The paths to "Eureka" moments: Teaching Mathematics in Secondary Education

Posts tagged ‘Lesson Plans’

Beg, borrow and steal?

As a new teacher, I’ve been told I should beg, borrow, and steal all materials I can get so as to not “reinvent the wheel”. I have found that this year, I have reinvented the wheel countless times, taken the wheel apart (kept what I wanted and trashed the rest), borrowed quite a bit, and screen-shot/stolen much!

Currently, I am in love with this 2nd-year teacher’s work on foldables in math journals. She is extremely creative in making the journals not only colorful and interactive, but also great study guides for students! With foldables, students are given self-made vocabulary, math facts, questions, and definitions all in a delightfully organized way! Ugh, someday I will be cool like her. For now, I will steal her ideas to help jazz up the end of the year.

Here is a lesson I am planning on using tomorrow in my Math 8 class: Exponent Rule Book

I’m pretty stoked, and I hope my students will see this as a helpful tool as they “study” for their unit test on Friday.


O2- Appropriate Challenges in Math

O2- Offer appropriate challenge in the content area.


Teacher-candidates plan and/or adapt curricula that are standards driven so students develop understanding and problem-solving expertise in the content area(s) using reading, written and oral communication, and technology.

This means that as a teacher, I design and adapt my instruction, based on the standards, to give students multiple pathways of success. My instruction challenges students to use reading, written and oral communication, and technology in order to problem-solve and demonstrate their understanding.

In concluding and reviewing the topic of transformations in my 8th grade algebra class, I designed a lesson plan which gave students multiple ways of articulating their knowledge, while challenging them to work with transformations using multiple perspectives.

Transformations Lesson 5

Specifically, this lesson had the following objectives. Students will write the learning target in their journal (read/write), use the learning target to remain on task during group work (reflect/problem-solve), discuss the learning target and why it is important during the closing discussion (oral communication), and finally, demonstrate proficiency by completing the exit ticket (graphing, written communication).

Throughout the unit on transformation, you-tube videos and online graphing sites where used compliment instructional materials.


After teaching this lesson, I learned about the differences of my students’ learning styles and the methods they prefer in demonstrating their understanding. In the future, I plan to use similar strategies for effective lessons on other topics. In addition, I will use give students more freedom of choice (differentiation by interest) in demonstrating their understanding.

Student Choice! Stations Lesson

H1-Honor student diversity and development.


Teacher-candidates plan and/or adapt learner centered curricula that engages students in a variety of culturally responsive, developmentally, and age appropriate strategies.

As a teacher, the content I teach must be accessible to all students of diverse learning profiles, readiness levels, and interests.

On the fifth day of our Algebra unit on functions, I decided to do a stations activity. The stations were designed to allow students to work on various ways of working with functions. The activity enabled students to choose the areas where they felt they needed additional practice.

Functions day 5

The stations were:

1)    Domain/Range: Worksheets with multiple ways of representing given information.

2)    Input/Output: Worksheets with many different functions and problems where students are asked to find either specific inputs or outputs.

3)    Graphing: Students are given several related functions (shifted along either the x or y-axis) and asked to graph them on different coordinate planes. (See graph paper)

DomainRange Worksheet     function_output      graphing_coordinate_plane 

As with other workdays, students were encouraged to work collaboratively and use dry-erase markers on their tables to demonstrate their work. “Go-to” people were designated at each station as peer leaders to whom students could direct questions before asking me.

After the stations activity a differentiated quiz was given to all students. The quiz had two versions based on student readiness level. The only difference between the quizzes was the complexity of the math involved; the function content was the same. Prior to giving the quiz,  I explained why I was giving two different quizzes. “Those who showed an understanding of functions (based on pre-assessment) receive a quiz with more complex math as well as functional notation. This is to challenge each student, not to label one group “smart” and another “dumb”. All students received the same type of questions, just different levels of math complexity.”

Functions Quiz 1   Functions Quiz 2

This lesson was planned so as to be learner centered. It allowed students to work with the content in a variety of ways and from multiple perspectives. Students were able to work collaboratively- challenging each student in a developmental way. Finally, the quiz was given in such a way as to give each student the opportunity to succeed and demonstrate their academic knowledge.

In creating this lesson I was able to grow in my understanding of how to differentiate instruction and assessments. I focused on individual student readiness levels and was able to formatively assess where students had strengths and weaknesses. By giving students the choice of which stations to work at, they were responsible for their own learning and quiz preparation.

In the future, I will continue to strive to make my lessons student-centered, differentiating my instruction to meet students where they are at developmentally.

The Classroom as an Environment for Learning: A Holistic Approach

H-3 Honor the classroom/school community as a milieu for learning. When the classroom and school community are respected as places of learning, student success is promoted and learning is uninhibited by unnecessary restrictions.

In the lesson plan presented below, students are encouraged to work collaboratively within groups of 3-6 students to solve for recursive equations given a sequence. Each group was given a different sequence and asked to solve using dry erase markers directly on their tables before then copying their work into math journals. In this way, students teach each other by discussing and writing their work for each other to see. Having completed their assigned problem, groups were then asked to review the work of at least two other groups and writing the others’ results in their personal math journals. Finally, one group was selected to demonstrate their work and rational in front of the class.

Recursive Review Lesson

IMG_20130117_113030Students were uninhibited by the tables as work spaces since they were able to use as much space as needed. Students were also able to quickly erase mistakes and make corrections. When the groups were satisfied with their own work, they were asked to leave it on the tables for other groups to review.  In reviewing the work of others, students were able to look to the entire class of peers as a resource for learning. They could learn from the work of others, ask questions, and then take notes in their personal math journals.


Finally, one group of students was asked to come forward and present their work in front of the class. Though their work was observed by several groups, the specific sequence they were given was at a level of greater difficulty and importance. In this way, all students were able to benefit from a more instructional time of learning (peer to peer instruction). The teacher, instead of directly instructing, led the presenting group through a series of questions about how they had solved their problem and why they were able to perform the operations they did. Not only did the students presenting have the opportunity to grow in communication and further understanding of their own work, but the entire class benefited from their work without having to struggle through it individually.


Through this lesson, I learned the power of peer instruction and collaboration. The teacher need not be the only source of learning. When students are in an environment which promotes peer communication and creativity in displaying their learning, they are able to thrive and grow as learners.

In the future, table tops will be continued to be used as resources for displayed work and examples. Additionally, I plan to continue selecting students to present in front of the class to demonstrate their work. I will especially look to encourage less confident students to do so (in content they display proficiency). I believe this to be one way to promote a healthy learning community where all students are valued.

Exceptionality in the Classroom

All students can learn. And I believe all students can learn math!



H1 – Honor student diversity and development. 

Attention Deficit Hyperactivity Disorder (ADHD) has become prevalent in the student body. As students struggle through the implications of such a disorder, it is important to recognize the behavioral and academic implications in the classroom. The article below provides some background and commonalities of ADHD as well as trends seen in the development of mathematics skills in students with ADHD.

Math Students and ADHD

Many students seem to find it difficult to transition from elementary addition of positive numbers to the addition of both positive and negative integers. And yet, this is a vital skill to learn. It is my belief that any student can develop the skills necessary and gain understanding of these concepts so as to achieve mastery in integer addition.

One important way to accomplish this is through lesson planning and the implementation of multiple learning styles. I have developed a lesson plan for the teaching visual and kinesthetic learners how to add and subtract with both positive and negative numbers.This is age appropriate for 7th grade students and meets appropriate OSPI standards as described in the lesson.

Teaching positive and negative addition to students with ADHD

Specifically, this lesson was designed with students with Attention Deficit Hyperactivity Disorder (ADHD) in mind. It is a dynamic and active lesson including games and the use of manipulatives to engage the students. In this way, students gain understanding though kinesthetic experience as well as stay engaged through visual reminders. Additionally, the lesson includes a self-monitoring sheet which allows the student to monitor his/her own behavior throughout the activities.  This creates a sense of ownership of the student’s learning which will positively influence future learning. In this lesson, we use colored chips to symbolize positive and negative numbers (as shown in the picture above). This demonstrates visually the differences between positive and negative integers allowing the student to develop a sense of “opposites”.

In writing the above article and designing the lesson plan, I have learned a great deal about the diversity of students with ADHD and how that will affect my teaching. I recognize I will need to integrate engaging activities and learning experiences in my lessons so that students are able to stay engaged. I also recognize the importance of self-monitoring aids that aid the student in developing an ownership of their behavior and learning. Though this lesson was designed for students with ADHD, it could and should be used for a wider demographic of students. It will be important in future lesson planning to consider the class being taught and the individual needs of the students. Additionally, taking advantage of other prompts and manipulatives will be key to presenting concepts to students with different learning styles.

Scaling Boxes: A math lesson integrating writing

Scaling a Compost Box

This lesson plan is for 6th grade honors students. Within the lesson, students will discover the relationship between the scale factor, dimensions, surface areas, and volumes of similar rectangular prisms.

This lesson includes:

1) Lesson Plan: Scaling Boxes lesson plan 6th grade

2) Textbook Pages: F&W Investigation 5

3) Answer Key: 7FWTGI52

4) Writing Worksheet and Launch Prompt: Scaling up Compost Box launch and questions

5) Student Work: Student Samples

Making Purple: A lesson in 6th grade Probability

Red+Blue = Purple !

This is a 6th grade lesson on experimental and theoretical probability. Attached are the following

1) Lesson Plan Part 1-5: Probability Lesson Plan 6th grade

2) Text pages: probability scan

3) Blank Worksheet: making purple blank worksheet