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**Using QR Codes for Problem-Solving**

I am excited to say that I teach in a one-to-one iPad classroom, and have committed to blog about my experiences. Here is one of my first attempts to use QR codes in my classroom! This free “apptivity” guides students through various apps on the iPad while engaging them in a problem-solving situation. QR codes, directions, and teacher notes are included. Students first scan one of five QR codes, and are guided to annotate a PDF file linked to the code, which helps structure the process of setting up and solving a simple equation. If you use the apptivity, will you please provide some feedback? How did you use it? How did your students like it? What would you do differently?

**Using Digital Photography for Problem-Solving**

Inspired to “dump” my digital photos somewhere, I recently created a resource! “The Math Cam” template is a great outlet for digital photos! Though I haven’t started using it yet with my students, I plan to soon! With the concept of “slope” on the horizon, I think students will easily be able to use their iPads to take some pictures around the school that we can analyze. In any case, this template can be used to encourage the problem-solving process with respect to a “real-life” photo for which students must generate the question(s) – we’ll see how it goes!

**Impressions with Expressions Parallel Practice: ****Exponents and Order of Operations**

Brain research supports that students benefit from being taught differences. “Focusing on and practicing differences gives learners the warnings and cues they need to identify them correctly in the future,” stated Carolyn Williamson in her session on the brain at a recent NCTM conference.

Inspired by this idea, I thought about students’ misunderstandings when it comes to simplifying expressions with exponents. Every year, students are presented with problems like (-2)^4 and -5^2, and they MIX IT UP, EVERY TIME! Why not be more explicit in presenting these differences to students?

That’s why I designed this “parallel practice” sheet – to help students very clearly see and practice the differences between various expressions containing exponents, while applying the correct order of operations. This structure supports brains better – give it a try.

**BIG HUGE PUZZLES – Fraction, Decimal, Percent Conversions and Simplifying Square Roots**

These have always been a big hit with students! Allow students to work in pairs or small groups to encourage math conversation as well as fluency for these basic skills. Consider laminating and making an interactive bulletin board. Fun with adult learners too! The goal is a BIG HUGE 4-by-4 puzzle such that every edge is touching an equivalent value.

**Slope – A Co-Created Graphic Organizer**

In my experience, students sometimes vary on timing when it comes to TRULY understanding the concept of slope. To walk them through this idea together, I have used a graphic organizer. Students help co-create its contents, and taking the time to explore the concept from different perspectives benefits all. I used a PDF to annotate on iPads, but a print copy would be just as effective… though maybe not *quite* as fun! 😉

**Classifying REAL Numbers Graphic Organizer**

Time and again, I have seen similar organizers in text books… except they are already done! Filled with examples, students are expected to just look at the completed G.O. and somehow understand how to classify numbers. Instead of staring at a page in a book, I’ve taken the idea and created this resource for students to interact with. First, students define each set of numbers, then small groups or individuals are given some numbers (on slips of paper) to classify themselves, based on the definitions and their understanding of how to use the G.O. Once all students present their classifications to the class, the G.O. has lots of nice examples, and everyone has experienced the organizer rather than just looking at it 😉

**Solving Systems of Linear Equations: ****Graphic Organizer for Problem-Solving**

After students learn how to solve systems by elimination, substitution, and graphing, this activity is the perfect icing for your proverbial cake! I designed the graphic organizer to help students break the problem-solving process into bite-sized pieces, and it has really helped!

Using 6 scenarios that will appeal to adolescents, students are prompted to:

* Define the variables

* Write the system of equations

* Solve the system

* Indicate which method was used to solve the system (students will circle the word “elimination” “substitution” or “graphing” in the graphic organizer)

* State the solution to the problem (specifically ANSWER THE QUESTION ASKED in the problem statement, with appropriate labels)

Included in this file are greyscale versions of the pages for easy photocopying, as well as colorful pages if you chose to annotate the PDF on an iPad. Sample key is also included, but the element of choice built in to this activity ensures your students may choose varying methods… which is a good thing!

**Relations and Functions “Representations Mat”**

The concepts of “relation” and “function” are very vocabulary-rich! Students sometimes struggle with all of the synonyms… inputs, x-values, domain, independent variable… and so on! I designed this “representations mat” to help students see and apply these concepts in a visual way. First, I generate a relation consisting of 5 ordered pairs. Next, students use the “mat” to identify the domain and range, represent the ordered pairs in a table, create a mapping diagram, plot the points in the coordinate plane, and finally decide whether or not the relation is a function. Students can even generate ordered pairs themselves.

In the past, I used this sheet as a template and placed it in a clear plastic sleeve, so students could use a dry-erase marker and re-use the “mat” for various relations, erasing and starting fresh each time. I now have iPads for every student, so I have used the PDF file in apps that allow students to annotate the “mat” and save each relation we walk through. A simple way to address multiple representations and reinforce key vocabulary!

**Distributive Property Versus the Order of Operations: A Solution to the Battle**

Every year, when I present The Distributive Property using only numerical expressions, students argue… “Why can’t we just use the Order of Operations?” To tell them they need the Distributive Property later in Algebra is not an acceptable answer, (trust me) so I designed this activity to allow students to validate and explore BOTH methods for simplifying numerical expressions. This task guides students through some expressions that are more easily simplified by using the Distributive Property, while others are simpler by following the Order of Operations. Allowing students to analyze both methods for each problem, then state their opinions about the methods, makes for a much more pleasant experience. A sample answer key is included.

I have a MathyCathy “store” on Zazzle.com featuring some math goodies I have created as gifts for colleagues. Easy to personalize, fun to give (even to yourself!) Check it out:

View more gifts at Zazzle.

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