Blog Archives

Intermediate Algebra Castle Learning Review Activity

Mrs. Magin, Mrs. Lagana, Mrs. O’Brien, Mrs. DiVirgilio, and Mrs. Benz engaged their Intermediate Algebra students in a review lesson on Castle Learning.  Students worked hard on finishing 12 multiple choice and 3 short answer problems that helped them to prepare for their final exams.  For more information on Castle Learning, visit

Well done teachers and students!

Check Out My Wordle

A few months ago, I explored a website called  As the website describes, Wordle is a toy for generating “word clouds” from text that you provide.  The clouds give greater prominence to words that appear more frequently in the source text.  You can tweak your clouds with different fonts, layouts, and color schemes.  The images you create with Wordle are yours to use however you like.  You can print them out, or save them to the Wordle gallery to share with your friends.

I love using for math vocabulary activities!

I encourage you to check it out for a creative activity, project, presentation, pre or post vocabulary lesson, or assessment.  You can type in words into the wordle website or copy text from an article.  A sample of a wordle that I created from my favorite education topics is below:

10 Ways to Ensure a Successful Credit Recovery Program

What happens when a student is not learning?  Athena High School has created a Tier 3 response to intervention (RtI) program called the “Algebra Opportunity Academy” (Click here for a blog about the specifics of this program).  As a result of this credit recovery program, 12 out of 12 students earned credit back for at least one quarter of Integrated Algebra.  These 12 students are now on track to pass Integrated Algebra.

In discussing this data with my colleagues, it was clear that there were many reasons why this program worked.  The following are a list of 10 ways to ensure a successful credit recovery program (in any content area):

  1. Colleague support:  This was the most essential piece of this program.  This credit recovery program was highly dependent upon the math teachers of these credit deficient students.  If the math teachers did not trust the rigor or the objectives of the program, we would not have been able to adjust student grades.  Colleague support was also important in the selection of students and in the selection of the power standards that were taught in the program.
  2. Administrator support:  As with most programs, administrators can either be a help or a hindrance.  The administrative team at our school supported the math departments efforts and assisted in contacting the students and parents.
  3. Parent/Guardian support:  All students in this program had parents that set the expectation that attendance was mandatory and supported the teachers in their efforts.  They also drove or arranged rides for their children when necessary.  The transportation component helps to ensure parent commitment.
  4. College student help:  There were 12 students enrolled in the program.  Some might argue that a 12:1 student to teacher ratio is acceptable.  Perhaps, but a 2:1 student to teacher ratio is better and offers much higher instructional intensity.  We arranged six math education college students to come in to assist us in the program.  Many of these students needed a much smaller group to fully master a topic.
  5. Quick and specific feedback:  As this program took place over a short amount of time, it was important to give the students as much feedback as possible to ensure that they were able to “correct” their mistakes.  The Castle Learning website assisted us in providing quick and specific feedback.
  6. Multiple modalities:  This program offered students an opportunity to experience many instructional models: direct instruction, small group activities, computer programs, SMART Response Clickers, Dry Erase Boards, and other lessons that required them to move around the classroom.
  7. Goal Setting:  All students knew their current grade in the course and set a specific numerical goal that they wanted to achieve.
  8. High expectations for behavior and academics:  Clear behavioral and academic expectations were given to students and parents verbally (each parent was called individually) and in written form.
  9. Targeted assessments:  Assessments focused on the essential understandings of the first 2 quarters of Integrated Algebra.  The assessments were a combination of written and electronic (Castle Learning).
  10. Food:  All students were given snacks and a lunch.  Some could argue that this is not needed, but the food resulted in higher student morale, greater student energy, and a positive motivator to work hard.

For more information, please E-mail or Tweet @AndyMaillet.

Algebra Teachers Differentiate

For the past two weeks, algebra teachers have been teaching their students the concepts of greatest common factor (GCF), difference between two perfect squares, and factoring trinomials using the grouping method.  Recognizing that these topics tend to be difficult for students to master, they tailored the design of their unit to accommodate for these multiple levels of understanding.  They accomplished this by using the computer program Castle Learning.

Most days of this seven day unit, students went down to the library and worked on several Castle Learning Problems.  This worked well for students because they were given instant feedback and explanations for any incorrect answers by Castle Learning.  Teachers examined the data from Castle Learning after every lesson.  A sample of a data analysis is shown below.  A check means that the student was correct on his or her first attempt, a check with an X means that the student was correct on his or her second attempt, and an X means that the student was incorrect for two attempts.  Based on those results, some students were pulled into a small group for a reteach lesson.  Student learning was increased as a result of teachers ensuring that what a student learns, how he/she learns it, and how the student demonstrates what he/she has learned matched that student’s readiness level (Tomlinson).  If a student was not ready to move on to the next lesson, immediate intervention took place until he or she was ready, and then he or she was able to continue with the rest of the class.

Authentic Assessment for Logic

Mrs. Gross used to create an authentic assessment for her students.  Xtranormal is a free website that allows its users to create their own animated videos.  A user simply types the dialogue between two characters and the website does the rest.  Mrs. Gross used this concept to assess her Geometry students on the topic of logic.  The task given to the students was to complete a logic movie that displays knowledge of the various topics of logic.  Her students were very creative in their projects and demonstrated their understanding of logical reasoning in a fun and different way.

According to the Xtranormal website, teachers can:

  • Enhance their lessons with a movie
  • Have students create their own movie
  • Get access to an entire library of characters and sets

The rubric that was used to grade the assignment is below:






The movie is not complete.

The movie has 1 example of logic statements.

The movie has at least 2 examples of logic statements.


The movie is not descriptive.

The movie gives fair examples and explanations of the logic topics.

The movie gives clear examples and explanations of the logic topics.


The work in this movie has many errors.

Most of the work in this movie is correct.

All work in this movie is correct.


Click on the links below to see some sample Logic projects from Mrs. Gross’ class:

Using the ENGAGING Framework, this lesson demonstrates the use of Active Learning and Authentic Assessment.  Students in Mrs. Gross’ class were engaged in an activity that allowed them to demonstrate their knowledge of logic by a performance of understanding.  They participated in creating an authentic video to help them explain the concepts of converse, inverse, and contrapositive.

Making Word Problems Come to Life

Ms. Ruggeri and her Integrated Algebra class transformed a word problem that many students may describe as “boring” or “difficult” into an exciting 30 second movie clip.  The problem on this video is a systems of equations problem that asks students to figure out the cost of one slice of pizza and one cookie.  After a couple students created the video, Ms. Ruggeri showed it to the entire class.  She plans to share the video in her other classes and with her colleagues.  After watching the movie, Ruggeri’s students were better understood what the problem was asking and they were more engaged in the problem solving process than they would have been if they just read it on paper.  Ms. Ruggeri plans to create more math videos with her classes using real world scenarios as a strategy to better engage in mathematics.

Using the ENGAGING Framework, this lesson demonstrates the use of Intelligence Interventions.  Students in Ms. Ruggeri’s class were engaged in an activity that was kinesthetic and visual/spacial.  They participated in creating an authentic video to help them solve complex math problems.


BuzzMath Helps Students Achieve Mastery

Today in Mrs. Davis’ Algebra class, students continued learning about graphing linear equations using the web program  As a result of this additional instruction and practice, all students in her class demonstrated mastery of the topic earning a gold star.  On, the gold star is earned by getting all 10 questions completely correct.  This program allows students to learn from their mistakes, make corrections, and demonstrate their understanding by giving them different problems.

When Mrs. Davis and I attended the 2011 Association of Mathematics Teachers of New York State (AMTNYS) conference in Rochester, New York, back in October, we talked with representatives from  They showed us their program and explained how it differed from other online programs, such as Aleks and Castle Learning.  Impressed with what we saw, we decided to try it in her class.  According to, “BuzzMath is the best way to practice your middle school math skills.  It’s fun, it has immediate detailed feedback and examples that allow you to progress at your own pace.”  It should be noted that it has many topics that are in the High School Algebra Common Core Standards.

This slideshow requires JavaScript.

Geometer’s Sketchpad in Action

Mrs. Mayer engaged her students using the dynamic software program Geometer’s Sketchpad.  In both of Mrs. Mayer’s 12:1:1 classes, she asked high level questions that challenged her students to think.  Her students responded with great answers using appropriate mathematical language and did an amazing job with the program!  Mrs. Mayer’s students used Sketchpad to measure the three angles of a triangle.  Even though all students in the class had different size triangles, they all came up with the same angle sum–180 degrees!  This was a great constructivist lesson that allowed the students to discover mathematics, rather than be told mathematics.  Teaching assistants Mrs. Arsenault and Mrs. Hale also did a great job working with students and facilitating conversations.

Students were also challenged to answer the following questions that pushed mathematical thought:

  • What is the sum of the angles in a triangle?
  • Could we have 2 right angles in a triangle?
  • How can you prove that this is an obtuse triangle?

Students commented on how fun Geometer’s Sketchpad was and asked if they could download it on their computers at home.  Mrs. Mayer and her students clearly met the learning objectives of the lesson and will likely remember them for a long time.  Well done!

This slideshow requires JavaScript.

Athena Middle and High Schools Receive SMART Response Grants

The Greece Education Foundation (GEF) awarded grants to both Athena Middle School and Athena High School for a set of 32 SMART Response Clickers!  The foundation paid over $1,500 per school.  The SMART Response system gives teachers the ability to instantly track quiz results and lesson comprehension to gain immediate insight into student learning and help increase overall retention and engagement.  These clickers are already in the hands of many students and teachers at Athena.  Academic engagement and achievement will be maximized as a result of this amazing foundation.

The Greece Education Foundation was formed in June 2000 to enrich and enhance educational opportunities for Greece Central School District students and staff in a manner that supports learning.  The GEF receives gifts, bequests, and donations from local businesses and community members and subsequently provides grant funding to enhance educational programs that cannot be readily financed through local tax dollars or other public resources reflected in the annual school budget.  These are beneficial projects that might not be initiated, improved, or maintained without outside funding.

Thank you Greece Education Foundation!

Maximizing Student Engagement with SMART Response Clickers

Teachers at Athena Middle and High School are using SMART response clickers!  Mr. Titus, Mrs. Schrieber, Miss Northrup (University of Rochester student teacher), and Mrs. Derleth have been utilizing this interactive technology in their classrooms.  The SMART Response system gives teachers the ability to instantly track quiz results and lesson comprehension to gain immediate insight into student learning and help increase overall retention and engagement.

Some activities that they have implemented in just a few weeks include the following:

  1. Warm-ups/Ticket out the Door:  All students will have a clicker in their hand and be expected to answer questions on a warm-up and/or ticket out the door.  These questions could be multiple choice, short response, true/false, etc.  As each student answers the question, the teacher will receive immediate feedback on topic areas of strength and opportunities for improvement based on their answers.  The teacher can use this information to modify and adjust his or her instruction based on the demonstrated student knowledge.
  2. Instant Questions: During a lesson, a teacher may want to assess if all students understand the content being taught.  Often times a teacher will ask, “Does anyone have any questions?” and no one raises their hands.  It is unlikely that all students understand what was being taught, but did not raise their hands or demonstrate knowledge of the topic.  With SMART response, a teacher can have the students answer an instant and spontaneous question to gage whether all students can answer the question.  If students need additional instruction or time on task, the teacher will instantly have the data to make that decision.
  3. Common Formative Assessments (CFAs):  The CFA process has been embraced by many in the Greece Central School District.  The CFA process means that teachers from the same grade or course ask the same questions to a similar group of students to collect data.  This data is analyzed and discussed by this common group of teachers to improve their instruction.  This collaboration will likely increase student and teacher learning.  One of the struggles for teachers in this process is that compiling data into a meaningful form can be difficult and time consuming.  The SMART response technology organized this data in seconds and can display it in graphs and charts.

Great job Athena!  Students are more engaged and instruction is continuing to improve.  You rock!

%d bloggers like this: