ALEX Learning Activity

  

Mondrian Factoring Models

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: DeLaura Downs
System:Jefferson County
School:Jefferson County Board Of Education
  General Activity Information  
Activity ID: 2211
Title:
Mondrian Factoring Models
Digital Tool/Resource:
Mondrian Factoring Models Instructions
Web Address – URL:
Overview:

Piet Mondrian is an artist famous for creating his masterpieces out of line art that utilized clean lines through rectangles. This activity will help us to create our own “Mondrian” by using our knowledge of factoring Quadratic trinomials through the use of Algebra tiles and area models.

This activity was created as a result of the ALEX Resource Development Summit.

  Associated Standards and Objectives  
Content Standard(s):
Mathematics
MA2015 (2016)
Grade: 9-12
Algebra I
7 ) Interpret expressions that represent a quantity in terms of its context.* [A-SSE1]

a. Interpret parts of an expression such as terms, factors, and coefficients. [A-SSE1a]

b. Interpret complicated expressions by viewing one or more of their parts as a single entity. [A-SSE1b]

Example: Interpret P(1+r)n as the product of P and a factor not depending on P.


Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.A.HS.7- Identify an algebraic expression involving one arithmetic operation to represent a real-world problem.


Mathematics
MA2015 (2016)
Grade: 9-12
Algebra I
9 ) Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* [A-SSE3]

a. Factor a quadratic expression to reveal the zeros of the function it defines. [A-SSE3a]

b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. [A-SSE3b]

c. Determine a quadratic equation when given its graph or roots. (Alabama)

d. Use the properties of exponents to transform expressions for exponential functions. [A-SSE3c]

Example: The expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.


Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.A.HS.9- Identify the expression that is the same as the one shown. (limit to two operations e.g. x^2 + 3x is the same as x(x+3).


Mathematics
MA2015 (2016)
Grade: 9-12
Algebra I
18 ) Solve quadratic equations in one variable. [A-REI4]

a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Derive the quadratic formula from this form. [A-REI4a]

b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square and the quadratic formula, and factoring as appropriate to the initial form of the equation. [A-REI4b] (Alabama)


Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.A.HS.18- Solve an equation of the form x2 = p, where p is a perfect square less than or equal to 225.


Learning Objectives:

I can factor a quadratic trinomial by using Algebra Tiles and area models. 

I can interpret the different parts of an expression such as factors, coefficients, and constants.

  Strategies, Preparations and Variations  
Phase:
During/Explore/Explain
Activity:

The instructions for students are included as part of the Google Doc. The teacher will need to provide a copy of the document to each student using Google Classroom, or by providing a hard copy. The teacher will provide Algebra Tiles. Other materials may be provided by the teacher or the students based on the teacher's discretion. 

Students will be able to factor quadratic trinomials using Algebra Tiles and will draw a representation of such models in order to create a Mondrian inspired piece of art. This activity is a great tool for having students independently practice factoring Quadratic trinomials through the use of Algebra tiles, therefore producing an equivalent form of the Quadratic expression. Students will factor given trinomials and draw the corresponding area models on graph paper to demonstrate an understanding of factoring. Students will be able to determine if factoring is correct by inspecting the model. Because students will be creating area models, they will be able to interpret the various parts of the expression easily, such as the coefficients, factors, and constants. The end product will be a creative representation of the factoring, which will also incorporate the artwork of Piet Mondrian.  Students will work independently.

Assessment Strategies:

The final product can be used by the teacher to determine whether or not student mastered being able to factor quadratic equations by modeling.


Advanced Preparation:

As an introduction, you may want to quickly show a few of Mondrian's works and relate those to models using the Algebra Tiles. 

You will need to provide a copy of the activity in Google Classroom or Docs. If students do not have access to technology, you can project problems on the projector, or give each student an individual copy.

Each student will need a piece of graph paper or a printed grid in order to draw models.

The teacher will need to have Algebra Tiles accessible.

The teacher may provide colored pencils or markers or have students bring their own coloring supplies.

Variation Tips (optional):

Could be adapted for lower grades by using area models rather than models using Algebra Tiles.

Quadratic trinomials with negative terms could be incorporated by changing the equations and adding red to represent the negative factors.

Notes or Recommendations (optional):

This activity can be completed independently or with partners. You can allow students to use Algebra tiles in order to allow kinesthetic learners to build models before drawing them.

  Keywords and Search Tags  
Keywords and Search Tags: area models, factoring, models, quadratic, trinomials