Rationale for
Sixth Grade Math Lessons

Context:

The Integers Test Review, Addition and Subtraction of Integers Test Review, and Probability math lessons can be used in a sixth grade classroom.  These lessons were created at Appalachian State University under the advisement of Dr. Lynch-Davis, Elementary Education Block II instructor,  and under the advisement of Teresa Wiles, a sixth grade teacher at Mountain View Elementary in Ashe County, North Carolina.  I completed these lessons as a requirement for CI- 4030, Teaching Mathematics in the Elementary School.  

These lesson plans refreshed, reviewed, and introduced mathematical concepts that sixth grade students were working on in my cooperating teacher’s block II math class.  The Integers Test Review, Addition and Subtraction of Integers Test Review, and Probability math lessons made students apply math skills to solve problems and relate everyday language to mathematical problems and symbols, The Addition and Subtraction of Integers Test Review focused on the students’ prior math skills to solve mathematical problems with positive and negative numbers. 

Impact:

The Integers Test Review lesson plan can be used to help students interpret integers on a number line, determine opposites of specific integers, absolute value, and comparison of integers using the correct mathematical signs for more than, less, or equal to.  During the lesson, students worked on creating a number line and place positive and negative integers properly on the number line. 

The Addition and Subtraction of Integers Test Review can be used to help students understand the following rules for addition of integers Rule 1: If the signs are the same, add the numbers, and keep the sign.  Rule 2: If the signs are different, take the larger number and subtract the smaller number.  Keep the sign of the larger number.  The test review also helped students with the subtraction rule for integers rewrite the problem.  Keep the first number exactly the same, and rewrite the rest by adding the opposite number.

The Probability lesson introduced students to probability.  It reinforced students’ math skills with fractions, decimal, and percentages.  Students worked on simplifying fractions, converting fractions to decimals, and converting decimals to percentages.  Students were also introduced to the following mathematical terms used in probability, equally likely, probability of an event, and outcome.

Alignment:

    These math lesson plans align with the following DPI program standards:

Standard 2: Elementary teachers have a broad knowledge and understanding of the major concepts in mathematics.

• Indicator 1: As I taught, the two Integers test reviews I had to illustrate, explain, and demonstrate integers on a number line, how to determine absolute value of integers, and how to compare positive and negative integers.  I also had to apply the basic operations of addition and subtraction to solve mathematical problems with positive and negative integers.  The probability lesson reviewed fractions, decimals, and percentages.  Students converted fractions to decimals, decimals to fractions, and decimals to percentages. 
• Indicator 4: As I taught the probability lesson, I stressed the importance of formulating the proper question in order to obtain reliable answers.  I introduced how to collect, organize, analyze, and summarize data in order to predict outcomes.

Standard 7: Elementary teachers use developmentally appropriate strategies to design and deliver instruction in all areas of elementary curriculum.  

• Indicator 1: As I developed and implemented the lessons, I aligned the objectives and standards to the North Carolina Standard Course of Study for sixth grade mathematics.
• Indicator 3: All three lessons built on the students’ prior mathematical knowledge, misconceptions, and interest.  The probability lesson was directed towards the students’ interest in outcomes.
• Indicator 4: As the lessons were taught, I implemented a variety of teaching strategies to ensure each student understood the mathematical concepts of integers and probability. 
• Indicator 6:   The class that I taught the lessons to had a hearing impair student, which allowed me to modify the lessons to meet her special needs.
• Indicator 7: I provided assessments for all three-math lessons.  Through the formal and summative assessments, I was able to determine the students understood how to add and subtract integers, interpret number lines, compare integers, and determine probabilities.

Standard 9: Elementary teachers understand and use the processes of problem solving, reasoning and proof, communication, connection, and representation as a foundation for the teaching and learning of mathematics.

• Indicator 1: As I taught, the probability lesson I built new mathematical knowledge through problem solving.  To launch the lesson the students were asked to determine the probability of a coin landing on heads.
• Indicator 3: As I taught, the two integer test reviews the students were encouraged to communicate mathematical thinking with group members and me, the teacher.  Students also analyze and evaluate the mathematical thinking of adding and subtracting positive and negatives of their peers.
• Indicator 4: The Integers and the Addition and Subtraction of Integers Test Reviews allowed students to make connections to mathematical ideas.  Students realized that subtraction of integers built on the mathematical concepts (rules) of addition of integers.  Students also realized that probability interconnects with fractions, decimals, and percentages.