Unit 1: Ratio and Proportions Time Frame: 3.5 weeks August ...• Unit 3 Activity 5 • Unit 3...

Lafayette Parish School System Math Essentials Curriculum Map

Unit 1: Ratio and Proportions Time Frame: 3.5 weeks August 15, 2011 to September 9, 2011

GLE #

GLEs

Evidence / Assessments of learning Instructional Notes/Strategies Differentiation

Essential: Big ideas/covered most frequently; 50% of content; 60-70% of instructional time; high # of test items on state assessment; mastery in current year 1 Important: Key knowledge/skills/covered less frequently; 30% of content; 20-30% of instructional time; fewer # of items on state assessment; Condensed: Less important/least frequently; 20% of content; 10-20% of instructional time; reinforcement; extension/enrichment

Unit Description This unit focuses on converting between units of measure, creating and interpreting maps and diagrams using scale values, and determining percentages. Student Understandings In this unit students will develop the ability to accurately use a ratio scale in a map or diagram to determine measurement of the actual distance or size. Additionally, students will be able to determine if a ratio represents a direct or inverse variation, as well as to solve for a variable in a given proportion, and to convert ratios into equivalent percent values. Note: Please incorporate calculator and non-calculator activities into this unit.

1 4 7

Read, write, and perform basic operations on complex numbers (N-1-H) (N-5-H) (Grade 12) Use ratios and proportional reasoning to solve a variety of real-life problems including similar figures and scale drawings (N-6-H) (M-4-H) (Grade 10) Use proportional reasoning to model and solve real-life problems involving direct and inverse variation (N-6-H) (Grade 9)

• Ratio and Proportion • Define • Notations • Real world examples

• Solving rates (speed, time, and distance) • direct proportions • inverse proportions Note: May not need to use terms “direct” and “inverse” with students. Can students solve real world using direct or inverse variation? Can students use proportional reasoning to solve for a missing quantity in a ratio?

Activity 1 - CC Algebra I text Section 3-6 JBHM 8th grade Unit 2 : SBIL 3 Activity 3 – CC Activity 4 w/ BLM – CC Geometry text Section 6-1 Bridges text Section 6-1, 6-3

4 days Activity 2 – CC use to guide teacher ** need activity to supplement direct and inverse proportion Reviewing Mathematics pub. Amsco page 172 - 175

Test 1 1 day 1 4 7

Read, write, and perform basic operations on complex numbers (N-1-H) (N-5-H) (Grade 12) Use ratios and proportional reasoning to solve a variety of real-life problems including similar figures and scale drawings (N-6-H) (M-4-H) (Grade 10) Use proportional reasoning to model and solve real-life

• Measurement, conversion and scales • scale drawings • Similar figures Can students use a scaled map or diagram to determine actual measurement? Can students use proportional reasoning to solve for a missing quantity in a ratio?

Activity 5 w/ BLM Algebra I text 11-6 Geometry text 6-2 Bridges text 6-2 Scale Drawing Project - see rubric in CC General Assessment page 10-11

6 days Reviewing Mathematics pub. Amsco page 176 - 178


Unit 1: Ratio and Proportions Time Frame: 3.5 weeks August 15, 2011 to September 9, 2011

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21

problems involving direct and inverse variation (N-6-H) (Grade 9) Determine appropriate units and scales to use when solving measurement problems (M-1-H) (M-2-H)(M-3-H)

Performance Task Assessment 1 day 1 4 7

Read, write, and perform basic operations on complex numbers (N-1-H) (N-5-H) (Grade 12) Use ratios and proportional reasoning to solve a variety of real-life problems including similar figures and scale drawings (N-6-H) (M-4-H) (Grade 10) Use proportional reasoning to model and solve real-life problems involving direct and inverse variation (N-6-H) (Grade 9)

• Percentages o Tax o Commission o Interest o Percent increase/decrease

Can students use proportional reasoning to solve for a missing quantity in a ratio? Can students use proportional reasoning to convert a ratio into an equivalent percentage

Activity 7 – CC Activity 8 w/ BLM– CC Activity 9 w/BLM – CC Algebra I text section 3-7 Bridges text section 7-1 – 7-6 Cord, Algebra I text section 3-2

4 days Reviewing Mathematics pub. Amsco page 179 - 196

Test 1 day


Unit 2: Probability Time Frame: 2.5 weeks September 12, 2011 to September 27, 2011

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Unit Description This unit focuses on providing an introduction to probability using counting techniques such as permutations and combinations, as well as, comparing theoretical and experimental probabilities. Student Understandings In this unit students will develop the ability to define and accurately compute probabilities for both dependent and independent events. Students will use counting techniques to compute probabilities as well as solve real life problems. Students will be able to represent experimental probability in a graphical representation. Students will be able to explain the relationship between odds and probability

21 22

Determine the probability of conditional and multiple events, including mutually and non-mutually exclusive events (D-4-H) (D-5-H) (Grade 10) Interpret and summarize a set of experimental data presented in a table, bar graph, line graph, scatter plot, matrix, or circle graph (D-7-H) Also GLEs 25, 31, 32(Grade 10)

• Experimental Probability • Probability terminology • Determine fairness in game playing

Activity 7 w/BLM: “Experimental Probability Activity 9 “Fairness” Bridges section 6-7 Cord, Algebra I section 6-2

2 days Activity 1: “Vocabulary” - use as focus activity or bellringer

32 24

Compute probabilities using geometric models and basic counting techniques such as combinations and permutations (D-4-H) Also GLE 31(Grade 9) Using counting procedures and techniques to solve real-life problems (D-9-H) (Grade 10)

• Permutations • Combinations

Can students determine which counting principle,

permutation or combination, is applicable to a variety of real-life problems?

Can students use permutations or combinations to solve problems in a variety of real life situations?

Activity 4 w/BLM: “Permutation or Combination”

Algebra I Section 14.2

4 days JBHM Unit 8 www.edhelper.com/interactive.htm ABC GEE 2nd Ed Ch 17

Test 1 1 day 21 22

Determine the probability of conditional and multiple events, including mutually and non-mutually exclusive events (D-4-H) (D-5-H) (Grade 10) Interpret and summarize a set of

• Explore probability written as a ratio • Independent and dependent events • Theoretical Probability • Compute odds of an event occurring • Use Venn diagram to show mutually and non-

mutually exclusive.

Activity 2: “Ratio to Proportion” Activity 3: “Outcomes of Independent and Dependent Events”

4 days Activity 5 JBHM Unit 8


Unit 2: Probability Time Frame: 2.5 weeks September 12, 2011 to September 27, 2011

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31 25 33

experimental data presented in a table, bar graph, line graph, scatter plot, matrix, or circle graph (D-7-H) Also GLEs 32(Grade 10) Define probability in terms of sample spaces, outcomes, and events (D-4-H) (Grade 9) Use discrete math to model real-life situation (e.g., fair games, elections) (D-9-H) (Grade 10) Explain the relationship between the probability of an event occurring, and the odds of an event occurring and compute one given the other (D-4-H) Also GLEs 21, 22, 24, and 31(Grade 9)

Can students accurately describe the differences between theoretical and experimental probabilities?

Can students determine the theoretical probability of both dependent and independent events?

Can students represent the outcomes of experimental data in a variety of graphical formats?

Activity 6 w/BLM: “Theoretical Probability” Activity 8 w/BLM: “Graphical Interpretation” Activity 10 w/BLM: “Odds Are” Algebra I Section 2-6, 14-5 Bridges Section 6-4 Cord, Algebra I Section 6-1, 6-3

www.edhelper.com/interactive.htm www.onlinemathlearning.com/math

Test 2 1 day


Unit 3: Statistics Time Frame: 3 weeks October 10, 2010 to November 4, 2010

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Evidence / Assessments of learning Instructional Notes/Strategies

Differentiation


Unit Description The unit will focus on graph construction, graph interpretation, determining bias, and basic descriptive statistics. Student Understandings In this unit students will develop the ability to read, interpret and analyze statistics presented in a variety of formats, including bar graphs, pie charts, box and whisker plots, and scatter plots. Students will be able to devise and conduct surveys and predict future outcomes from the data collected, including the limitations of their predictions. 27 Determine the most

appropriate measure of central tendency for a set of data based on its distribution (D-1-H) (Grade 9)

• Determine most appropriate measure of central tendency • Box & Whisker Plot

Can student determine which measure of central tendency for a set of data based on distribution?

Reviewing Math Unit 10.3 Mean, median, mode Math GEE Unit 14: Statistics

2 Days • Unit 3 Activity 4

Algebra Prerequisite Skill:12(p.818) Reviewing Math Unit 10.4 Stem-and-Leaf Plots and Box-Whisker Plots

Test 1 1 Day 28

Identify trends in data and support conclusions by using distribution characteristics such as patterns, clusters, and outliers (D-1-H) (D-6-H) (D-7-H) (Grade 9)

• Identify trends in data and support conclusions • Types of Graphs

• Bar • Histogram • Stem and leaf • Circle • Venn diagram

Can student identify trends in data and support conclusions by using distribution characteristics such as: patterns, clusters, and outliners?

Algebra 1 Section 2-5 Statistics: Displaying and Analyzing Data Algebra 1 Lesson 13-4 Measures of Variation Unit 3, Activity 2 Unit 3, Activity 3 BLM Bridges Section 2-1 – 2-7

3 days • Unit 3 Activity 5 • Unit 3 Activity 5 BLM

Reviewing Math Unit 1.7 Patterns Reviewing Math Unit 10.2 Frequency Tables and Histograms Algebra Requisite Skills: 5 (p.806) Textbook: Algebra 1 Lesson 13-3 Histograms ABC GEE 2nd Ed Ch 14, 15

Performance Task Assessment 1 day 29 Create a scatter plot from a set

of data and determine if the relationship is linear or nonlinear (D-1-H) (D-6-H) (D-

• Create and determine if a scatter plot is linear or nonlinear

• Write equations for lines of fit using graphing calculator

Textbook: Algebra I Lesson 5-7: Statistics: Scatter Plots and Lines of Fit www.algebra1.com/other_calculator_

2 days • Unit 3 Activity 7 • Unit 3 Activity 7 BLM


Unit 3: Statistics Time Frame: 3 weeks October 10, 2010 to November 4, 2010

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Differentiation


7-H)(Grade 9)

Can students create scatter plot form a set of data? Can student determine if scatter plot is linear or nonlinear?

keystrokes Textbook: Algebra Lesson 4-3: Relations (tables, graph, mapping)

Quiz 1 day 17 18

Distinguish between samples and populations (D-1-H) (Grade 11-12) Devise and conduct well-designed experiments/surveys involving randomization and considering the effects of sample size and bias (D-1-H) (Grade 11-12)

• Distinguish differences between samples and populations

• Devise and conduct well designed random experiment/survey

Can students distinguish differences between samples and populations? Can students devise and conduct experiment and surveys using randomization? Can students determine the effects of sample size and bias?

Activity-Specific Assessments Unit 3 Activity 4 & 5 (p. 36) – Use as lead in to project. Textbook: Algebra 1 Lesson 13-1: Sampling and Bias Textbook: Algebra 1 Lesson 14-4: Probability Distributions: Random Variables Textbook: Algebra 1 Lesson 14-5: Probability Simulations: Experimental Bridges Section 6-8

2 days • Unit 3 Activity 8 • Unit 3 Activity 6 & 9 • Unit 3 Activity 6 BLM • Unit 3 Activity 9 BLM

Performance Task Assessment/Presentation

3 days **Use Activity 9 Rubric.

22 Explain the limitations of predictions based on organized sample sets of data (D-7-H) (Grade 11-12)

• Explain the limitations of predictions based on data from students’ presentations.

Can students explain limitations of predictions based on organized sample sets of data?

Reviewing Math Unit 10.8 Experimental Probability Textbook: Algebra 1 Lesson 14-5: Probability Simulations:

Experimental

**Discussion of student data as presented. Stats Modeling the World: Ch 23 Inferences About Means – What can go wrong


Unit 4: Topics in Geometry Time Frame: 6 weeks November 7, 2010 to January 9, 2011

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Unit Description This unit will focus on spatial visualization of geometric figures as well as determining the quantitative measurements of two and three dimensional objects. Study of right triangle geometry and trigonometry, including Pythagorean theorem is also included. Student Understandings In this unit students will understand basic geometric concepts such as distance, midpoint and the Pythagorean Theorem. Students will understand and use trigonometric ratios. Students will understand how to transform polygons in a coordinate plane. Additionally, students will understand the relationship between surface area and volume of rectangular prisms and cylinders. 2 12 16 23 12 26

Evaluate and write numerical expressions involving integer exponents (N-2-H) (Grade 9) Apply Pythagorean Theorem in both abstract and rela-life situations(G-2-H) (Grade 10) Represent and solve problems involving distance on a number line or in the plane (G-3-H) (Grade 10) Use coordinate methods to solve and interpret problems (e.g., slope as rate of change, intercept as initial value, intersection as common solution, midpoint as equidistant) (G-2-H) (G-3-H) (Grade 9) Evaluate polynomial expressions for given values of the variable (A-2-H) (Grade 9) Generalize and represent patterns symbolically, with and without technology (P-1-H) (Grade 10)

• Simplifying Radicals • Distance on the number line • Distance in the coordinate plane • Midpoint on the number line • Midpoint on the coordinate plane • Pythagorean Theorem • Pythagorean Triples Can students determine the distance between two points? Can students determine the midpoint of a line segment given the two endpoints? Can students use the Pythagorean Theorem to solve right triangle problems?

Geometry text Pre-Req Skills : Square Roots & Simplifying Radicals (p. 744-745 7.2 Pythagorean Theorem and It’s Converse p. 350 1.3 Distance and Midpoint p. 21-27

Unit 4 Activity 1 (could be used as intro to entire unit) Unit 4 Activity 2 Geometry Activity : The

Pythagorean Theorem p. 349 Unit 4 Activity 3 Unit 4 Activity 4 6 days



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Test 1 1 day 3 8 18

Define sine, cosine, and tangent in ratio form and calculate them using technology (N-6-H) (Grade 10) Model and use trigonometric ratios to solve problems involving right triangles (N-6-H) (M-4-H) (Grade 10) Determine angle measures and side lengths of right and similar triangles using trigonometric ratios and properties of similarity, including congruence (G-5-H) (M-4-H) (Grade 10)

• Defining basic relationships of sine, cosine, and tangent • Find the sine, cosine, and tangent with and without

technology • Solve missing angles and missing sides of a right triangle

using sine, cosine, and tangent – with and without technology

Can students define sine, cosine, and tangent in ratio form and calculate them using technology?

Geometry text 7.4 Trigonometry p. 364-370

Unit 4 Activity 5 w/ BLM 4 days

Test 2 1 day 25 14 16

Perform translations and line reflections on the coordinate plane (G-3-H) (Grade 9) Develop and apply coordinate rules for translations and reflections of geometric figures (G-3-H) (Grade 10) Represent translations, reflections, rotatiosn, and dilations of plane figures using sketches, coordinates, vectors, and matrices (G-3-H) (Grade 11-12)

• Translations • Reflections • Rotations Can students develop and apply coordinate rules for

translations and reflections of geometric figures?

Geometry Text: 9.1 Reflections p. 463-469 9.2 Translations p. 470-475 9.3 Rotations p. 477-482

Unit 4 Activity 6 w/BLM 3 days

Test 3 1 day

12

Evaluate polynomial expressions for given values of

• Perimeter of regular and irregular shapes • Area of

Geometry Text: 11.1 Area of Parallelograms

Unit 4 Activity 7 w/BLM Unit 4 Activity 10



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9 10 26

the variable (A-2-H) (Grade 9) Construct 2- and 3-dimintional figures when given the name, description, or attributes, with and without technology (G-1-H) (Grade 10) Form and test conjectures concerning geometric relationships including lines, angles, and polygons (i.e., triangles, quadrilaterals, and n-gons), with and without tehcnology (G-5-H) (M-4-H) (Grade10) Generalize and represent patterns symbolically, with and without technology (P-1-H) (Grade 10) Translate among tabular, graphical, and symbolic representations of patterns in real-life situations, with and without technology (P-2-H) (P-3-H) (A-3-H) (Grade 10)

o Rectangles o Triangles o Parallelograms o Trapezoids o Shaded region/irregular polygons

• Circumference and Area of a Circle • Volume and Surface Area of

o Prisms o Cylinders o Cones o Spheres o Regular Pyramids

Can students determine the volume and surface area of

rectangular prisms and cylinders and apply these concepts in real-world applications?

p. 595-597 11.2 Area of Triangles, Trapezoids, and Rhombi p. 601-604 11.3 Area of Regular Polygons and Circles p. 610-612 11.4 Area of Irregular Figures p. 617-618 12.2 Nets and Surface Area p. 643-648 12.3 Surface Area of Prisms p. 649-654 12.4 Surface Area of Cylinders p. 655-659 12-5 Pyramids 12-6 Cones 12-7 Spheres 13.1 Volume of Prisms and Cylinders p. 688-694 13 – 2 Volume of Pyramids & Cones 13 – 3 Volume of Spheres Bridges Ch 12

Unit 4 Activity 11 Unit 4 Activity 12 10 days **Note: If needed, separate skills into 2 tested areas.

Test 4 1 day 9 Construct 2- and 3-dimintional

figures when given the name, description, or attributes, with and without technology (G-1-H) (Grade 10

• Orthogonal Drawings • Corner View • Identify 3-dimensional objects given a net Can students create orthographic and foundation drawings of

three-dimensional objects from isometric drawings of three-dimensional objects?

Can students create isometric drawings given orthographic and foundation drawings of the objects?

optional 12.1 Three-Dimensional Figures p. 636-642 12.2 Nets and Surface Area p. 643-648

Unit 4 Activity 8 w/ BLM Unit 4 Activity 9 w/ BLM 1 day



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10

Form and test conjectures concerning geometric relationships including lines, angles, and polygons (i.e., triangles, quadrilaterals, and n-gons), with and without technology (G-1-H) (G-4-H) (G-6-H)

• Calculate the area of irregular shapes • Calculate the area of shaded regions • Calculate the geometric probability of

o Hitting shaded region o Choosing at random o Etc.

Can students apply the concepts of geometric probability?

Geometry Textbook: Section 11-3 Area of Regular Polygons and Circles p. 610 – 612 Section 11-4 Areas of Irregular Figures p. 617 – 618 Section 11-5 Geometric Probability p. 622 – 627 Note: Keep it simple!

Geometry Unit 6 Activity 11 2 days ABC GEE 2nd Ed Ch 16

Test 5 1 day


Unit 5: Exploring Linear Functions Time Frame: 8 weeks January 4, 2012 to March 2, 2012

GLE #

GLEs


Differentiation


Unit Description This unit will focus on exploring linear relationships and linear equations from given data, as well as interpreting and creating the graphs of linear functions Student Understandings In this unit students will understand the difference between relationship and function. They will translate among tabular, graphical, algebraic, and verbal representations of functions. Students will determine the equation of a line given two points, a point and the slope, and the y-intercept and slope. Students will determine the line of best fit of a scatter plot. 8.

Use order of operations to simplify or rewrite variable expressions (A-1-H)(A-2-H) (Grade 9)

• Use order of operations Can students simplify or rewrite variable expressions using order of operations?

Textbook: Algebra I Lesson 1-2

2 days AMSCO Unit 5-1 Math GEE 2ed. Chapter 1, page 33 Century Board Activity (See Demarcus)

Test 1 1 day

11 Use equivalent forms of equations and inequalities to solve real-life problems. (A-1-H) (Grade 9)

• Solve Linear Equations • Solve Linear Inequalities Can students solve multi-step equations and inequalities?

Textbook: Algebra I Lesson 3-1 - 3-5 (Solving Equations) Textbook: Algebra II Lesson 1-3 Solving Equations Textbook: Algebra I Ch 6-1 – 6-3 (Solving Inequalities) Textbook: Algebra II Lesson 1-5 Solving Inequalities

10 days AMSCO Unit 5-4 – 5-7

Test 2 1 day 10 35 36

Identify independent and dependent variables in real-life relationships (A-1-H) (Grade 9) Determine if a relation is a function and use appropriate function notation (P-1-H) Identify the domain and range of functions. (P-1-H)

• Relation • Function • Domain • Range • Vertical line test • Distinguish between independent and dependent variables • Evaluating functions Can students represent relations and functions using a mapping or table, (symbolically), graphically, algebraically, and verbally?

Textbook: Algebra I Lesson 1-8 Graphs and functions Textbook: Algebra I Lesson 4-3 – 4-4, 4-6 (Relations & Functions) Textbook: Algebra II Lesson 2-1 Relations and functions

4 days JBHM Unit 3 SBIL-1 Math GEE 2ed. Chapter 10, page 145 & 155 AMSCO Unit 11.1



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Differentiation


Can students determine the graphs, domains, ranges, intercepts, and global characteristics of linear functions by hand and using technology? Can students determine the real-world meanings of domains, ranges, intercepts, and global characteristics of linear functions? Can students identify independent and dependent variables in real-life relationships?

Test 1 day 25 Explain slope as a

representation of “rate of change” (G-3-H) (A-1-H)

• Slope Can students determine the slope of a line and classify lines as perpendicular, parallel, same or neither?

Textbook: Algebra I Lesson 5-1 Textbook: Geometry Lesson 3-3 Textbook: Algebra II Lesson 2-3

JBHM Unit 3 SBIL-3 JBHM Unit 4 SBIL-2 JBHM Unit 4 Student Handout 5, 6 AMSCO Unit 11.4 3 days

Test 1 day 13 Translate between the

characteristics defining a line (i.e. slope, intercepts, points) and both its equation and graph (A-2-H) (G-3-H)

• Writing equations of lines (slope intercept form, standard) • Parallel & perpendicular • Linear regression • Graphing linear equations Can students graph linear equations using slope-intercept form, standard form, and point-slope form of a linear equation? Can students write a linear equation given:

a. two points? b. a point and the slope? c. the y-intercept and the slope?

Can students use a scatter plot to identify the correlation manifested by a set of data and create a line of best fit with and without graphing technology?

Textbook: Algebra I Lesson 4-5 Graphing Linear Equations Textbook: Algebra I Lesson 5-3 – 5-7 (Writing equations of lines) Textbook: Geometry Lesson 3-4 Equations of Lines Textbook: Algebra II Lesson 2-4 – 2-5 (Equations of lines)

Unit 5: Activities 6 - 10 JBHM Unit 3 SBIL-4 AMSCO Unit 11-2 Math GEE 2ed. Chapter 7, p. 102 6 days

Test 1 day



GLE #

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Differentiation


14 Graph and interpret linear inequalities in one or two variables and systems of linear inequalities (A-2-H) (A-4-H)

• Graphing linear inequalities in 2 variables Can students graph linear inequalities?

Textbook: Algebra I Lesson 6-6 Graphing Inequalities in Two Variables Textbook: Algebra II Lesson 2-7 Graphing Inequalities

Unit 5: Activity 11 AMSCO Unit 11.3 3 days

Test 1 day 16 Interpret and solve systems

of linear equations using graphing, substitution, elimination, with and without technology, and matrices using technology (A-4-H)

• Solving systems of equations • Solving systems of inequalities

Textbook: Algebra I Lesson 7-1 – 7-5 (Solving systems of equations and inequalities) Textbook: Algebra II Lesson 3-1 – 3-3 (Solving systems of equations and inequalities) Optional

4 days

Test 1 day


Unit 6: Exploring Step, Piecewise, Absolute Value, and Quadratic Functions Time Frame: 8 weeks March 5, 2012 to May 11, 2011

GLE #

GLEs


Differentiation


Unit Description This unit will focus on exploring non-linear functions: step, piecewise, absolute value and quadratic functions. Students will interpret and create graphs of step, piecewise, absolute value and quadratic functions with and without using graphing technology. Student Understandings In this unit students will develop the ability to create and translate graphs of these non-linear functions: absolute value functions, step functions, piecewise functions and quadratic functions related to real-world situations and examples. Note: Depending on level of students, concepts from this unit may be replaced with some of the hands-on activities from Unit 7. 12 2 8

Evaluate polynomial expressions for given values of the variable (A-2-H) (Grade 9) Evaluate and write numerical expressions involving integer exponents (N-2-H) (Grade 9) Use order of operations to simplify or rewrite variable expressions (A-1-H) (A-2-H) (Grade 9) Compare and contrast the properties of families of polynomial, rational, exponential, and logarithmic functions, with and without technology (P-3-H)

• Monomials • Product of Powers • Power of a Power • Power of a Product • Quotient of Powers • Zero Exponents • Negative Exponents Can students factor expressions using the greatest common factor, factor binomials containing the difference of two perfect squares and the sum and difference of two perfect cubes?

Algebra I : BLM Unit 7 # 1 JBHM Unit 7 –SBIL 1 8.1: “Multiplying Monomials” (p.410) 8.2: “Dividing Monomials” (p.417) Algebra I BLM Unit 7 # 6

5 days

• Test 1 day 2 8 15

Evaluate and write numerical expressions involving integer exponents (N-2-H) (Grade 9) Use order of operations to simplify or rewrite variable expressions (A-1-H) (A-2-H) (Grade 9) Translate among tabular, graphical, and algebraic representations of functions and real-life situations (A-3-H) (P-1-H) (P-2-H) (Grade 9)

• Polynomials • Arrange in Descending Order • Add Polynomials • Subtract Polynomials

Can students apply adding and subtracting of polynomials?

JBHM Unit 7 –SBIL 1 8.4: “Polynomials” (p.432) 8.5: “Adding and Subtracting Polynomials” (p.439) M.E. Unit 7 Activity 2 Use algebra tiles Algebra I BLM Unit 7 # 7

1 day

• Test 1 day



GLE #

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Differentiation


2 8

Evaluate and write numerical expressions involving integer exponents (N-2-H) (Grade 9) Use order of operations to simplify or rewrite variable expressions (A-1-H) (A-2-H) (Grade 9)

• Multiply polynomials by monomials • Simplify Expressions • The distributive property

Can students select the appropriate technique for

factoring? Can students multiply polynomials and identify special products? Can students apply multiplication of binomials and factoring to geometric problems? Can students factor expressions using the greatest common factor, factor binomials containing the difference of two perfect squares and the sum and difference of two perfect cubes? Can students factor perfect square trinomials and general trinomials? Can students factor polynomials by grouping?

M.E. Unit 7 Activity 3, 4, 5, 6, 7 JBHM Unit 7 –SBIL 1 8.6: “Multiplying Polynomials by a Monomial” (p.444) 8.7: “Multiplying Polynomials” (p.452)

5 days

Test 1 day • Factoring polynomials

9 days

Test 1 day 9 Solve quadratic equations by factoring,

completing the square, using the quadratic formula, and graphing Also, 1,2,5,6,8,24,29

• Zero product property • Completing the square • Quadratic formula and discriminant Can students factor in order to solve polynomial equations using the Zero–Product Property? Can students relate factoring a polynomial to the zeroes of the graph of a polynomial? Can students complete the square to solve a quadratic equation? Can students solve a quadratic equation by factoring and using the Quadratic Formula?

Textbook: Algebra II Lesson 6-3 – 6-5 (Solving quadratic equations)

Algebra II CC Unit 4: Act. 2 BLM 9 days



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Differentiation


TEST 1 day • Graph exponential functions with a > 1 and 0

< a < 1 • Identify exponential behavior •

Algebra I unit 10-5: “Exponential Functions” (p.554)

2 days

• Test 1 day 15 27 36 8

Translate among tabular, graphical, and algebraic representations of functions and real-life situations (A-3-H) (P-1-H) (P-2-H) (Grade 9) Translate among tabular, graphical, and symbolic representations of patterns in real-life situations, with and without technology (P-2-H) (P-3-H) (A-3-H) (Grade 9) Identify the domain and range of functions (P-1-H) (Grade 9) Categorize non-linear graphs and their equations as quadratic, cubic, exponential, logarithmic, step function, rational, trigonometric, or absolute value (A-3-H) (P-5-H) (Grade 11-12)

• Identify step function and piecewise function • Indicate domain, range and intercept of each

function

Can students determine the graphs, domains, ranges, and intercepts of step functions, and piecewise linear functions, then verbalize the real-world meanings of these?

M.E. Unit 6 Activity 5 M. E. Unit 6 Activity 6 Piecewise function resources:

http://archives.math.utk.edu/visual.calculus/0/functions.13/index.html www.onlinemathlearning.com/piecewise-functions.html http://my.nctm.org/eresources/repository/shared/concord/resources_files/Piecewise.html 1 day

8 10

Categorize non-linear graphs and their equations as quadratic, cubic, exponential, logarithmic, step function, rational, trigonometric, or absolute value (A-3-H) (P-5-H) (Grade 11-12) Model and solve problems involving quadratic, polynomial, exponential, logarithmic, step function, rational, and absolute value equations using technology (A-4-H) (Grade 11-12)

• Identify absolute value functions • Solve absolute value functions Can students determine the graphs, domains, ranges, intercepts, and global characteristics of absolute value functions, step functions, and piecewise linear functions, both by hand and by using technology, then verbalize the real-world meanings of these? Can students solve absolute value equations and inequalities and state their solutions in various forms when appropriate?

M.E. Unit 6 Activity 7, 8, 9

1 day

10

Model and solve problems involving quadratic, polynomial, exponential,

• Graph step function and piecewise function • Determine the real world meaning of each

Optional Math Essentials BLM Unit 6

1 day



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GLEs


Differentiation


logarithmic, step function, rational, and absolute value equations using technology (A-4-H) (Grade 11-12)

function

Can students determine the graphs, domains, ranges, intercepts, and global characteristics of absolute value functions, step functions, and piecewise linear functions, both by hand and by using technology, then verbalize the real-world meanings of these?

Activity 6: Senior Trip

TEST 1 day


Unit 7: Applied Mathematics Time Frame: 2 weeks May 14, 2011 to May 24, 2011

GLE #

GLEs


Differentiation


Unit Description This unit will focus on exploring the application of mathematic concepts within the career clusters. Student Understandings In this unit students will develop the ability to apply algebraic and geometric concepts as they relate to real world situations. This allows the teacher to provide opportunities for differentiated instruction through the use of project-based learning. NOTE: The activities listed are only guidelines but offer examples of tasks that would provide for real world learning. Use as time permits. 7 21 4 1

Use proportional reasoning to model and solve real-life problems involving direct and inverse variation (N-6-H) (Grade 9) Determine appropriate units and scales to use when solving measurement problems (M-1-H) (M-2-H)(M-3-H) (Grade 9) Use ratios and proportional reasoning to solve a variety of real-life problems including similar figures and scale drawings (N-6-H) (M-4-H) (Grade 10) Read, write, and perform basic operations on complex numbers (N-1-H) (N-5-H) (Grade 11-12)

• Measurement • Standard and metric • conversions

• Use of geometric concepts • Symmetry • Scaled drawings

Quilter’s Project – http://www.esd112.org/edtech/no_limit/rs_archive.cfm#quilts Designing a school for the future – http://www.edutopia.org/mountlake-terrace-schools-2050-project Create Scaled Models of the Pyramids – http://www.pbs.org/wgbh/nova/pyramid/geometry/index.html The Geometry of Lenses – http://www.pbs.org/teachers/mathline/concepts/movies/activity3.shtm

3 – 4 days 10 days for full project Can modify to design something smaller like a putt-putt golf course for less days. This is a great guide for any project. 1 - 2 days 1 - 2 days

31 32 33

Define probability in terms of sample spaces, outcomes, and events (D-4-H) (Grade 9) Compute probabilities using geometric models and basic counting techniques such as combinations and permutations (D-4-H) (Grade 9) Explain the relationship between the probability of an event occurring, and the odds of an event occurring and compute one given the other (D-4-H) (Grade 9)

• Use and interpret quantities and units correctly in graphs and data displays

• Understand that statistical methods take variability into account to support making informed decisions based on data collected to answer specific questions or explain real world situations

• Organize and display data using appropriate methods and technology

• Evaluate published data by considering the source, the design of the display to identify and explain the use or misuse of the data

The Stowaway Adventure – http://www.ciese.org/curriculum/shipproj/ Down the Drain – http://www.ciese.org/curriculum/drainproj/

6 days 6 days 3 – 4 days



GLE #

GLEs


Differentiation


21 22 24 25

Determine the probability of conditional and multiple events, including mutually and non-mutually exclusive events (D-4-H) (D-5-H) (Grade 10) Interpret and summarize a set of experimental data presented in a table, bar graph, line graph, scatter plot, matrix, or circle graph (D-7-H) (Grade 10) Use counting procedures and techniques to solve real-life problems (D-9-H) (Grade 10) Use discrete math to model real-life situation (e.g., fair games, elections) (D-9-H) (Grade 10)

Gun shots by the numbers – http://learning.blogs.nytimes.com/2004/08/19/gunshots-by-the-numbers/

28 18 22

Identify trends in data and support conclusions by using distribution characteristics such as patterns, clusters, and outliers (D-1-H) (D-6-H) (D-7-H) (Grade 9) Devise and conduct well-designed experiments/surveys involving randomization and considering the effects of sample size and bias (D-1-H) (Grade 11-12) Explain the limitations of predictions based on organized sample sets of data (D-7-H) (Grade 11-12)

• Design simple investigation or survey to collect data to answer questions of interest

• Explain how the outcome of an event can be predicted by the estimated probability

2010 Census Project - http://learning.blogs.nytimes.com/2003/01/23/the-minority-majority/ Matching Birthdays Activity – http://webcache.googleusercontent.com/search?q=cache:TyBot5Rngo0J:https://pumas.gsfc.nasa.gov/files/06_07_99_1.doc+matching+birthdays+activity+nasa&cd=1&hl=en&ct=clnk&gl=us&client=safari

2 – 3 days 2 days

9 11 15

Model real-life situations using linear expressions, equations, and inequalities (A-1-H) (D-2-H) (P-5-H) (Grade 9) Use equivalent forms of equations and inequalities to solve real-life problems. (A-1-H) (Grade 9) Translate among tabular, graphical, and algebraic representations of functions

• Recognize and solve problems that can be modeled using a linear equation in one variable

• time/rate/distance problems • percentage increase or decrease problems • ratio and proportion problems

Photos of real-world equations http://www.digitalwish.com/dw/digitalwish/view_lesson_plans?id=1403 Finding our top speed – http://illuminations.nctm.org/LessonDetail.aspx?ID=L254

1-2 days 3 days



GLE #

GLEs


Differentiation


5 37 27

and real-life situations (A-3-H) (P-1-H) (P-2-H) (Grade 9) Write the equation of a line of best fit for a set of 2-variable real-life data presented in table or scatter plot form, with or without technology (A-2-H) (D-2-H) (Grade 10) Analyze real-life relationships that can be modeled by linear functions (P-1-H) (P-5-H) (Grade 9) Translate among tabular, graphical, and symbolic representations of patterns in real-life situations, with and without technology (P-2-H) (P-3-H) (A-3-H) (Grade 10)

Grandpa’s Social Security Activity – https://pumas.gsfc.nasa.gov/examples/index.php?id=44 When a ruler is too short activity - https://pumas.gsfc.nasa.gov/examples/index.php?id=96 Walk the Plank – http://illuminations.nctm.org/LessonDetail.aspx?id=L682

3 -4 days 2 days 3 days

37 27

Analyze real-life relationships that can be modeled by linear functions (P-1-H) (P-5-H) Translate among tabular, graphical, and symbolic representations of patterns in real-life situations, with and without technology (P-2-H) (P-3-H) (A-3-H)

• Recognize and solve problems that can be modeled using a system of two equations in two variables

• Recognize and solve problems that can be modeled using a system of two inequalities in two variables

Greenbacks or Green space Project - http://www.envisionprojects.org/cs/envision/view/env_p/88

10 days

27 24

Translate among tabular, graphical, and symbolic representations of patterns in real-life situations, with and without technology (P-2-H) (P-3-H) (A-3-H) (Grade 10) Model a given set of real-life data with a non-linear function (P-1-H) (P-5-H) (Grade 11-12)

• Recognize and solve problems that can be modeled using a quadratic equation • Motion of an object under the force of

gravity

A Real learning curve – http://www.edutopia.org/impact-academy-catapults-quadratic-equation

3 – 4 days

15 24

Translate among tabular, graphical, and algebraic representations of functions and real-life situations (A-3-H) (P-1-H) (P-2-H) (Grade 11-12) Model a given set of real-life data with a non-linear function (P-1-H) (P-5-H)

• Recognize and solve problems that can be modeled using an exponential function • Compound interest

Dream Job Activity - https://pumas.gsfc.nasa.gov/examples/index.php?id=40

2 days



GLE #

GLEs


Differentiation


(Grade 11-12) 1 26

Read, write, and perform basic operations on complex numbers (N-1-H) (N-5-H) (Grade 11-12) Generalize and represent patterns symbolically, with and without technology (P-1-H) (Grade 10)

• Makes reasonable estimates of arithmetic results without a calculator

• Distinguish relevant from irrelevant information, identifying missing information and either finding what is needed or making appropriate estimates

Right Place, Wrong Time Activity – https://pumas.gsfc.nasa.gov/examples/index.php?id=70

2 – 3 days

• Make connections between careers and mathematics

http://www.bls.gov/k12/index.htm http://thefunworks.edc.org/SPT--homeflash.php

2 – 3 days to explore careers and complete a report, technological or visual display

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