Teaching equations using the cover-up or blob method

I have a group of struggling algebra students. They were taught to solve equations last year in 8th grade. When we approached the Mystery Bags activity (which covers solving equations with variables on both sides) I gave them some simple one-step equations and realized that they needed some more practice - especially with equations involving integers. The first day I "retaught" solving equations using inverse operations it did not compute with the majority of the class. I discussed with Mrs. New whether or not I should try to find a creative way to teach equations. After teaching using our Meaningful Math books in which we have a context and discovery/inquiry based activities it was so hard to just teach by giving notes and examples. I had seen a cover-up method for solving equations but the worksheet I had was a little confusing. Mrs. New had learned about a Cover Up Math app when she was at ISTE last Summer. I decided to let the students work with the app and see their reactions. When they told me that they understood it better using this method I did a little more searching. I found this worksheet along with this video which teaches solving equations with a method very similar to the Cover Up Math app. I had some students really grasp hold of this method because it made more sense to them. I still would kind of go to the side a be a "real" math teacher and talk about inverse operations. I had one student who did great using the traditional inverse operations.

Now...fast forward a week or so and we are now working on solving inequalities. I have realized that since I have so many students in the class that did not solve by inverse operations it is difficult to explain to them about when they need to change the direction of the inequality. We did an exploratory activity in Cookies where they discovered that when you multiply or divide by a negative (when solving inequalities) that we have to flip the inequality for the statement to remain true. However, when we looked at solving inequalities and we "reached back" to the blob/cover up method we do not  talk about multiplying or dividing by a negative. So...in order to modify for the students to get the answers correct I told them to do these steps:

1. Replace the inequality symbol with an equal sign and solve the equation. (It is amazing how happy some of my students were when they didn't have an inequality symbol anymore.)
2. Draw a number line and decide whether or not to use an open or closed circle based on the inequality symbol (we had already discussed this)
3. Test a value on either side of the circled number to see if it makes the original inequality true. If it does shade on that side and if it doesn't shade the opposite side.
4. Lastly, make sure your "solution" matches the graph. This helps them to write the inequality with the sign going in the correct direction.

I did not write these steps on the board. We just worked through several together. I can't help but stand there thinking that it would be so much easier to just use the inverse operations with the "flip if you divide or multiply by a negative" rule. I had a few students tell me today that it all made sense to them now. I just wanted to say, "Really??"

So, I write this entry with a conflict brewing in my head over whether or not I have done the right thing. My reasoning for using the other method was that the students had been taught last year and  this year with the inverse operation approach and it just did not seem to work for them. The math teacher in me tells me that it is so important for them to understand how to solve using inverse operations. The common sense portion of my brain says if I can get these students to improve their ability to solve 1 and 2-step equations then I am doing good. These are students whose math confidence level is so low.

As we go through these problems I often show the inverse operations method beside the cover up/blob method in order to show them the connection between the two. I want them to get to where they can understand the formal mathematics of what they are doing.

Solving Equations Scavenger Hunt - Thanks Mr. Webb

It is great to have fellow algebra teachers that share their fun activities! Mr. Webb is another algebra teacher at Etowah High School and he made a scavenger hunt using QR codes in which the students had to solve equations in order to find the missing digits in the next room number. He bought cupcakes for the winners and we also awarded bonus points to the top 2 teams (everyone got a grade for participating). So during 5th period today we combined our  classes and created random teams of students.  Each team got a paper with a QR code that gave them an equation to solve in order to get the next room number.  They ran all over the school!

They had to get the room numbers in the correct sequence to win so they often returned to my checkpoint a little frustrated...

They do eventually get the hang of it though and they seemed to have alot of fun too! This was a great way to spend the last class of the day on the Friday before Spring Break! (And I got to eat a cupcake too!!)

Thank you again Mr. Webb for creating this activity and sharing with us!

Winners eating their cupcakes:)

IMP Overland Trail - solving equations using mystery bags - 5th period

I really enjoyed using Mystery Bags and Scrambled Equations. However, when I gave my students some "naked math" one-step equations they have really struggled. I have one class that is taking all year to work through the 1st half of algebra. They were identified to possibly have a struggle in algebra. I have several incredibly bright students in there. I have often thought - why was this student put in this class...   I had an eye-opening experience today. There were a few of my students who excel when we work in our IMP books who really struggled with today's work. I mean...the ones who are always "piping up" to answer the questions and seem to just "get" the big picture. One student even started the age-old, "When am I ever going to use this? This is stupid!" It took hearing him say that for me to realize that I have not heard that near as often since we started using our IMP Meaningful Math Algebra I books.

Ok...I am rambling a bit in this post so I am going to resort to using bullet points to make sure I get the main ideas that I am trying to convey:

• If I am teaching students who are struggling math students I am going to have to supplement material to help them learn to solve 1 and 2 step equations ...for sure. When integers were thrown in (after mystery bags) it has totally blown their minds. I think I am going to go "old-school" tomorrow and just teach the process in steps.
• After today I have a greater appreciation for how the context and story lines in the books give the algebra more meaning. I think it helps all students but I think it makes an even bigger difference in struggling students who don't usually do well in math.

IMP Alice Day 3 - Logic POW and Mystery Bags revisited

Today my Algebra IB students took a short quiz on systems of equations. The grades were not all that great but Ms. Whitt (my incredible coteacher) and I did our best to talk to each of the students about what they missed. The students will be given the opportunity to retake the quiz within the next week.

Ms. Whitt tutoring a student one-on-one on solving systems of equations.

 After the students turned in the quiz they were instructed to start working on the Logic POW. This is a very different POW than any that we have done before. It gives the students several pairs of statements and asks them to figure out if there is a logical conclusion that can be made. Some of the pairs do not have logical conclusions. I think this is a great way to introduce them to the type of thinking and reasoning that is required in geometry!

My 5th period Algebra IA class started Mystery Bags this week. Today we did the More Mystery Bags activity. I appreciated the context the first time I went through this last semester. I went back and read the blog I wrote after that day. The first time through most of my students seemed to have a pretty firm grasp of solving basic equations. However, my 5th period class needed more prompting. When the students had a problem like 5M +3 = 2M + 15 the context gives me such an easy way to explain why you would first want to take 2 Ms (or mystery bags) from each side of the equation (balance). In the mystery bag activity the constants are referred to as the weights that are on the balances. Therefore it once again makes logical sense that the next step is to take 3 ounces of weight from each side. We want to get mystery bags only on one side and weights only on the other side. Almost every student then understands to divide the amount of weight by the number of bags. (They are told that each mystery bag has the same amount of weight in it.)

Tomorrow they will be thrown some problems with some negative numbers. I explained to them today that the concept of getting all the mystery bags (variables) on one side and all the constants (weights) on the other will still work.

IMP Day 47 - The Mystery Bags Game and More Mystery Bags

Today my students completed 2 "mystery bag" activities. These activities are designed to provide a contextual understanding of solving equations. I have used an activity that used the idea of using a balance before but there wasn't a story to go with it. Once again I believe the context helped my students to grasp hold of the concept. Supposedly my students learned how to solve all types of equations last year. I could definitely tell that they were better at solving equations than previous years. However, I retaught solving equations before we started our new books.

The IMP Mystery Bag activities assumes that students have already been exposed to solving equations. Doing this activity makes me wonder how many times it takes our students to see a topic for them to retain it.