Linear Functions Practice with Stations

My algebra 1 class only has 11 students who all work at very different paces. I don’t really like doing traditional stations because they tend to talk and not do their work, especially if the answers are at their table.  I arranged this activity based off of math sprints from I love Math. I changed the activity to focus on everything we’ve focused on this unit.

Each student started off with sheet #1. . I had all of the answers for all four sheets glued on the inside of a folder that I kept upfront with me. When students finished the first sheet they came to me to check their answers. When they got one incorrect I would circle it and send them back to their seats.  When students came to me with a completed and correct sheet they were able to get the next sheet.  I personally thought the sheets became slightly harder as class went on.

Because students were checking their answers with me, I was able to see what each student understood and how they improved throughout the class.Because every student worked at their own pace I was able to help every student. I was also able to see what the class as a whole was struggling on. I’m not sure how this would work in a  larger class, but in my class of 11 very hyperactive students it was perfect! They loved getting to move around and get instant feedback on their work.

At the end of class I had them staple all four sheets together and told them this was their Linear Equation Book (so far). I’ve found that they also love having practice problems and notes all in one place (the more compact the better). I teach very interactive, so students tend not to take detailed notes in my class. I’d rather them be engaged all during class and have this small book of practice problems to refresh their memories.

Their linear equation books include. . .

Sheet #1: Finding slope between two coordinate points

Sheet #2: Graphing Linear Equations

Sheet #3: Finding the equation of a line when given a graph

Sheet #4: Finding Equations of Lines given two coordinate points

I taught students how to find equations of lines given two coordinate points during the beginning of class using a Writing an Equation from 2 Points Template from the Algebra Toolbox Blog. Every student had a template in a sheet protector and a dry erase marker. We did a few together and I walked them through the template. I then put coordinates on the board and had students create equations by themselves.  After every equation, we would check them! My students love to compete against each other so they would race to see who finished first. They love the template, but it’s been difficult weaning them off of it. I plan to have them journal quickly at the beginning of class about what they are actually doing in the template to gage their understanding.

Radical Jail … Prison Break Edition!

We just finished up our triangle congruence proofs and were moving on to exploring the pythagorean theorem and special right triangles. I noticed that my students heavily relay on their calculators for EVERYTHING, so I decided to include a lesson that explored roots (which I realized they never learned?) and simplifying radicals.

I started the class by giving students a root exploration activity created by Julie Reulbach. I told my students that they could work with a partner and each at least one person needed a graphing calculator. This activity explored the relationships between squauring and taking the square root, and cubing and taking the cubbed root of a number. When my students first saw a cubed root I was asked “Do we multiple 3 by the square root of 5?” It did not occur to be that this was the first time that they ever saw a cubbed root. They worked through the activity and then we discussed the answers.

 

Next, I told my students to get one whiteboard and one marker for each group of 2. I told them today they were going to learn how to break out of radical jail.  I started out by putting the square root of nine and asking them how they knew it was 3. They told me because 3 times 3 was 9. I then gave them the square root of 8 and asked how we could put this is simpliest form without using a calculator. My students knew that we had to use prime factorization!

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I told my students to think of the radical symbol as a jail cell and anything inside the radial is in jail. When we are simplifying radials we want to them escape radial jail. When we are helping them escape we use prime factorization to break up the inmates into prime people. I had my students circle every prime person. We talked about how a prime person could NEVER escape radical jail alone. The index tells the students how difficult it is to break out of the jail and how many prime people there need to be escape. When we were taking the square root I told my students that they need two prime people who are the exact same in order to escape radical jail. I had students put a box around the groups of two. If a prime person didnt have a partner in crime then they were stuck in jail. If they did have a person only one of them made it out alive but they needed each other to make it out of jail. 

My students loved this! I put problems up on the board and told them to help them get out of radical jail! I had them work with the person next to  them on their whiteboard. I love only giving each group one marker. It makes sure that they are talking about how to figure out the answer and not just working indivually.

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I used this lesson to lead into using the pythagorean theorem to find the relationships between the sides of special right triangles! Overall, it was a pretty fun and successful lesson! Let me know if you have any questions about escaping radical jail!

Using Manilla Folders to increase classroom engagement

One day I was sitting at my desk trying to figure out a way to keep my students engaged in class. I wanted students to be able to work through multiple problems and see multiple examples at their own pace. This is when I saw my box of manilla folders.

I first used the folders for an activity in Geometry where my students discovered the converse, inverse, and contrapositive.  Each pair of students worked on the activity together on the manilla folder, and at the end of class they were passed around. Students were able to see multiple examples and figure out the patterns of converse, inverse, and contrapositive without having to do multiple problems.

I next decided to use these folders in my algebra 1 class for teaching word problems. This particular class has A LOT of energy. It’s hard to get them to focus and take notes. I’ve been trying to figure out a way to have them practice word problems (perimeter, consecutive numbers, uniform motion). Students already filled in notes with notes with me and had examples of every type of word problem. Instead of giving students multiple problems to practice, I broke the class into partners and gave each group a word problem. It was each group’s job to complete the word problem and call me over when they finished. Once a group completed the problem correctly they had to copy their problem onto the manilla folder. On the front of the folder, they had to write the word problem. On the inside of the folder, they had to draw a chart (if necessary) and show their algebraic work. They also had to write their answer to the question out in complete sentences.   Students finished at different rates so this activity gave me plenty of time to walk around and help students and check for understanding.

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For homework that evening I had my students do the same thing, but this time they had were given a specific type of word problem and they had to create and solve their own problem. I wrote down the different types of problems on slips of paper and put them in the cup. Students got to reach into the cup to pick the problem they had for homework. This added a sense of excitement for getting the homework that night. I had students send me pictures of their problem before they copied it to the folder.

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In class the next day, students passed around the folders from their homework and from class the days before. The problems were on the front of the folder and the answers were on the inside. This was great because students were able to practice a variety of problems that they SOLVED and CREATED and were able to check their work instantly. This activity freed me up to be able to answer questions without the hassle of checking if every student had the right answer. This also gave my students the autonomy to create their own problems, decorate the folders, and work at their own pace. This activity took a little more time than just giving students a worksheet, but it was definitely worth it.  A worksheet would only keep this class engaged for a quarter of the time, but using folders kept them engaged the entire class.

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Exponents exponents and more exponents.

After our zombie apocalypse game about exponents I decided to check my students understanding of exponents by doing a hands on activity. I passed out a stack of cards to each students. In each stack there were 15 white cards (the questions) and 15 blue or green cards (the answers). Each student sat at a table with one other student. Each table had one stack of blue cards and one stack of green. The questions in each stack were different, so students were able to work with their partner if they had questions, but they still did their work on their own.

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I told my students to glue/tape the questions (white cards) to one side of their paper and the answer on the other, leaving room to do work between them. This caused my students to work out the problems (on paper) before matching it with the answer. It was AMAZING to see how much the students learned about exponents from the day before.

My students loved having manipulatives as they worked through the problems. This activity was much more effective than using a worksheet to check my students understanding. My students actually asked if I could organize our test in the same sort of way.  Although I’m not planning on using manipulatives I may make test matching (with more answers than questions) and create boxes for students to show their work.

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I got the cards forthis activity from Don’t Panic, the Answer is 42. I changed her directions around from being a class activity where questions or answers would be up on the board to a way that gave me tangible information about each students’ understanding of exponents.


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The Zombie Apocalypse of Exponent Rules

Today my Algebra 1 students started to learn about exponents. They’ve briefly worked with exponents in the past, but they have a very basic understanding. The idea for my lesson first came from Sarah Hagan’s Blog. I first asked students to draw seven X’s (I recommend less) on their dry erase boards. My students love using the white boards, so they were really excited when I told them we were going to learn exponent rules through a Zombie Game using the boards. I put the rules on the Smart Board for my students to read while I was explaining the direction. I have found that my students miss a lot of directions if they don’t see it in writing asScreen Shot 2015-08-31 at 7.39.17 PM well as hearing it.

I next used the exponent rules proof worksheets from Don’t Panic, The Answer is 42 to organize the game. My students had all of the sheets in a packet that they had turned over on their desk.  I put problems one at a time on the board for students to students to answer in 20 seconds. When time was up they all held up their white boards and I reveled the answer. My students then had 15 seconds to go erase an X from someone’s board if they got the answer correct. This is the point where this game got a little crazy. My class of 11 started running all over the place trying to erase their friends X’s. My students realize they needed to “defend” their X’s so they start trying to hide their boards from each other. It order to get my students back in their seats in time I told them if they weren’t in their seats by the end of my countdown then I would take one of their X’s. I split the game into 3 sections that covered four exponent rules, and their were 4 questions in each section. When each section was over they would complete the page in the packet dealing with that rule. Students would haveIMG_5723 to find a different partner for each rule. I told my students that completing each page was a necessity for surviving the zombie apocalypse. Students were only given5 minutes to work on each worksheet, so they were all very focused to complete it.  After they completed each worksheet we would come up with an algebraic rule together and then move on to the next rule. During class today we were able to cover the Product Rule, the Distributive Property of Products, the Quotient Rule, and Zero Exponent Rule.

 

This activity was great because it gave students the opportunity to explore the exponent rules and understand where they come from through a worksheet, but also have fun solving practice problems in order tIMG_5725survive the apocalypse. I was going back aIMG_5724nd forth between which order to organize this lesson. I decided to give my students practice and exploration problems on the board before they even knew they were working on a certain exponent rule. When they started working on each worksheet they already felt confident on what to do because they just saw a few examples.

If I were to do this activity again I would position the room so students wouldn’t trip and hop of over desks and chairs trying to get each other. My class got a little wild trying to make their peers Zombies. I would also create more rules in the beginning (no running, yelling, standing on chair, ect,). I wasn’t anticipating on how rowdy they would get. Over all I think that this was a very successful lesson. Students stayed engaged the whole time!