I have been teaching one student who is an English language learner who came to me at semester how to add and subtract proper fractions for the past three days. Everyday they come in I feel like I am starting from square one each day. I tried teaching by one example at a time, didn't work. I tried teaching using visuals like fraction circles and bars, that failed. The student was getting more and more frustrated, because they weren't moving forward.

I tried a different way. The other students in my class are to graphing linear inequalities. A majority of students in this class speak limited English and/or struggle with mathematics. One of the students finished early and I asked them to help this student.

This was their discussion back in forth in Spanish. It was a great way for both students to move forward mathematically and feel confident going forward.

Link to conversation in Spanish: https://chirb.it/ntn5mD . The sound byte is a minute and a half of the whole conversation which took about 5 minutes.

The girl in the audio does an excellent job of breaking down the problem and used fraction bars to represent the fractions in the problem. You can hear her counting out the fraction bar in the first part of the audio, eventually she moves towards release of instruction where they did a problem together, then she watched as the student did one guiding through the entire process.

I need to find ways of incorporating more peer teaching for my other students, I wonder how I can help guide them through the steps of asking questions and dialogue between each other better?

### Peer Teaching with ELL Students

### Orthographic Projection with Merge Cube

Merge Cube has been a hit with stores like Walmart offering the simple flexible cubes for a dollar a piece. Merge cube is a simple way to get students using augmented reality in a QR code way. Students scan the Merge Cube with an app and a magical world appears.

One of my favorite apps using the Merge Cube is Dig!

Using the app changes a simple cube with a bunch of symbols looking like hieroglyphics into another world. You can build and deconstruct the cube that looks almost exactly like Minecraft. The reason I like this app the most is that students can build using the app.

One of my favorite apps using the Merge Cube is Dig!

Using the app changes a simple cube with a bunch of symbols looking like hieroglyphics into another world. You can build and deconstruct the cube that looks almost exactly like Minecraft. The reason I like this app the most is that students can build using the app.

My students at the beginning of the year struggle with this concept of orthographic projection and being able to correctly sketch the block layout. Having students use the Merge Cube students can grasp that conceptual understanding that they don't get from a sketch. Last year I borrowed some of the wooden blocks our construction teacher uses and it was a great way for some of the students to see the finished product. The app allows students to see around each object looking at it from the sides and from the top.

What I would like to see is have students create their own and have stations at each group where students correctly draw the orthographic projection of their groups creation.

TIP: If you can't get a Merge Cube for each student, there is a shortcut. I printed a picture of one side of the Merge Cube and you can't rotate it like a Merge Cube showing each side, but students can use that one side to create especially using the Dig! app.

### Graphing Polynomials Using Vases 📈🏺

Polynomials is one of the hardest sections to teach, over the past four years I have acquired different handouts, activities, lessons, and tasks for Algebra 2 students and almost no material for the section on polynomials. Adding, subtracting, multiplying, and dividing polynomials always seemed like an algebraic process and not so much visual or hands on.

Now I have one activity!!! Graphing polynomials was always tricky, but teaching quadratics before made it seem like a piece of cake for them. One of my favorites is graphing polynomials using vases, yes vases.

So to preface this I with I spent a week searching all the Goodwills in the Omaha metro area for different vases and this is basically what I found when you take all of the repeats out.

Now I have one activity!!! Graphing polynomials was always tricky, but teaching quadratics before made it seem like a piece of cake for them. One of my favorites is graphing polynomials using vases, yes vases.

So to preface this I with I spent a week searching all the Goodwills in the Omaha metro area for different vases and this is basically what I found when you take all of the repeats out.

I did replace the big one in the middle and the one on the far right, well you can tell why.

The way I set this up is I provided each group a vis-a-vis marker, ruler, set of measuring cups, and a vase. Students were given the following directions:

1. they needed to mark off every inch on the outside of the glass

2. make a table for how many mL in every inch.

3. Put the table into Desmos

4. Find the line of best fit on Desmos (I gave them the different equations)

5. Look at the R squared value to find which one is best.

6. Present your vase to the class the following day.

I had students present from their iPads, but having them create a poster would have been better so they could compare and contrast the vase with the graph to identify key attributes.

What is even better the day before the students presented they practiced with a Desmos activity. At the end of the activity students had to create their own vase and graph.

Below are some photos of my students working on their vase.

Labels
activity,
algebra 2,
desmos,
graphing,
polynomials,
vase,
vases,
water line

### Transversal Tag 🏃

One of my favorite geometry activities I did this year was Transversal Tag. I set up the gym so it had the pattern of a transversal, like the picture below:

Students were randomly assigned a number 1-8 and then a tagger was randomly chosen. I am sure this game would have been much better to play with 3-4 taggers and play freeze tag, but we played that if you were tagged you became a tagger as well. Also if you went to the wrong area you could be tagged and become a tagger as well.

The taggers had to decide which angle congruency to say to get the most amount of people. For example, a favorite to choose was alternate exterior angles, because half of them had to run to the other side of the gym. The taggers also had to be smart about choosing ones where the runner will be going.

Especially closer to the end of the game the taggers had to come together to talk about which one would move the most amount of people and get a specific person out.

Students used the following:

Alternate Exterior

Alternate Interior

Corresponding

Consecutive Interior

Vertical

Linear Pair

It was a quick fun game that would have lasted longer if it was freeze tag, but the students had fun, used vocabulary, and had fun running around the gym for 20 minutes instead of being in class.

Labels
alternate exterior angles,
geometry,
tag,
transversal

### Head's Up: Review Game 🗣️

Head's Up! is a game of charades where the person puts their iPad or iPhone on their head and the audience performs and nods down for correct and backwards for pass. For students this was one of the best review games we used for vocabulary for geometry.

Students stood up in front of half the class and used my phone to show the students. This was excellent for students coming up with moving actions for such words as vertical angles and supplementary angles. Students were better able to self define vocabulary words better than previous, plus students had more fun reviewing.

It costs .99$ for the app and an additional .99$ to make your own cards. Well worth the money.

Students stood up in front of half the class and used my phone to show the students. This was excellent for students coming up with moving actions for such words as vertical angles and supplementary angles. Students were better able to self define vocabulary words better than previous, plus students had more fun reviewing.

It costs .99$ for the app and an additional .99$ to make your own cards. Well worth the money.

Labels
geometry,
Heads up,
review game,
vocabulary

### Coding Inequalities 💻

Coding in the classroom has always been an interest to me, Hour of Code is a great resource for any teacher especially those just starting out. For the past two years we have been doing Hour of Code during the Hour of Code week and that has been the most coding we do all year. What I wanted in my classroom was more coding, because I think coding could be the future for most of my students. I also believe that coding can be a gateway to other mathematical principles that are taught in the classroom such as: growth mindset, support productive struggle, and promote reasoning and problem solving.

So we have started in the math classroom is using one day a unit to work on these skills by implementing a way for students to apply their mathematical knowledge and coding. Students are given a task write code to make a calculator to solve an inequality. Students had to write code in Trinket.io to write their inequality.

We were going to use Swift by my Seniors do not have the iPads supported to do it, so we decided for everyone to use Trinket. Some students really loved the problem solving aspect of coding, using the blocks to get the numbers to do what they want them to do. Other students were not happy about trial and error process to finding the answer.

So we have started in the math classroom is using one day a unit to work on these skills by implementing a way for students to apply their mathematical knowledge and coding. Students are given a task write code to make a calculator to solve an inequality. Students had to write code in Trinket.io to write their inequality.

I have some other upcoming units to try this out with like Pythagorean Theorem.

Labels
coding,
inequality,
io,
mathematical principles,
trinket

### How I Teach Direct Variation

I use to teach direct variation by having students take notes, but the past few years I have been using Jon Orr's Water Bottle Flip.

There is an excellent Desmos activity that goes along with it. This year I copied and edited my first Desmos activity which was this one.

https://teacher.desmos.com/activitybuilder/custom/57f788035db373e705868c8b

I added two slides:

[New Post] Flippity Flip, Bottle Flip! Volume, rates, equations. https://t.co/FQ2QyFJ8Rf #mtbos #bottleflipping pic.twitter.com/tyMtBtyCX8— Jon Orr (@MrOrr_geek) October 7, 2016

There is an excellent Desmos activity that goes along with it. This year I copied and edited my first Desmos activity which was this one.

https://teacher.desmos.com/activitybuilder/custom/57f788035db373e705868c8b

I added two slides:

I wanted to emphasize direct variation and ask them deep meanings of graphs. One of the questions I asked was looking at the graph on the bottom, what inferences can you draw?

On September 8, there was the NATM (Nebraska Association of Teachers of Mathematics) Conference. During Lenny VerMass presentation, Smoke and you Croak or Huffing and Puffing to Understand Slope, he had a very interesting task.

Students had to measure how much air filled their lungs. So we exhaled into a balloon and measured (3) breaths and the circumference of the balloon. Then on a big sheet of paper we had to plot all of our data points for the following graphs and interesting things happened. Try it with your students.

Labels
balloon,
bottle flip,
direct variation,
graphing,
Lenny VerMass,
lines,
NATM,
task

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