UNIT PLAN: LEARNERS/INSTRUCTIONAL PLAN
Unit Plans
i.
Learning goals
1. Classroom Description
Demographics: Age: 13 Years old (25) 14 Years old (30) 15 Years old (5) 16 Years old (1)
Race: Caucasian (51) African American (5) Hispanic (2) Asian (3) Other (0)
Gender: Male (39) Female (22)
SES: 21 students qualify for free or reduced lunch.
Grade Level: 8 Course: Math 3 Course Code: 1205070
Student’s skill level is below average to average. Students posses an understanding of basic math
operations.
The school environment is warm and inviting. The students are provided with many extra-curricular
activities. The community is generally safe, and is working class to middle class.
Students sit at individual desks in six rows. The walls have many posters and bulletin boards. The
students are taught using a white board and occasionally an overhead projector.
MA.8.A.6.4- Perform operations on real numbers (including integer exponents, radicals, percents,
scientific notation, absolute value, rational numbers, and irrational numbers) using multi-step and
real world problems.
ii. Assessment Plan
2. Screening – Design and administer a pretest addressing the specific student learning outcomes
for the Unit Plan. (worksheet, multiple-choice tests, quiz etc.)*
Data Analysis and Probability Pre-Test A bag contains 2 red cubes, 3 white cubes, and 5 blue cubes.
(1-4)1. What is the probability of randomly choosing a red cube?
2. What is the probability of randomly choosing a blue cube?
3. What are the odds of randomly choosing a white cube?
4. What are the odds of randomly choosing a red cube? Tell whether the events are
independent or dependent. Then find the probability.
(5-6) 5. Your teacher randomly calls on you to answer the question. She then randomly chooses
another student from the remaining 17 students.
6. You flip a coin and it lands heads up. You flip it again and it lands heads up. The state of
Florida wants to know if residents favor increasing the driving to 18. Tell whether the method
could result in a biased sample. Explain. (7-8)
7. Ask middle and high school students. 8. Ask every 25th person listed in the phone book.
3. Progress Monitoring – design and administer multiple assessments based on learning goals to
monitor student progress. Assessments should address higher and lower levels of thinking and
questioning skills.*
Formative Assessment
Day 1: p. 634-635 2-20 even 21-25 all This assessment includes 8 number based problems about
probability and odds. The assessment also includes 8 word problems about probability and
odds.
Day 2: 12.7 Practice B This assessment includes 10 number based problems about probability
and odds. The assessment also includes 10 word problems about probability and odds. This
assessment is more practice on probability and odds from day 1.
Day 3: p. 642 2-10 all 12, 14, 16 This assessment includes 6 number based problems about the
probability of dependent and independent events. The assessment also includes 8 word
problems about the probability of dependent and independent events. For the word problems
students must determine if the events are independent or dependent in order to solve them
properly.
Day 4: 12.8 Practice A This assessment includes 6 number based problems about the probability
of dependent and independent events. The assessment also includes 7 word problems about
the probability of dependent and independent events. For the word problems students must
determine if the events are independent or dependent in order to solve them properly. This
assessment is more practice on the probability of dependent and independent events from day
3.
Day 5: Hands-on Activities This assessment will be based on students� ability to work
cooperatively in their groups. The assessment will also be based upon the students� ability to
follow directions and show understanding of probability and odds.
Day 6: p. 645 1-8 all This assessment includes 4 problems dealing with biased and random
samples and biased and unbiased survey questions. Students will determine if each scenario is
biased or unbiased and explain why.
Day 7: p. 629 7, 23, 25, 27, 29; p. 635 11-19 odd; p. 642 5-15 odd; Samples review sheet This
assessment provides a test review over all the skills taught about data analysis and probability.
The problems include several real-world based word problems dealing with probability odds and
samples.
4. Outcome-based Assessment – Design and administer a post test addressing the specific learning
outcomes for the Unit Plan.*
Data Analysis and Probability Test
1. A piggy bank holds 3 quarters, 7 dimes, 5 nickels, and 2 pennies. If a coin is chosen at random,
what are the odds that it is worth less than 5 cents?
2. One of the 5 letters B, I, N, G, and O is picked when playing the game bingo. What is the
probability of picking the letters G or N? What are the odds of picking the letters G or N?
3. A vase contains 13 red marbles and 15 green marbles. What are the odds against picking a
green marble?
4. Find the odds in favor of the event described when rolling a number cube. Roll a number less
than 3. Events A and B are independent. Find the missing probability.
5. P(A)= ?
6. P(A)=0.9 P(B)=0.8 P(B)=0.25 P(A and B)=0.48 P(A and B)= ? Events A and B are dependent.
Find the missing probability.
7. P(A)= ?
8. P(A)=0.9 P(B given A)=0.8 P(B given A)= ? P(A and B)=0.72 P(A and B)=0.27 Tell whether the
situation describes independent or dependent events. Then answer the question.
9. Two urns contain green ball and black balls. Urn I contains 6 green and 6 black, and urn II
contains 4 green and 2 black. A ball is drawn from each urn. What is the probability that both
balls are green?
10. A drawer contains 2 black socks, 7green socks, and 4 blue socks. Without looking you draw
out a sock and then draw another without replacing the first sock. What is the probability that
the two socks you draw are grey? Tell whether each question could produce biased results.
11. Do you like French fries or tater tots best?
12. Would you rather stay at the magnificent Grand Hotel or the Motel 7? SGA wants to
determine a theme for Friday�s dress up day. The choices are: Favorite sports team, Tacky
Day, or Camo Day. Tell whether each sample could produce biased results.
13. SGA decides to poll members of the hunting club.
14. SGA decides to poll 5 random students from all first period classes. Bonus: What is the
probability of a flipping a quarter three times and it lands on heads all three times?
iii. Instructional Plan
5. Addresses all 5 areas of reading: phonemic awareness, phonics, vocabulary, fluency,
comprehension.
OR
Skill based unit (dependent on topic) addresses concept building, mechanics, and knowledge
application; (real-world problems, dependent on topic, etc.)*
Content Instruction Plan
Day 1- Probability and Odds Prior knowledge: Ability to reduce fractions. Basic mathematics
operations. The lesson will begin with me showing students a spinner with 4 even sections.
Three sections are red and the other is blue. Next, I�ll ask the students the percent chance of
landing on blue. On red? And the probability of not landing on red. Through discussion we will
conclude that: Probability = # of favored outcomes / # of possible outcomes. Using a die. Find
the probability of rolling a 3? Find the probability of rolling an odd? Spinner. We want blue. How
many favorable outcomes are possible? How many unfavorable outcomes are possible? What
are the odds of landing on blue? What are the odds of landing on red? Through discussion we
will conclude that: Odds = # of favorable outcomes / # of unfavorable outcomes. Discussion
questions: How are odds and probability different? How are they related? Given the probability
that an event occurs, determine the probability that the event will not occur. Ex. 1 70% Ex. 2
0.35 Ex. 3 2/7 Find the probability and odds of randomly choosing a green marble from the bag
of marbles described. Ex. 4 3 green and 6 red Ex. 5 7 green and 2 red
Day 2- Probability and Odds Prior knowledge: Ability to reduce fractions. Basic mathematics
operations. Review and practice from day 1. How do you represent probability? How do you
represent odds? Given probability, find probability against. Ex. 1 63% Ex. 2 9/11 Ex. 3 0.51 Ex. 4
The weather man says there is a 30% chance of rain tomorrow. What are the odds that it will
rain tomorrow? Ex. 5 25 Students were asked what their favorite meal is. What is the probability
that a randomly chosen student chose pizza? What are the odds that a randomly chosen student
chose hamburgers? What are the odds that a randomly chosen student did not choose pizza?
Day 3- Independent and Dependent Events Prior knowledge: Ability to solve for unknown
variables. Basic mathematics operations. What is independent? What is dependent? Through
discussion we will develop in formal definitions. Using poker chips, 2 blue, 3 red, and 5 white, in
a bag. I�ll pull out one chip replace it and draw another. Is this dependent or independent?
Then I�ll pull out one chip not replace it and draw another. Is this dependent or independent?
Then, as a class we will determine the probability of the independent event of pulling a red chip,
replacing it, and drawing a white chip. Then, as a class we will determine the probability of the
dependent event of pulling a red chip, not replacing it, and drawing a white chip. Why are they
different? Repeat a few times. Using dice. Is rolling dice two times a dependent event or
independent event? What is the probability of rolling a 1 and then rolling a 2? Repeat a few
times with other examples. Dependent or Independent? Ex. 1 You are beginning a 500-piece
puzzle. The first piece you randomly choose is a corner. The next piece you randomly choose is a
corner. Ex. 2 You spin a spinner on a board game and it lands on �spin again.� On the
second spin you land on �spin again.� Given probabilities find the missing probability.
Events are independent. Events are Dependent. Ex. 3 P(A)=0.3 Ex. 4 P(A)=1/6 Ex. 5 P(A)=0.6 Ex. 6
P(A)=0.9 P(B)=0.1 P(B)=2/5 P(B given A)=0.4 P(B given A)=? P(A and B)= ? P(A and B)= ? P(A and
B)= ? P(A and B)=0.09 Ex. 7 A jar contains 5 oatmeal cookies, 6 sugar cookies, 8 frosted cookies,
and 9 chocolate cookies. You choose a cookie randomly, keep it and randomly choose another.
What is the probability that you choose a frosted cookie, then a chocolate cookie?
Day 4- Independent and Dependent Events Prior knowledge: Ability to solve for unknown
variables. Basic mathematics operations. Review and more practice from day 3. When one event
affects the outcome of another, the two events are ____________. When one event does not
affect the outcome of another, the two events are ____________. Find the missing probability.
Ex. 1 P(A)=0.2 Ex. 2 P(A)= ? P(B)=0.9 P(B)=0.5 P(A and B)= ? P(A and B)=0.3 Ex. 3 Each day, the
person who gets the lucky tray at lunch gets a free snack. 127 people buy lunch on Wednesday
and 134 buy lunch on Thursday. What is the probability that you win both days?
Day 5- Hands-on Probability and Odds Prior knowledge- Understanding of probability and odds,
basic math operations. Students will be put into pairs. Students will complete 3 activities. CardsStudents will cut a piece of paper into 8 equal sections. They will number them 1-8. One person
in the group is represented by the card 1 and the other member is represented by the card 2.
Students will then shuffle the cards and choose 2 randomly and record the results. Then
students will repeat for a total of 10 trials. Next, we will compile the class results. Then we will
calculate the experimental probability. And then the actual probability. Compare the two. If we
did 100 trials each would the experimental probability be more accurate? Explain why? Poker
chips- Each pair receives a bag with 10 random red, white, and blue poker chips inside. Don�t
look inside. Students will then record the results of 50 trials of choosing a random poker chip,
replacing it and randomly drawing another. Students will then calculate the experimental
probability for each color. Then using this information, students will guess the number of each
color contained in the bag. Next, students will check their guess and find the actual probabilities.
Dice- Now the pairs will be split into 3 groups. Each pair will make a chart for favorable
outcomes over unfavorable outcomes. One group is trying for a 1 or 2, another is trying for a 3,
and the other is trying for an odd number. After many trials are run the groups compile their
results and compare the experimental odds with the actual odds they calculate.
Day 6- Samples and Data Analysis Prior knowledge: Understanding biased and unbiased. What is
population? Develop an informal definition through discussion. What is a sample? Develop an
informal definition through discussion. What is a random? Develop an informal definition
through discussion. What is a biased? Develop an informal definition through discussion. Next
we will relate these definitions to complete the following examples. Ex. 1 The student council
wants students to help decide on a theme for a costume dance. Students can choose one of the
council�s three theme ideas: movies, famous historical figures, sports and games. Surveying
all the students would take too long, so a sample will be surveyed. Tell whether the survey
method could produce biased results. Explain. a. Survey members of the movie club. b. Survey
students as they enter the school. c. Survey students on the football team. Ex. 2 Tell whether
the question could produce biased results. Explain. a. Do you support the unfair policy of
requiring students to do a time-consuming community project? b. Do you like our new apple-nut
yogurt flavor, now on sale in stores everywhere?
Day 7- Test Review Day 8- Test
6. Differentiated Instruction: List specific activities, strategies or techniques used to provide
instruction for diverse students, including ESOL students. Please list this information here even if
you wrote it into the plans above. *
2 students are learning disabled 1 student is classified as homeless because they are sharing
other�s home due to hardships Modifications for these students include preferential seating,
shortened assignments, extended time for tests and assignments, and allowed to retake failed tests.
UNIT PLAN: ANALYSIS AND REFLECTION
iv. Analysis of student learning
1. Analyze the effectiveness of your instruction using the Pre/Post test. Explain the results of your
graph. What conclusions can you reach about your students and your teaching?*
The graph shows the results of the Pre-test in blue alongside the results of the Post-test in red. The
grades for the Pre-test were 8 D’s and 53 F’s. After the unit was taught, the scores on the Post-test
were 18 A’s, 13 B’s, 19 C’s, 7 D’s, and 2 F’s. All students improved from before the unit to after the
unit as shown by Pre- and Post-test scores. Students also displayed learning gains by the
observations I made of the continuous assessment of practice assignments and questioning.
Learning gains were also observed as student applied their knowledge of Probability and Odds to
the hands-on activities that required this knowledge to complete. Through observation and
reviewing of the Post-Test scores students showed significant learning gains as a result of the unit
being taught.
2. Record the results on a chart or table.*
60
50
40
30
Pre-Test
20
Post-Test
10
0
A
B
C
D
F
v. Reflection and self-assessment
1. Reflect on the effectiveness of your Unit Plan. Why or why not was your plan effective? *
I feel the plan was effective because of the observed and quantitative learning gains that the
students displayed. I was well prepared for each day with the right materials and knowledge of what
is being taught. I feel that my preparedness enhanced the effectiveness of the lesson. All of the
formative assessment materials and activities were appropriate in providing practice for students.
This unit, I feel, was clearer in describing the flow of the lesson as it allows for student participation
than my first unit. This unit also included better prepared outlines of modifications for differentiated
instruction that allowed me to implement them more effectively. I also feel that the Post-Test
assessment was better prepared for this unit and allowed for the test to effectively measure student
learning gains.
2. Reflect on your teaching effectiveness. What are your teaching strengths? What can you change
to enhance student learning? What would you do differently? *
I feel that the teaching was effective because of the observed and quantitative improvements in
students’ skills from the Pre-test to the Post-test. After the unit, students understand the necessary
vocabulary and possess the skills needed to evaluate probability, odds, and other data analysis
problems. I feel that my teaching strengths include a mastery of the content, sufficient
preparedness, and the ability to answer questions effectively. I feel that my understanding of
mathematics is more than sufficient for teaching at this level. I also feel that my preparation before
teaching the unit makes my teaching effective because I am able to focus more on responding to
student needs rather than scrambling for what to do next. My effectiveness at answering students’
questions is effective because I can explain again or explain in a different way so that students can
understand. Time management is an area that I have struggled with for some time. I feel that I have
improved my time management of the classroom as I have become more familiar with the settings. I
feel that this area could still improve, but has improved greatly since the first unit. To improve my
time management I will observe other teachers to learn some of the ways they manage time.