Student Loans Provide Interesting Topic for Math Students

As a Texas math teacher, I’ve just implemented a series of new math standards in my classrooms. One critical part of the new standards is personal financial literacy. The Texas legislature has decided that students need to be aware of the impact financial knowledge and decisions can make on their lives, and I wholeheartedly agree. One of the standards requires sixth grade students to “explain various methods to pay for college, including through…student loans” (TEKS 6.14G, 2012). In our lessons, we explored the costs to attend various colleges and what could happen if students decided to take out student loans. I also told them my own student loan story.

My parents always stressed that “I would never have to pay for a higher education,” if I kept my grades up. I worked hard and earned partial scholarships in undergraduate and graduate school, but I still decided to take out students loans to cover the rest of my college expenses. I made sure I was an informed borrower, even trying to pay the interest that began to accrue while I was still in school. Once I graduated and began working in the “real world,” it was time to pay back the loans. I struggled a bit at first, but found a balance that worked. When I changed careers, the salary I made barely covered my living expenses and loan payments. I began what I like to call “the student loan dance.” I moved through a series of deferments and forbearances and finally ended up on an income-based plan that has given me a sense of peace.

One of my students asked what would happen if “I decided not to pay [my student loans].” I explained the concepts of default, lawsuits, and garnishment. In Texas, defaulting on a student loan would result in losing my educator’s license. I’m sure many other states have similar measures. Ultimately, I told my students that when I decided to get student loans, I was taking out a mortgage on myself – and that’s not a bad thing. My personal “mortgage” gave me the opportunity to get a great education and impact the lives of hundreds of students over the years. And, just as I work hard to keep a roof over my head, I work hard to make sure that one day, I will make that last student loan payment. One day…

A quick lesson in student loans:

• Allow students to research the cost to attend college for four years
• If you have access to computers or tablets, direct students to one of the online student loan calculators. Bankrate.com has a good one: http://www.bankrate.com/calculators/college-planning/loan-calculator.aspx
• After students find their potential repayment amounts, have them search for their potential annual salaries based on their future careers. I totally rely on the United States Bureau of Labor Statistics: http://www.bls.gov/oes/current/oes_nat.htm
• Students should then calculate how much of their potential salaries will be used on student loan payments.
• In a writing prompt, ask students if the amount of the loans and their potential salaries will impact their decisions on where they want to attend college.

Creating Posters for Reviewing Concepts

As testing season moves into full swing, I've been thinking of ways to keep students engaged as we review various math concepts. In the past, we made review books, but there are so many new standards that it is not possible this year. How could I balance the need to cover dozens of new concepts with the need to be creative? And, how could I keep students from being overwhelmed? My solution: part anchor chart, part poster, and part challenge for students. Before challenging my students, I had to create an example.

Why CORN?

The first topic we cover class is rational numbers. Each year, I bring in ears of corn to represent whole numbers (corn in the husks), fractions (cutting the husk into parts), and decimals (removing the husks to reveal the kernels). I also use the acronym "corn" for conversion of rational numbers. When creating my own review poster, it was the perfect fit.

Creating Corn

Cut shapes first

Add notes after attaching

Making a corn review poster is simple. I started by cutting out 12 pieces of husks and six pieces of corn. Next, I joined two husks and taped them to a sheet of easel paper. Then, I inserted one piece of corn and added notes. I repeated the process five more times and my review poster was complete!







Blending review and technology

Poster image on phone

Zoom on converting














Once my sample was complete, it included information on each topic we covered that focused on rational numbers. I told students they could take pictures of the poster with their phones so that they could review the poster anytime. If they want to focus on a certain topic, they can use the zoom feature on their phones for the almost perfect review feature.

 
Almost perfect

The project would be complete (and perfect) when students created their own review posters. Instead of one student trying to cover each topic, I focused on eight major categories: rational numbers, integers, ratios and rates, expressions and equations, geometry, data analysis, measurement, and personal financial literacy. I allowed students to work in groups and told them I would post all of the posters in the hallway. Students could then pick and choose which posters they wanted to take pictures of and use for review at home. I limited their creation time to one hour, five minutes. (20 minutes for planning and 45 minutes for poster creation).

Students were engaged and I took so much joy in the creative juices flowing around the room during this activity. Students (and adults) have a competitive streak, and they were soon attempting to best one another in creative design. I am so proud of their effort and their results. Ultimately, I hope the posters will continue to help them prepare for testing and to help them retain the information long after testing is done.

I was so excited by my students' creativity!!!

"Egg-cellent" Expressions

One of things I've learned over the years is that presentation can really capture students' attention and
maintain interest in a topic throughout a lesson. When I have to cover difficult material, or when I'm reviewing for standardized tests, I like to create different types of lessons and activities. Since I have 140+ students, it's been a struggle to be budget-conscious while creating activities that all of my students can use. Dollar Tree and the clearance rows in many stores have become my favorite lesson-planning hunting grounds.

Last week, I picked up some plastic eggs and beautiful baskets from Dollar Tree (I still cannot believe the baskets were three for a dollar!). I also purchased a couple of bags of grass. My mission: to create a lesson to help students review equivalent expressions and the properties of operations.

I. Make a list of equivalent expressions.

I made the list first so I knew which expressions to write on the eggs.

II. Separate the eggs.

I planned on having students work in pairs with 8-10 eggs each. I counted out the eggs and put them in separate trays. In order to separate the eggs, you may have to cut or break a bit of plastic holding the egg together.



III. Write expressions on the eggs

After separating the eggs, I wrote the equivalent expressions on different colored eggs. When I finished writing the expressions, I connected the eggs based on the same colors.



IV. Select the basket, fill with grass and eggs.

Here's where the presentation is important. The lesson has truly transformed from a boring worksheet on identifying equivalent expressions to an activity where students get to interact with their work.



Using "Egg-cellent Expressions

 

 

1. Group students in pairs
2. Give them one basket with 8-10 eggs each
3. Instruct students to separate the eggs and connect the equivalent parts.
4. On paper, student should write the equivalent expressions and the applicable property of operation. For example, for the equivalent expressions 7 + 5 and 5 + 7, the commutative property of addition applies.



The entire activity should last 10-15 minutes.

I hope your students enjoy "Egg-cellent Expressions"!!!

Despite Technological Progress, Students Will Always Need Teachers

Full disclosure: I have had a computer since I was 12 years old. I have been exposed to them even longer. I love computers, love programming, and I love that computers and programs can make our lives so much easier. I took one of the first "computer-based" English classes at college and I was hooked. When I first started teaching, the idea that each student would have access to a computer (or cell phone) was unrealistic. I couldn't let go of the idea of giving students the opportunity to work on computers, so I begged teachers at my school to give up their classroom computers and we put a make-shift computer lab together. It was a success! Within 5 years, our school received COWs and the lab became unnecessary. Now, I don't have to move my students. The computers come to them. Gone are the days of floppy disks and CD-Roms. We have the Cloud. Today's students have more access to information than I could have ever dreamed of in my youth.

It seems that computers could solve many of the needs of today's classrooms. Online-based programs have allowed me to grade work faster, giving students also immediate access to their grades. Videos break down the steps to many of the concepts my students struggle with in class. Math-related games and other activities provide fun-filled enrichment that keep students engaged. At one point, my students were on computers so much that I wondered if I was needed anymore. And then...

One day, like many days, my students were working out problems I had posted on my online classroom. The program I use gives hints and provides step-by-step solutions. As I walked around monitoring student work, a student raised his hand. I asked him if there was a problem. He responded, "No, I just want to see if I got this problem right before I enter in the answer." I thought about reminding him that the computer would give him the answer, but I was curious about his thinking. So, I asked him to explain how he arrived at his answer. It took him some time, but he went through each step, carefully explaining his work. When he finished and pointed his pencil at the answer, I smiled and gave him a thumbs-up. He beamed and pumped his fist. Then, he told me, "See, I told you I could do it." Our exchange ended with a fist bump. Buoyed by that personal interaction, I asked the class, "Does anyone else want to explain their answers?" My entire class raised their hands.

That day taught me a lesson. Computers are great. Technology is wonderful. These things will never replace that personal touch that students need to grow, learn, and retain concepts in any subject. They need a person, a real person, to give them that boost of confidence, a smile, or even a fist bump. They need human interaction and recognition that a program will never be able to give them. That's one reason, among many reasons, that students will always need teachers and the world will always need physical classrooms in which to bring students and teachers together.

Real World Area: Infusing Interesting Topics into Math Lessons

Image from official Norway website

I was planning for this week's math lesson on area when I thought about an article I read last year. It
was about Rjukan, a town in Norway that does not receive a lot of sunlight during the winter months. To "illuminate the issue," they decided to use giant mirrors to direct sunlight on the town. At the time, I shared the article with students and asked them to answer a question based on the article. I gave extra credit for responses I received from students. This year, I want to actually incorporate the article into a lesson for my students. I don't want it to take the entire class period, but I do think it will give them a chance to explore a topic beyond the polygons they'll deal with on paper for the next couple of weeks.

Start with the article

The story about Rjukan is short, which makes it ideal for introducing to my math classes. I'm going to insert the link on my class website so that students can read it independently. I'll give them 3 minutes to finish the article. Time permitting, I'll also ask them to visit the official project website. Thankfully, the article includes that link.

Link to News Article about Rjukan

Get to the math

According to the article, the mirrors will create a 6,500 square foot beam of light for Rjukan for the town square. It does not mention the dimensions of the beam. I will direct students to prepare a page in their notebooks with the title, "Rjukan's Beam of Light." Students will need to determine possible dimensions of the town square and justify their dimensions. Area is given, but they will also need to calculate possible perimeters of the town square. Their notebook entries will also include a sketch of the dimensions. Students will have 5-10 minutes to complete their entries.

Answer expectations

Most students will use rectangles to complete the task. I'll be looking for proper algorithms, as well as sound justifications for responses (that means complete, detailed sentences!). Students will have to share their answers with a partner before we discuss their responses in a whole group setting. I know they'll be several different responses. We'll discuss the reasonableness of responses. For example, if a student gives dimensions of 10' by 650', I will ask, "Do you think the town square is only 10 feet wide/long?"

Lesson lead-in

I've found these types of "lesson lead-ins" keep students more engaged in the lesson. Students aren't always exposed to some of the reasons "why we're doing this in class." Exposure to real-world math applications is critical in increasing students' math competency. We'll be working on area formulas for the next week and a half, so I'm hoping to find a few more lesson lead-ins such as this one. Hopefully it's something other teachers can use in their classrooms.

Football Fun with Equivalent Rational Numbers

The Super Bowl is coming! The Super Bowl is coming! I wanted to plan a review lesson that incorporated football with one of our more challenging concepts. While browsing through Walmart, I  noticed some football-themed napkins and plates on clearance. I looked at the football laces on the napkin images and a number line came to mind. At that moment, I knew how I could use the napkins for an enrichment lesson on rational numbers.

Students needed a label, a napkin, and a notecard for the project.

First, I purchased enough napkins for all of my students. With clearance prices, I spent nearly $4.00 on the napkins. The plates were more expensive, so I only purchased 1 set of 8 plates. I already had white circle labels, and I remember paying about $2.00 for those labels. Each page of labels contained 15 stickers. It did take some time to write equivalent rational numbers on the labels. Without the labels, I would have created a document with sheets of the numbers, printed them, and allowed students to cut and paste them along the football laces.

We worked on the first lace together. Students later worked in pairs.

 
After setting up the plates, I spread out the napkins. Due to the design, each napkin yielded two football images. After distributing the napkins and labels, I instructed students to identify the equivalent rational numbers and order them from least to greatest along the laces. We briefly discussed the similarities between the laces and a number line. I allowed them to work in pairs. The conversations about how to position the labels were interesting, and all students were engaged (which made me very happy!)

Image of completed napkin.

After completing the footballs, there was one label remaining. Students were required to write an equivalent decimal (we are working on repeating decimals, so it was a great quick review). They also had to make a model.

Students used a notecard to write equivalent rational numbers for the last label.

The lesson took 20 minutes to complete, and I truly believe it was a success.

The plates are more expensive, but I love them!

Is it Possible to Re-invent Homework?

Okay. I'll admit it. There are times I just want to give up. Not my teaching position, of course, but on homework! Let's face it, many kids just don't like homework. I've often found some of my students trying to complete it before the bell rings. Don't get me started on incomplete or messy homework. I've tried to find ways to make it more meaningful, but I still have a percentage of students who can't seem to get it done.

For 2015, I've made it a mission to "re-invent" homework. I want as many students as possible to complete their work. I've heard the arguments for and against homework, but I believe work outside of the classroom is important to developing study skills needed for college.

So, how am I re-inventing homework? I'm doing it in "three-two-one." I challenged my students to complete six problems a day, four days a week. I'm distributing one page of homework (front and back) a week. Students complete the assignments and parents (or other adults) sign them before students submit them for grading. All of the concepts covered on the homework pages are review. For example, the first week of "Three-Two-One" focuses on basic calculations and rational numbers (the first concept covered this school year). I think students are less likely to get stuck when reviewing concepts as opposed to completing problems on new concepts.

I've also decided to place more emphasis on flipping the classroom. Sometimes students fall behind when taking notes in the classroom. Flipping can help with that issue. It will also give me an opportunity to focus on problem-solving during class.

I don't know if my "re-invention" will work, but I'm hopeful. I told students will keep the new format until Spring Break. I'll keep everyone updated on the results.