Upload
doandien
View
215
Download
0
Embed Size (px)
Citation preview
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
5
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.
6
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
7
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)
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)
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)
The student will demonstrate an understanding of the mathematical processes and tools used in problem solving.(SE 8.14, 8.15, 8.16)
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.
9
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
10
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.
11
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.
12
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.
13
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.
14
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.
.
15
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.
16
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
17
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.
20
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.
22
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:
23
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
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 9.
24
The warm-up questions are similar to the assessment questionsfor the objective.
Second 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.
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.
26
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?
28
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
The problems from the warm-up do not necessarily correlate to the lesson taught that day
30
The warm-up questions are a review for Objective 10.
The warm-up questions are similar to the assessment questionsfor the objective.
Fourth 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
31
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
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.
33
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.
34
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.
35
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
Temperatur
e
36
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?
37
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.
38
39