Building Enduring Mathematical Understanding, one lesson at a time.

Archive for the category “msSunFun”

msSunFun: Musical Math Partners

One of the “math games” we play in my classes that I would like to share for

is “Musical Math Partners.”

It is quite flexible, gets kids out of their seats, and gives students an opportunity to use mental math skills.


Each student receives some sort of “card” depending on the topic of the day.

Some sort of “path” is designed for students to travel around the room without too many “log jams.”
Here is a diagram of how I make it work in my room:

Students follow a path around a “row” of four pairs of desks, but at the end of the row they may choose to turn either left or right and continue around that “row.” (Even though there are two arrows in the diagram, students are single file when walking between the desks.)

As the teacher plays their choice of music, students “travel” around the path – usually only 10-15 seconds. Once the music stops, students take a seat in the nearest desk and become “partners” with the person in the adjacent seat. (If you have more desks than students, you might want to identify some of the desks as “out of the game.” As it is, you will often have students that must continue to “travel” after the music stops in order to find a partner. If you have an odd number of students, the “leftover” person becomes partners with the teacher.)

Students “do the math” (more details below) – usually trying to finish more quickly than the other person – followed by a short debriefing regarding how they solved the problem, and then they trade cards so that they have different experiences with each new partner.

Possibilities. . .
The possibilities are only limited by your imagination / ingenuity. 🙂

Integer Operations
Each person holds a card with an integer. (A deck of playing cards work well for this: black = positive and red = negative.) When the music stops, the teacher randomly flips an operation card and students perform the operation from “left card” to “right card.” (I would only recommend division if you are interested in also focusing on fractions and mixed numbers.)

Fraction/Decimal Operations
Similar to the Integer Operations, only cards have fractions (or decimals.) I am fairly certain I would not include multiplication if decimals were involved, unless they were single digits. 🙂 For subtraction, if students are not yet familiar with negative numbers, students can subtract the lesser value from the greater one.

Fraction/Decimal/Percent Comparisons
Each student has a card containing a number. (You could do all fractions, all decimals, or a mix.) When the music stops, students race to decide which value is greater.

Evaluating Algebraic Expressions
Each student has a card containing two pieces of information: an algebraic expression (as simple or complex as you wish) and a numerical value (also as simple or complex as you wish – including negatives, decimals, or fractions – but remember the goal is for students to evaluate fairly quickly.) When the music stops, students must evaluate the expression of the left card by the number on the right card and then vice versa.

Operations on Algebraic Expressions
Each student has a card with an algebraic expressions. When the music stops, teacher randomly selects add or subtract and students perform the operation from left to right. If the expressions are binomials, multiplication could also be included. (I am not sure I want students multiplying trinomials using mental math.)

Solving Linear Equations
Two options using cards throw the previous two “games” if the expressions are fairly simple.
Option 1: For the cards that have the expression and the number, students set the left expression equal to the number on the right card and solve, then switch to number on the left equal to expression on the right.
Option 2: For the cards that all have algebraic expressions, students set the two expressions equal and solve. (This would work best if the expressions were fairly simple, but again, it is up to the teacher depending on the level of students and the current unit of study.)

Measures of Center and Spread
Each student has a card containing a fairly small data set. When the music stops, the two data sets are combined, and students are to find median, mode, and range. Depending on the size of the sets and the values, you could also have students find mean or the quartiles and interquartile range.

Plotting Points
Each student has a card with an integer and each desk pair contains a coordinate grid. When the music stops, students point to the location on the coordinate grid (of course, the left card is x coordinate, and the right card is y coordinate.)

Pythagorean Theorem
Each student has a card with a value representing a side of a right triangle. When the music stops, the teacher either chooses “two legs” or “hypotenuse and leg.” Students find the remaining side. (Since relatively small values should be chosen in order for students to compute mentally, there would be some duplication. If students with equal values became partners, the second option could provide some interesting discussion!)

Distance on a Coordinate Plane
Each student has a card containing the coordinates of a point. When the music stops, student locate the two points and find the distance between them.

That’s about all for now. Feel free to add more ideas in the Comments. This is certainly an activity to use only after students have a fairly strong understanding of the concepts used in the tasks. Teachers need to be careful when choosing the values / expressions on the cards so that mental calculation is fairly accessible.


msSunFun: Homework Hassles

Somewhere along the clogged up Google Reader, I missed the topic for this week’s:


It didn’t take more than opening up Flipboard to find out that the dreaded “Homework” is what’s on the menu today.

I have taught Middle School Math for the past four years. Until this year I have always taught sixth along with “something else.” Beginning Wednesday I will have three classes of Algebra (8th graders) and three classes of Math 8. I must admit that I am not exactly looking forward to the “Homework Hassles.”

I use Standards Based Grading in all of my classes, and one of the tenets that I feel strongly about is that a student’s grade is based purely on their understanding of math concepts and not on “participation,” “effort,” “behavior,” or “homework.” Therefore, even though I assign homework fairly regularly in my classes, it does not factor into their overall grade. Let me rephrase that: There are no “points” from homework involved in their grade, but I do feel there is a fairly strong correlation between a student’s homework completion rate and their overall grade. Unfortunately, (surprisingly enough,) not all middle school students necessarily have that same philosophy.

From my (albeit brief) observation of student behavior, sixth graders are much more “regular” in regards to homework completion. I think that whatever habit they developed in Elementary School tends to stay with them as the begin their life as a middle schooler. At some point, for some of the students, “grades” start to get in the way. If an assignment for another class counts as a part of their “grade” then it surely takes precedence over their math homework that “doesn’t really count” for their grade. By the time they are eighth graders, the percentage of the student population who find “more important things to do with their time” has definitely increased. Instead of completing a set of practice problems that your teacher has assigned in order to help you learn and retain the math concepts, school has become a series of earning “points” (or not earning them) to reach a desired “grade.”

Enough ranting, here is my “multi-pronged” approach for this year.

Math@Home Logs
For at least the first month of school, all students will be required to fill out a log, tracking the date, the assignment, time spent, whether it was completed, student initial, parent initial, and teacher initial.

This will be kept in the front “pocket” of their math notebook. I will stamp (or not stamp) daily and collect the log on Fridays. A “bulk” email will be sent home to any students who were negligent in completing the assignments and/or having their parent/guardian sign off on their log.

If a student has been successful at completing their homework for the first month of school they will be excused from completing the log unless their habits begin to change.

No Homework Notice
As I circulate and check off (stamp) homework, student who did not complete the assignment (didn’t start, didn’t finish, or didn’t show process) will be given the following reminder:

and will then be required to fill out a GoogleDocs form detailing the reason why they didn’t complete the homework along with a plan for completion.

I can print off the spreadsheet whenever necessary. As students do complete the assignment I can delete that row from the sheet.

Morning Math / Learn @ Lunch / Afternoon Academy
These are just my fancy ways of saying before school / during lunch / after school. Each Monday, students with assignments still missing will need to choose 15-60 minutes (depending on how much is missing) of time in which they will come to class and work on their missing work. (I have a cool grid on my board all ready to go for this. Students will each have a magnet with their name that can be placed in the location of their “first appointment.” No picture today – maybe later this week when I am at school.)

Making Homework Accessible and Appropriate.
Why have homework? What is my goal for my students when I assign it? These are important questions to consider when making decisions about a lesson each day. One goal I have for this year is to make sure I don’t assign problems “too early” in the concept development cycle. Just because a topic was introduced in class that day, doesn’t mean that students are really ready to “practice” on their own. Instead an assignment might focus on previous skills that will be helpful in solidifying the current concepts. This will take careful consideration, since I am not always sure how much progress will be made in class each day.

For some units I design quite a bit of the homework assignments myself, trying to incorporate some “puzzle/problem” solving activities that require students to come up with strategies that will, in the long run, help develop their understanding of math concepts. (See the example in this “Tricky Tables” post.)

In addition, I hope to make textbook homework less “rote” and more “reflective” at least SOME of the time. A few posts by David Coffey that I read recently share how to “flip homework” so that students are really analyzing a set of problems instead of just “cranking out answers.”

I certainly don’t have the “magic bullet.” I forced myself to refrain from reading today’s posts before composing this one, but I am looking forward to finding some ideas that will be useful. 🙂

msSunFun: Start, Stop, Continue


For this week’s msSunFun, I will have to opt for the goal-setting post, as my room is still somewhat in chaos. (I “inherited” a room from a retiring teacher and he left me lots of “gifts.” It took hours to sort through and decide what I wanted to keep, so now I am finally making some headway. We don’t actually start with students until September 5, but we do have an Open House a week from Tuesday – yikes!) After using 12 different rooms over the past 17 years, sharing with another teacher in all but one, am I hopeful that I have found a “home” for awhile!

Soooooo, on to the “real post.” Not much discussion – just a list. (I rambled on far too long yesterday for the New Blogger Initiative post.)


-Blogging about one lesson (success or “failure”) each week to share/get feedback.

-Incorporating the use of “monster” whiteboards in group problem solving.

-Implementing ideas I read about on blogs/twitter by figuring out how they will work best in my classroom.

-Introducing other teachers in my school/district to some of the ideas I read about.


-Staying up too late and/or falling asleep while reading with my daughter and then not being able to fall asleep later.

-Thinking critically about teachers who teach in an “ultra-traditional” manner and try to look for ways to help them see things differently. (Ok, that’s a stop/start.)

-Putting off following through on incomplete/missing student work. Help students understand how much I value homework even if it isn’t part of their grade. (Another stop/start.) 😉

-Allowing “little things” to disrupt the learning environment without addressing them in a simple non-threatening way.

-Applying too much pressure on myself to be the “perfect teacher.”


-Trying to focus on EMU (Enduring Mathematical Understanding,) especially when first developing concepts in the classroom.

-Using SBG to help students (as well as myself) see where they are really at in terms of their learning.

-Thinking “outside the book” when it comes to planning lessons and activities in the classroom.

-Writing posts for the New Blogger Initiative and msSunFun on a fairly regular basis (depending on the topic) and throw in a little Made4Math Monday and My Favorite Friday for good measure.

-Reading all the wonderful ideas that others are willing to share while attempting to find time to comment on them as well!

I think that’s all for now. I’ll check back in about a month and see. . .

MS Sunday Funday: “My Own Math” Notebooks

For the past few years I have required my students to have either a spiral notebook, a composition notebook, or a three-pronged pocket folder filled with paper. I have provided them one if they do not have one (finding the penny or dime deals) but I have not collected many from the sales this summer. I do have some useable three-pronged folders to hand out for those in need. Most students end up using more than one during the year, but I do not have them “start over” each quarter or semester. They just start a new one whenever the finish one off. (I had some sixth grade girls that wrote microscopically last year and were able to finish the year using only one notebook, but that is the exception.)

My notebooks are not so much “interactive,” but EVERYTHING goes in their notebook, with the exception of assessments (which are stored in class, in their math portfolios.) Students record daily learning targets, vocabulary, responses to class activities, partner activities, writing prompts, whiteboard activities (paper and pencil first), practice problems, homework, and I am sure some other things I left off the list. We also do activities that are entirely hands on and/or verbal. (They are usually quite excited when I tell them they DON’T have to write it down.) Each day they record the date along with “Today’s Targets” and start where they left off. I do have handouts, etc. for them to “attach” to their notebooks. I have used both glue sticks and mini-staplers in the past, but I “inherited” a bunch of rolls of masking tape from a retiring teacher, and I think I have found a way to make good use of that gift!

There are a few new features I plan to add this year. Unless students have the three-pronged pocket folder, I will be giving them a piece cut from an old file folder (another “inheritance”) to tape on the inside of the front and back covers. This will serve to hold handouts temporarily if there is not enough time to attach them in class that day. It will also store a few “ongoing handouts” that I use for formative assessments. These are one page “booklets” (folded the hamburger way) that have space for eight responses. Students will turn them in on days we use them and receive them back with feedback the next day to store for the next use. Another item to be stored in their “pocket” is a homework log on which they record the time spent on homework each day along with a parent signature. I will collect these weekly and return each Monday.

I also am working on designing a generic “foldable” for vocabulary (“Words of the Day.”) I will probably modify the Frayer Model that has been mentioned by others, as my vocab slides include definitions, examples, non-examples and use in a sentence. I do like the idea of including “characteristics” as well. The “tri-fold” below allows either the word OR the definition to be folded on top, so students can quiz themselves either way.


Students will store “blanks” in their “pockets” and pull one out whenever we need them.

Last year I collected notebooks every few weeks. (I had fewer students than I will this year.) I am not sure it was worth the time I spent creating a checklist and paging through them. I use Standards Based Grading, so their notebook is not actually part of their grade. It is important for students to understand the idea that the value in the notebook is in the thinking and recording that happens as they create the notebook, and the resource it becomes for them as they progress through math, not the “points” they earn. Some students need gentle reminders to stay focused, record their ideas, and show their work, whether I collect their notebook or not. The physical and verbal cues I give them in class do more than written comments at the end if the week. We will see how well it works if I don’t collect them this year. 🙂

I guess that last paragraph sums up the Enduring Mathematical Understanding that I want them to learn from using notebooks. The math they learn is THEIR OWN. They are in control of their own thinking, their own ideas, and their own strategies, as well as what they gain from others. Their notebook is a place to store all that they learn!

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