooperative Groups • Participation & Discussion • Projects • Flip model Academic Strategies and/or Resources

Skill-Based Task: One application of the Pythagorean Theorem is finding the distance between two points on the coordinate plane. Students build on work from 6th grade (finding vertical and horizontal distances on the coordinate plane) to determine the lengths of the legs of the right triangle drawn connecting the points. Students understand that the line segment between the two points is the length of the hypotenuse.

Glencoe Math Course 3 Chapter 5 • Lesson 7 pp. 431-438

• Supplemental

textbooks • Technology Software • SMARTBOARD • Graphic Organizers • Manipulatives • Grid/Graph Paper • Rulers


in text and website: • Math in the Real World • Chapter Foldables for Notes • Note Taking within the text • Graphic Novel • Quick Review • RTI & Differentiated Instruction • Standardized Test Practice • Real World Link • Rate Yourself • Online Tutor • Watch out (error or misconception


NOTE: The use of the distance formula is not an expectation Problem-Based Task:

Find the length of AB using the Pythagorean Theorem


• Multiplication Tables • See web resources

below


Stage 2 – Assessment Evidence

Suggested Performance Tasks: • Exemplars • Extended projects • Math Webquests • Writing in Math/Journal • Inquiry Labs • Problem Solving Investigations • 21st Century Careers




Lesson

Objective

Opening/Do Now

10-15 minutes

Homework Review

5-10 minutes



15-20 minutes

Independent/Partner/Group Work YOU DO

20-30 minutes


10 minutes Using 3-part, student-friendly language. Ex. With 80% proficiency, I will solve 10 addition word problems.








• Technology • Problem-based/Skill-based Task • Vocabulary Work • Writing in Math • Art/Music Connections







UNIT NAME: STATISTICS and PROBABILITY

Grade level: 7th grade Accelerated District-Approved Text: Glencoe Course 2 and 3

Unit 6

Stage 1 – Desired Results Enduring Understandings/Goals: • The rules of probability can lead to more valid and reliable predictions about the likelihood of an event occurring

Essential Questions: • How is probability used to predict the outcome of future events? • How can simulations help you understand the probability of something happening? • How do you know which type of graph to use when displaying data? •


Standard: Standards Content Key- (Identified by PARCC Model Content Frameworks). [M] Major Content [S] Supporting Content [A] Additional Content




Suggested Resources

Standards Content Key- (Identified by PARCC Model Content Frameworks). [M] Major Content [S] Supporting Content [A] Additional Content

7.SP.1 [S] Understand that statistics can be used to gain information about a population by examining a sample of the

Explain why the validity of a sample depends on whether the sample is representative of the population

• Instruct students to generate a survey, compile, and display the data. Then interpret their results

Skill:

[S] 7.SP.1: 10-1, 10-2, Ch. 10 PSI • Pg. 793-800, 801-808, 821-823 • www.illuminations.nctm.org


population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

Explain that random sampling tends to produce representative samples

• Given a population, have

students analyze various sample groups as being representative or not.

• Discuss means of obtaining a random sample.

What is the range and interquartile range of the data displayed in the box plot? Task: Trenton Middle School is considering the following locations for a Grade 7 field trip: science museum, state park, or ballet company. The principal wants to survey a sample of students to find which location Grade 7 students would prefer. Should the principal select the members of the science club for the sample? How can the principal get a random sample of Grade 7 students?

• www.quantile.com • CCSS Investigation 5:

Variability

7.SP.2 [S] Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction

Understand that information can be gained about a population by examining statistics of a representative sample of the population, where random sampling tends to produce representative samples. Draw inferences about a population based on data from a random sample. Generate or simulate multiple samples of the same size to gauge the

• Obtain multiple samples of the same size for a given population and explore variability and differences in estimates of measures of central tendency

• Use a random number generator to create a random sample

Skill: Students asked 10 of their peers their favorite music. The results are show below. Student 1: 4 Pop, 6 Country Student 2: 1 Pop, 9 Country Student 3: 6 Pop, 4 Country What would student 1 say about the proportion of students who prefer Pop? If, in fact, 75% of the student body prefers Pop, what is the error in each student’s estimate? Task:

[S] 7.SP.2: 10-1, IQL 10-2, 10-2 • Pg. 793-800, 801-808, 809-812

• www.illuminations.nctm.org • www.quantile.com • CCSS Investigation 5:

Variability


might be.

variation in estimates or predictions. Informally assess the degree of visual overlap of two data distributions with similar variabilities and express the difference between centers of the distributions as a multiple of a measure of variability.

Given the first name of all students in your grade. Predict the most common

name in the U.S. for 7th

graders. How good an estimate do you think your sample provides? Explain your reasoning.

7.SP.3 [A] Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

Find the difference in the mean or median of two different data sets

Demonstrate how two data sets that are very different can have similar variabilities

Can draw inferences about the data sets by making a comparison of these differences relative to the mean absolute deviation or interquartile range of either set of data

• Use dot plots to observe visual overlaps for measures of center and spread to compare data such as temperatures in Honolulu, HI and Los Angeles, CA,

• Use an area model to analyze the theoretical probabilities for two-stage outcomes

Skill: The average temperature in City 1 is 70 degrees and in City 2 it is 80 degrees. The mean absolute deviation of City 1 is 5 degrees and in City 2 it is 5 degrees. Compare the data using measures of center and spread. Task: Measure the heights of the girls versus boys in your class. Calculate the measures of center and measures of variability for each group. Describe the similarities and differences.

[A] 7.SP.3: IQL 10-4, 10-4 • Pg. 825-826, 837-838

• www.illuminations.nctm.org • www.quantile.com • CCSS Investigation 5:

Variability • Data Distributions (Inv. 2)

7.SP.4 [A] Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about

Can compare two populations by using the means and/or medians of data collected from random samples

• In small groups, compare and contrast similar data from two populations to make inferences

• Use the Pair Problem

Skill: Measure the heights of the girls versus boys in your class. Calculate the measures of center and measures of variability for each group.

[A] 7.SP.4: IQL 10-4, 10-4 • Pg. 825-826, 827-836



two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

Can compare two populations by using the mean absolute deviations and/or interquartile ranges of data from random samples

Solving; where A problem-solving technique in which one member of the pair is the "thinker" who thinks aloud as they try to solve the problem, and the other member is the "listener" who analyzes and provides feedback on the "thinker's" approach

What inferences can you make about the height of girls versus boys? Will these inferences be the same your Senior year? Support your answer with a description of the overlap of the two distributions and numerical calculations for means and variability. Task: Decide whether girls or boys take longer to get ready for school in the morning. Justify your answer using measures of center and spread.

7.SP.5 [S] Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

Define probability as a ratio that compares favorable outcomes to all possible outcomes

Understand the distinction between unlikely, likely, and equally likely events

• Group discussions regarding the likelihood of situations, i.e. will the sun rise tomorrow, you toss a coin twice and get two heads, you toss a coin twice and get at least one head

• Use brainpop videos as a visual and brainpop hands-on activities to help student understand the Law of Large Numbers

Skill: There are three choices of jellybeans – grape, cherry and orange. If the probability of getting a grape is !

!" and

the probability of getting cherry is !

!, what is the

probability of getting orange? Task: The container below contains 2 gray, 1 white, and 4 black marbles. Without looking, if Eric chooses a marble from the container, will the probability be closer to 0 or to 1 that Eric will select a white marble? A gray marble? A black marble? Justify each of your predictions.

[S] 7.SP.5: 9-1, 9-5 • Pg. 711-718, 757-764



7.SP.6 [S] Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

Use probability to predict the number of times a particular event will occur given a specific number of trials

Use variability to explain why the experimental probability will not always exactly equal the theoretical probability

• Use spinners, dice, cards, etc. to have students generate data, make predictions, and experiment with probability

• Use brainpop videos as a visual and brainpop hands-on activities to help student understand the Law of Large Numbers

Skill: Roll a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. Task: A bag contains 100 marbles, some red and some purple. Suppose a student, without looking, chooses a marble out of the bag, records the color, and then places that marble back in the bag. The student has recorded 9 red marbles and 11 purple marbles. Using these results, predict the number of red marbles in the bag.

[S] 7.SP.6: IQL 9-2 • Pg. 719-720


7.SP.7 [S] Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

Can develop a simulation to model a situation in which all events are equally likely to occur Utilize the simulation to determine the probability of specific events

• In groups of two, have students create their own area models and present to class

• Have students create spinners or paper dice, then students should develop three associated questions; may select a question to incorporate in an assessment

Skill: Using a probability tree, find the number of possible choices when you choose one item from each category: 3 desserts, 2 drinks, 5 vegetables Task: Devise an experiment using a coin to determine whether a baby is a boy or a girl. Conduct the experiment ten times to determine the gender of ten births. How could a number cube be used to simulate whether a baby is a girl or a boy or girl?

[S] 7.SP.7 9-1, IQL 9-2, 9-2 • Pg. 711-718, 719-720, 721-728,

729-732 [S] 7.SP.7a 9-1, IQL 9-2, 9-2 • Pg. 711-718, 719-720, 721-728,

729-732 [S] 7.SP.7 IQL 9-2, 9-2 • Pg. 721-728, 729-732



b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? 7.SP.8 [S] Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event. c. Design and use a simulation to generate frequencies for compound events. . For example, use

Can use sample space to compare the number of favorable outcomes to the total number of outcomes and determine the probability of the compound events

Design and utilize a simulation to predict the probability of a compound event

• Use problem solving cards: have students complete one of three options involving a word problem, spinner problem, or tree diagram problem

• Have students create compound event situations; may develop spinners, tree diagrams, or organized list, then students should develop three associated questions; may select a question to incorporate in an assessment

Skill: If you toss a coin three times, what is the probability of flipping at least 2 heads? Task: A couple wants to have exactly 2 children. Assume that the chance of one boy or one girl is equally likely at each birth (no multiple births). What is the probability that they will have exactly 2 girls?

[S] 7.SP.8: 9-3, IQL 9-4, 9-4, Ch. 9 PSI, 9-5, 9-6, IQL 9-7, 9-7 • Pg. 733-740, 741-748, 749-752,

753-755, 757-764, 765-772, 773-774, 775-782

[S] 7.SP.8a: 9-3, 9-5, 9-6, 9-7 • Pg. 733-740, 757-764, 765-772,

773-774, 775-782 [S] 7.SP.8b: 9-3, 9-5, IQL 9-7, 9-7 • Pg. 733-740, 757-764, 773-774,

775-782 [S] 7.SP.8c: IQL9-4, 9-4, Ch. 9 PSI, IQL 9-7 • Pg. 714-748, 749-752, 753-755,

773-774 • www.illuminations.nctm.org • www.quantile.com


random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?


• Exemplars • Extended projects • Math Webquests • Writing in Math/Journal

Other Evidence: • Classwork • Exit Slips • Homework • Individual and group tests • Open-ended questions • Portfolio • Quizzes


Stage 3 – Learning Plan Lesson Format

Lesson Plan Template

Lesson Objective

Opening/Do Now

10-15 minutes

Homework Review

5-10 minutes


Mini Lesson I DO/ WE DO 15-20 minutes


20-30 minutes


10 minutes Using 3-part, student-friendly language. Ex. With 80% proficiency, I will solve 10 addition word problems.




• Contain a writing in math type of prompt/question for students to explain their thinking, etc.








UNIT NAME: GEOMETRY



Enduring Understandings/Goals: Equation solving skills from algebra are applied to the Pythagorean Theorem. Formulas provide an efficient method to problem solving. Numbers should be written in the best form for the context of the problem. Essential Questions: Why is it helpful to write numbers in different ways? Why are formulas important in math and society? How can algebraic concepts be applied to geometry? Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

Standard: M= Major

S=Supporting A= Additional


Suggested Instructional Strategies Suggested Assessments

Suggested Resources

IQL= Inquiry Lab

PSI= Problem Solving Investigation

21CC= 21st Century Careers

8.SP.3 [S] Use the equation of a linear model to solve problems

S.L.O. 1 Using a linear equation to model



Skill Task: Given a scatter plot determine slope and y


684


in the context of bivariate data interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

real life problems then solve it by interpreting the meaning of the slope and the intercept.

Groups/flexible groups Instruction • Center based learning • Technology • Demonstration • Cooperative Groups • Participation & Discussion • Projects • Flip model Academic Strategies and/or Resources in text and website: • Math in the Real World • Chapter Foldables for Notes • Note Taking within the text • Graphic Novel • Quick Review • RTI & Differentiated Instruction • Standardized Test Practice • Real World Link • Rate Yourself • Online Tutor • Watch out (error or


intercept Problem Based: Based on data, create a scatter plot, determine line of best fit, and write the equation. Explain the meaning of the slope of the line within the context of the problem. Assessments from text: • Quick Check • Editable assessments online • Mid-Chapter Check • Chapter tests Built in Checks for understanding: • Stop and Reflect • What’s the math? Ticket out the Door

• IQL pp. 685-686

• Supplemental

textbooks • Technology Software • SMARTBOARD • Graphic Organizers • Manipulatives • Grid/Graph Paper • Rulers • Multiplication Tables • See web resources

below

8.SP.1 [S] Construct and interpret scatter plot for bivariate measurement data to investigate patterns of association between two quantities.

S.L.O. 2 Construct and interpret scatter plots for bivariate measurement data and identify and interpret data patterns (clustering, outliers, positive



Groups/flexible groups Instruction • Center based learning • Technology • Demonstration • Cooperative Groups • Participation & Discussion • Projects

Skill Task: Students represent numerical data on a scatter plot, to examine relationships between variables. They analyze scatter plots to determine if the relationship is linear (positive, negative association or no association) or nonlinear. Students identity a line of best fit given a scatter plot.

Glencoe math Course 3 Chapter 8 • IQL pp. 663-663 • Lesson 1 pp. 556-

674 • IQL pp. 675-676


• Technology Software


Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. 8.SP.2 [S] Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

or negative association, possible lines of best fit, and nonlinear association).

• Flip model Academic Strategies and/or Resources in text and resources: • Math in the Real World • Chapter Foldables for Notes • Note Taking within the text • Graphic Novel • Quick Review • RTI & Differentiated Instruction • Standardized Test Practice • Real World Link • Rate Yourself • Online Tutor • Watch out (error or


Problem Based: Data for 10 students’ Math and Science scores are provided in a chart. Describe the association between the Math and Science scores. Given a linear model, students write an equation. Assessments from text: • Quick Check • Editable assessments online • Mid-Chapter Check • Chapter tests Built in Checks for understanding: • Stop and Reflect • What’s the math? • Ticket out the Door

• SMARTBOARD • Graphic Organizers • Manipulatives • Grid/Graph Paper • Rulers • Multiplication Tables • See web resources

below

8.SP.4 [S] Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative

S.L.O. 3 Construct frequency/relative frequency tables to analyze and describe possible associations between two variables.



Groups/flexible groups Instruction • Center based learning • Technology • Demonstration • Cooperative Groups • Participation & Discussion

Skill Task: Students understand that a two-way table provides a way to organize data between two categorical variables. Data for both categories needs to be collected from each subject. Students calculate the relative frequencies to describe associations Problem based:


696 • PSI pp. 697-699 • Mid chapter check

pp. 700



frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have curfews and those who have chores?

• Projects • Flip model Academic Strategies and/or Resources in text and website: • Math in the Real World • Chapter Foldables for Notes • Note Taking within the text • Graphic Novel • Quick Review • RTI & Differentiated Instruction • Standardized Test Practice • Real World Link • Rate Yourself • Online Tutor • Watch out (error or


25 students were asked whether they have a part time job and then whether they get 8 hours a sleep at night. The data is summarized in a table. The students use relative frequency to describe possible correlations. What percent of students that work do not get 8 hours of sleep a night? Justify their answers. Discuss other possible explanations. Assessments from text: • Quick Check • Editable assessments online • Mid-Chapter Check • Chapter tests Built in Checks for understanding: • Stop and Reflect • What’s the math? • Ticket out the Door


below


8.G.9 [A] Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

S.L.O. 4 Know and apply the appropriate formula for the volume of a cone, a cylinder, or a sphere to solve real-world and mathematical problems.



Groups/flexible groups Instruction • Center based learning • Technology • Demonstration • Cooperative Groups • Participation & Discussion • Projects • Flip model Academic Strategies and/or Resources in text and website: • Math in the Real World • Chapter Foldables for Notes • Note Taking within the text • Graphic Novel • Quick Review • RTI & Differentiated Instruction • Standardized Test Practice • Real World Link • Rate Yourself • Online Tutor • Watch out (error or


Skill-Based Task: • Construct cylinders – What shapes are

needed to construct a cylinder? How many blocks are needed to fill the cylinder? How could find the volume mathematically?

• Construct a cone with the same height as the cylinder. How many blocks are needed to fill this shape?

• Construct a sphere of similar height to the cone and the cylinder. How many blocks are needed to fill the sphere?

• Students find the volume of cylinders, cones and spheres to solve real world and mathematical problems. Answers

• could also be given in terms of Pi. •

Problem-Based Task:

Pablo's Icy Treat Stand sells home-made frozen juice treats as well as snow-cones. Originally, Pablo used paper cone cups with a diameter of 3.5 inches and a height of 4 inches.

Conical Cup A

His supply store stopped carrying these paper cones, so he had to start using more standard paper cups. These are truncated cones (cones with the "pointy end" sliced off) with a top diameter of 3.5 inches, a


• IQL pp.584- 588 • Lesson 1 pp.

589-596 • Lesson 2 pp.

597-604 • Lesson 3 pp.

605-612 • PSI pp. 613-615 •



below


bottom diameter of 2.5 inches, and a height of 4 inches.

Cup B

Because some customers said they missed the old cones, Pablo put a sign up saying "The new cups hold 50% more!" His daughter Letitia wonders if her father's sign is correct. Help her find out.

1. How much juice can cup A hold? (While cups for juice are not usually filled to the top, we can assume frozen juice treats would be filled to the top of the cup.)

2. How much juice can cup B hold? 3. By what percentage is cup B larger

in volume than cup A? 4. Snow cones have ice filling the cup

as well as a hemisphere of ice sticking out of the top of each cup. How much ice is in a snow cone for each cup?


5. By what percentage is the snow cone in cup B larger than the snow cone in conical cup A?

6. Is Pablo's sign accurate?


Lesson Plan Template

with suggested pacing for required 80 minute math block










Lesson Objective

Opening/Do Now

10-15 minutes

Homework Review

5-10 minutes



15-20 minutes


20-30 minutes

Summary and

Exit Slip 10 minutes









• Technology • Problem-based/Skill-based Task • Vocabulary Work • Writing in Math • Art/Music Connections


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