Download 7th Math Genetics and Bioengineering

Unit Title: Genetics & Bioengineering
10 Days
Algebra
Lesson Plan
2013-2014 School Year
7th Grade Mathematics Teacher
Grade:
7th Grade Mathematics
Lesson Title:
Genotypes vs. Phenotypes
STRANDS
Probability
Permutations
Combinations
LESSON OVERVIEW
Summary of the task, challenge, investigation, career-related scenario, problem, or community link.
In this unit, students will be learning about Genetics. The unit will start with a brief discussion of Bioengineering. Students will have the opportunity to do
a taste test of traditionally grown foods. They will make observations to determine the difference in taste, texture, and color and record this data on bar
graphs. Students will analyze this data in math class later in the unit. Students will also be discussing probability with a professional statistician and
discussing how probability is used in real-life. Students will be using what they know about probability to make predictions. Students will also make a
connection to Science by completing a task on experimental v. theoretical probability and how it relates to genetics.
MOTIVATOR
Hook for the week unit or supplemental resources used throughout the week. (PBL scenarios, video clips, websites,
literature)
The taste test activity during the Bioengineered Foods Project will serve as the motivator for the unit. Students will taste foods of four different lettuces
and recording their physical traits.
DAY
Objectives
(I can….)
1
I can create a
bar graph to
show
frequencies of
certain
physical traits.
Materials &
Resources
Data from class
involving hair
color
Data from Taste
Test using
different breeds
of lettuce
iPads
Instructional Procedures
Differentiated
Instruction
Assessment
EQ:
-
How can graphs be used to communicate data from an
experiment?
-
How can I create a bar graph showing frequency in a real world
situation?
½ Project Day – Bioengineered Foods
Set

Graphing
calculators
Graphs PPT
Students will respond to the following questions:
1. What are bar graphs?
2. How are bar graphs related to measures of frequency?
3. How are they different from other graphs, give examples?
4. Provide two different scenarios that could be communicated
utilizing bar graphs.
Teaching Strategy



Direct Instruction
Graphs
Whole Group Discussion
How can I best represent data in math class and beyond?
Students will review their bar graphs created during today’s project.
Students created bar graphs by recording quantitative data
from the taste test of different lettuce types. The bar graphs
were based on the traits of the lettuce.
Students will analyze the data from their frequency graphs.
Summarizing Strategy

Project Reflection Think-Pair-Share
- Students will work in pairs to discuss their individual
project reflections.
- Students reflected the frequency of physical traits and
what it has to do with genotype as opposed to
phenotype. Students reflected on what they felt, tasted,
Enrichment:
1) Same Data, Different
Graphs: Using scale and
interval to represent
data differently.
Students will represent
the class data using bar
graphs with different
scale of frequency and
intervals.
2) Heterogeneous
grouping
3) Peer tutoring via
student grouping
Remediation:
1) Teacher will provide
students with several
different graph scales
and intervals to choose
from.
2)
IXL Practice: Interpret
bar graphs, line graphs,
and histograms.
3) IXL Practice: Create
bar graphs, line
graphs, and
histograms.
Formative:
1) Informal
observation
2) Whole Group
Discussion
3) Student-created
bar graphs.
4) Project Reflection
Think-Pair-Share
Summative:
1) Bioengineered
Foods Project
etc. from today’s experiment?
2
I can
determine
interquartile
range from a
box plot
Calculators
EQ:
Quick Write /
Quick Draw
Template
Box and Whisker
Plots PPT
What are Box and Whisker Plots?
-
How can I make a five-point summary of a data set (use box
and whisper plot) and find the interquartile range?
Set

Ice cream data
sheet
iPad
Exit Ticket
-
Students will complete a Quick Draw / Quick Write on the following
topic:
What is your favorite ice cream flavor?
How did you determine this is your favorite flavor?
Teaching Strategy


Direct Instruction
Box and Whisker Plots
Ice Cream Data Challenge
Give students a data set of different brands and flavors of ice
cream with information describing the ice cream that has
artificial additives and those with just natural flavoring.
Use this data to create box and whisker plots to model this data
with a five-point summary.
Students will also find the interquartile range.
Show students that the ends of the “box” is the endpoints of
50% of the data and therefore the subtraction of the endpoints
of this “box” will always give the interquartile range.
Summarizing Strategy

Students will complete an exit ticket including the following
questions:
1.
Summarize their procedures and why the “box” will always
have 50% of the data set.
Enrichment:
1) CK-12 March Madness:
Real-World Application
of Box and Whisker
Plots (Alternatively,
similar data may be
tailored to meet
student interest while
demonstrating realworld application)
Remediation:
1) Individualized
instruction for
developing learners
during the Ice Cream
Data Challenge.
2) IXL Practice: Interpret
Box and Whisker Plots
Formative:
1) Informal
observation
2) Quick Draw/Quick
Write
3) Box and whisker
in-class activity
4) Discussion
5) Exit Ticket
3
I can
determine
theoretical and
experimental
probability.
I can explain
reasoning and
persevere in
solving
problems.
Eight pair of dice
Explain why the difference of the two endpoints of the “box”
will always give the interquartile range.
-
How can I determine theoretical and experimental probability?
How can I explain reasoning and persevere in solving
problems?
EQ:
iPad
Theoretical and
Experimental
Probability PPT
Doceri app
2.
Set

Students will complete a Venn Diagram on the following topic:
What is the difference between theoretical and experimental
probability?
How is reasoning and persevere related to problem solving?
Teaching Strategy


Direct Instruction
Theoretical and Experimental Probability
Probability Challenge
Ask students what number (sum of two dice) would they
choose to be rolled the most often on a pair of dice.
After allowing different opinions and why, tell them that as
groups we will all roll a pair of 50 times and record the sums.
Students will learn about experimental probability and
theoretical probability through this challenge.
Have students make bar graphs above the numbers
2,3,4,5,6,7,8,9,10,11, and 12 to show frequency of the number
(sum) rolled.
Airplay or project to display different graphs and discuss the
reasons they are different.
Have students make a 6x6 area model grid to find the
theoretical probability. The theoretical grid has 36 possible
outcomes, while the experimental chart we created was based
on 50.
Enrichment:
1) Article: Is a pregnant
woman’s chance of
giving birth to a boy 50
percent?
2) Heterogeneous
grouping
3) Peer tutoring
Remediation:
1) Heterogeneous
grouping
2) Peet tutoring
3) Use of calculator
4) IXL Practice:
Theoretical
Probability
5) IXL Practice:
Experimental
Probability
Formative:
1) Venn Diagram
2) Informal observation
3) Probability Challenge
4) Mini Poster
-
Have students list probabilities for both (e.g., P(1)= ,P(2)=
,P(3)= ,etc.) the bar graph and the grid.
Summarizing Strategy (5 to 10 minutes in length)

4
I can
determine
expected value
and therefore
conclude if a
game is fair or
not.
Presentation
with practice
problems
EQ:
Enrichment:
-
iPads
Expected Value
PPT
How can I determine expected value?
How can I determine if a game is fair (e.g., expected value is
equivalent for all players)?
Set

Video Challenge
Independent
Practice
Students will work in table groups to create a mini poster on Doceri
to respond to the following questions:
Why does experimental probability approach theoretical
probability?
Discuss and list the differences between theoretical and
experimental probability.
What is the Law of Large Numbers (the larger the number of
events, the closer the experimental probability approaches the
theoretical)?

Reflection
Template
Show students an area model that has at least two colors and in
patterns of squares or rectangles.
Students will create a think, write, draw writing task on the
following topic:
Ask them which color would be more likely to be landed on if
all areas of the rug have equal chances of being landed on
(make sure the colors are not half and half).
Teaching Strategy


Direct Instruction
Expected Value
Video Challenge
Students will watch a video of a board game (video clip of
participants playing the game or commercial clip for a board
game).
1) Peer tutoring
2) Heterogeneous
grouping
3) Expect Madness:
What is the
relationship
between expected
value and the
NCAA Basketball
Tournament?
Remediation:
1) Peer tutoring
2) Heterogeneous
grouping
3) Use of calculator
Formative:
1) Think-Write-Draw
2) Video Challenge
and Independent
practice
assignments
3) Individual
Reflection
-

The students will be directed to pay special attention to the
spinner used in the game.
Students will create a visual representation (of their choice –
utilizing their iPad technology) that explains which color or
space on the spinner is most likely to be landed on during this
game.
Students will share with their visual representations with their
assigned table groups.
Student table groups will share their best visual representation
and explain how their illustration is related to expected value.
Students will post their visual representations to the class
website.
Independent Practice
This lesson involves various area model worksheets to be used
to divide the up the areas of different colors to determine
probability and also expected value.
The expected value will come into play when points or values
are given to the colors.
The expected value is figured by multiplying the probability (of
a color being landed on randomly) times the points or value
(given that color).
Before working on each area model ask students which color
they would choose to win. After figuring the expected value,
they will see the theoretical answer to their question.
Summarizing Strategy

Individual Reflections
-
5
Students will write a reflection explaining why probability of an
area model is different from the expected value of that same
area model if points or values are added as conditions for the
area models’ colors.
Project Day – Genetics Guest Speakers
6
I can use
counting
techniques,
such as
permutations
and
combinations,
to determine
the total
number of
options and
possible
outcomes.
Entrance Ticket
EQ:
-
Fundamental
Theorem of
Counting PPT
Fundamental
Theorem of
Counting Guided
Practice
How can I use counting techniques, such as permutations and
combinations, to determine the total number of options and
possible outcomes?
Set

Sandwich
topping
manipulatives
Mathematics
exit ticket
iPads
Entrance Ticket – Students will respond to the following question:
Your family is ordering a family-sized submarine sandwich.
There are four toppings from which to choose (ham, cheese,
lettuce, tomato).
You have a coupon for a three-ingredient sandwich.
Determine all the different three-ingredient sandwiches you
could order.
Create a list, diagram or table on chart paper to show possible
outcomes and counting techniques.
Teaching Strategy
Graphing
calculators
Three, Two, One
Writing Activity
Template



Direct Instruction
- Fundamental Theorem of Counting
Guided Practice
- Fundamental Theorem of Counting
Challenge
Students will work in teams of three to complete the provided
challenge.
Students will explore combinations in a variety of applications.
Assign each situation to two groups so the groups may
compare results after completing the task. There will be a
minimum of 3 sets of challenge situations (total of 6 teams of
3).
Challenge scenarios include:
1. How many different ways can you choose two ice
cream toppings from three?
Enrichment:
1) Peer tutoring
2) Heterogeneous
grouping
3) Allow students to
choose a real life
commodity of their
choice and apply
the fundamental
counting theorem.
Remediation:
1) Peer tutoring
2) Heterogeneous
grouping
3) Vary the number of
combinations by
beginning small
and progressing to
more complex
problems/tree
diagrams.
Formative:
1) Entrance Ticket
2) Guided Practice
3) Individual
Reflection
4) Challenge
Scenarios
5) 3-2-1 Writing
Activity
2.
-
-
-
-
How many different ways can four students be seated
at two desks?
3. How many different ways can two food items be
chosen from six food items?
4. How many ways can you choose three chores from
five to do before dinner (clean your room, feed the
fish, take the trash out, cook dinner, wash dishes)?
Direct groups to create lists or tree diagrams to organize the
data and then use counting techniques to determine a
numerical result for each situation.
Model how to create a tree diagram or list if necessary.
Have groups share with another group and teach that group
about their problem situation, or compare solutions with the
other group completing the same scenario.
Assess students understanding by observing their methods for
organizing (i.e., tree diagrams, lists or other) and listening to
their discussions.
Each team will complete three challenge scenarios for practice.
Summarizing Strategy

7
I can use
counting
techniques,
such as
permutations
Sandwich
topping
manipulatives
Combinations
PPT
Three, Two, One Writing Activity
- Students will rate their level of comprehension through
this simple self-assessment writing tool.
Students will create a pyramid graphic organizer the
includes:
The base:
3 concepts that they have learned during today’s lesson.
The middle:
2 questions that they have about this lesson.
The top:
1 math problem related to today’s topic
EQ:
-
How can I use counting techniques, such as permutations and
combinations, to determine the total number of options and
possible outcomes?
Enrichment:
1) Peer tutoring
2) Heterogeneous
Formative:
1) Think-Pair-Share
2) Class Discussion
3) Individual
Reflection
and
combinations,
to determine
the total
number of
options and
possible
outcomes.
Mathematics
exit ticket
Set
grouping

iPads
Graphing
calculators
Short homework
assignment
Digital
presentation
Think Pair Share – Students will work with a partner to respond to
the following question:
Think about the sandwich ingredient combinations you found
in the previous lesson.
You chose three ingredients from four.
Determine how many ways you can assemble a sandwich with
ONLY three ingredients.
This will depend on the order that ingredients are placed on the
sandwich.
For example, putting on ham, then tomato, then cheese is
different than putting on tomato, then cheese, then ham.
Working with your Think, Pair, Share partner create a list,
diagram or table on chart paper to show possible outcomes
and counting techniques.
Teaching Strategy



Direct Instruction
Combinations
Whole Class Discussion
Review the term “combination”.
Explain that they have been finding combinations over the past
two days, and ask them to describe/explain the processes they
used and what they believe a combination is.
Be sure students understand the concept and term before
proceeding.
Give students an opportunity to write a definition for
combination in their own words in journals or notebooks.
Challenge
Present the following scenario and discuss reasonableness of
using tree diagrams and/or lists to count possible outcomes.
The Innovation Academy Eighth Grade Mathematics Team won
the county Math-a-Thon Competition. The reward was a six
topping pizza. At the local pizza parlor, 10 toppings were
offered. How many combinations of six-topping pizzas could be
chosen?
Discuss if a tree diagram or a list is appropriate to determine
Remediation:
1) Peer tutoring
2) Heterogeneous
grouping
3) IXL Practice:
Compound events
4) Challenge Scenario
5) Exit Ticket
-
-
the total number of ways to choose six pizza toppings from 10.
Why or why not?
Students begin to realize that if the numbers are too large,
these methods may be too tedious to be efficient.
Have pairs of students create two problem situations that can
be solved using combination methods for solution.
Each situation should use lists or tree diagrams and counting
techniques.
On separate pieces of paper, students find the numerical
solutions for each situation.
Remind them to consider if their solutions are reasonable.
Have pairs exchange problem situations with another pair and
solve for numerical solutions for each other’s problem
situations.
Have pairs verify numeric solutions and methods used to find
the solution.
Summarizing Strategy

Exit Ticket
-
Ask students to describe a combination in their own words with
a partner or by writing a Mathematics Exit Ticket.
They should include a definition and an example of a
combination in their description.
Collect the tickets as students leave at the end of the class.
Use tickets as a formative assessment by quickly reading to
determine what students understand after the lesson.
Use the analysis to inform future instruction.
8
Project Day – Pedigrees-Family Health History
9
I can use
probability to
iPad
horse race
EQ:
-
How can I use probability to make logical decisions?
Formative:
make logical
decisions.
I can explain
reasoning and
persevere in
solving
problems.
calculation stats
Probability and
Mathematics
PPT
How can I explain reasoning and persevere in solving
problems?
Set



Students will watch a short video of a horse race.
Students will choose a horse and based on its record (go to
calculation stats) will calculate it’s expected value of winnings.
Based on this calculation, they can predict the horse’s earnings on
all future starts.
Teaching Strategy



Direct Instruction
- Probability and Mathematics
Research
Students will learn work in teams to research statistics
associated with horse racing – particularly statistics of wins and
prizes won by horses, jockeys, and owners.
Partners Practice
Students will work in pairs to calculate the expected value of
their choice (horse, jockey, or owner) and predict the horse’s
(or jockey’s or owner’s) earnings on any future start.
Student groups will present their results to each other and the
whole class, discussing expected value as a tool that helps to
level out data to make informed predictions.
Enrichment:
1) Opening set
problem.
2) Class Discussion
3) Exit Ticket
1) Peer tutoring
2) Heterogeneous
grouping
Remediation:
1) Peer tutoring
2) Heterogeneous
grouping
3) Use of calculator
4) IXL Practice:
Probability
Summarizing Strategy

10
I can
determine
compound
probability,
Permutations
PPT
Exit Ticket
Students will write a reflection of their idea of probability of an
event in comparison to the expected value of an event.
EQ:
-
Skittles
probability
How can I determine compound probability, combinations, and
permutations?
Enrichment:
1) Peer tutoring
Formative:
1) Opening set
problem.
combinations,
and
permutations.
activity sheet
Set
iPad
Skittles fun
packs (one per
student)



Students will watch a short video of a horse race.
Students will choose a horse and based on its record (go to
calculation stats) will calculate it’s expected value of winnings.
Based on this calculation, they can predict the horse’s earnings on
all future starts.
Teaching Strategy


Direct Instruction
Permutations
Explain that they have been finding permutations, ask them to
describe or explain the process they used and what they
believe a permutation is.
Be sure that students understand the concept and term before
proceeding.
Give students an opportunity to write a definition for
permutation in their own words in journals or notebooks.
Challenge
Provide problem situations that allow students to explore
permutations in a variety of applications.
Divide students into groups of three or four.
Assign each situation to two groups.
Scenarios include:
1. How many different ways could four students exit a
room?
2. How many different ways could the letters K, A and B
be ordered?
3. How many different ways could the following colors be
arranged in horizontal stripes to create a flag? (red,
black, yellow, orange and green)
4. How many different ways could four students be
placed at two desks? (Desk A, Desk B)
Direct the groups to organize the data and then use counting to
determine a numerical result for each situation.
Regroup students by taking one person from each of the
scenario groups and combining them.
2) Heterogeneous
grouping
3) Students can be
given more
challenging
permutations and
combinations with
the skittles to
determine all
possible
combinations.
Remediation:
1) Peer tutoring
2) Heterogeneous
grouping
3) Use of calculator
4) IXL Practice:
Permuations
5) Students can be
given fewer choices
to calculate easier
combinations and
permutations.
2) Challenge
3) In-class practice
4) iMovie closure
-


Each student shares the solutions for the problem situation and
explains the strategies used. Each student in the group
presents.
This instructional strategy makes every student accountable for
understanding the problem situation and teaching it to others.
Tree Diagram Practice
Present the following scenario to discuss reasonableness of
using tree diagrams and lists to count possible outcomes: The
softball coach was putting together a batting order for the first
game of the season. There are nine players whom the coach
has to order. How many possible ways could the coach order
the batters?
Discuss whether a tree diagram or a list is appropriate to
determine the total number of ways that you could arrange
nine players in a batting order. Why or why not?
Students will begin to realize that if the numbers are too large,
these methods may be too tedious to be efficient.
Have students create two problem situations that use
permutation methods to find possible outcomes.
Students solve situation using lists or tree diagrams and
counting techniques.
On separate pieces of paper, students find the numerical
solutions for each situation.
Remind them to consider if their solutions are reasonable.
Instruct pairs to exchange problem situations with another pair.
The pairs continue to exchange papers and solve problems until
about 10 minutes remain in the period.
Observe student discussions and solutions.
Pairs join those with whom they exchanged papers to verify
numeric solutions and methods used.
Probability Practice
Students will be completing a probability activity with fun packs
of skittles.
They will start by finding basic probabilities of selecting a
specific color of skittle.
Students will then move on to finding compound probabilities
such as a red or green OR a red and green.
-
Students should find the compound probabilities when skittles
are replaces and when they are not.
Finally, students should find the possible combinations or
permutations of skittles based on their favorite flavor
combinations.
Summarizing Strategy

STANDARDS
iMovie
Students will create a short movie discussing their favorite
skittle combinations and how likely they are to pick this
combination (or permutation) out of a bag of skittles.
Identify what you want to teach. Reference State, Common Core, ACT
College Readiness Standards and/or State Competencies.
7.SP.C.7 - Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain
possible sources of the discrepancy.
CP.A.1 - Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other
events (“or,” “and,” “not”).
CP.A.2 - Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to
determine if they are independent.
CP.A.3 - Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same
as the probability of A, and the conditional probability of B given A is the same as the probability of B.
CP.A.4 - Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to
decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among
math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other
subjects and compare the results.
CP.A.5 - Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung
cancer if you are a smoker with the chance of being a smoker if you have lung cancer.
CP.B.9 - Use permutations and combinations to compute probabilities of compound events and solve problems.
MD.B.5 - Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
MD.B.5a - Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant.
MD.B.5b - Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various,
but reasonable, chances of having a minor or a major accident.