7 T H – 8 T H GRADE MATH PORTFOLIO

Kaycee Dammann

Richfield Public School Academy2009-2010

Bulletin Boards

Each month a new question is posted outside my classroom to challenge students and encourage them to work together.

Student Led Daily Warm Ups

“I felt encouraged to try the problems even when I wasn’t sure of the answer. I received support and help every time.”~Chantel Reedy

Workshop

Workshop takes on all different meanings in my classroom. It can be a tough logic puzzle, a hands on brain building activity, study island, or small group instruction. “I enjoyed the logic puzzles because it challenged my brain and kept me focused so I wasn’t talking.” ~Kyler Jarvis

THROUGHOUT THE YEAR STUDENTS USED HANDS ON ACTIVITIES, TECHNOLOGY, AND B OTH VISUAL AND VERBAL

REPRESENTATIONS TO LEARN ALGEBRA AND THE GRADE LEVEL CONTENT EXPECTATIONS FOR 7 T H GRADE.

7th Grade Math

7th Grade Unit DataAt the beginning of each chapter I assessed students prior knowledge. After each chapter, I formally assess what knowledge they had acquired. The green bars indicate the percentage of knowledge students gained each chapter.

Topics covered include: data and probability, understanding expressions, signed numbers, linear relationships, solving equations, ratio and proportion, interpreting graphs, and similarity.

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7th Grade STAR Math Data

7th Grade students took STAR Math five times this year. On average, the 7th grade students increased their STAR Math Grade Equivalent by two and a half grade levels. The discrepancy in January was due to a lack of test monitoring which was corrected for the final two tests. Se

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Chapter 10: Graphing

In this chapter, students learned to represent and interpret data using circle graphs, stem and leaf plots, and box-and-whisker plots. Students also used their prior knowledge to practice plotting points on the Cartesian plane. Geo boards were used to provide students with a concrete foundation of plotting points.

“I really like the stem and leaf plots because it was easy to see the pattern and interpret that data it represented.”

~Adriana Ruiz

Chapter 1: Understanding ExpressionsStudents learned to understand the basic properties of real numbers including common known identities.

Students used algebra tiles to practice combining like terms, and to show their understanding of the distributive property, associative property, and commutative property This provided students with a hands on approach to Algebra.

“I enjoyed using Algebra tiles in math class. I was able to manipulate them to find the answers to the equations. They were also helpful in checking my answers.”

~Emmanuel Solis

Chapter 4: Signed Numbers

Students solved problems involving operations with integers as well as performing basic operations on positive and negative rational numbers.

Students used counters to practice adding, subtracting, multiplying, and dividing positive and negative numbers.

“The counters helped me see and understand subtracting numbers with negative signs.”

~Marcelina Alaniz

Chapter 5: Linear RelationshipsStudents identified directly proportional and linear relationships through teamwork and presentations. Students created posters that outlined the basic characteristics of directly proportional and linear relationships and presented them to the class. They had to give examples and non-examples, and explain how to identify the relationship.

“I learned the difference between the relationships and understand it better because I was able to show my work through pictures.”~Alyson Countryman

Chapter 6: Solving Equations

Students solved one and two step Algebraic equations. They practiced using bags and blocks to help them visualize the concept of a variable. Also, students used interactive whiteboard scales to keep their equations properly balanced.

Higher level learners where challenged with more complex multi-step equations.

“What I liked most about math this year was how to solve an algebraic equation using bags and blocks.”

~Asonte Miller

Chapter 8: Ratio & Proportion

Students solved proportion problems and solved for the rate of change. They used the scale factor to enlarge and shrink objects, such as the sailboat to the right. Students also constructed similar figures out of blocks. These introductory activities laid the foundation for students to understand more complex proportion problems.

“I like using the graph paper to draw scale drawings. This helped me understand the rest of the chapter by starting with this project.”

~Anthony Johnson

Chapter 9: Interpreting GraphsStudents used the topics learned in Chapter 5 to apply it further to inversely proportional relationships.

Students created posters, each with a different equation, stated whether the relationship was directly proportional, linear, or inversely proportional. They had to explain their reasoning and show their results in a graph. Each group presented their findings to the class and discussed the differences between the three relationships.

“I enjoyed learning about the different graphs of equations and how we were able to create posters that had a different equation so we could learn from each other.

~Emmanuel Solis

Chapter 7: Geometry & ConstructionsProtractors, compasses, and rulers were used by the students to create similar figures. Students where challenged to identify congruent shapes and to construct both similar and congruent shapes. Students learned the main angle relationships and characteristics of triangles.

Lower level learners used trace paper to visualize, measure, and compare different figures.

“I truly learned geometry. I will remember this for a long time because we used compasses and protractors the correct way.” ~Kaycee Kolar

7th Grade Student Reflections

“I enjoyed learning Algebra this year. I liked how fast I got at solving equations using the opposite operation. I feel that I learned how to study for math and problem solve.”~Dominique Walker

“I learned the order of the four blocks of writing and I found that using it makes problem solving easier. It helps me organize my ideas and solve problems in order.”~Kaycee Kolar

“What I liked most about math this year was when we created the pi chain on pi day.”~Jerricka Goodlow

“Mrs. Dammann helped me in math by showing me the right way to use a compass and protractor.”~Roshaad Grass

“Mrs. Dammann has helped me in both being in groups and working independent better from the beginning of the year to the end of the year. She has helped me become a better student at math.”

~Grant Humphrey

THROUGHOUT THE YEAR STUDENTS USED HANDS ON ACTIVITIES, TECHNOLOGY, AND B OTH VISUAL AND VERBAL REPRESENTATIONS TO MASTER ALGEBRA AND THE GRADE

LEVEL CONTENT EXPECTATIONS FOR 8 T H GRADE.

8th Grade Math

8th Grade Unit DataAt the beginning of each chapter I assessed students prior knowledge. After each chapter, I formally assess what knowledge they had acquired. The green bars indicate the percentage of knowledge students gained each chapter.

Topics covered include: probability, linear relationships, quadratic and inverse relationships, exponents, solving quadratics, functions and their graphs, and measures of central tendency.

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8th Grade STAR Math Data

8th Grade students took STAR Math five times this year. On average, the 8th grade students increased their STAR Math Grade Equivalent by more than two and a half grade levels. The discrepancy in January was due to a lack of test monitoring which was corrected for the final two tests. Se

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8th Grade STAR Testing2009-10 Grade Equivalent

Grade Equiva-lent

Chapter 9: ProbabilityStudents learned how to apply the Basic Counting Principle to find the total number of outcomes possible for independent and dependent events. They created lists, tree diagrams, and formulas to find the sample space. Students debated the difference between both theoretical probability and experimental probability as well as independent versus dependent events. They created real world examples that could be applied to the topics they were learning.

Advanced learners were taught the difference between permutations and combinations and how to calculate the solutions.

“Using hands on activities and simple formulas helped me understand probability. This was my favorite chapter”~Aaron Rowell

Chapter 1: Linear Relationships

Students studied the difference between linear functions, quadratic functions, and other simple functions. They used color coded flash cards to identify a direct or indirect variation. Students created their own examples of basic functions using tables, graphs, and equations.

“The cards helped me figure out the equations by remembering a color coded system. On the test I visualized the cards and was able to easily recall the correct answers. I can use this skill in all of my classes”

~Tyler Panek

Chapter 2: Quadratic & Inverse Relationships

Students learned how to relate an equation to its graph through a parabola project where students researched where parabolas could be found in the real world. Some students built catapults out of pencils and rubber bands, while others showed that parabolas can be found when shooting a basketball. Students then demonstrated their project to the class which included explaining how to find the related equation and graphing the curve.

“I liked the way the project fit with my love for skating. It helped me remember the hard equations by linking it with the vision of my hockey stop”

~Austin Molina

Chapter 3: Exponents

Students learned how quickly exponential functions grow by folding or cutting a piece of paper in half or in thirds as many times as possible while counting the number of folds or cuts. Students were able to visualize exponential growth and understand how exponents work. Technology is often integrated in the classroom so the students can demonstrate what they discovered to their classmates.

The children’s book One Grain of Rice was used in class to show exponential growth and to give students a visual aid to help their learning.

“It was interesting because we interacted with different activities that were fun. I liked using the story book with our lesson.” ~Breona Rehil

Chapter 4: Solving Systems of EquationsStudents learned how to solve systems of linear equations by graphing, substitution, and elimination.

Advanced students were taught the Gaussian Elimination method using operations on matrices.

Lower level learners were encouraged to use algebra tiles and other visual aids to learn how to substitute an expression into an equation for a variable.

Students were taught to use their calculators to graph equations and solve systems of two linear equations.

“I found that solving systems of equations was challenging and fun at the same time!”

~Devon Lahring

Chapter 6: ExpressionsStudents learned how to expand simple quadratic equations with integer coefficients. Groups of students were given different sets of equations that follow common formulas and directed to “find the rule.” Students had to work together to find what was in common among each set of equations and disregard what was inconsistent. Each group came up with their rule, created a poster, and presented how the rule works to the class on the smart board.

“I found this chapter easy to understand because we used the acronym– FOIL – and we also created our own acronyms for other math ideas, which will be a great tool in my life.”

~Quientin Lee

Chapter 7: Solving QuadraticsStudents demonstrated their knowledge of factoring using algebra tiles and showing all of their steps. Students also worked together to write out the steps of more complex factoring computations, and explained the properties needed to solve for the variable. Posters covered the room as students discussed the different methods they discovered to solve a quadratic function.

“Using Algebra tiles, I was able to figure out how to break down long equations to solve for x.”

~Michael England“I liked square roots because it was easy for me to understand and find the answers.”

~David Rice

Chapter 8: Functions & Their Graphs

Students focused their learning on relating various families of graphs to their functions. They learned how to identify, write, and graph equations that have had various shifts and translation applied to the original equation. Students studied the effects of a shift on parabolas and cubic functions. In the posters to the left students

“This chapter showed me that through practice I could get the task done quicker and knew the material better.” ~Josh Price

Chapter 10: Measures of Central TendencyStudents used their prior knowledge of the measures of central tendency to analyze and determine which best represented a data set. They also learned to recognize practices of collecting and displaying data that may bias the presentation or analysis.

“What I liked most about the measures of central tendency was that a lot of it was based on prior knowledge so it was easier for me to learn the new material with a strong understanding of it already.”

~Dae-Shawn Spencer

Michigan High School Secondary Credit Assessment.

For the first time in Richfield PSA’s history we have had students pass this test! Hopefully we can get them right into Geometry starting next year. These students (from left): Seth Vankooten, Devon Lahring, Tori Promenchenkel, and Michael England worked very hard all year, and proved that hard work pays off!

8th Grade Student Reflections

“Mrs. Dammann is a great teacher. She is a funny person whose serious about peoples education. She always helped me by going through problems with me and making sure I succeeded at times I felt I would fail. She would go out of her way to make sure I understood, even when I made little mistakes she would help me correct the error.”

~Michael England

“What I liked most about math class was creating parabolas and watching the videos that the other students in my class created. I learned to recognize parabolas in everyday objects.”

~Rayven Layton

“My favorite part about math this year was the individual attention I got from the teachers. Mrs. Dammann worked hard to keep me on track and motivated.”

~Mark Roy

“This year I really enjoyed math. I am glad I have had a math teacher like Mrs. Dammann. She is always there for me when I need help and when I don’t understand she sits and explains it to me until I get the point. To be honest, math isn’t my favorite subject, but now I have a teacher who would never give up on me and I take more interest in math.”

~ CJ Brett

MMLAImproving Student’s knowledge of Numbers and Operations

School Improvement!

Our school improvement goal was to increase students knowledge of the numbers and operations GLCE’s. Students practiced their skills daily through warms ups and mental math practice sessions. De-

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Richfield Park Team Building Fieldtrip: Students participated in relay games and various activities to form bonds at the beginning of the year.

Students worked together to decorate the classroom door for National Literacy Month.

Team Building & Field Trips