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

Archive for the ‘O2’ Category

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.

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

Creating a “Lightbulb” effect! How do smart readers think?

How can students engage in their reading?

How can students engage in their reading?

As a teacher, it is my job to teach reading strategies which enable students to think and become smart readers. One method I can use to accomplish this is through reading activities that emphasis techniques students can use before, during, and after reading.

For “before” reading, I like the KWL activity where students are asked to identify first what they Know about a particular subject, then what they Want to know, and then following the reading end with what they Learned. Through this activity, students will use their prior knowledge to spark interest and use scaffolding to build a new layer of knowledge. This activity relates to Standard T2: Intentionally Planned, as it is a planned exercise for students to complete before moving into new subject matter.

In terms of Mathematic State Standards, using a reading strategy like KWL addresses and enhances the category of Core Processes: Reasoning, Problem Solving, and communication. When my students are equipped with reading strategies they will be able to tackle tough word problems, work through new definitions, and dig deeper into class content.

Question to consider:

* Besides asking the students questions, what are some methods for inspiring an inquisitive mind? In other words, how can I encourage a lot of content for the “W” part of the exercise?

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Citation: Chapters 3-6 Subjects Matter: Every Teacher’s Guide to Content-Area Reading,

by Harvey Daniels and Steven Zemelman

Showcase Lesson Plan – Functions as Literal Equations

As a result of the conclusion to my first quarter in the Education Program at Seattle Pacific University, I have completed my first showcase lesson plan!

Please view it, and give me your feedback!

Attached are four documents which make up a showcase lesson plan centered around a lesson titled: Functions as Literal Equations.

The documents are as follows:

1) Unit Plan Alg1

2) csc function lesson

3) Functions as a Machine of Literal Equations Rational

4) Function Lesson