The Distributive The Distributive Property and Property and Power Point Power Point

PresentationsPresentationsAn Action Research ProjectAn Action Research ProjectBy Linda Faulk, Davena Burns-Peters, & By Linda Faulk, Davena Burns-Peters, &

Katheryn RedKatheryn Red

OverviewOverview 2 Algebra I classes at Colton High 2 Algebra I classes at Colton High

SchoolSchool

Difficulties with Distributive PropertyDifficulties with Distributive Property

Series of Power Point presentations to Series of Power Point presentations to reteach and give practicereteach and give practice

Weekly quizzes to assess students’ Weekly quizzes to assess students’ progressprogress

Literature ReviewLiterature Review

Research QuestionResearch Question

Do variety in Do variety in lessons, using sound using sound and animation in Power Point and animation in Power Point instructioninstruction, assist with the learning assist with the learning of the distributive property?of the distributive property?

SubjectsSubjects

Used a beginning quiz to determine Used a beginning quiz to determine who was having difficulty with the who was having difficulty with the propertyproperty

18 students from two Algebra I 18 students from two Algebra I classes at Colton High Schoolclasses at Colton High School

Range from ninth to twelfth gradesRange from ninth to twelfth grades

Students’ ProblemsStudents’ Problems

One of three types of errors were One of three types of errors were made.made.

Correct Example: Correct Example:

3 (x + 1) = 3 * x + 3 * 1 = 3x + 33 (x + 1) = 3 * x + 3 * 1 = 3x + 3

Student Answers: Student Answers: 3 (x + 1) = 3 * x + 1 = 3x + 13 (x + 1) = 3 * x + 1 = 3x + 1 3 (x + 1) = 3 * 1x = 3x3 (x + 1) = 3 * 1x = 3x 3 (x + 1) = 3 * x + 3 = 6x3 (x + 1) = 3 * x + 3 = 6x

Action!Action! 3 Power Point presentations3 Power Point presentations

The lesson as a whole consisted of a review of vocabulary, a lesson about it, and several examples that were copies from the adopted textbook from the district. Problems were given to students the next day to complete.

The second lesson demonstrated the distributive property being completed using an area model. Two days later, they were given problems to complete.

The final Power Point lesson was given one week later and immediately upon completion the students were given a problem to complete.

Weekly quizzesWeekly quizzes

The Why, What and How….

Part 1 of a series by Mrs. Faulk

Distributive Property

Distributive Property

For any numbers a, b, and c,

a(b + c) = ab + ac

a(b - c) = ab - ac

For any numbers a, b, and c,

a(b + c) = ab + ac

a(b - c) = ab - acWhen a number or letter is separated by parentheses and there are no other operation symbols – it means to distribute by multiplying the numbers or variables together.

Find the sum (add) or difference (subtract) of the distributed products.

Use the Distributive Property

Use the Distributive Property

For any numbers a, b, and c,

a(b+c) = ab+bc

Our problem is 3(x + 1) and our result is now

ab+ac3(x) + 3(1)= 3x + 3,

Remember, this cannot be simplified because 3x is not the same kind of term as 3, they are NOT like terms

For any numbers a, b, and c,

a(b+c) = ab+bc

Our problem is 3(x + 1) and our result is now

ab+ac3(x) + 3(1)= 3x + 3,

Remember, this cannot be simplified because 3x is not the same kind of term as 3, they are NOT like terms

Multiply 3 times x and then multiply 3 times 1, then add

them together.

Multiply 3 times x and then multiply 3 times 1, then add

them together.

1,,3 now cxba

Multiply 3(x + 1)

Another one of Mrs. Faulks’ Fun and Exciting PowerPoint Lessons

Try Another:

2(3X - 1)

STEP 1: DRAW A RECTANGLE

 STEP 2: COUNT HOW MANY TERMS YOU HAVE

MULTIPLY 2(3X - 1)

1 TERM 2 TERMS

LET’S TRY A PROBLEM

STEP 3: SECTION YOUR RECTANGLE INTO NUMBER OF TERMS. YOUR LENGTH HAS 1 TERM: 2, YOUR WIDTH HAS 2 TERMS: (3X - 1)

 

MULTIPLY 2(3X - 1)

43X-1

 

 

STEP 4: FIND THE AREA OF EACH SECTION AND COMBINE

2

=6X

=-2

AREA = 6X - 2

X32

12

Distributive Property

Use the same concept that was applied with multiplication of integers, think of the first factor as the counter.

The same rules apply 2(X+1)

Two is the counter, so we need

two rows of (X+1)

Let’s try a problem• The counter indicates how many rows to

make. It has this meaning if it is positive.

X1

1

X

X X

1 1

2X + 2

2X + 2

2(x + 1) = means two rows of (x + 1)

Row 1

Row 2

Data Collection and Data Data Collection and Data AnalysisAnalysis

Initial Unsuccessful Students:  Total Students  

Far Below Basic

Below Basic Basic

       

Gender:   Male   13   5 6 2

    Female   5   1 4  

Ethnicity:   White   3   2 1  

  African-American 2 1 1  

    Hispanic   13   3 8 2

Grades;   9   8   1 5 2

  10 3 3  

  11 2 1 1  

    12   5   4 1  

Results and DiscussionResults and Discussion

     

Results of quiz prior to the first Power

Point lesson  

Student Results after the

first Power Point  

Student results after the Second

Power Point lesson  

Student results after the

Third Power Point

lesson

  # Students # Students # Students # Students  

           

Students successful     58       58       64       66   

Students Exhibiting Error Type 1 10       10       8       5  

Students Exhibiting Error Type 2 5       3       3       1  

Students Exhibiting Error Type 3 3       4       1       2  

ConclusionsConclusions

50% of students improved50% of students improved Other factors Other factors Further researchFurther research

ReferencesReferences