One of my favorite warm ups is the game 24. The goal of the game is to take the 4 numbers on a card and use any of the 4 basic operations and grouping symbols to equal a total of 24. You must use all 4 numbers and you cannot repeat a number. You cannot use the numbers as exponents nor put them together to create a new number (like 5 and 8 cannot be put together to make 58.)

​I project one of each level (the dots in the corners represent the levels) and students work on a level of their choice. They record their solutions in their journals.

There are so many concepts that we cover during this once a week warm-up.

Out of all of our warm-ups (except maybe math fights when we do them) students enjoy 24 day the most.  They get quite competitive in trying to get the answer first. What I find amazing is many students don't want to told what the answer is and they HATE when I tell them time is up before they've found all 3 solutions! 

Here is a sample record of what we talked about today in class. Notice my error of putting in +4 instead of +14...we fixed it eventually, but I'd already snapped the pic. :)

​The purpose of the journals is twofold.

First, it is a place students can place resources and references for what we've been learning about. I've tried Interactive Student notebooks in the past, but it was too much of a management issue for me. It also allows me to "review" their journals at my leisure without having to collect notebooks from the students.

Second, it is a reflective journal. By giving students an opportunity to share what they learned or their thinking about a topic I can easily search for misunderstanding or interesting comments to discuss individually or as a class.

I use Google Classroom to pass digital materials out to the students. On the day we started our journals I assigned a view only copy of the journal with a title page and table of contents. Students made a copy in their drive and were able to make it their own. We discussed how to add links to the table of contents so they could easily find information.

Students had to title their journal "P#-name" but could decorate and format it however they want.

When I have a new page I want students to add to their journals, I simply add it to my original copy. Then students can open it up from Google Classroom, copy the page and paste it in to their slides.

Students do NOT need to type their reflections in the journal...they are more than welcome to hand write their journals. All I ask is they take a picture of their written work and insert them onto the slide.

I chose to make the slides portrait instead of landscape because I felt like more information could be added. Students are more than welcome to switch this in their journals.

I chose Google Slides instead of Docs because I liked how the table of contents could easily link to a specific slide and the link would stay associated with that slide even if they were rearranged. It's also easy for students to copy and paste an entire slide without having to select specific text.  I don't like that Draw isn't an insert function, but there are definitely ways around it.

Here are 2 examples of reflection prompts I asked students to complete:

Here is an example of "notes" students were asked to complete:

I was super nervous to try a digital journal this year but I'm glad I stepped out of the box with this one! I think the kids have picked up on the management piece of it pretty quickly (helps that they used Google Classroom last year), so now we need to start discussing quality of answers.  

I need to be sure to allow at least 10 minutes for students to journal. I asked them to finish for homework, but many did not, so they had to finish in class the next day. I don't think students need to journal every day, but I will do it after a big lesson or idea.

Having students share their journals is extremely important. So far I've been pretty good about giving them time to share with a partner, but I need to get better at looking through them and pulling out things I think could make good conversation so we can have some classroom discussions.

I can only see this form of note taking getting better as myself and my students use it more. If you use digital journals/notebooks or have ideas, let me know in the comments below.

Today in my 7/8 class, we started working with squares and square roots. This was done on a block day which are 90 minutes long. I pushed all the tables out of the way and put down some tape as a simple number line. Then I passed out square tiles and put up the following prompt:

All groups came up with a 2x2 square for question 1 and the 8x8 square for question 2. I challenged them to see if they could come up with another square that satisfied questions 1 and 2.

• Most groups were able to rationalize that a 2x2 was the only possible answer for question 1, but thought if you could make a big enough square you'd be able to make another for question 2.
• One group determined it was impossible to make a square other than 8x8 where the perimeter was half the area because after the 8x8 square the area was increasing faster than the perimeter. 
• After a class discussion about questions 1 and 2, I asked again if they could come up with another possible square for each and if not, why. Most groups still thought they could create another square for number 2, so I brought out Desmos.

We graphed the perimeter line and did a quick notice and wonder. Before graphing the area line I had them predict what they thought it would look like and draw a quick sketch on their whiteboards. Most lines were straight, through the origin and steeper than the perimeter line. Their responses after graphing it were:

• "WHAT???"
• "It's curved!"
• "Wait, it doesn't go in to the negatives."

I wasn't expecting to go in to this detail today, but I'm glad it happened.

We had a conversion about perfect squares which led in to square roots. Most of the kids have heard of square roots but now had a better understanding of what they actually were. I had each student create a number line on their dry erase boards similar to the one on the floor and I wrote √25 on a card. I asked one student to place the card on the number line while the rest placed it on their white boards.

I kids place a few more perfect squares and finally presented them with √7. The student who I gave the card to placed it between 3 and 4 which I couldn't have planned better...it allowed great conversation between students about the differences between square rooting and dividing by 2.

Eventually, I started rolling dice to randomly choose numbers for them to square root and place on their number line. (I used a 10 sided die and a 30 sided die to make 2 and 3 digit numbers.) For those students who caught on quickly, I had them try to approximate the square root to a decimal as accurately as they could.


Overall, I think the lesson went well. The students were engaged and the different tasks allowed me to have conversations with those students who were struggling and let those kids who understood have little competitions among themselves to see who could come up with the most accurate placement on the number line.

One of the things Common Core is asking students to be able to do is create real life situations or problems that relate to a given expression. Here's an example from the 7th grade standards:

This is something that even teachers struggle with. I remember a professional development I went to early in my career where the District Math coach asked a group of middle school math teachers to create a situation that resulted in division of 2 fractions. Most had no concept of what the problem even meant. From that point on I made an effort every year to stress the meaning of the operations when looking at any problem. 

This year, I decided to make writing real life situations one of my classroom routines and called it "What's Your Story?" We're just getting in to our rational numbers unit, so I'll start soon (Right now I'm stressing number talks.)

I haven't decided yet how I'm going to manage this warm up: Paper or digital, individual or group, if digital what platform will I use? So I did a possible method with my advanced 7/8 class. I created 1 Google Sheets document to share and had the kids work in groups to write a story for 3 expressions. This is what one group came up with:

And this is is what the whole page looked like:

• Overall, I thought the activity went great. They had a little trouble thinking about a fraction divided by a fraction. Most groups were in a "cake" or "pizza" mind frame when it came to fractions, so thinking about separating 7/10 of a pizza into groups of 1/5 was difficult for them to comprehend. I prompted them to think about other areas of life we typically use fractions. Several students brought up cooking and other forms of measurement. This made the problem a bit more manageable.
• Before letting groups work on the document, they had to work on paper for about 10 minutes.
• I loved having all the kids working on the same document because they could see what other groups were working on and get inspiration if they were stuck.
• I had the groups set permissions for their group section so other groups couldn't change their slides on accident. However, when groups inserted a picture, it wasn't inserted into a cell...it was just placed on top of the sheet. This caused a little trouble when the picture covered another group's work. I reminded students that no one was doing anything malicious and to be patient while the problem was fixed.
• When I start doing this for a warm up I will need to shorten it a lot (this took a 60 minute period, so even if I only completed 1 problem it would take good 20 minutes. Most likely I will print out a document to go in notebooks.

​The final document can be found here.

I love nrich's game Up, Down, Flying Around to introduce operations with integers to my students. Last year I made the decision to focus solely on the number line method to explore this topic. In the past, I had used the chip method, but students picked up on what happens when you add or subtract integers so quickly using this game that I chose to make it my method of choice. It even translated to multiplication fairly well (we just added or took away sets of hot air or sandbags. The problem with only using the number line method is that I use algebra tiles to explore expressions and equations. Without having learned the chip method previously, the students weren't as comfortable with zero pairs and taking away things that weren't actually there (like subtracting a negative x from a positive x.)

This year, I decided I will explore both methods and let students decide which works best for them in certain situations. Since I introduced the number line method with a game, I thought it would be fitting to do the same with chips! This is what I came up with (with the help of my daughter, who came up with some of the rules.)

Witch's Potion Game

Materials: 

• 1 die labeled with 3 addition and 3 subtraction (or a chip that can be flipped)
• 1 six sided die
• Set of algebra tiles or two colored chips. I use algebra tiles that have yellow as the positive and red as the negative...hence the pictures on the game board (yellow brick road for good and red apple for bad.)
• Witch's Potion game board (laminated or in a plastic sleeve)
• Dry erase marker

Setup:

• Have the chips where both students can reach.
• If desired, you can add in equal amounts of positives and negatives to represent 0 in the cauldron. This way zero pairs will most likely not need to be added immediately.
• Mark the overall charge of the cauldron as 0 on the line using dry erase marker.

Rules

1. Decide who is going to be the good witch and the bad witch. The good witch can only add or remove the positive chips from the cauldron. The bad witch can only add or remove negative chips. (The only exception to this rule is if zero pairs need to be added...then a witch can add the same number of their chips with the same number of the opponent's chips.)
2. Decide on who is going to go first (however works for your kids...I am going to assume good goes first.)
3. The Good Witch rolls both the operation and number dice. The operation tells them if they add or remove the number of positives that are revealed on the number die. For example, if they roll "add" and "4", they will add four positives. If they add "subtract" and "4" they will take out 4 positives. After chips are added or removed, adjust the overall charge accordingly. 
4. The play continues with the bad witch either adding or subtracting negatives and changing the overall charge.
5. If at any point a player doesn't have enough of their tiles to take away, they may add enough zero pairs so they can.

Winning the Game
I haven't decided yet on how I'm going to handle this part. I have 2 options:

1. If the overall charge gets to 20, the good witch wins, if it gets to -20 the bad witch wins (or any number that seems reasonable.)
2. Play for 5-10 minutes and at the end of the time if the overall charge is positive the good witch wins, if it is negative the bad witch wins

I plan on using this game later this week, but I'd love to hear thoughts or feedback!

I'm sure most middle and high school teachers can empathize with the idea that we tend to get better at teaching a lesson throughout the day. It sucks and I hate the fact that my 1st period doesn't get the same quality of my time as my later classes. Here's just the most recent example.

I gave the following Illustrative Mathematics task:

I gave this as a partner preassessment to get student's level of understanding on how operations affect numbers on the number line.  In my 1st period class, I started by giving the groups the worksheet and going over the directions together. They understood the directions just fine and got started. Very quickly I noticed something that almost every group was doing. They had assigned the value of 2 to the variable "a". I had a conversation with almost every group about what they noticed about where "a" was located in relation to the other numbers on the number line. All groups said that it was closer to 1 than 1 was to 0, so a couldn't be 2 and it must be a decimal. I realized this was an idea that could have been alleviated very easily by letting students look at the number line before working on the problem....as in a notice and wonder!

Quickly during break, I did a cut and paste and created this:

The next classes went much smoother, with students immediately noticing that a could not be 2 before even knowing what they were going to do with the number line. But really...why didn't I think to do this originally?

Eventually, I hope to make the differences between my 1st and later periods less extreme...this reflection blog should help.

Here are a few more observations about this activity:

• My students either never learned how to add and subtract on a number line, or they have since forgotten (due to lack of usage, I'm sure). Most groups chose to assign a number value to a and b in order to answer the question. For example, they would say that letter a is positive because it's about 1 1/2, and 1 1/2 - 1 would still be positive 1/2. Similarly, for question b, they said 1 1/2 - 2 would get you into the negatives. Most groups did not look at using the number line to "jump" one or two places to the left.
• Question c allowed great conversation! There was confusion and blown minds...it was great! Most groups said -b would be negative, but a few figured out the idea that it would be the opposite of b (or a positive).

I hope to post some student work soon.

I'm a gamer. I love games...video games, card games, board games. I love playing games by myself or with groups...chance or strategy. There are few games I've played that I didn't at least moderately enjoy. The other day amazon had strategy games on sale up to 30% off and I was in heaven. One of the games I purchased was a very simple dice rolling game called "Roll for it!" I originally became aware of this game on a You Tube web show called Tabletop. You can watch it here.

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​Image courtesy of Amazon

The object of the game is to roll your 6 dice and attempt to be the first to create the dice combinations on the cards that are shared in the middle of the table. As I was playing my mind kept drifting to the thought that this game could very easily involve math. Instead of having dice patterns, there could be empty boxes for the dice to fit in (similar to open middle problems.)

Now, if you actually read what makes an open middle problem "open middle" it's not just the fact that it has boxes that kids fill in to achieve a specific goal. Here's what it says on their website:

• they have a “closed beginning” meaning that they all start with the same initial problem.
• they have a “closed end” meaning that they all end with the same answer.
• they have an “open middle” meaning that there are multiple ways to approach and ultimately solve the problem.

So, I'm not sure if this game I'm contemplating actually preserves the "open middle" status...but I'm hoping it will be fun and thought provoking, anyway.

Classroom games are not usually my favorite. I don't typically play them because I feel like so often they are DOK level 1 questions where kids compete to earn points. Sure, the "game" part might be a break from much classroom monotony, but the "thinking" just isn't there. I enjoy strategy games and I feel like with this game there could be some good opportunities for students to actually utilize that frontal lobe of theirs (note: I think that's the part of the brain associated with problem solving???) as well as practice those specific standards. Anyway...I felt like it was a game that I would actually enjoy playing, which is kind of the barometer I use to determine if it's good enough for my kids.

I didn't really start this blog for anyone to read, but if anyone does and you'd like to give your input about this game...maybe you've played something similar...maybe you see a glaring problem with it or a way to make it better...maybe you'd like to give it a try and let me know how it goes...I'd greatly appreciate it! I don't have all the cards made up yet, but I'll link them when I do. 

One of my favorite things to read about in blogs is what everyone does on their first day of school. Nothing gets me more excited about starting a new year than hearing about the amazing activities everyone has planned. In fact...it's a little overwhelming. Wouldn't it be awesome if school consisted of 180 first days? Then...maybe...I could do every first day activity I've ever wanted to do.

It may be due to the fact that there are such a plethora of great ideas that I tend to stick with what I've always done. I'm all about growth and change, but there's something about this activity that speaks to me and keeps me coming back to it year after year. It's not an amazingly great activity. It's pretty simple, actually. And it came from my first year teacher self's desire to "NEVER WASTE A DAY!" Get them talking about and doing math from Day 1!  

So here's...for the most part...what I've always done since my first day of teaching (with 1 major exception. This year I'm using name tents which I've never done before. Thanks Sara VanDerWerf for the inspiration!)

1. When students come in, I'll have them make a name tent and they can decorate it however they want...doesn't have to be mathy.

2. While they're working on their name tents I tell them we're going to have a little competition. I want them to predict how many names I'm going to get phonetically wrong. I do this for 1 major reason...not all students feel comfortable telling their teacher they're wrong...but when it's made in to a game at the least their friends will speak up for them! I'm sure to write the phonetic spelling of their name on the roster so I get it right the rest of the year (hopefully). 

3. Then we play a game called "Numbers About Me" or "My Numbers" (I think the name changes every year.) I put 4-5 numbers up on the board and tell the students "These numbers say something about me."

    Last year I used 4, 1/3, 602, 36.25 and 54,000. 

Then I let the kids guess what they think these numbers mean or represent about me. I love this part. It really lets me see how kids view numbers. We use numbers in so many ways in our lives (values, identification, ages, etc...) it gets them thinking about all the different representations. After some guesses (some are pretty wild) I show them 1 descriptor...for example, "My age" and they guess which number that belongs to. Then I give them another and continue the process. I don't tell them if they're right or wrong until the end. 

By the way...here are the other descriptors:
   The amount of time in a day I am asleep
   Area code of my cell phone number
   Approximate number of miles on my car
   The number of people who live in my home

4. The rest of the class period (we have early release on the first day, so there's not much time) I let the students create their own set of numbers. I ask that the use at least 1 non whole number. We'll spend a few minutes each day through the week for students to get up and share their numbers until everyone's had a chance to go.

And that's it! It's not the most fabulous thing anyone has ever done...and I'd probably be smart to try something else sometime. But, the kids always talk about how much they enjoy it...and they LOVE having the opportunity to be able to get up and present their numbers to the class which I find surprising sometimes...but that probably comes with the comfort-ability students feel going to school at a K-8...just like I feel comfortable with this first day activity. 

So my big ideas about the first day of school are:
1. It's never too early to have the kids start thinking about math in math class
2. It's so incredibly important that we learn to say our kids' names correctly!

Oh, and my favorite moment about the activity is when (no fail) a student suggests that I have $54,000 in my bank account...ahhh to be able to dream like a 12 year old!

Last year I attempted to keep a classroom blog. This was before I dove head first in to #Mtbos (Math Twitter Blogosphere: A learning community of educators who are trying to be better at this "teaching math" thing we do.) Its purpose was to communicate daily to parents what we've been doing in class as well as keep a record for myself to look back on. Unfortunately, I dropped the ball and only posted about 20 times. Looking back on it, it's understandable that I failed miserably at blogging for one major reason...I absolutely DETEST writing. Truly. I would rather clean my house (including the floors) than sit down and write anything. Plus, I'm pretty sure I write like a 5th grader...so there's that...
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Me when I have to sit down and write something.
#Phepsface




So....why try to start again? Honestly, I have no idea. I guess it boils down to the fact that I want my kids to have a growth mindset. I'd never accept "this is too hard" or "I'll never be good at this" from them, so why should I accept it from me? 

But if writing isn't something I enjoy...why choose to do it? Easy. I need to reflect better on what goes on in my classroom. I'm guilty of doing lessons with my kids and never looking back on what went well, what bombed and what was just ok. In the moment, I may have thoughts about what I can do differently next time, but I rarely keep record of those ideas so what's to stop me from doing the same thing again next year? And, even though I rarely have an original lesson and I'm the WORST (or should I say best?) at stealing from others...occasionally I may do something that someone else may find useful.

Ok, then...what's going to make this blogging experience different? Well for one, this blog isn't going to be a communication to parents, it's going to be a collection of reflections  on lessons, teaching and math in general. I'm not going to try to blog every day...just when I have something I need to reflect on. 

So, I'm not sure what's going to happen. It's the beginning of the school year, and I have an "I can do it" attitude. I know things change through the course of the school year and this may be another failed venture...but at least I'm giving it a try, right???