This lesson is an introduction to Polynomials. It includes some activities that will help the teacher to assess student's understanding of several concepts (integer addition and subtraction, combining like terms), which are essential to polynomial operations. Through engaging activities involving candy and chocolates, students will learn to add, subtract, and multiply polynomials!
General Information
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Suggested Technology:
Computers for Students, Internet Connection
Instructional Time:
45 Minute(s)
Resource supports reading in content area:Yes
Freely Available: Yes
Keywords: polynomials, combine like terms, closure, integers, addition, subtraction, multiplication, wonka, gum drop, chocolate, box, monomial, binomial, function, functions
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Lesson Content

Lesson Plan Template:
General Lesson Plan

Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will be able to:
 Define and identify polynomials.
 Add and subtract polynomials.
 Multiply polynomials using the distributive property, and then simplify.
 Understand the concepts of combining like terms and closure of polynomials for addition, subtraction, and multiplication.

Prior Knowledge: What prior knowledge should students have for this lesson?
The students should already:
 Understand integer properties and operations, including closure.
 Be able to add and subtract like terms.
 Understand the distributive property.
 Be familiar with combining like terms.

Guiding Questions: What are the guiding questions for this lesson?
 What is a polynomial? (combination of monomials which are numbers, 4, variables,x, or product of real numbers and variables,. The polynomial would be ).
 How are polynomials classified? (by the number of term: each section between the plus or minus signs; by the number of degrees: highest number of exponents. Above example has 3 terms and 2 degrees).
 How are polynomials added and subtracted? (by combining like terms: terms whose variables and exponents are the same i.e. 5x, 8x the coefficients do not have to be the same).
 What strategies can be used to multiply polynomial expressions?(use the distributive property)
 What mathematical concepts will be useful in adding, subtracting, multiplying, and dividing polynomials?

Teaching Phase: How will the teacher present the concept or skill to students?
Students will complete the formative assessment activity in the beginning of the class. At the bottom of the page, students have an opportunity to complete a selfassessment which is based on a proficiency scale.
 Handout slips of paper with #1, 2, 3, 4 (or whatever method you choose) as students enter the room.
 Teacher will instruct students with #1 and 3 to work on Gum Drop activity and #2 and 4 "Wonka Box". Teacher will give an introduction to all students on the Wonka Box however, the box will be used for the second activity for this lesson. Wonka Box Instructions.docx
 "Gum Drop" students should work individually while you assist "Wonka Box" students (remind them to include units), if needed. Then, allow "Gum Drop" students to share with a partner. (one that also was working on "Gum Drop")
 The teacher should walk around the room to observe methods that students use and listen to conversations which will provide ideas for discussion. (Record anecdotal records of student performances, prompting with guided questions as needed).
 After about five minutes, have the students switch activities. Again, have "Gum Drop" students work independently while assisting "Wonka Box" (if needed), then students working on "Gum Drop" should share with a partner.
 When the students are finished, transition (using whatever cue you have established in your classroom) to a group discussion of "Gum Drop".
Teacher will facilitate a class discussion based on student response to the activity. Mention positive observations and start with questions that will engage students on every level.
 Are there any similarities/differences with the numbers? (Some have x^{2}, x, or no variable with them).
(These are called Monomials)
 What connections can you make between what you have done and other mathematical concepts covered in this course? (Adding and subtracting integers, combining like terms. Maybe remind students integers are only +/ whole numbers)
 Ask for volunteers to share their answer. (Select two students who you observed to have different approaches to the problem).
 Have students explain how they came up with the answer.
 The teacher will encourage students to openly express disagreements and sharing various methods to solve the problems.
 Ask other students which argument is most convincing? Why?
(Some students may have come up with an answer that looks more like a list, 28x^{2}, 11x,  30 or 5x2, x, and 5 numbers; meaning they counted rather than combined the monomials. Be sure to address common errors observed).

Guided Practice: What activities or exercises will the students complete with teacher guidance?
The teacher will utilize discussion to help students define and identify polynomials; through the initial assessment and discovery students should be able to add and subtract polynomials.
 Any errors should be corrected at this point. Explain to students that 28x^{2}  11x  30 is a polynomial, which is a combination of all of the separate terms, monomials.
 Discuss polynomial classification. Each monomial in the polynomial is referred to as a "term". How many terms are there? (3; called a trinomial) What is the highest exponent? (2nd degree polynomial. The degree of a polynomial is the largest of its monomial exponents.)
 Polynomials are classified according to the number of terms or degrees. If a one term polynomial is called a monomial, what would we name a two term polynomial? (Binomial)
 Just as we did with the Gum Drop activity, polynomials can be combined using addition, subtraction, and multiplication.
 Example, (2x^{2} + 10x  3) + (x^{2}  11x + 7) = x^{2}  x + 4
 Explain multiplication using the example: (4x + 1)(2x  5) = 18x^{2} + 18x  5
During this lesson, the teacher will give instruction and provide examples for students. The teacher will utilize discussion to help students define and identify polynomials; through the initial assessment and discovery students should be able to add and subtract polynomials.

Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
The discussion and polynomial practice problems will act as the transition point for independent practice. Students will have all of the information they need to complete the Box of Chocolates Activity. Students will be working as a group for this part. Have students take out boxes (if they are not on the desk already). Go over materials needed (in case you missed something) and an overview. Remind students to rate their understanding (bottom right of activity sheet).
Box of Chocolates and Answer Key.docx
 Review the activity on the following day. This can be your assessment for moving on with multiplying polynomials.
 (5p^{2} + 3) + (2p^{3}  3p^{3}) = 3p^{3} + 7p^{2} + 3
(be sure to point out the convention of writing polynomials descending order of exponents)
 (4x  5)(7x + 6) = 28x^{2} + 24x  35x  30 = 28x^{2}  11x  30

Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The teacher will use the Summative Assessment Activity to bring the lesson to a close. After review of students work, teacher will facilitate a discussion according to elements from the lesson that students need to improve upon.
Golden_Ticket_and_Answer_Key.docx

Summative Assessment
Students will complete The Golden Ticket activity. Teacher will grade and use this as a tool to help develop review questions for the next day.
Golden_Ticket_and_Answer_Key.docx

Formative Assessment
Students will work individually to complete the Gum Drop Activity at the start of the class. The teacher will determine students' prior knowledge of basic integer operations and combining like terms by taking notes during observation of student discussion. You may want to use a grade book or some sort of log to jot down student selfassessment levels on the activity sheet. During the discussion, teacher can assess prior knowledge as well; this would be more observational to help determine the types of questions to ask in order to guide students in discovery.

Feedback to Students
At the end of the lesson, student will have an "Exit Slip" activity. This is a quick assessment tool to help gauge the concepts that the student has/has not mastered during the lesson. You can grade this and return to students the next day along with a review. By doing so, it will help the students to get a better understanding of what they need to improve upon prior to the formal assessment.
Another option is to monitor students as they are completing the "Exit Slip" (The Golden Ticket) activity and provide immediate feedback. You may use a rubric to develop your grading scale (there is a sample attached to this lesson).. Be sure to explain to the students all of the elements of the rubric so that they are clear on the requirements for becoming successful in your classroom.
Assessment
 Feedback to Students:
At the end of the lesson, student will have an "Exit Slip" activity. This is a quick assessment tool to help gauge the concepts that the student has/has not mastered during the lesson. You can grade this and return to students the next day along with a review. By doing so, it will help the students to get a better understanding of what they need to improve upon prior to the formal assessment (exam).
Another option here is to actually walk around while students are completing the “Exit Slip” (The Golden Ticket) activity and give a classwork grade. You may use a rubric to develop your grading scale. If you do not have rubrics, there is a sample attached. Be sure to explain to the students all of the elements of the rubric so that they are clear on the requirements for becoming successful in your classroom.
 Summative Assessment:
Students will complete The Golden Ticket activity. Teacher will grade and use this as a tool to help develop review questions for the next day.
Accommodations & Recommendations
Accommodations:
"Gum Drops": Have a number line available for students who have difficulty with integer operations. Different colored counting blocks (if available) or any object (pencils, pens, dry erase markers) may be useful to help students understand "like terms". You may give a hint that there are 5 gumballs for each bag. This will help students who may be stuck.
"Box of Chocolates": Have a few prefolded boxes for students who may have difficulty. If students need reminder on calculating volume, let them research in a textbook. You may want to have each step of the folding activity available (maybe taped to the board or on an extra table) for the visual learners.
Provide practice with peer tutors for students who are having difficulty.
Extensions:
Students who finish their work may work independently or together on coming up real world word problems that relate to the topic. Give the students index cards to write the questions and use as problem or two for the morning "warm up" activity on the following day. To make this fun, you can have a student volunteer draw a card out of a box and that will be the question posed. If you have computers in the classroom, allow the students to research questions as well.

Suggested Technology: Computers for Students, Internet Connection
Special Materials Needed:
Materials for Student Use:
Construction paper (vary the shape and sizes), tape, rulers, scissors, index cars, pens, pencils, and/or markers, computer with internet access
Materials for teacher use:
Use different shape and size blocks (or anything) to create "Wonka Bars" for the "Box of Chocolates" activity. Cover the blocks in your own creative way! Label the bars or colorcode them and have students note this on their papers.
If possible, bring in actual mini and snack size candy bars that the students can eat at the end of the lesson.
Further Recommendations:
Classroom Setup: You may want to have the room split so that the students are working on either side of the room in groups and there is space for free movement. Also, it may be good to have two boxes of different sizes on display.
Additional Information/Instructions
By Author/Submitter
This lesson plan has several documents attached to assist with Formative Assessments, Student Feedback, Summative Assessments, and a Sample Rubric.
It also covers MP Standards (MAFS.K12.MP.1.1: Make Sense of Problems and Persevere in Solving Them and MAFS.K12.MP.3.1: Construct Viable Arguments and Critique the Reasoning of Others) through teacher facilitated discussion and student presentation.
Source and Access Information
Contributed by:
SYLIKA CAMACHO
Name of Author/Source: SYLIKA CAMACHO
District/Organization of Contributor(s): Osceola
Is this Resource freely Available? Yes
Access Privileges: Public
* Please note that examples of resources are not intended as complete curriculum.