Description
Looking for a comprehensive, editable resource to teach your students or child how to construct rough graphs of polynomials using their zeros and end behavior? Need to teach them how to factor a polynomial when it has a greatest common factor (GCF) of some degree of x? This set of lesson notes, extra practice (homework) worksheet, and exit ticket to check understanding of the lesson is excellent in helping students achieve mastery of this objective.
These scaffolded notes begin with a few warm-up questions to activate students' prior knowledge of how to solve quadratic equations by factoring. Then, notes jump into how to find the roots of a polynomial given in factored form, introducing the vocabulary word multiplicity. A graphic organizer is provided for clarity about what happens on the x-axis with zeros of different multiplicities. Once students are understanding all the different parts, everything is put together as a whole process, having students factor polynomials (we haven't factored by grouping or difference/sum of cubes yet, so all polynomials require a GCF of some degree of x to be factored out, leaving a quadratic polynomial that is factorable, such as with y = x^5 - 2x^4 - 8x^3), identify the zeros & end behavior, and then constructing a rough sketch of the graph. A lot of independent practice is provided, including some extension questions asking students to identify some of the other features of the graph (domain, range, y-intercept, positive/negative intervals) and some end-of-year state test style questions.
This lesson was thoughtfully planned to meet the needs and rigor of the following Common Core high school math standard: CCSS.MATH.CONTENT.HSA.APR.B.3 - 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.
The extra practice (homework) includes a lot of independent practice of this whole process of factoring polynomials and constructing sketches of graphs from their zeros and end behavior, including two pages of end-of-year state test style questions.
Objective(s):
By the end of this lesson, students will be able to factor polynomials, find their zeros, identify the multiplicities of those zeros, and then construct a rough graph of the polynomial using the zeros, multiplicities, and end behavior.
What's Included:
- Notes: 4 pages + answer key
- Extra Practice: 3 pages + answer key
- Exit Ticket: Two identical exit tickets are included (this is meant to be cut in half to save paper) + answer key
Editable Format:
- As a google doc, all text is editable.
- Graphs are NOT editable, but can be replaced with your own.
Random Tidbits:
- One of the things that I thought to do on each exit ticket that is super simple, but paid off huge dividends relationally with my students, is adding a sentence stem along with asking for their names. 1) Students almost never forgot to write their names on the exit ticket. 2) Daily, students would leave chatting with each other about what they wrote to answer the sentence stem. 3) It gave me something personal to chat with students about the next day as they entered class or I passed back exit tickets and helped me get to know them. 4) Even if students struggled on the exit ticket, I noticed that they never seemed to leave class feeling down or defeated because they could always at least answer the prompt about themselves.
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Highlights
Description
Looking for a comprehensive, editable resource to teach your students or child how to construct rough graphs of polynomials using their zeros and end behavior? Need to teach them how to factor a polynomial when it has a greatest common factor (GCF) of some degree of x? This set of lesson notes, extra practice (homework) worksheet, and exit ticket to check understanding of the lesson is excellent in helping students achieve mastery of this objective.
These scaffolded notes begin with a few warm-up questions to activate students' prior knowledge of how to solve quadratic equations by factoring. Then, notes jump into how to find the roots of a polynomial given in factored form, introducing the vocabulary word multiplicity. A graphic organizer is provided for clarity about what happens on the x-axis with zeros of different multiplicities. Once students are understanding all the different parts, everything is put together as a whole process, having students factor polynomials (we haven't factored by grouping or difference/sum of cubes yet, so all polynomials require a GCF of some degree of x to be factored out, leaving a quadratic polynomial that is factorable, such as with y = x^5 - 2x^4 - 8x^3), identify the zeros & end behavior, and then constructing a rough sketch of the graph. A lot of independent practice is provided, including some extension questions asking students to identify some of the other features of the graph (domain, range, y-intercept, positive/negative intervals) and some end-of-year state test style questions.
This lesson was thoughtfully planned to meet the needs and rigor of the following Common Core high school math standard: CCSS.MATH.CONTENT.HSA.APR.B.3 - 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.
The extra practice (homework) includes a lot of independent practice of this whole process of factoring polynomials and constructing sketches of graphs from their zeros and end behavior, including two pages of end-of-year state test style questions.
Objective(s):
By the end of this lesson, students will be able to factor polynomials, find their zeros, identify the multiplicities of those zeros, and then construct a rough graph of the polynomial using the zeros, multiplicities, and end behavior.
What's Included:
- Notes: 4 pages + answer key
- Extra Practice: 3 pages + answer key
- Exit Ticket: Two identical exit tickets are included (this is meant to be cut in half to save paper) + answer key
Editable Format:
- As a google doc, all text is editable.
- Graphs are NOT editable, but can be replaced with your own.
Random Tidbits:
- One of the things that I thought to do on each exit ticket that is super simple, but paid off huge dividends relationally with my students, is adding a sentence stem along with asking for their names. 1) Students almost never forgot to write their names on the exit ticket. 2) Daily, students would leave chatting with each other about what they wrote to answer the sentence stem. 3) It gave me something personal to chat with students about the next day as they entered class or I passed back exit tickets and helped me get to know them. 4) Even if students struggled on the exit ticket, I noticed that they never seemed to leave class feeling down or defeated because they could always at least answer the prompt about themselves.
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