findingEMU

Building Enduring Mathematical Understanding, one lesson at a time.

Archive for the category “Made4Math Monday”

Made4Math Monday: Formative Assessment Forms

I definitely left some things “hanging” on my last SBG post, so I thought I would “kill two birds with one stone,” so to speak, and write about some of the ways I incorporate formative assessment into my daily routine.

A lot of people have written about “Exit Tickets,” and I guess, in a way, that’s what this is. I LOVE Sarah’s recent post at Everybody is a Genius (I’m not sure about everybody, but she IS a genius!) about the laminated dry erase ones ๐Ÿ™‚ I think I might try that for my more “reflective” tasks to end the period, but I like the “permanence” of the system that I have set up.

Here is my:

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Question of the Day
After we have spent a bit of time on a concept (but before it is time for a Mini-Assessment (Quiz)) I use Question of the Day to assess where students are at on a concept and us it to guide my instruction for the next few days. I will put up a slide such as this:

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at the end of class and given them about five minutes to work on it. (Depends on the task.) Rather than just using quarter sheets of paper (or anything dry erase) I wanted to have a tool that I could use to provide feedback and also to have students keep as a record of their growth. I came up with the following simple “form”:

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I print out four copies and then use the “booklet” app on our copy machine so that it shrinks it down and prints all four onto an 8.5 x 11 sheet. The original copy has more “space” on the top section because when it shrinks down there is an extra “gap” at the bottom of the page. This provides opportunities for 8 QOD’s before the students need a new sheet. They will store them in the “pocket” of their Math Notebook once they receive them back the following day. I use colored markers to write their number at the top so it’s easier to sort and hand back to color or number groups. The specific standard (CCSS) is written on the form, and we update scores on their Tracking Sheets (see SBG post) fairly regularly. When the forms are “full” students store them in their Math Portfolio – a hanging file folder in a crate that contains their tracking sheet as well as other “larger” formative assessments. Since there is only one question (ok, there’s usually two to three parts though) they don’t take long to grade and record. I can also “sort” the forms to create “Just for Today” seats (also on Sticks and Seats post) to either differentiate instruction or provide support for students who have not yet mastered the concept.

Writing About Math
I have students write in math class quite often,

20120903-130039.jpg but I haven’t always spent the time reading and commenting on their responses as I should. This year we are implementing the Common Core State Standards, and there are more than a few that employ the use of the verb “explain” or “describe.” I am looking forward to challenging students to meet standard on those in addition to the more skill-based ones. I decided to modify my Question of the Day form to use it for Writing About Math prompts as well.

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Sometimes the prompt will be tied to a particular standard and graded/recorded as such, but other times I am just looking into their thinking about a concept and wanting a way to provide feedback.

Recording System
Since I record multiple scores for each standard (and multiple standards on each assessment) I needed a way to organize that information so that I can see the progressions of scores in each area. I created a “grade book” form that allows for up to four scores (more if I sneak in a re-assessment score next to the original) for each standard with room for three standards on each sheet:

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Once I have my class lists I will enter them on a blank copy, make four copies of that, and again use the booklet feature on the copy machine. This time I transfer them to the 8.5 x 14 size, otherwise it shrinks down more than I want. When folded they create a nice size for up to twelve standards. I usually don’t have more than that in any one unit, so I create a new “grade sheet” for each unit. When I am entering grades into the online Gradebook, I just have to look at the most recent column and update scores that have changed from previous assessments.

Final Note: QOD and WAM are not always relegated to “end of period tasks.” I also use them at the beginning of the period. After I collect them we discuss possible responses. I am excited to use “My Favorite No” either when we do them at the beginning of the period, or the following day as a re-cap / remediation activity!

Made4Math Monday: Sticks and Seats

One of the benefits of working part time for a NUMBER of years was that I could find the time to be a “parent volunteer” while my own kids were in Elementary School. I must say that it was a valuable experience as a teacher as well. Most of my teaching experience up until that point was at the high school level, so many of the classroom routines were new to me:) One of those ideas was “picking with Popsicle sticks.”

Sticks

The question is. . .how do you pick sticks when you have six different classes? Do you have six different cups of sticks? After a few years of “refinement” I have a method that works well for me. I picked up a package of big, brightly colored “craft sticks” at the dollar store. There are actually six different colors, but I generally only use four. I wrote the numbers 1-8 on the bottom of the sticks and I am good to go for a class of up to 32 students. Each student is assigned a color and a number (which they remember quite readily after the first few days.) I, on the other hand, have a “cheat sheet” that I post on the board and “borrow” during class so I can actually call on the student’s name instead of just the “color-number combination.”

Here is my “Wizarding World of Harry Potter” butterbeer cup that I will being using this year. (I am finally retiring my University of Minnesota cup with the lettering all worn off, but I am still using it to hold my little six inch rulers.)

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Here is one of the (currently empty) “cheat sheets” that will be filled with names once our class lists are finalized.

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(Ha! I just noticed the Yellow column twice. I must have used my class that only had three colors last year and copied and pasted a new column. It’s supposed to say Green!)

Soooo. . . what if you have more than 32 students in a class? I’m glad that you asked. There are a number of different ways that you can deal with this issue. Since there are more than four colors available, you can certainly use more colors and fewer sticks of each color if you wish. Last year I had a class of 34 students and I included two blue sticks (in addition to the red, orange, yellow and green ones) numbered 1-2. If you have far fewer than 32 students (less than 24, for instance) you can eliminate one color all together, and never “pick” that color during that class. I have an additional “rule” that I follow as well. If I pick a stick that does not “belong” to anyone in the class (not just because they are absent) then I am the one who must answer the question! (Occasionally I have a class with lots of “unclaimed sticks” and I end up “calling on myself” more often than I wish, so I will put a limit on how many times I can answer in a period.)

I rarely use the sticks for “total cold calls” in class. Quite often students work on a problem, discuss it with a partner, and then I pick a stick to share their response. Other times I will have students work on five or six problems and as I begin to pick sticks, the first person chosen is allowed to decide WHICH of the five or six problems he or she wishes to share. (If no choice is made, I will choose!) By the time the last person is chosen, at least we have already discussed the other problems – even if the most challenging one was left for last. However, this is certainly not always the case. Some students definitely WANT to share their response to the toughest problem! I do not allow students to “pass,” even if they have not completed the problem. I will instead ask questions, questions, and more questions, to help them reach a solution. I will also call on raised hands after a problem has been shared if students wish to add more information, an alternative process, or an alternative solution. I generally leave the stick out of the cup for the rest of the period. I am not sure this is a “good thing.” Some students then “relax” knowing they won’t be called again. Others are disappointed that they won’t get “picked” another time.

I have to chuckle sometimes at the responses I get when I start to pick a stick. (Some times I will have already grabbed it, just waiting for the time to call.) Since they know their color, some are happily anticipating that it might be them, while others are nervously hoping it WON’T be them! Often the people up front will see the number as the stick is drawn (apparently I’m not very adept at hiding it) and actually KNOW the particular student before I can even look it up! Occasionally a student professes “disbelief” because they (let’s be honest, it’s usually a “he!”) “called it” that he would be picked. Oh, sixth graders – I will miss them this year ๐Ÿ˜ฆ

Seats

Why all this hassle just to assign a stick to a student? I have ulterior motives. ๐Ÿ™‚ The color-number combination is also often used to assign seats! On a daily basis, students enter the room and need to figure out where they are sitting and who they are sitting with for that particular day. (I alluded to this in my First Day post, but here is the full text version.) Some days the desks will be in groups of four and they might be sitting with their number groups or “half” of their color groups (evens and odds or highs and lows.)

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Other days they will be sitting in two’s where they are generally paired up with someone else in their color group.

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Since there are usually six or seven other people in their color group, this partner will also change from day to day. Part of my reason for posting the lists is that they act as a “cheat sheet” for the students as well.

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You may have noticed signs above the class listings that notify students the groups for the day. I have laminated (double-sided so I can just flip for a new option) all of the different seating choices available. For the “color pairs” there are seven different signs that all have each number paired with a different “partner.” (Now there’s a math problem for you!) I also have laminated signs for each number group that I set out on the groups of four, and for each color group that I place out to determine the “row” or “section” for that color. These are all stored in a basket right under the section of the board I use for group assignments.

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Just to make things even MORE confusing, I also have a few additional ways of picking the groups for the day. One is “Find Your Match” (pairs or trios) that I described in my post on Math Cards. The other is “Just for Today” groups (pairs, trios, or quads.) I often use this option after a formative assessment or during review activities where I purposely group students so that at least one person in the group has a strong understanding of the concepts. I sort their formative assessments and put them in groups, then jot down the names on a blank seating chart in a page protector using an overhead pen (I guess they still have their uses!)

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I assign new “color groups” every quarter. (I used to do it more frequently, but it can be time consuming, and with eight people in group, plus the other options, they get quite a variety throughout the quarter.) Initially the groups are usually alphabetical. By the second quarter I put some work into assigning groups. I often have the highest performing students with the same number (or two to three numbers) so that I can choose to use “Number Groups” when I want to differentiate a bit. (Those groups would “receive” a more challenging problem than some of the other groups.) I am also aware of when I end up with “high-low” pairings so that I either take advantage of built in “tutors” or at least I do not plan an activity in which partners might be “competing” against each other. A definite part of my lesson planning involves deciding how students will be grouped for the day. Finally, for the last quarter I usually allow some student input regarding who they would like to have in their group. I take requests of 2-3 people for each student and I can usually place them all in a group with at least ONE of the people they requested, often with two (or another in their number group.) Again, THIS is a challenge as well!

Back to Sticks

There were blue sticks I used in my class of 34 last year. When in “Number Groups,” they just created a group of five. When in color groups pairs they were my “Wild Cards.” They took the place of students who were absent for the day or sat together as a pair. (I also randomly drew sticks that they would switch with so each day there were different student’s sitting in the “Wild Card” seats.) For odds/evens or high/lows, if everyone was present, I would have them join a “convenient group” with the most extra space to form groups of five. I would also probably do this for a class of 25 or 26 instead of having four color groups with “lots of empty seats.”

Last year I came up with a new way to use the sticks during group work. If the students were in Number Groups, I would walk around with one stick of each color in my hand. When stopping to check on a group or to answer a question, I would place the sticks behind my back, mix them up and pick one to determine who to call on to either ask or answer a question. If students were in Color Groups, a collection of sticks with different numbers could be used. (Although I also used an octahedron, but this sometimes resulted in MANY rolls if I was at an “even” group and the numbers kept coming up “odd.”)

Whatever For!?

Sticks: I am TERRIBLE at calling on “purely random” students, so the sticks help me to do that on a more regular basis. (We also have class discussions that don’t involve sticks – it depends on the particular activity.)

Seats: I want every student in the class to be comfortable and familiar working with every other student in the class. We all have our strengths and weaknesses that we bring to a group and I want student to be aware of that fact, and looking for opportunities to share their strengths while acknowledging and working on their weaknesses. Not every student “enjoys” working with every other student in the class, but they know it will change the next day. Sometimes we will stay in the same groups for two consecutive days, but really no more than that. Some students swear to me that they have been with the same partner waaaay too often because they “happen” to end up partners in find your match (over and over. . .), they are IN the same color group so they are in pairs and quads with that person, AND I even put them together in a “Just for Today” group!! Oh, the injustices of being a middle school student!

Minor Pitfalls

Last year my sixth graders were my first class of the day. The buses arrive by 7:30 and class starts at 8:00, so more than a few of them would “hang out” in class for awhile. Then, I started noticing some patterns. Within a “column” of eight seats, the pairs can choose their spots on a first come – serve basis. Some students would quickly “claim” spots so that they could be just across the aisle from their “BFF” – who they were not actually in a group with (on purpose, from my point of view) but wished to sit near them anyways. I began to be quite careful about where each color groups was assigned, or where each number group was placed to try to avoid the “cliques.” I was not always successful. This year I have 8th grade Algebra students first thing in the morning. I am not sure they will “hang out” in class before school, but if so, I think I will wait until closer to 7:55 to make the group placements for the day!

Whew! “Leadership Team” meeting this morning, working in my room all afternoon, and I still finished this post at a decent hour – West Coast Time! Still nine more days ’till students arrive – unless you count out Open House on Wednesday, but I think I’m ready for that ๐Ÿ™‚

Made4Math Monday: Monster Whiteboards

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Yesterday I finished getting my “monster” whiteboards ready and I brought them into my classroom today. I am far from the first to have created these learning tools. Frank Nochese sang their praises here, and Anna followed up with another post as well. I use the little mini-whiteboards quite regularly with pairs, and they will still have a place in my class, but the opportunity for groups of three or four is really exciting! I especially envision using them for problem solving, such as the chessboard problems for my First Day Activities. I am concerned that we will not always have enough time to complete the “solving” as well as the “sharing” in one class period, but my solution will be to at least take photos of all of the boards and project them on the screen the following day as groups present. Another intriguing use will be the Mistake Game, as described by Kelly O’Shea. (Go there! Read it!) Sooooooo looking forward to trying this out – especially with my Algebra students because I think they will thrive on it. However, in the long run I predict it will be incredibly valuable to my Math 8 students in freeing them from fear of failure. The classes on the whole are not full of students who have been successful in the past, and developing a classroom culture where mistakes are acceptable and even celebrated as ways to learn concepts more deeply (EMU!) will be a huge step for their learning.

I bought mine at the local Home Depot for about $13.50 per sheet. I picked up two that they cut (for free!) into the six 24″ x 32″ pieces recommended by Frank. (I considered going 2′ x 2′, but I am very glad I went with the extra inches on the length.)

My next task was to put duct tape (or duck tape) on the edges to keep them from degrading. This is where Anna gets all the credit! I had planned on “buying” some of my daughter’s stash

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until I “did the math!” Each board requires almost ten feet of tape (112 inches of perimeter, plus a bit extra on either end that I cut off while taping.) Since I had twelve boards, the 120 feet of tape would have decimated her supply. (As it was she wasn’t going to give me the “fancy” stuff anyways.) I decided to go with my school colors and picked up a blue roll and a yellow roll of 20 yds each. Needless to say, there’s not much left. (Maybe just enough to use for periodic “repairs.”) The tape cost $7 for the two rolls, for a grand total of $34 + tax, or about $3 a board. (The cuts were free, and didn’t take long at all, but the taping process took me over an hour!)

Here they are!

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Notice as well, the PERFECT storage space that is holding the other ten!

Now, for the writing instruments. I am always frustrated by how quickly the dry erase markers die. Last year I picked up some of the Crayola Dry Erase Crayons. Other than the periodic breakage, they seem to “last” much longer. (Hey, when they break, one crayon turns into two!) In addition, I have to watch out for pieces that accidentally “chip” off, are left on the floor, and then get ground into the carpet.๐Ÿ˜ž The crayons look pretty sharp (sharp = awesome, not sharp = pointed) on these boards, and the color variety is great, with the exception of the yellow crayon – whoever thought it would work well on a whiteboard was sadly mistaken. I guess they sell yellow markers as well – maybe it’s for those black dry erase surfaces. I “inherited” a number of boxes of the crayons (eight colors in a box plus an eraser “mitt” and sharpener) when I moved into this classroom – enough that each group could have their own box! (I will generally only use eight boards at one time.) The kids liked markers better, but maybe the different colors will “sell it.”

One more note about the duct tape. In hindsight I don’t think yellow was a great choice. As I was erasing one of the boards today I realized the dry erase particles will accumulate along the edges of the tape, so lighter colors will start to look “grungy” after awhile. Oh, well.

One “short” story about my whiteboard history. In the early nineties (yes. . .I am dating myself, but I have already done that on a previous post) I was teaching Calculus. I had one particular student who repeatedly asked if he could go up and work out problems on the corner of the board while the class was working on a set of problems. It was certainly fine with me. He commented on how his thoughts seemed to “flow” from his brain when he used a whiteboard. It was not long before he bought himself a 1′ x 2′ framed board to use at home, as well as another one that he brought to school (and stored in the classroom) to use at his desk. I have no idea where he found these boards, as I had never seen them in stores. At the end of the year he gave me the one he had brought to school and I still have it to this day. (It was one of the last years that I taught Calculus. Not many years later, I went on maternity leave and then came back to teaching just part time. My own kids scribbled and doodled on it while they were toddlers.) Jump forward about ten years, when I was volunteering in my son’s first grade class, I observed his teacher using a class set of mini-whiteboards with her students. Within about a year, I had a set for my classes. Now I am on to the next phase – MONSTER whiteboards!

(Ok, it wasn’t so short. Have I mentioned that I ramble . . .?)

Made4Math: Math Cards

When I was taking Math Ed. classes in college we had to choose one manipulative and describe all of the different ways they could be used in the classroom. I chose Legos, and came up with quite a list of activities. Many of them involved using Legos as replacements for other manipulatives, therefore allowing you to spend less by “just” buying Legos. I guess I was frugal even back then ๐Ÿ™‚ (Of course, that was before I knew just how EXPENSIVE Legos are!) Almost all of the Legos at our house are “claimed” by my son, and those that are left belong to his sister, so I have yet to use them in the classroom. (I did “sneak” some Duplos to school when they were younger, but those are all now in storage.)

Anyways, I originally developed the idea of “Math Cards” just for the “Find Your Match” activity listed below, but it has morphed into much more. See what other ideas you can think of!

Find Your Match
The first incarnation of Math Cards involved having students pick a slip from a bucket when they arrive in class and find their partner for the day based on their card. Now, the cards are not identical (this is middle school math, after all) but “match” in some way. Maybe they are equivalent. Maybe one card is the solution to the equation on another. Maybe they are different representations of the same linear relationship. The sky’s the limit on what you can create. Here are some I have made for this year.

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I also have “Find Your Match Trios” cards where groups of three will “find each other.”

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Each year, I would print out the sheet and cut it up for the class to use. I would create new “cards” for different concepts to add to my collection. (I have quite an assortment for 6th Grade, where we have a two period block with the students.) The next year I would find the file, print it out, cut it up . . .
I found that students would “cheat” (in my opinion) by putting their “answer” on the back of their slip and THEN finding their match, but in reality the “game” involves NO talking, and students are holding up their card and looking at other cards (analyzing them mentally) to find their match. The idea is that they will have to “do the math” for every other student’s card until they find their match.

Sooo, my brilliant idea was, hey, I can have these laminated and reuse them for years and they also won’t write on them! I took it up a notch and glued them on construction papers before having them laminated. Color coding made them easier to keep in sets. I had a TA first semester last year and it kept her busy quite often. Here are some of the finished products:

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THEN, other uses started flowing into my brain. Below are “two more ways” that I have been using the cards, but within those two categories are MANY more uses ๐Ÿ™‚

Math Greetings
I have mentioned this briefly in other posts: First Day and Magnets, and I plan to do a more in depth post on it in the future. As students enter the room, they are required to “do math” in some way. I can put a set (or part of a set) in a “bucket,” have a student draw a card and “do it.” Sometimes it means solving the equation, sometimes it means changing the fraction to a decimal, sometimes it means finding the slope for the near relationship, sometimes it means just doing the arithmetic on the card. Again, the possibilities are endless.

Some cards are just numerical values (fractions, decimals, percents, square roots, cube roots) so I combine the cards with student magnets and they plot the values on a number line.

I have also combined the cards with dice.
-Draw a card with an algebraic expression, roll a die, evaluate the expression for that value of the variable.
-Draw a card with an algebraic expression, roll a die, set the expression equal to the value and solve.
-Draw a card with a fraction, roll a die, multiply (or divide!)

This year I plan to add some more “twists.”
-Set out a 4 by 4 grid of cards. Students find a match, I take the cards and place out two new ends.
-Pick two “ax + b” cards: set equal and solve, just add them together, or multiply together.

I really value the brief 1-on-1 with each student. It allows me a quick assessment of where they are at on a particular skill or concept. Often 2-4 students are “answering” their Math Greeting at the same time, so it really keeps me on my toes! Sometimes it really opens my eyes as to the general level of understanding that remained after 23 hours, and this may alter my plans for the day ๐Ÿ™‚

Review Games
At the end of each Unit, I often have a variety of different activities that rotate among groups of students. Many of these end up involving the cards in some way.
-Math Race: Flip a card from a stack, race to answer it, keep the card if you “win” OR everyone writes down their answer, earn one point for getting it right and one for being first (IF you are correct.)
-Match Game: Lay out cards upside down. Flip pairs and try to find a match.
-Go Fish: Students play the game while “fishing” for cards that match the ends in their hands.
ANY of the Math Greetings activities can be modified slightly as well.

Final Thoughts
Most of the time I am quite intentional in the problems I choose. For instance, for the scientific notation set in the first image, there are only two different mantissas (had to look that up) so plenty of opportunities to demonstrate conceptual errors. The Exponent Rules set provides for the same “opportunity for error.” Does 2^20 รท 2^5 = 2^4? Students who think so will “find the wrong match.” However, in the factoring/multiplying set, I could have done a better job just switching two values so that the “a and c” in the quadratic are the same. I once turned my brain into mush coming up with sets of five values where each card matched with two other cards having the same mean, but also matched with two different cards having the same median. It made for a good discussion of outliers!

Once I figure out the “tech side of things” I do plan to post links to them on a page here on this blog, but for now, feel free to come with your own ideas!

Part of Enduring Mathematical Understanding comes through practice, and Math Cards certainly provide that opportunity. However, deeper understanding comes from dialogue. “Find Your Match” is often followed up by questions regarding “why” two particular cards are a match. It’s always interesting to hear the conclusions!

Made 4 Math Monday: Student Magnets

I use magnets (about 3/4″ diameter, 1/4″ thick) for a variety of activities in class. Originally, I had one set labeled with colored/numbered sticky dots (each student is assigned a color and number to determine seating assignments) but last year I had students design their own. They really seemed to claim ownership and enjoy activities more, so I will repeat that this year, even though I will have to purchase more magnets to do so ๐Ÿ™‚ (I believe I found them at Michael’s before, and I have a 40% off coupon!) One of the First Day/First Week activities involves decorating and “claiming” a magnet.

I store each class set on a magnetic mini-whiteboard and pull it out for the students to “find” their own each time we use them. Many of the activities are related to a “Math Greeting” I have as students enter the room. I only have pictures of a few that happen to still exist on my iPad. I hope you understand the others based on my descriptions.

Data Gathering
Data collection is a common use, whether it is regards to the students themselves:

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These would be followed up by questions on slides relating to the data. I will often take a snapshot of each set of class data and the next day follow it up by having students compare and contrast the various classes. When data is gathered from an experiment, I will usually complete a few more trials to make the total a “nice” number for analyzing. (See the plain black magnets on the second image.)

Class Poll
Towards the end of a Unit, I will often make a list of the concepts we have studied and have students place their magnets on the concept they found most challenging. (Some students are adamant that there should be a “none” option, but I remind them that it doesn’t have to mean that they find it challenging anymore.) This gives me some feedback regarding where I should focus my review activities.
I have also used this idea by choosing a current concept and having students rate their understanding on a scale of 1-5. I am not thrilled with the outcome for a few reasons. Students tend to inflate their level of understanding due to the presence of other students (and other magnets,) and “level of understanding” often implies “I can do it” rather than “I understand.”

Number Line Plots
I have draw a very long number line on the board, often with values marked only at the ends and equal intervals between the endpoints. Students “draw a card from a bucket,” pick up their magnet, plot the point with their magnet, and attach the card “label” by sticking the corner under the magnet with the value still showing. The values on the cards can vary, depending on what we are studying: decimals, fractions, mathematical expressions, square roots to estimate. . .
As a class we analyze the number locations. Students have the opportunity to move their own magnet if/when they recognize errors in their thinking, and also recommend changing the placement of other magnets they feel are inaccurate.

Coordinate Plane Plots
One option is similar the the activity described above, but the cards contain ordered pairs for students to plot. This is just for practicing accuracy with plotting. Class discussion follows.

Another option involves drawing 2-4 sets of axes (different colors) on the board with a different rule written above each one. The card drawn will indicate the color and the x value. Students will plot “their” point and record the value in a table. After a class discussion for accuracy, follow-up question on a slide will provide opportunities for more analysis and comparison.

A third option arises when looking at bivariate data. Class scatter plots can be created based on students data or based on student opinions (on a scale of -10 to 10, chocolate on the x-axis and vanilla on the y-axis – or whatever “variables” you want to investigate.) Again, follow-up questions provide opportunity for analysis.

Magnet Relays

The class is divided into 3-4 teams, lined up behind an imaginary “exchange zone” line. Each player has their own magnet (with an extra magnet for someone to go twice, in case the teams aren’t even.) Each team is assigned an area on the board that may include a number line or a coordinate plane. A stack of cards (one per relay “leg”) is on the tray at the whiteboard. On “go” the first person goes to the board, picks up the top card and plots the point (similar to the activities described above.) When they are done, they tag the next player, who takes the next card. .. etc. Only “you” can move your own magnet. If you see a teammate make an error, you can help them change their location, but only verbally. Only ONE person at the board for your team at a time, so if you plan to move your magnet, it must be “between” two of your teammates. There is a 30 second penalty for each incorrect location, so you are better off helping fix the error before the end of the race. Once your team is done, ALL hands are raised to signal your “finish.”

The Enduring Mathematical Understanding comes not as much from the participation in the activities, but in the follow-up discussion and analysis.

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