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Ninth Grade Mathematics:Intervention Materials Utilizing Personal Response Systems

by

TRACI KIMBERLY STURGEON

December 2010

A Project Submittedin Partial Fulfillment of

the Requirements for Degree of

MASTER OF SCIENCE

The Graduate Mathematics ProgramCurriculum Content Option

Department of Mathematics and StatisticsTexas A&M University-Corpus Christi

APPROVED:_______________________________Date________________Dr. Jose Giraldo, Chair

_______________________________Dr. Tim Wells, Member

_______________________________Dr. Elaine Young, Member

Style: APA

ABSTRACT

The ninth-grade Texas Assessment of Knowledge and Skills (TAKS) exam

for mathematics is an integral part of each student’s high school career since it

can determine their class schedule for the following year. However, 33% of the

ninth-grade students failed this exam during the 2008-2009 school year (TEA,

2010). The test is based on the objectives from the Texas Essential Knowledge

and Skills (TEKS) taught in Algebra I and in eighth-grade mathematics. The

objectives that are most frequently not met by all students are those taken from

the eighth-grade mathematics TEKS.

Across the state and locally, students regularly fail this test by only a few

incorrect answers. The purpose of this project is to write intervention materials

addressing the objectives identified with the lowest performance that will help

improve student scores on the ninth-grade TAKS test for mathematics. The

materials will incorporate the use of interactive response systems or clickers to

engage students and to help the teacher identify misconceptions and gaps in

student learning.

2

TABLE OF CONTENTS

Abstract………………………………………………………………………….2

List of Tables……………………………………………………………………4

Introduction……………………………………………………………………..5

Literature Review………………………………………………………………9

Results………………………………………………………………………….12

Summary……………………………………………………………………….15

References.…………………………………………….………………………16

Appendix A – Objective 8……………………………………………………..18

Appendix B – Objective 9……………………………………………………..24

Appendix C – Objective 10……………………………………………………30

3

LIST OF TABLES

Table1: Percent of Ninth Grade Students Who Answered the Objective Correctly……………………………………………………………. 7

Table 2: High School Mathematics Objectives with Student Expectations…………………………………………………………………………8

4

INTRODUCTION

In a traditional mathematics classroom, a great number of students are

passive in their learning environment, which is supported by the class setting and

activities done in the classroom. In a typical class setting the students are seated

facing the chalk/white board while the teacher presents the lesson. In the

author’s experience, the teacher stresses major points and concepts while most

students are diligently writing down everything that is said or are simply taking

detailed notes. As a way to assess their understanding of the concepts

presented, the teacher asks leading questions, but consistently only a few

students participate by volunteering their answers. This is the main opportunity

the teacher has to provide feedback to the students about the concepts

discussed. However, this feedback is based only on the answers from the

students who participated with their answers, which means that it becomes more

difficult for the teacher to determine the extent of learning for students who are

not participating.

As a follow up assessment after the teacher completes the lesson, the

teacher assigns a set of problems for homework that resembles the concepts just

conveyed to the students. The students, whether they learned the concepts or

not, then work independently on their attempts to complete the day’s assignment,

which is graded the next class day. Sometimes the teacher has time to look at

the students’ answers to determine if they learned those concepts. However, a

quick formative assessment would improve the whole learning process by

allowing the teacher to evaluate the learning of concepts at anytime during the

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lesson, and immediately redirect or correct any misconceptions, especially before

any high stakes test.

In Texas high schools, students are required to take high-stakes tests

(TAKS) that will eventually determine if they will graduate from high school. Even

though the students are not required to pass the ninth grade TAKS tests in order

to graduate, their test scores are still an important factor in determining their

class placement for the following school year. If a student fails the ninth grade

TAKS test, they could be placed in a TAKS tutorials class instead of an elective

of their choice, such as band or athletics. With the state increasing the number of

mathematics and science credits needed to graduate, there is little room on a

student’s schedule for an extra class such as TAKS tutorials. TAKS tutorials

would be considered a local credit and does not count as one of the four

mathematics courses required by the state of Texas for graduation.

The ninth grade mathematics TAKS test includes ten objectives, five of

which correspond to material taught in the eighth grade (see Table 1). Of these

five objectives, objectives 8, 9 and 10 are most often not mastered by students in

a local district and across the state.

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Objective2007 2008 2009State State StateLocal Local Local

Objective 1-The student will discuss functional relationships in a variety of ways.

61% 61% 65%60% 63% 66%

Objective 2- The student will demonstrate an understanding of the properties and attributes of functions.

65% 65% 70%

70% 68% 71%Objective 3-The student will demonstrate an understanding of linear functions.

65% 65% 69%68% 66% 73%

Objective 4- The student will formulate and use linear equations and inequalities.

62% 65% 67%63% 67% 66%

Objective 5- The student will demonstrate an understanding of quadratic and other nonlinear functions.

70% 68% 72%78% 78% 75%

Objective 6- The student will demonstrate an understanding of geometric relationships and spatial reasoning.

73% 68% 71%

73% 70% 75%Objective 7- The student will demonstrate an understanding of two- and three- dimensional representations of geometric relationships and shapes.

64% 67% 72%

65% 70% 73%Objective 8- The student will demonstrate an understanding of the concepts and uses of measurement and similarity.

57% 57% 62%56% 55% 63%

Objective 9- The student will demonstrate an understanding of percents, proportional relationships, probability, and statistics in application problems.

64% 65% 64%

61% 64% 68%Objective 10- The student will demonstrate an understanding of the mathematical processes and tools used in problem solving.

62% 64% 65%

60% 70% 65%Table1: Percent of Ninth Grade Students Who

Answered the Objective Correctly

The eighth grade TAKS objectives are not taught in the ninth-grade

curriculum, which may be a possible reason for low performance. In the ninth

grade mathematics class, Objective 6 is reviewed when the class is discussing

the coordinate plane and linear functions. Objective 7 is one of the higher

performing objectives not only on the ninth-grade TAKS test, but also on the

eighth-grade TAKS test since it is not as abstract as the others. The objectives

with the lowest performance are Objectives 8, 9, and 10. A proposed resolution is

to tie the concepts included in these objectives to activities in the ninth-grade

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mathematics curriculum. Regular in-depth reviews and understanding of common

errors is expected to increase student performance in the TAKS test, taken in

late April each year. The interventions in this project will target the three widely-

missed objectives that are taught in the eighth grade and tested not only in the

ninth grade but also in subsequent grades and are, ultimately, included on the

Exit Level TAKS test. Table 2 shows how Objective 8, 9, and 10 are the same for

the ninth, tenth, and EXIT level exams. Except for objective 8 in the EXIT level

exam, the student expectation is also the same. The student expectation (SE) is

when the student is expected to know that knowledge.

9th Grade 10th Grade Exit Level

Obj. 8

The student will demonstrate an understanding of the concepts and uses of measurement and similarity (SE 8.8, 8.9, 8.10)

The student will demonstrate an understanding of the concepts and uses of measurement and similarity (SE 8.8, 8.9, 8.10)

The student will demonstrate an understanding of the concepts and uses of measurement and similarity (SE G.8, G.11)

Obj. 9

The student will demonstrate an understanding of percents, proportional relationships and statistics in application problems (SE 8.1, 8.3, 8.11, 8.12, 8.13)



Obj. 10

The student will demonstrate an understanding of the mathematical processes and tools used in problem solving.(SE 8.14, 8.15, 8.16)



Table 2: High School Mathematics Objectives with Student Expectations

8

To reach the main goal of improving student test scores in the ninth grade,

this project will produce intervention materials to review the key concepts

involved in those three objectives and questions for assessment purposes that

will be carried out using the response systems or clickers. Clickers will be used to

facilitate reviews, warm-up activities and assessment activities that will engage

students while providing feedback about student learning and gaps in achieving

individual objectives. The principles guiding this project are:

1. The intervention materials will concentrate on the three objectives with the highest failing rate.

2. The materials used should actively engage the students, foster their participation, and lead to meeting the objectives to be tested.

3. The assessment questions will be created based on existing statistical information about the mentioned objectives, so that the statistical analysis can provide feedback on weak points that need to be revisited.

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LITERATURE REVIEW

The Principles and Standards for School Mathematics (NCTM, 2000) state

that technology is an essential tool for teaching and learning mathematics. For

years mathematics teachers have considered the use of calculators as sufficient

technology to keep the students engaged. However, the use of response

systems (hereafter referred to as “clickers”) in the classroom provides itemized

analysis of the questions used to determine the level of understanding of the

concepts tested as well as possible misunderstandings. This information may be

used to modify or create new activities leading to correction of identified

problems. The teacher is able to determine the errors that are taking place and

the misconceptions or gaps that students might have.

The clickers that were used in this project are similar to that of a cell

phone. They have an LCD screen with alpha/numeric keys. A receiver is

attached to the teacher’s computer that reads what the students have keyed in.

The answers can be multiple choice, numeric, or a single word or phrase. The

program immediately identifies which clicker has answered and what percentage

of students obtained the correct answer, providing the teacher with immediate

feedback as well as item analysis. Answers are completely anonymous to other

students in the classroom, but each clicker is registered to the student by a

number so the teacher may keep records on the progress of each student.

Clickers allow students to give input without fear of public humiliation or without

more vocal students dominating the discussion (Martyn, 2007). D’Inverno, Davis

and White (2003) documented that clickers displayed the progress of

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comprehension level during the lectures for not only the teacher but also for the

student. This in returned guaranteed that the key concepts where not only

repeated by the students but that knowledge was gained.

D’Inverno, Davis and White (2003) explained that clickers allowed

students to “take a breather and to refocus” (p. 165). Even if students are taking

notes, the teacher may question how much of it is actually being learned during

this process. The use of clickers made lessons more student-centered and

supported the development of a better learning environment.

King and Robinson (2009) used clickers with engineering students in a

university mathematics classroom and described a chain reaction between the

teacher and the student. The students were not only interacting with the

instructor but also with their neighbors before, during, and after the voting

process. One of the engineering students in the study said the clickers “keep

people awake and attentive during the lectures and stop boredom” (p. 4). The

researchers also noted that it gave students an understanding of not only what

the learning gap was but also an idea on how to close the gap.

Bode and colleagues (2009) reported that 70.1% of students stated they

became more aware of their own misunderstandings, 76.1% of students found

that questions asked during clicker sessions helped them to understand what

was expected of them in class, 84.8% agreed that using clickers helped teachers

to become more aware of student difficulties with the subject matter, and only

9.2% responded that they remembered less after a class with the clickers than

other classes.

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Clicker technology can compensate for the passive, one-way

communication inherent in lecturing as well as the difficulties students experience

in maintaining sustained concentration. When used correctly, students are likely

to be more interactive in the classroom. Teachers must plan ahead,

communicate with students on what to expect before the clickers are used,

spend time training the students on the clickers, keep a positive attitude, and

encourage classroom communication between both the teacher and the other

students (Caldwell, 2007). Mistretta (2005) reported that the first step for

integrating any technology into the classrooms is to prepare the teachers. Stiff

(2006) explained that all students can learn if their teachers are skilled and teach

the material in a variety of ways.

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RESULTS

Objective 8 (the student will demonstrate an understanding of the

concepts and uses of measurement and similarity), Objective 9 (the student will

demonstrate an understanding of percents, proportional relationships, probability,

and statistics in application problems), and Objective 10 (the student will

demonstrate an understanding of the mathematical processes and tools used in

problems solving) are only taught in the eighth grade but are tested on the ninth

grade, tenth grade and Exit level TAKS tests. Research shows that they are the

lower scored objectives on the ninth grade TAKS test because of only being

taught in eighth grade. This project produced a set of warm-up problems, an

activity, and an assessment for each of these ninth grade objectives. The goal of

the project was to address and review the learning gaps that might exist through

the warm-up problems, the activity would aide in clearing up the misconceptions

and the assessments will determine if the teacher was successful.

The ninth-grade mathematics curriculum was reviewed to identify suitable

places to link objectives to the activities that were created. The project begins

with a timeline that illustrates what lesson is being taught on a given day, what

warm-up questions are done that day, and when is an appropriate time to do the

activity and assessment during the grading period. The author’s district is

revolves around six grading periods, so the timelines are formatted to match. If a

teacher in another district is using these warm-ups, activities, and assessments,

the timeline may have to be adjusted.

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Each objective has a set of 20 warm-up questions, to review and work on

during the grading period. The students will spend about 5 to 10 minutes at the

beginning of each period working on these questions and discussing them with

the teacher.

One activity per objective was created that is used to practice the

objectives in consideration. Two days were allowed in each timeline for the

activities. A teacher in another district may choose to only spend one day on the

activity and have the students finish up the activity outside of the classroom.

After the activity and warm-ups have been completed, an assessment will

be given. A set of 20 assessment questions was created for each of the three

objectives. The assessments closely resemble the warm-up questions. The

assessment questions verify whether the gaps identified in previous data have

been fixed.

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SUMMARY

The ninth-grade TAKS test consists of ten objectives that are tested.

Objective 8, objective 9, and objective 10 are only taught in the eighth grade, but

continue to be tested through the Exit Level TAKS test. This projected created

warm-up problems, activities and assessments to review these objectives and

clear-up any misconceptions there might be.

As a ninth-grade teacher, I determined a timeline that displays where

these warm-up questions, activities, and assessments will be utilized. Since

these objectives are also tested in the tenth grade and Exit Level TAKS test,

those teachers can also use these items. This format can also be adapted to

other objectives tested on all the TAKS tests. Eighth-grade teachers may also

use the warm-ups, activities, and assessments as part of their review after they

are taught in the classroom and before the eighth- grade TAKS test is given.

.

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REFERENCE

Beal, C. R., Lee, L. Q., & Lee, H. (2008). Mathematics motivation and achievement as predictors of high school students' guessing and help-seeking with instructional software. Journal of Computer Assisted Learning, 24(6). 507-514.

Bode, M., Drane, D., Ben-David Kolikant, Y., & Schuller, M. (2009). A clicker approach to teaching calculus. Notices of the AMS, 56(2), 253-256.

Caldwell, J. E. (2007). Clickers in the large classroom: Current research and best practice tips. Life Sciences Education, Retrieved January 21, 2010, from www.lifescied.org/cgi/content/fill/6/1/9

Cline, K.S. (2006). Classroom voting in mathematics. Mathematics Teacher, 100(2), 100-104.

d'Inverno, R., Davis, H., & White, S. (2003). Using a personal response system for promoting student interaction. Teaching Mathematics and Its Applications, 22(4), 163-169.

Joshi, R.N. (1995). Why our students fail math achievement. Education, 116. Retrieved February 16, 2010, from http://www.questia.com/

King, S.O. & Robinson, C.L. (2009, October). Formative teaching: A conversational framework for evaluating the impact of response technology on student experience, engagement and achievement. Paper presented at the 39th ASEE/IEEE Frontiers in Education Conference, San Antonio, Texas.

Kloosterman, P. (1997). Assessing student motivation in high school mathematics. Paper presented at the annual meeting of the American Educational Research, Chicago, Illinois.

Martyn, M. (2007). Clickers in the classroom: An active learning approach.EDUCAUSE Quarterly, 30. Retrieved January 21, 2010 from http://www.educause.edu/EDUCAUSE+Quarterly/EDUCAUSEQuarterlyMagazineVolum/ClickersintheClassroomAnActive/157458

Mistretta, R. (2005). Integrating technology into the mathematics classroom: The role of teacher preparation programs. The Mathematics Educator, 15(1), 18-24.

National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.

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Texas Education Agency (TEA). (2007). TAKS Information Booklet Mathematics Grade 9, Retrieved March 5, 2010, from http://ritter.tea.state.tx.us/student.assessment/taks/booklets/math_g9.pdf

Texas Education Agency. (2009). Statewide Item Analysis Reports. Retrieved March 5, 2010, from http://tea.state.tx.us

Thompson, L. (2006, August). Why do teens fail math? "It ain't the kids". The Seattle Times, Retrieved February 16, 2010, from http://seattletimes.nwsource.com/html/education/2003168064_mathconference02n.html

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APPENDIX A

Timeline - Algebra I First Six Weeks Objective 8 - Warm-up, Activity, and Assessment

Topic

Problems from Warm-

up

Number of

Days

First Day Information conversion chart 1I. Rational Numbers

a.identifying and relating real numbers with absolute value 1, 2 1

b. operations with real numbers 3, 4 1c. order of operations 5, 6 1d. order of operations with exponents 7, 8 1 Review 9, 10 1 Test 1II. Variablesa. substituting values (introduce formula chart) 11, 12 2b. properties with emphasis on Distributive Property 13, 14 1c. combining like terms 15, 16 1d. translations 17, 18 2 Review 19, 20 1 Test 1 Activity: Sorting out Solids (Objective 8) 2 Assessment: Objective 8 1III. Equationsa. adding and subtracting 1b. multiplying and dividing 1c. multiple steps 2d. tricks for fractions and decimals 1e. inequalities with one step 1f. multiple steps inequalities 1 Review 1 Test 1 BENCHMARK – NOTEBOOKS 1 Discuss Benchmark 1 TOTAL DAYS 29

The problems from the warm-up do not necessarily correlate to the lesson taught that day

The warm-up questions are a review for Objective 8.

The warm-up questions are similar to the assessment questionsfor the objective.

18

First Six Weeks – Timeline Explanation

When the tardy bell rings, students enter the classroom, look up

at the assignment board and are reminded of the material that the

class will be working on that day. The timeline on the assignment

board is a chronological listing of the topics that will be discussed, the

number of days that will be spent on the topics and the warm-up

problems that students will work on each day at the beginning of class.

The warm-up problems do not necessarily correspond to the lesson

that is taught that day, since they are problems that review the eighth

grade topics that are tested on the ninth grade Math TAKS Test but are

only taught in the eighth grade.

All of the students have their warm-up packets in their

notebooks, so the assignment board simply instructs the students on

the two (2) problems they will work on each day. Students will be

allowed the first five (5) minutes of class to work on and answer the

two (2) problems using clickers. The teacher will be able to quickly look

at the board to see if everyone has answered. For approximately five

(5) minutes, the teacher will discuss the two (2) warm-up problems for

the day, answer student questions, and clear-up any misconceptions

about the two problems. The remainder of the period will be used to

teach the lesson of the day.

After all of the twenty (20) warm-up problems have been

completed in about a two week period, students will work on an

19

activity for two days that reinforces the concepts that were discussed

in relation to the warm-up problems. After the activity is completed,

there will be an assessment using clickers. The assessment will

resemble the warm-up problems that were discussed during the first

six weeks and will provide feedback to the teacher on student

understanding of the eighth grade topics.

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Objective 8 ActivitySORTING OUT SOLIDS

GOALIn this activity the students will associate objects commonly used in daily life to geometric solids. They will identify and calculate the necessary measurements to estimate attributes such as surface area and volume of prisms, pyramids, cylinders, cones and spheres using concrete models and nets.

EXPECTATIONSThe students will demonstrate an understanding of the concepts of surface area and volume and uses of measurement and similarity with these geometric solids.

The student is expected to:8.8A find lateral and total surface area of prisms, pyramids, and cylinders using concrete models and nets (two-dimensional models).

8.8B connect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume of these objects.

8.8C estimate measurements and use formulas to solve application problems involving lateral and total surface area and volume.

MATERIALS Objects from daily life with the shape similar to geometric solids

(cube, rectangular prism, pyramid, cylinder, cone, sphere) Metric ruler (centimeters) Poster board Colored pencils, crayons, markers (anything used to design your

poster board)

PROCEDURE1. The day before the activity, form groups of two or three students.

2. Each group will bring to class a three-dimensional figure, such as a cube, rectangular prism, pyramid, cylinder, cone, or sphere. These solids should have been discussed prior to the day of the activity. Different groups will have to choose different solids. In case there are more than 6 groups, solids will be repeated.

21

3. The title of the poster board is the name of the figure for your group.

4. Divide the part of the poster board below the title area into four sections. Label the sections as indicated.

a) 3D – Representation

b) Net of the Solid

c) For the solid, assigned to your group, include the formulas and do the corresponding calculations with proper units:

o Lateral Surface Areao Total Surface Areao Volume

d) Characteristics: (This is not included in the objective, but a good opportunity to review vocabulary used on the TAKS test.)

o Number of Verticeso Number of Edgeso Number of Faces

5. Draw a 3-dimensional representation on the poster board.

6. Draw a net of the solid, using the colored pencils to shade the faces with equal areas.

7. Measure the necessary information of the solid to the nearest tenth of a centimeter and label the 3D representation and its net accordingly.

8. Write the formulas that are necessary to find the lateral surface area, the total surface area, and the volume for the solid. In front of each formula indicate the corresponding values (with units) needed to do the calculation. Calculate the lateral surface area, total surface area, and volume of the solid, including the correct units.

9. Identify the number of vertices, edges, and faces of the solid.

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TITLE3D Representation Net of Solid

Formulas and Calculations

Formulas

Measurements

Needed (units)

Calculations

(units)Lateral Surface

AreaTotal

Surface Area

Volume

Characteristics

Number of Vertices:

Number of Edges:

Number of Faces:

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APPENDIX BTimeline - Algebra I Second Six Weeks

Objective 9 - Warm-up, Activity, and Assessment

Topic

Problems from

Warm-up

Number of Days

I. Equations and Inequalitiesa. compound inequalities 1, 2 1b. ratios/proportions/similar figures 3, 4 1c. percents 5, 6 1d. writing and solving equations and inequalities 7, 8 2 Review 9, 10 1 Test 1 Activity: Catch the Rainbow (Objective 9) 2II. Linear Equations/Functionsa. literal equations 11, 12 1b. independent and dependent quantities 13, 14 1c. coordinate plane 15, 16 1 vocabulary/plotting ordered pairs domain and range sorting d. functions 17, 18 1 representing data determining if a set of ordered pairs is a function determining if a continuous graph is a function find domain and range of graph and/or data e. evaluating functions 19, 20 1 Review 1 Test 1 Assessment: Objective 9 1

III. Graphing Linear Equationsa. graphing lines using a table of values 1b. x and y - intercepts 1c. finding slope - algebraically and describe 1d. graphing a line with a point and a slope 1 Review 1 Test 1 BENCHMARK - NOTEBOOKS 1 Discuss Benchmark 1 TOTAL DAYS 32



24


Second Six Weeks – Timeline Explanation





















25

After the first test there will be an activity for two days that

reinforces the concepts that were discussed. After the activity is

completed, the class will continue discussing the remainder of the

warm-up questions. There will be an assessment, using the clickers.

The assessment will resemble the warm-up problems that were

discussed during the second six weeks and will provide feedback to the

teacher on student understanding of the eighth grade topics.

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Objective 9 ActivityCatch the Rainbow

Goal In this activity the student will be able to evaluate experimental probability and theoretical probability, and distinguish between them.

Expectations The students will demonstrate an understanding of experimental probability and theoretical probability and use these probabilities for prediction.

The student is expected to:8.11A find the probabilities of dependent and independent events.

8.11B use theoretical probabilities and experimental results to make predictions and decisions.

MaterialsStyrofoam cupsSkittles (36 yellow, 9 red, 18 purple, 9 green,18 orange)

ProcedureThe activity will be done in groups of 3 to 5 students. Proceed to form the groups.

A. Experimental Probability:

1. Put the Skittles into a cup. Shake up the Skittles and pick out 45 Skittles without looking. Record the results below.

Sample Yellow Red Purple Green Orange#1

2. Complete the table below for the experimental probability of each color. A total of 100 Skittles should have been sampled.

27

Experimental Probabilities of Each ColorColor Fraction Decimal Percent YellowRed

PurpleGreen

Orange

B. Theoretical probabilities:

Given that a collection of Skittles contains: 36 yellow 9 red 18 purple 9 green 18 orange

1. Complete the tableTheoretical Probabilities of Each Color

Color Fraction Decimal PercentYellowRed

PurpleGreen

Orange

2. If 45 Skittles were randomly selected from the collection, predict how many of each color would be expected. Round to the nearest Skittle.

3. Compare the answer to question 2 on theoretical probability to the answer above on experimental probability with 45 Skittles.

4. What is the probability of randomly selecting a red Skittle or a purple Skittle?

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5. What is the probability of randomly selecting a red Skittle and then a purple Skittle with replacement? What is the probability of randomly selecting a red Skittle and then a purple Skittle without replacement?

6. In the table below record the combined class data for Part A. Find the probability of each color. How do these compare to the theoretical probabilities in Part B?

Theoretical Probabilities of Each ColorColor Class Count Fraction Decimal PercentYellowRed

PurpleGreen

Orange

7. If 45 Skittles were randomly selected as a sample, predict how many of each color would be expected using the classroom sample data. Round to the nearest Skittle. How does this compare to theoretical probability in question 2? Are they the same? Why or why not?

29

APPENDIX CTimeline - Algebra I Fourth Six Weeks

Objective 10 - Warm-up, Activity, and Assessment

Topic

Problems from

Warm-up

Number of Days

I. Systems of Linear Equations and Inequalities a. graphing method and special systems 1,2 1b. combination method 3, 4 2c. writing linear systems 5, 6 2d. graphing systems of linear inequalities 7, 8 2 Review 9, 10 1 Test 1II. Polynomialsa. rules of exponents 11, 12 2b. naming, classifying and determining degree 13, 14 1c. adding and subtracting polynomials 15, 16 4d. multiplying polynomials 17, 18 2e. polynomial operations with geometry 19, 20 1 Review 1 Test 1 Activity: Sorting out Solids (Objective 10) 1 Assessment: Objective 10 1III. Factoringa. adding and subtracting 1b. GCF, factoring out monomials 1c. factoring trinomials 3d. solving quadratics by factoring 1 Review 1 Test 1 BENCHMARK - NOTEBOOKS 1 Discuss Benchmark 1 TOTAL DAYS 33


30



Fourth Six Weeks – Timeline Explanation



















31



After all of the twenty (20) warm-up problems have been

completed in about a two week period, students will work on an

activity for two days that reinforces the concepts that were discussed

in relation to the warm-up problems. After the activity is completed,

there will be an assessment using clickers. The assessment will

resemble the warm-up problems that were discussed during the fourth

six weeks and will provide feedback to the teacher on student

understanding of the eighth grade topics.

32

Objective 10 ActivityProblem Solving in Centers

Goal The students will demonstrate an understanding of the mathematical processes and tools used in problem solving.

Expectations The students will demonstrate an understanding of collecting data, modeling the data on a scatter plot and predict the population from the data collected.

The student is expected to:8.14A identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics.

8.14B use a problem-solving model that incorporates understanding the problem, make a plan, carrying out the plan, and evaluating the solution for reasonableness.

8.14C select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.

8.15A communicate mathematical ideas using language, efficient tools appropriate units and graphical, numerical, physical, or algebraic mathematical models.

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8.16A make conjectures from patterns or sets of examples and nonexamples.

MaterialsGraph paperGraphing calculatorTimer

Procedure1. There will be 4 centers separated in the classroom.

Center A: Problem solving with graphs.Center B: Problem solving with tables.Center C: Making conjectures and checking.Center D: Changes in scale

2. Proceed to form 4 groups with equal members.

3. Each group will start at a different center. The groups will be allowed 10 minutes at each center to discuss and solve both problems.

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Center A: Problem solving with graphs

1. Determine a story plot that describes Lynne’s Car trip. Include as many details in the story as possible.

2. Determine a story plot that describes both graphs. Include as many details in the story as possible.

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A.

B.

Time Time

Center B: Problem solving with tables

1. The table shows the number of E. coli bacteria in a Petri-dish.

Hours Bacteria0 601 1202 2403 480

With the trend shown in the table, predict the number of bacteria the Petri-dish contains after 10 hours.

Estimate the time when there will be around 25,000 bacteria in the dish.

2. A-1 Rentals charges a $50 set-up fee and $15 per hour to rent a moon-jump. Kiddy Rentals does not charge a set-up fee, but does charge $25 per hour to rent a moon-jump. Using a table, determine

Temperaturee

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e

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how many hours are needed for A-1 rentals to be cheaper than Kiddy Rentals.

Center C: Making conjectures and checking

1. Alex is building a set of mosaics that follow the pattern below. How many tiles will he need to build the 10th mosaic?

2. A student stated that in any list of numbers the range can never be greater than the mean, median or mode. Is this a true or false stamen? Why?

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Center D: Changes in scale

1. Phil’s mom has asked him to put the Christmas balls used to decorate the Christmas tree into a bin for storage. Each ball is 3 inches in diameter and fits snuggly into the bin to keep from breaking. The bin measures 2 feet by 3 feet by 1 foot. How many bins is Phil going to need if there are 300 balls to store?

2. A model airplane, that grandpa Stan is working on for Charlie’s birthday present, measures 12 inches from nose to tail. The actual airplane is 180 feet long, with a 120 feet wingspan and 25 feet tall from the ground to the top of the plane. Grandpa Stan wants to mail it to Charlie, but needs your help determining the dimensions of the smallest box that can be used to ship the package.

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