What's My Rule?

I used the 'What's My Question?' format to have the sixth graders practice writing rules (or as Everyday Math calls them, 'general cases') for various patterns.

I first demonstrated how to write a rule: (the constant difference/ or change) times the variable plus (or minus) the constant/ what doesn't change. Example: the perimeter of a triangle is 3. When 2 triangles are placed side by side so that one side touches, the perimeter is now 4. Three triangles side by side have a perimeter of 5. etc. So the change is +1. So 1T +2 (that doesn't change)=the total perimeter.

The "What's My Question?' format worked great! I left the previous examples up and reviewed the basics in between each pattern. The students had partners to help them out. They were very engaged, motivated, and excited. Writing one rule after another like this was very powerful for many of them. I could see the light in their eyes, and they're growing confidence.

Try it!

--Lauren

Cooperation vs. Competition

When choosing a game format to practice math skills, we often have to choose between cooperation and competition.

Cooperation encourages risk-taking, promotes self esteem, and positive interactions among students.

Competition increases motivation, promotes self esteem (with the students' abilities are similar and neither one always wins or loses), and encourages positive interactions among the students.

I have found the perfect game format: it's called 'What's My Question?' and it involves both cooperation and competition. Students work with partners competing against another team. It can be used for any and all math skills/ concepts. The only requirement is that the students be capable enough to not need the teacher's support and input. It works best when you have homogeneously mixed teams so that the stronger students can teach their peers.

To begin, draw 12 to 20 squares on a black or white board, and number them. The teams take turns throwing something at the board to determine which question is theirs. If the team that threw gets it correct, the square is theirs and they may mark it accordingly. If they miss it, the other team gets to try for it. Should they have the correct answer, the square is theirs.

The first team to get 3 in a row (with 12 squares), or 4 in a row (with 20 squares) wins the game.

I have created questions based upon the skills they are currently working on, written on index cards, or used worksheets with problems. They sometimes like the worksheet format because they get to see the question before they throw and can try to pick the questions that they feel most comfortable answering. The card format works well if you want to pick the level or difficulty or type of question based upon the team members.

Try it out and let me know what you think.

--Lauren

S.T.E.M.

Wendy Cleaves, the Math Coordinator at the Regional Science Resource Center @ UMMS
222 Maple Ave., Shrewsbury, MA 01545, wrote, "The Central MA STEM Network has created a STEM Career Awareness video that focuses on middle school students. The intent of the video is to highlight opportunities for middle school students to connect with the world of STEM. Local STEM activities are highlighted in the video. The link is http://www.youtube.com/watch?v=NOhFEf_Q0Dc

You can also go to You Tube and search for Central MA STEM Network.
Charter Cable will be airing a half hour TV show ( STEM Career Awareness) in December with expanded footage of these activities and a panel. Please share as you see fit."

It's a very well done video about Science, Technology, Engineering, and Math applications as they relate to the middle school student. Several students were interviewed. They are well spoken, enthusiastic, and interesting. I think that you and your students will enjoy this video.

--Lauren

Multiplying Decimals

A teacher asked me today for help in explaining/ instructing/ illustrating multiplication of decimals. While decimals tend to be easier for students to handle than fractions, they might still get confused by the rules/ algorithms: when to line up the decimals; when to count them; and what do you do when you divide??! 

I shared some worksheets that I have that highlight the pattern involved, as every problem on the sheet has to do with multiplying or dividing by multiples of ten. I then ask the students to tell me what happened to the decimal? It moved to the right because you were multiplying; to the left because you were dividing... 

Some students catch on to this. They learn well when presented with number patterns. Others still look confused. For some it's the medium: the paper's too busy, so fold it in half. For one boy I worked with recently, this was still too difficult for him to see. So I wrote each digit on a separate piece of paper and I took out a counter to be used as the decimal. Then I had him physically move the counter to show me what his answer looked like. 

He got it! He now saw what I meant by the decimal point moving. 

Others still might look confused. I had one student represent the decimal. The students had to tell him/her how to move and how far to move. (Because decimals can't think for themselves.) This worked very well for some of the students. I combine this with my own 'decimal dance': where every time I mention the decimal moving to the right, I move to the right that number of spaces. And every time I mention the decimal moving to the left, I move to the left that number of spaces. This usually gets some weird looks and laughter from the students and helps them to remember what to do and why. 

How do you help your students to multiply/ divide decimals? Please send me your ideas as what I'm doing is surely not going to reach every one and there will be a day soon when I  need to do something new. Together we can teach the world: one child at a time. --Lauren   

Game Playing

Nrich is a great website. It has a lot of great online games involving strategy and critical thinking: including Sudoku and many types of discrete math topics (such as nets, NIM games, etc.).

It also has 3 articles worth checking out:

• The Value of Games
• Evaluating Games
• Making Your Own Games

Check them out then let me know what you think.

--Lauren

No Child Left Behind

I had a great week! My students were motivated, hard working, and --best of all--successful!

This is even better than it sounds, because I work with students who need a little extra support in order to succeed at Math.

It's easy for these students, (who are now in middle school, and may have had difficulties with Math for 6 or more years already) to give up: on their teachers; on Math; and, worst of all, on themselves.

When they come to me I refuse to let them give up. There is no "I can't." in my room. There is no giving up. Not trying is not an option.

That said, they sometimes still just go through the motions: doing as little work while with me as possible, and counting the minutes until class ends.

That is why this week was so special: not just for me, but for them. Because this week 2 of my students, who have been struggling mightily lately, had some success! And it makes all the difference!

Once a student who has been struggling succeeds, they begin to believe that they CAN DO IT! Their focus is better. They work harder. They continue to succeed. It really is a cycle.

We talk about this phenomenon in sports all of the time: winners' momentum. It's real. It's out there. And it can make a difference.

So-- in order for our students to begin to succeed, they need to begin to succeed. Or-- in order to believe in themselves, they have to see proof that they can do it.

So, how to begin this process?

Please send me your ideas.

--Lauren

Math Tutorials

I just found a great website with math videos. It's got everything!

Check it out!

http://tulyn.com/

Do you have a website for math videos that your students really like?

We use Brain Pop Videos (http://www.brainpop.com/) a lot in our school, but they don't have all of the concepts I'm looking for.

How about you? What do you use?

--Lauren

Math Games!

I just found an exciting site which features online math games. Games are a great way to practice skills: they are engaging; repetitive; and fun!

Check it out!

http://www.math-play.com/Middle-School-Math-Games.html.

I also heard about a software program that allows you to create your own games:

http://www.quia.com/web. Unfortunately, there is a small fee (about $40-$50 a year).

Do you have a favorite website for math games? Which games do your students most enjoy?

--Lauren

I've been working with my sixth graders on reading and ordering decimals. This can be tricky as a number like 7.521 seems to be much larger than the number 7.6 because, in our previous experience the more digits a number has, the greater the number.

I always relate decimals to money. When we relate a math concept and skill to real life and place it into a context that the students encounter on a regular basis than it makes more sense to them.

Today I did a google search for teacher blogs that commented upon ordering decimals. I found this great powerpoint/ video. Check it out.

Comparing and Ordering Decimals View http://www.authorstream.com/presentation/afabbro-68217-comparing-ordering-decimals-compare-order-entertainment-ppt-powerpoint/
Presentation Description Learn how to compare and order decimals By afabbro	Presentation URL
	http://www.authorstream.com/presentation/afabbro-68217-comparing-ordering-decimals-compare-order-entertainment-ppt-powerpoint/
	Presentation Description
	Learn how to compare and order decimals By afabbro

Rate * Time = Distance Problems

I have long wondered why our textbook teaches rate*time= distance problems in chapter 2. It's only October, the students are still fairly new to algebra. We have just reviewed integers, 1-step equations and the distributive property. They have recently been introduced to 2-step; multi-step; clearing fractions and decimals; "identity" and "no solution" equations. Are they really ready for what arguably are the most challenging problems in all of algebra?

These are the problems that frequently are quoted as being representative of algebra; often in regards to how much someone hated or failed at Math. Are we setting up our students to experience defeat? Are we asking too much of them?

For the first time one of my students truly surprised me: He Got It! He truly Got It! Is this my star student? Is he gifted? Perhaps-- but as soon as a week ago he was struggling to remember what he had learned about adding integers; who had forgotten what he had learned about solving 1-step equations. This is a student whose teacher and parent have been concerned about. I had spoken to him the previous day about the possibility of coming to the Math Specialist program more often, or seeing me after school.

He not only understood the rate*time= distance problems; he came in excited and eager to share. He was able to help the other students to do and understand the problems as well! These are the times when we are amazed and impressed by our students. These are the times when we bow to the wisdom of our textbook writers. These are the times that we know why we are teachers!

Perhaps we ask the students to do these difficult problems so early in the year so that they might understand the power that is algebra. Perhaps we ask the students to do these problems so early in the year so that they might come to see themselves as capable, able to meet challenges and overcome them. Perhaps we ask the students to do these problems so early in the year so that they might shine-- as this student did.

What do you think: should we save these challenging problems for later in the year? How do you help/ scaffold/ guide your students to succeed at these difficult problems?

What exciting times have you had as a teacher?

Answering Questions via Circle Graphs

I tried something new with my 6th graders this week. I encouraged them to generate questions that might be answered through our sports survey data.

At first all of the questions posed were of the type: "How many students...?" I wanted to go more in depth; so I suggested that the questions we ask might start with the phrases, "Do more...?"; "Which sport do more ___?"; etc. The questions that we asked had to make a comparison of some sort in order for the circle graph to give us any information.

Perhaps I shouldn't have been so explicit. Would they have understood the power of circle graphs more if I had allowed them to continue as they were, asking questions that would net only one quantity, then making circle graphs that were always completely shaded in?

How have you enabled your students to ask data questions? How much guidance is needed and how much is too much?

My sixth graders came to me confused this week about finding the median from numbers in a table. I determined that they must have been talking about a frequency table.

First, I helped them to understand what each number represented: in our case, the number of houses that had the given number of dogs.

Then we tried to visualize what all of the numbers would look like if they were written on index cards and hung from a rope with clothespins. I drew a few of the cards: we said that there were 13 houses with 0 dogs, so I drew five cards and wrote "0" on them.

Then I asked one of the students to help me to demonstrate what that might mean on a rope. We each held an end then I folded it in the middle, and asked the students, "What number would be here?"

It worked! They could visualize the process and seemed to have a clear understanding that the median is actually the middle of something: in this case a rope. They understood that half of the responses, in this case the numbers of dogs each household had, would be on one half of the rope and the other half would be on the other half, with the median right in the middle!

If you have other ideas for teaching the meaning of frequency tables or how to find the median, without writing out 73 numbers in order, please send in your ideas and suggestions. --Lauren

Expressions vs. Equations?

Have you ever had difficulty helping students to understand the difference between expressions and equations? Between evaluating and solving?

I tried something new this past week with my 7th graders: I wrote various algebraic expressions on index cards then asked the students to evaluate them. "How?" They asked. They didn't know what the variables equaled: EXACTLY!

I then gave them a dice and said that they needed to record what they rolled so that I would know what each variable was equal to. This highlighted the fact that variables can be anything.

What have you done to help students understand variables and the difference between expressions and equations?

--Lauren

Welcome to "Math Makes Sense"!

This site is under construction, but check back for great lesson plans, activities, and links that support Math in middle and high school. Feel free to send in your own suggestions.

Lauren McCluskey