ALEX Learning Activity

  

Adding and Subtracting Polynomials: The Thinking Tree

A Learning Activity is a strategy a teacher chooses to actively engage students in learning a concept or skill using a digital tool/resource.

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  This learning activity provided by:  
Author: Kristy Lacks
System:Marshall County
School:Douglas High School
  General Activity Information  
Activity ID: 2652
Title:
Adding and Subtracting Polynomials: The Thinking Tree
Digital Tool/Resource:
The Thinking Tree
Web Address – URL:
Overview:

After a lesson on adding and subtracting polynomials, the students will complete an exit ticket by picking three questions from The Thinking Tree to answer.

This resource was created as a result of the ALEX Resource Development Summit.
  Associated Standards and Objectives  
Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 9-12
Algebra I with Probability
7. Add, subtract, and multiply polynomials, showing that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use the repeated reasoning from prior knowledge of properties of arithmetic on integers to progress consistently to rules for arithmetic on polynomials.
  • Accurately perform combinations of operations on various polynomials.
Teacher Vocabulary:
  • Polynomials
  • Closure
  • Analogous system
Knowledge:
Students know:
  • Corresponding rules of arithmetic of integers, specifically what it means for the integers to be closed under addition, subtraction, and multiplication, and not under division.
  • Procedures for performing addition, subtraction, and multiplication on polynomials.
Skills:
Students are able to:
  • Communicate the connection between the rules for arithmetic on integers and the corresponding rules for arithmetic on polynomials.
  • Accurately perform combinations of operations on various polynomials.
Understanding:
Students understand that:
  • There is an operational connection between the arithmetic on integers and the arithmetic on polynomials.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGI.7.1: Combine like terms of a given expression
ALGI.7.2: Define monomial, term, binomial, trinomial and polynomial.
ALGI.7.3: Multiply polynomial expressions (quadratic).
ALGI.7.4: Multiply polynomial expressions (linear).
ALGI.7.5: Subtract polynomial expressions.
ALGI.7.6: Add polynomial expressions.
ALGI.7.7: Use order of operations to evaluate and simplify algebraic and numerical expressions.
ALGI.7.8: Identify the terms in a polynomial expressions.
ALGI.7.9: Explain the distributive property.

Prior Knowledge Skills:
  • Identify properties of exponents.
  • Give examples of the properties of operations including distributive, commutative, and associative.
  • Recall how to find the greatest common factor.
  • Combine like terms of a given expression.
  • Recognize the property demonstrated in a given expression.
  • Simplify expressions with parentheses (Ex. 5(4 + x) = 20 + 5x).
  • Simplify an expression by dividing by the greatest common factor (Ex. 18x + 6y= 6(3x + y).
  • Define linear expression, rational, coefficient, and rational coefficient.
  • Combine terms that are alike of a given expression.
Learning Objectives:

Students will add and subtract polynomials.
  Strategies, Preparations and Variations  
Phase:
After/Explain/Elaborate
Activity:

The Thinking Tree

  1. After a lesson on adding and subtracting polynomials, the teacher would instruct the students to look over the Thinking Tree and pick three questions to answer.

  2. The students would be instructed to think about each question and answer fully. They will also be instructed to use strategies and explanations of adding and subtracting polynomials in their answers. 

  3. The students will be instructed to turn in the exit tickets as they leave the classroom.
Assessment Strategies:

The teacher would assess student content knowledge by reading student exit tickets, looking for strategies and explanations involving adding and subtracting polynomials.

Also, the teacher could reinforce the next day using some of the best exit tickets that the students turn in the day before.
Advanced Preparation:

It is suggested that the teacher get a poster-sized copy of The Thinking Tree to hang in the room.  This would facilitate the use of this activity for multiple lessons.  If that is not available copies could be made for the students.
Variation Tips (optional):

The Thinking Tree can be used as an exit strategy with any lesson.  The exit tickets could also be shaped like leaves either by a die-cut machine or hand cutting.

When the lesson runs long, the teacher could instruct students to only pick one topic to write about.

The teacher could group students and have them come up with answers together.
Notes or Recommendations (optional):

ALCOS 2019

Alg One 7) Add, subtract, and multiply polynomials, showing that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.
  Keywords and Search Tags  
Keywords and Search Tags: add, difference, like terms, polynomials, subtract, sum, terms