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MacKinnon Math Masters = M3

The mathematics faculty at Wharton Borough Public School's Alfred C. MacKinnon Middle School proposes to increase students' achievement in mathematics through creation of Learner-Active Technology Infused ClassroomsTM.  Learner-Active Technology-Infused ClassroomsTM are a signature product of the educational experts affiliated with Innovative Designs for Education (IDE) Corporation, the school district’s partner in this project.  These classrooms incorporate problem-based learning, differentiated instruction, technology-infusion and other principles of learning correlated with high student achievement.  Through intensive training, on-site and remote mentoring, and summer institutes, IDE consultants will provide professional development programming designed to identify and promote curricula and teaching strategies that integrate technology effectively into the school’s mathematics program and maximize student learning.


In order to aide in the accomplishment of these goals, the MacKinnon Middle School applied for and received grant funding through MATRIX, a program affiliated with the New Jersey Department of Education.  For details regarding the MacKinnon MATRIX grant and Wharton's year one abstract visit: .


Click here to view the Year Two Abstract which will be posted to the NJDOE MATRIX site soon.



Fall 2005 Update

The MacKinnon MATRIX Year Two Team is off to a terrific start!  The eight member team of mathematics teachers have already engaged their sixth, seventh and eighth graders in several of the technology enriched web quests and activities planned during the summer '05 workshop.  Teachers and students have enjoyed several visits from IDE Directors Tanya Boscoe and Sharon West. The team also participated in a LoTi workshop focusing on web-based multimedia projects.  All look forward to a great year exploring technology enriched mathematics.


The MATRIX Team 2005-06

The 2005-2006 MATRIX Team lines up with all of MacKinnon's math teachers.  Michelle Freeman continues on the team as a seventh grade math teacher.  Betsy Riordan teams up with three sections of this year’s sixth graders.  Our bilingual students are led through the MATRIX by their instructor, Karen Vaughan.  This year Tim McGrail is instructing one section of grade six mathematics and one section of grade seven mathematics.  Colleen Silvestri and Amy Laudati are new to the MacKinnon MATRIX Team this year.  Both teachers instruct special needs students in the Resource Room as well as in class support.  Also new to the team this year are eighth grade math teachers, Ann Marie Cunha and Carol Pillsbury.


We have a strong, knowledgeable team of veteran teachers and we look forward to some very exciting lessons!


How the West Was One + Three x Four

 During the month of September Mr. McGrail's sixth grade math class participated in a tournament for championship of "How the West Was One..."  The "West" math game allows students to develop their mastery of the mathematical order of operations through a challenging adventure game.  Students also used computers in the classroom and in the Tech Lab to write letters to  fifth graders explaining the order of operations.  The results of these activities are impressive and the students look forward to doing more tech enriched math lessons.




Who's the Best?   The Data Tells!

In September, Mrs. Freeman’s seventh grade math classes worked on a web quest entitled “Who’s the Best Player in the Major Leagues?” This particular project was designed to go along with Chapter 1 in the seventh grade math text; focusing on the use of several types of graphs and measures of central tendency. The students had to come up with their own definition of the best player. Searching varies websites on six current major league players; they obtained several statistics to determine who might be the very best. Once students gathered their data, MS Excel was used to represent the information in a spreadsheet. The final product was displayed in poster format, including pictures of players, hand written and computer generated graphs, spreadsheets including the measures of central tendency, and an explanation of the player they surmised to be the best in the MBL.


Create A Graph Online!

Mr. McGrail's seventh graders used the mobile lab to create one each of  a bar graph, line graph, and circle graph.  The students enjoyed learning to use the Create A Graph  website tools to complete this task.  Students were instructed to use 'amounts' for the bar graphs, 'change over time' for the line graphs, and 'percents or parts of a whole' for the circle graphs. Students will continue to explore this complex topic in math.


Technology + Math =Fun

 MacKinnon eighth graders recently completed the first of the MATRIX Math units created during the teachers' summer workshop.  In this math activity, Which Airline is Best?, the students were able to create a table of solutions for various linear equations; graph these lines; relate them to a point; and analyze the results.  In addition , the eighth graders used the classroom computers to graph these equations on the Graphing Calculators Program.  Using a "How To"  sheet, the students were able to complete this task, save the screen to a clipboard and then to their folders, and print out a picture of the screen.  The students truly enjoyed this activity!



"Order of operations--PLEASE HELP!!"  This has been the phrase humming through sixth grade classes in September for years.  This year the students in MacKinnon's sixth grade math classes helped other students with this process by writing letters to different grade levels. The overall project allowed the students to sharpen their skills on the computer by making power point presentations, downloading graphics, finding examples from a variety of web sites as well as discovering that in England "BEDMAS" is the acronym used for remembering. The letters include a complete explanation of the order of operations when evaluating numeric expressions.  Because this can be a difficult task, the students also wrote mnemonic phrases to help others to remember  PEMDAS.  Many of the projects include web site addresses that can be visited to help them with the procedure.  Handouts and examples were added for further reference.  We are all anxious to see what impact this project has on other classes who are studying the process.


Are There Really Vampires?        

With Halloween approaching, everyone is asking if Vampires really do exist. Sixth graders used calculators to work on this problem.They determined that if Vampires were real and had the ability to infect others by a simple bite,  we would all be Vampires in less than one month.  With the world population just over 6,000,000,000 people, students proved that in less than one month one Vampire could have the ability to infect the entire planet if they bit only two people each day.  Well, we certainly are not all it must mean that the bat-like creatures are just for fun on Halloween!!!


Click here to see the great rubric the teachers used to assess the students work.

Wecome, Mrs. Silvestri

New to our school system and MATRIX Team is math teacher, Colleen Silvestri.  Mrs. Silvestri kicked off the new year with some terrific technology enriched math lessons for her MacKinnon students.  Click the picture below to take a closer look at an eighth grade lesson using the coordinate plane.


Fall Updates

Mrs. Riordan's  and Mr. McGrail's sixth graders completed the "Vampire Project" shortly after working with exponents.  We discovered that if one vampire were to infect two people, and those two people infected two more people and so on; within a little more than a month the entire planet would be infected!  Since I am not a vampire and you are not a vampire then they really do not exist!!


This project afforded the students the opportunity to browse Web sites that kept statistics on world population.  We also did a lot of work learning how to solve equations with variables.  We are looking forward to our shopping project this holiday season!


Mrs. Silvestri's  sixth grade class work included  a unit on word problems, patterns and sequencing. These students also are looking forward to the school wide shopping project coming up next month.


Rumor Race

Mrs. Silvestri's 8th graders have been working on a very exciting project:


Since Sydney and Ben were both born on December 21st, the date of the winter solstice, they decided that it would be great not to have school on that day. Therefore, they decided to start a rumor that school will be closed to celebrate the winter solstice on December 21st. So, on December 1st, Sydney told two of her friends that school would be closed and continued doing this.  While Ben decided he did would tell 3 people every other day.  If there are 8,000 students in each school district, did Sidney and Ben start the rumor early enough for everyone to have heard it in their school?  Whose plan allowed for their entire school to be told first?



·        Make a predication.  Were the rumors started in time?  Whose entire school will know first?

·        Make a table or calendar to illustrate your calculations.

·        What was your conclusion?  Did Sidney and Ben start the rumor in time?

·        Who’s plan allowed for their entire school to be told first?



You will be graded as follows:


Prediction (20 pts)                            _____

·        Did you write in complete sentences?

·        Is your hypothesis logical?


Math Calculations     (60 pts)           _____

·        Did you show your work?

·        Did you check your work?

·        Did you put your work in table or calendar form?


Conclusion (20 pts)               _____

      • Did you back up your conclusion with the facts from your calendar?
      • Did you use complete sentences?


More Updates

During the month of October Mr. McGrail's seventh grade students worked on a WebQuest entitled Who Is the Best Major League Baseball Player? The students were given links to the Internet where they could study statistics of their favorite players.  Their research led them to create a power point presentation to persuade their classmates of their choice.


Mrs. Freeman’s 7th grade Pre-Algebra class was given a task to determine which airline would be best to bring them closest to an amusement park. Each airline used different algebraic equations to set up its flight plan. Students had to choose two airlines and use the corresponding equation to try to reach the park with the shortest distance remaining, since none of the airlines flew there directly. They were told that after landing they’d have to rent a car and drive the remaining miles. With that in mind, students had to determine which airline to use. Seventh graders were responsible for creating a sheet of solutions, plotting the two lines for each flight plan  on graph paper, graphing and printing points from a graphing calculator, and writing a letter to a travel agent explaining  which airlines they chose and why.


An interesting update from our grade six math teachers....

It is the holiday season and many of us are busy shopping for wonderful presents for our loved ones.  This year's sixth graders are no exception.  Beginning in the month of November the sixth grade mathematics teachers introduced students to MacKinnon's "Holiday Shopping Spree"!  Each student will be putting together a booklet for their family which includes a wish list of presents they would give if money were no object.  This is a great opportunity for them to dig deep into their values and find the ultimate gift, explore the Internet to discover all of the resources available to them and incorporate the mathematics skills they have learned this year.  We are all anxious to see the final result!!


Hmm, I wonder what they "pretend" bought me!!!


Mrs. Silvestri Reports...

8th graders in Mrs. Silvestri's class joined in the shopping project with an unlimited budget to spend on their family.  They had to figure out the discount amount and sales tax for each item they purchased. 


Mrs. Silvestri's 6th graders are learning the metric system and participated in a metric scavenger hunt. Her 7th graders are starting a project to determine if the weather in one region of the United States is more predictable than in other regions.  Each student has to select four cities; one from each quadrant of the United States.  Students track the daily temperature for seven days and compare the findings to the average monthly temperature for that city.  The seventh graders will have to plot their city locations on a coordinate plane and compare data gatehered by fellow students to make a draw a conclusion about the predictability of the weather.


Grade Seven Likes Shopping, Too!!

Not to be out done by grade six, the MacKinnon seventh graders are also on a fantasy shopping spree; however, some challenges have been added.  The older students have been given a budget!  Seventh graders are finding out just how far $5,000 will go and they are also required to apply coupons to their purchases. Students are calculating the cost of their purchases before and after applying those money saving coupons.


What a great way to teach budgeting and cost cutting!!


Eighth Graders Shop With Class!!

Our 8th graders are taking the MacKinnon shopping project even further!  They are formatting spreadsheets to calculate discounts and sales tax and then creating circle graphs to categorize their purchases.  Students have been instructed to complete all of their calculations by hand and with calculators prior to making their spreadsheets functional.  The functional spreadsheets enable the eighth graders to check the accuracy of their mathematical calculations. 


Who knew that shopping involved so much math


Students Celebrate Hispanic Heritage Month With Math

In celebration of Hispanic Heritage Month the MacKinnon bilingual class read different articles about Hispanic populations of the United States. The first article identified ten states with Hispanic populations. The students used this data to create bar graphs in Microsoft Excel to analyze and compare these populations. The second article identified the Spanish - speaking countries with the highest number of immigrants to the U.S. The students created pie charts in MS Excel and on the web site Create A Graph to depict this data.

The students also explored additional statistics on the data.


This was a great way to celebrate National Hispanic Heritage Month , to learn about Microsoft Excel, and to use the web site Create A Graph from the National Center for Educational Statistics.


En celebracion del mes de la herencia hispana la clase bilingue de la escuela Mackinnon leo varios articulos sobre las poblaciones de hispanos en los estados unidos.  El primer articulo identifico diez estados con poblaciones de hispanos. Los estudiantes usaron esta información para hacer graficas de circulos para analizar y comparar aquellos poblaciones. Usaron la programa Microsoft Excel y el sitio electronico, Create A Graph.  El segundo articulo identifico los paises donde hablan español y han tenido el mayor numero de inmigrantes hacia los estados unidos. Los estudiantes tambien exploraron mas estatisticas relacionadas con la misma iformacion. Fue una manera maravillosa para celebrar el mes nacional de la herencia hispana , para aprender sobre Microsoft Word y usar el sitio electronico Create A Graph del centro nacional de estatisticas educacionales.


Bilingual Updates

This month our class continued working on learning to organize and display data on varoius types of charts and graphs. They have also been studying the order of mathematical operations. They worked both in the computer lab under the guidance of Mrs. Leary and in our classroom.


Each student wrote five interview questions to ask each other, and  then recorded  responces on bar graphs and pie charts. Their questions ranged from "How long have you lived in the U.S.?" to "What is your favorite animal ?" Some students decided to use clip art to make the charts more appealing.


Students were also introduced to, and have been playing a computer math game called How the West Was 1+3*4  which pits their  own mathematical skills against the computer while reinforcing order of operations.


Additionally a few students enjoyed using Kidspiration to make beautiful time lines about their own lives. They combined ESL, Social Studies and Math in this activity.




Math in Daily Life

The first thing students need to understand about math is… IT IS USED EVERYDAY!  This is a great site for ideas to help students understand the connection from skills learned in the classroom to daily life.


Do We Need Mathematics?

A great resource for parents and teachers to explain to students the correlation between math and why they need to know math in today’s society. 


Glossary of Terms


Math Glossary – 6th grade

A sixth grade interactive math glossary.  Easy to use and gives examples of many functions that are defined. 


Math Glossary – 7th grade

A seventh grade interactive math glossary.  Easy to use and gives examples of many functions that are defined. 




Fraction Game

The National Council of Teachers of Mathematics created this a great interactive tool allowing students to understand size and equivalence of fractions.  The site also provides suggestions for collaborative work. 


Fraction Math

Harcourt School Publishers provides this interactive tool for students to review basic fraction operations. 




Bar Graph
How do you divide your day?  Students enter the data of how they spend a 24 hours in a day.  The focus is on the input and analysis of the data in the bar graph rather than on the technical aspect of building the graph. 


Circle Graph
How do you divide your day?  Students enter the data of how they spend a 24 hours in a day.  The focus is on the input and analysis of the data in the circle graph rather than on the technical aspect of building the graph. 


Spanish Resources for Math:


Math Lesson in Spanish:

This site gives ideas for teaching middle school math for bilingual or ESL students.


Interpreting Graphs in Spanish

A site written in Spanish for ESL students in middle school math to understand and decipher graphs. 


Spanish Math Resources

From the Internet Math Library, this site is provided in Spanish for ESL and bilingual teachers. 





Pentominoes is the general name given to plane shapes made by joining squares together. Note that the squares must be 'properly' joined edge to edge so that they meet at the corners.



These are brain teasers obtained when digits in numerical calculations have been replaced by letters.  Cryptarithms are a great way to reinforce or introduce concepts of problem solving while promoting group collaboration between peers.  Some of these are also available in Spanish.