7 T H – 8 T H GRADE MATH PORTFOLIO

Kaycee Dammann

Richfield Public School Academy2010-2011

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

“Doing the warms ups on the board made me feel smarter because I could show everyone else what I learned”~Alexia Wilson

Workshop

Workshop takes on 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 liked the riddles and logic puzzles because I had to think through the problem to get the answer” ~Gabriel Reese

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 orange 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 Ed Performance Data

7th Grade students took Ed Performance Math four times this year.

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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 liked learning about stem-and-leaf plots because it wasn’t confusing and made sense.” ~Kadesjah James

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 liked that I could use algebra tiles and balances to get the answers when I was solving equations.”

~Arriona Davis

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.

“I have fun playing the pirate boat game because it was fun and educational. It helped me learn how to solve problems with integers.” ~Michael Stormer

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 thought it was fun figuring out the slope, it was kind of like a puzzle.” ~Gregory Wilborn

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.

“I liked learning to solve equations because I learned how to solve for x or y easily. I liked being able to see the bags and blocks”

~Alexia Wilson

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 liked drawing different sizes of the same thing and learning the relationship between the sizes.”

~Kadesjah James

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 liked making posters that showed everything we have learned. I liked the graphs.”

~Thomas McGinnis

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 liked learning this because it comes in handy in everyday life.” ~Jace Ryno

7th Grade Student Reflections

“What I liked most about math this year was learning Algebra and solving equations. Mrs.Dammann taught me how to do Algebra in math.”

~Brendan Smith

“What I liked most about math this year was learning a lot of different topics.” ~Marquez Collins

“Mrs. Dammann helped me in math by showing me how to do the work. I liked learning about the x and y intercepts with Mrs. Dammann.”

~Alexia Wilson

“My favorite part of math this year was having Mrs. Dammann by my side to help me with everything I did not get”~Kadesjah James

“I like Math class because it is organized and I know what we are going to do everyday. I liked learning about linear relationships.” ~Mikayla Stevens

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 orange bars indicate the percentage of knowledge students gained each chapter.

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

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8th Grade Ed Performance Math Data8th Grade students took Ed Performance in Math four times this year.

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8th Grade Ed Performance Test-ing

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Unit 1: Real Number Concepts

Students learned to solve different problems involving rational and irrational numbers. Students used geoboards to find square roots of perfect and non perfect squares. Students also made human number lines to understand how to order and compare numbers

“I liked starting off the year with decimals and square roots.” ~Dominique Walker

“I liked when Mrs. Dammann taught me how to convert fractions into decimals.” ~Myles Clemons

Unit 2: Solve percent problems

Students learned to solve problems involving percentages, compound interest, and weighted averages. Students found the cost of going out to eat including the tip using menus from a local restaurant, and calculated their grades based on different weighted averages. They were then able to compare and contrast different systems to choose the right one.

“I liked when Mrs. Dammann taught me how to find discounts on sale items at stores. I liked the percent problems the most because I feel like they were the most useful in real life. ~Emmanuel Solis

“I liked learning compound interest when we got to calculate money because it deals with real life situations” ~Adriana Ruiz

Unit 3: Linear and Non-Linear FunctionsStudents learned to identify and represent linear, quadratic, and inverse functions, as well as direct and indirect variation, and population growth. 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.

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.

“I liked when Mrs. Dammann taught me about functions because there was a lot of graphing.”

~Alyssa Barrington

Unit4: 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 also learned to visualize a system of equations using centimeter cubes.

“This chapter was challenging, but once I learned it, it seemed simple.” ~Dominique Walker

Unit 5: Factoring QuadraticsStudents learned how to expand simple quadratic equations with integer coefficients. Students used Algebra Tiles to model expansions and factors. 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 liked factoring most because it was the most fun. I liked FOIL it was interesting.” ~Christopher Bilicki

“I liked that when I finally learned it I was proud of myself because in the beginning it was really hard.” ~Myles Clemons

Unit 6: Solving Quadratic Equations

Students 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.

Students developed knowledge through discovery learning while being asked to think about their graphs and how a change in one variable affected the other

“The chapter I liked this year was solving quadratic equations because we used calculators and did hands on activities.” ~Kaycee Kolar

Unit 7: The Pythagorean Theorem

Students were led through a variety of activities to develop a concrete understanding of the Pythagorean Theorem. This built on previous knowledge learned through out the year. They then applied what they had learned to solve more advanced real world problems involving distance.“I liked the chapter on the Pythagorean

Theorem the most because it was fun, and easy to learn” ~Clyde Huddleston

Unit 8: Complex FiguresStudents used prior knowledge to divide figures and find the perimeter, area and circumference.

Students used hands on activities and exploration activities to discover formulas and find patterns among the shapes.

“I liked learning all of the formulas.”~Adriana Ruiz

“I liked when we found the area and perimeter of the letters in our name.”

~Joe Huddleston

Unit 12: 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. Students created their own experiments and tested their predictions. Then used this information to discuss the difference between the main topics.

I liked the Probability chapter the most because we had a lot of hands on things in this chapter and we also played a lot of games in this chapter. ~ Kayla Knight

“I liked this unit because we were playing games, but actually learning.” ~Shaniya Martinez

Michigan High School Secondary Credit Assessment.

At the end of the year students take a final exam that covers all material learned in Algebra I. If they pass, they get the high school credit and get to move into Geometry!

This year we had three students pass the test, Emmanuel Solis, Cecelia Luna and Kaycee Kolar.

Cecelia Luna, Kaycee Kolar, & Emmanuel Solis

8th Grade Student Reflections

“My favorite part about math this year was learning Quadratic Functions. I also liked all of the different activities and fun things we did.”~Kaycee Kolar

“What I liked best about math this year was that I had two teachers that didn’t let me quit, no matter what my mood was in class. I really learned a lot from these two teachers.”~Kristian Garcia

“What I liked best about math this year was how Mrs. Dammann tried her best to make all the topics we covered fun in a way, and I also liked the different ways Mrs. Dammann taught the topics, such as using cubes and cubic tiles”

~Kayla Knight

“What I liked best about math this year is the improvement I showed throughout the year in math and scoring the highest on Ed Performance”

~Cashay Brownlee

“I like when Mrs. Dammann taught me that math does not have to be boring. It can be a lot of fun. She would teach me new ways to solve problems.”

~Christopher Bilicki

Peace Builders

“I liked the Duck Sense lessons because it helped some people stop bullying others and it was fun.”~Andrew Pieron

“Writing Peace Notes was a good thing because it helped some students be encouraged to do nice things.” ~Chelsey Emery

MATH Night!

Learning integer operations with playing cards!