Algebra II, Grudge Ball Review Game
Unit Objective:
Students will be able to simplify, factor, solve, graph, classify zeros, and find all real zeros of
polynomial functions.
Materials Needed:
Ti-Nspire Calculators, Mini Whiteboards (1 per team), Dry Erase Marker (1 per team), Nerf
Basketball Hoop, Nerf Basketball
Homework:
Prepare for the test by reviewing old notes, examples, and quizzes.
Accommodations:
Our two students with a vision impairment will receive an enlarged version of the question right
before the question is asked to the class. This will help these students when they are practicing
with their teammates because they will be able to see the question, and will even the playing field
when it is their turn to answer the question on the mini whiteboard.
Common Core Standard:
CCSS.MATH.CONTENT.A-APR.2: Identify zeros of polynomials when suitable factorizations
are available, and use the zeros to construct a rough graph of the function defined by the
polynomial.
Instructional Objectives:
Students will be able to simplify, factor, solve, graph, classify zeros, and find all real zeros of
polynomial functions.
Assessment:
Grudge Ball
Time Frame: 50 minutes
Instructional Outline:
1. Review of the overarching essential equation
2. Grudge Ball
Steve Zajac
The Rules of Grudge Ball
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Students are broken up into 5 teams
Each team gets 10 x’s (10 lives) to start
One person from each team gets to answer a question on their own
 If they get the question right, they get to take away 2 x’s away from another team, or
take away one from one team and one from another
 Before they take the x’s away, they get to shoot a nerf ball from either the 2 point line
or the 3 point line
 If they make the 2 point basket, they can take away an additional 2 x’s away
from another team for a total of 4 x’s
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If they make the 3 point basket, they can take away an additional 3’s away
from another team for a total of 5 x’s
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If the student misses, they still get to take away 2 x’s away from the another
team
 You can not take x’s away from your own team
When a team is eliminated, they still answer questions to get back into the game
 To do so, they must answer the question correctly and make either a 2 point basket or
a 3 point basket
 If they make a 2 point basket, they can add 4 x’s to their team
 If they make a 3 point basket, they can add 5 x’s to their team
Students on each team who are not currently answering the question, are working as a team
teaching one another how to solve the problems
 Teamwork is stressed a lot because in order for your team to do the best they can,
everyone on your team needs to know how to answer the questions
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Hopefully students will be teaching one another so students who may be
struggling are getting more one on one help from peers, and higher achieving
students are deepening their knowledge by teaching it to someone else
http://toengagethemall.blogspot.com/2013/02/grudgeball-review-game-where-kidsattack.html
Steve Zajac
Teacher Action
Greet students as they walk into the room and ask them how
they are doing today.
Anticipatory Set: (10 minutes)
“Alright class today we are going to play Grudge Ball to review
for the test tomorrow. But before we start to play the game, you
need to prove to me that we understand the overarching essential
question for the unit. “How can simplifying and factoring
polynomials help solve real-world problems?” With you teams,
write down your answer to the essential question. In order for
the class to play Grudge Ball, at least 4 out of 5 teams must
answer the question correctly.
The teacher is checking the students’ responses to see if at least
4 out of 5 teams understand the essential question.
“Great job everyone! Every team answered the essential
question correctly. Can I have team Barracuda come up and read
their answer to the class?”
Grudge Ball: (35 minutes)
Today is a very important day to ask questions if you do not
understand. Most of these questions will be similar to the
questions on the test tomorrow. Can I have one player from each
team come up and grab a white board? Everyone else stay in the
back of the class with your team. You can practice each of the
questions, but you will have to remain silent. After the students
up front finish the question and give me their response, you can
discuss as a group the solution. Remember, you are a team. You
will want to teach one another how to answer the questions
because every member of the team will take turns answering the
questions. The winning team will get to take a piece of candy of
their choice. Now if people start acting unsportsmanlike, I will
end the game and pass out homework instead. “Who’s ready to
play some GRUDGE BALL?” With that said, “May the odds be
ever in your favor!”
Student Action
Students will get out paper, pencil, and their Ti-Nspire
calculator.
Rationale
Students will be ready to learn as the bell rings.
Also, the teacher will be building relationships
with the students by getting to know them
better.
Students get very excited to play grudge ball, the students
already know the rules from playing the game previous times
throughout the year. Students discuss their ideas with one
another from each team. Students will turn in their answer to
the teacher when they are finished.
The review will not do the students any good if
they do not understand the essential question
for the unit. If the students do not know how to
answer the question, the teacher might want to
push the game back a day to reteach some of
the critical parts of the unit.
While the teacher is looking over the students’ responses, the
teams are reviewing with one another to prepare for the
game. Students are answering each other’s questions.
Grudge Ball is a team game, where every
student will be asked to individually answer a
question. Therefore, students will want to help
one another to prepare for the game so they
have the best chance to win.
A member of team Barracuda comes up to read their
response. “Our team has realized the importance of solving
polynomial equations because of their correlation to real
world problems. Our factoring and simplifying skills have
helped us answer questions regarding area, predicting values,
and finding the cost of something. Having these skills in our
back pockets will help prepare us for any future problems!”
The teacher wants to showcase a group’s idea
to the class, and to give that team recognition
for their hard work. This will motivate students
to submit quality answers.
Each team gets pumped up to begin the game!
Students need to be reminded of sportsmanship
because of the competitive nature of the game.
Each team sends one player to answer the question first, and
the other team members will be in the back answering the
question silently.
Steve Zajac
Teacher Action
The first question is to simplify the expression and tell which
properties you used of x3 * x2 * x-4. The teacher will write the
question on the board for all of the students to see. Then the
teacher will pass out the enlarged vision for the two students
with a vision impairment. The teacher will do this after each
question.
Student Action
The students in the back of the class will be working with
their teams quietly, and the students up front will be
answering the questions on the mini white boards.
“What were your answers?”
All students in the front answered, “We got x! We used the
product of powers property”
“Nice job! Now take your 2-point or 3-point shot at the nerf
basketball hoop. Students in the back, did you get x as well?”
Ok we will move onto the next question. Can I have a new
member from each team come up to the front to answer the next
question? Make sure you bring up your calculator with you!
Rationale
This allows the students with vision
impairments to be able to see the problem and
practice it like the other students.
We did!!
Another student will come up to answer a question for their
team and will bring their calculator with them.
Since all of the students answered the question
correctly, I will not take time to explain the
solution.
I want you to create a table of values and then graph those
points. The polynomial function is f(x) = x5 – x4 - 9
Great work! Does anyone need a refresher about how to graph
or create a table?
“Nope! We are ready for the next problem!”
Ok the next problem asks you to perform the indicated
operation. (3x – 2) (x2 + 4x -7)
“Did all of the students in the back get the correct answer too?”
Awesome! Who is ready to factor? Send your next teammate up
to the whiteboards. Make sure everyone in your group has gone
before the next person goes twice. I know there are some people
that have not gone yet.
“Yes we did! We feel pretty confident about all of the
material so far!”
Students who have not gone yet will come up to the front of
the class to answer the next question.
All students need to practice on their own to see
what things they need to work on. This also
adds to the team mentality. You are only as
strong as your weakest link.
Steve Zajac
Teacher Action
The next question asks you to factor the polynomial completely.
x3 – 3x2 -4x +12. I will give you 3 minutes to work on the
problem.
Student Action
The students take the full 3 minutes and seem to be
struggling with the problem.
How many people want me to review how to do this problem?
Anticipated Problem That Students May Need Help With:
Many of the students raise their hands. “This problem is
tough!”
“Well let me walk you step by step and help you factor this
polynomial.”
Rationale
Students have a hard time grasping how to turn
each of the factored parts back into a whole
equation. (From line 3 to line 4)
“That makes much more sense!”
The next question asks you to find all of the zeros of the
function. You must show your work!
f(x) = x3 – 5x2 + 3x + 4. After a few minutes, “What were the
zeros of the polynomial function?”
Students begin to work on the problem, and are able to find
the zeros. “I found the zeros to be x = -0.618, 1.62, and 4.”
“How did you find the zeros?”
“I graphed the function and used the analyze function to find
the 3 zeros.”
Did someone find the zeros using a different method?”
Another student raises their hand and says, “I used a graph to
find out what the zeros were. But instead of using the
decimals, I found out their exact value. Since 4 is a zero, I
used synthetic division to find the quotient of
(x3 – 5x2 + 3x + 4) ÷ (x -4). Then I used the quadratic
formula to find the exact values.
Students need to realize that there is more than
one way to solve a problem because we all
think a little differently from one another.
Steve Zajac
Teacher Action
Student Action
Rationale
I really liked how you found the exact answers for the zeros. On
tomorrow’s test you will be asked to find the zeros of a function
and will need to show your work. An answer such as this will
receive full credit.
Check for Understanding:
“Two of these zeros are an example of what rule we learned
yesterday?”
“Great job!” Now who’s ready for the next problem?”
“This is an example of the irrational conjugates theorem!”
It is very useful to make references to previous
lessons so that students can make connections.
Students come up to the whiteboards to answer the next
question.
The next question asks you to write a polynomial that has
rationale coefficients, a leading coefficient of 1, and the given
zeros of 6 and 2i.
“Great answer! Way to think about it step by step.”
Check for Understanding:
“Our function has degree of 3, but we only have two zeros
listed. Why do you believe that is?”
Let’s find the zeros using our calculator to see if you are correct.
“When we tried to find what 2i was equal to we found that to
be plus or minus the square root of negative 4. Therefore the
zeros of the function are 6, 2i and -2i.
Asking students to think critically is an
essential step in mastering the concepts in
mathematics.
Students get out their calculators to solve to find the complex
zeros.
“Super Duper!”
Steve Zajac
Teacher Action
“Lets do one more problem, so we can have a few minutes to
answer any questions you may have for tomorrow’s test. Using
Descartes’ Rule of Signs, determine the possible numbers of
positive real zeros, negative real zeros, and imaginary zeros of
x3 - 4x2 + 8x + 7.
Student Action
Another student comes up to the front of the class to the mini
whiteboards to answer the next question.
“Great job of explaining your steps! Does anyone want
clarification on how to solve these types of problems?”
“Nope! We are feeling pretty confident for the test!”
Closure: (5 minutes)
“All of the teams were very good sports today, and I am very
proud of you. You may want to practice how to factor a few
more times so you are ready for the test tomorrow. Overall, you
did very well answering the questions today. The exam will
cover the same types of questions that I asked you today! Now
does anyone have a question about the test tomorrow?”
Anticipated Question:
“How many questions are on the test and are there any story
problems?”
Rationale
Students always seem concerned about the
number of questions on the test and story
problems.
“There are 17 questions on tomorrow’s test and 2 of them are
story problems. You will do great!”
Steve Zajac