Math Practice #5 for Teachers

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The other day I was trying to decide which of the many tools in my bag of tricks I wanted to use for a quick formative assessment. My usual routine is just to have students raise their hands to answer my questions and provide enough wait-time for everyone to think about it, or to have them write their answer on their individual whiteboards. But no matter how much wait-time I provide, there's either that one student who calls out the answer so everyone else stops thinking, or the student who just waits for someone else to answer so they don't have to. Over this past summer I read Total Participation Techniques and swore I was going to use some of these strategies to get everyone involved in answering, but I really haven't done a good job with that.

So back to my decision of which tech tool to use - here are my usual go-to choices:

• Nearpod
• Socrative
• Google Forms
• Plickers
• Classkick
• Google Classroom Question

I'm looking for something that is quick and easy, will record everyone's answers for later review, and gives everyone an equal opportunity to provide an answer. I'm trying to assess how my students are understanding the pattern lessons we've been exploring from the book From Patterns to Algebra. I want to see if they can explain their thought processes using words, not just drawing or building the next position in the patterns. I want to see if they can explain how they determine the constant and the multiplier. This is really important as we are going to move on to patterns where all the tiles are the same color instead of having the constant stand out with a different color. I want to have a good class discussion afterwards to reveal all understandings and also correct misconceptions.

So, my first option - Nearpod - requires me to set up the presentation and have students sign in. I can see the results in real time and it does save the data for later. I can even share out good responses and those that are lacking so we can discuss them as a whole class which I like.

The next option - Socrative - also allows me to set up questions ahead of time. I could use the Quick Question option, though, and Short Answer Quick Questions can generate reports for later review.

Next up - Google Forms - again requires prior setup to use, but it does save the data. But reviewing the data is awkward when it's short answer questions as I'm planning to use. Forms are also good for multiple choice because they can be graded automatically when set up as a quiz, but this was not the case here.

Next is Plickers - my students love Plickers, but they're only good for multiple choice, so that option is off the table.

Classkick is another option, but I find this is a better option for using the drawing tool to solve problems, not so much for typing responses.

My last choice is the Google Classroom Question feature. My students are already signed into Classroom all the time, so that makes it quick to access. And adding a question on the fly is quick and easy too. I have a class that I named "Templates" where I add questions that I use over and over again. So when I want to use one, I go to Classwork, choose "Create," then "Reuse post," and pick the question I want to ask. I love that I can see how many students have submitted their answers and how many have not. I also find it easy to review their short answers by simply scrolling through them. I can also provide feedback to them by means of a private comment if I wanted to do that afterwards.

We talk about students' mathematical habits and the 8 Common Core Standards for Mathematical Practices that we want them to become proficient with. I realized as I was trying to find the "just-right" tech tool for this formative assessment that I was paralleling Math Practice #5 - "Use appropriate tools strategically":

Just as students choose appropriate tools to solve mathematical problems, teachers choose tools to assess student thinking. For me, that means weighing the strengths and limitations of formative assessment tools—Nearpod, Socrative, Google Forms, Plickers, Classkick, and Google Classroom—and using them to analyze students' understanding.

As I was going through my options for formative assessment ("consider the available tools"), I was making decisions about each tool's strengths and weaknesses ("recognizing both the insight to be gained and their limitations").

I don't think I've ever put this much thought into choosing a tech tool to use. Going forward, I think I will always make a more conscious effort to "use appropriate tools strategically".

What do you look for when choosing tech tools for formative assessments?

From Patterns to Algebra (part 3)

I'm continuing to blog about my experiences with using the great ideas from the book From Patterns to Algebra. In case you missed my first 2 blog posts, you can read the first one here and part 2 here.

So we worked on lesson 4: pattern building with composite rules this week. The first pattern I showed them was the one on the right below with the yellow diamonds. They were struggling a bit so I showed them the very first pattern we had worked with a few weeks ago (the one on the left without the yellow diamonds) and asked them what they noticed. I started to hear some "ah-ha's".

My students are starting to get more flexible with this concept. I can ask them different questions and they can apply what they know about the pattern rule to answer my questions. For example, for the first few days, all I asked of them was to come up with the rule and what position 4 would look like. Then I started asking them to show me position 0, or position 10, or how many tiles will there be in position 8, etc.

A few of my students can draw position 4, but are having a difficult time writing the rule independently; I have to prompt them with questions like "what's staying the same?" or "what's changing in each position?" for every pattern. I have 8 students in this class and about 5 or 6 can come up with the correct rule and patterns for the positions I ask for fairly easily each day. My big challenge going forward is to figure out how to help the last 2 or 3 make the connections needed to do this independently.

The last few days I really challenged them - I did not use 2 different colors, making it more difficult for them to determine the constant. About half of my students were able to identify it after a few minutes of productive struggle. I love watching them all really thinking and talking about these patterns!

Here are the patterns we worked on this week:

I'm looking forward to the next lesson in which we work in reverse and I give each student a secret pattern rule and they must build what their positions 1, 2, and 3 look like. Stay tuned...

Check out the rest of my series on From Patterns to Algebra here:

From Patterns to Algebra (Part 1)
From Patterns to Algebra (Part 2)
From Patterns to Algebra (Part 4)
From Patterns to Algebra (Part 5)

From Patterns to Algebra (part 2)

(In case you missed my last post on using the book From Patterns to Algebra, I highly suggest you check it out before you read this post.)

The next 2 lessons in the book were similar to the first 2, but instead of just multiplying, now my students needed to think in 2 steps (can you say "nice connection to two-step equations"?) by first multiplying then adding. We started with the "Guess My Rule" game as before. The first day I used the rule x2+2 as suggested in the book. I had my students volunteer the random numbers for the input column and I gave them the output numbers one at a time. After 3 sets of input/output numbers I asked them to try to think of the rule. Many were stuck. One student (the same student I mentioned in part 1 as a matter of fact) said "This is hard!" (again). But once she figured it out, she again changed her tune and said "Oh, this is easy!" Most of my students just needed scaffolding to help them come up with the rule. I asked them to start by looking at just one pair of numbers - "What can you multiply the input number by so that you get close to but don't go over the output number? OK, then what do you have to add to get to the output number? Now see if that rule works for another pair of numbers in the table." Basically trial and error. Eventually most of them were able to figure this out.

The next day I started by giving them the first pair of input/output numbers and told them "I can think of 6 different rules for this, can you?" Loving a challenge, they all set out to work. That same girl I mentioned several times already had 4 correct rules and said she couldn't think of any more. That's when I broke into my rant about perseverance and productive struggle. With my prompting she went back to work and easily came up the last 2 rules. After we had all 6 rules written on the board, I added a new pair of inout/output numbers. I asked them "Now which rule is the only rule that works for both sets of numbers?" A few minutes later most had written down the correct rule on their whiteboards.

The third day we started out the same way with one pair of input/output numbers and me challenging them to find 4 rules. Once they had figured out the 4 rules, I gave them another input number and asked them to write down the output number using our rule. This was easy for them now that they had the rule, but then I gave them an output number and asked them to figure out what the input number was. Wow! You would have thought I'd asked them to explain Einstein's theory of relativity! We're in the middle of a unit on two step equations so I hinted at the connection. Love this! I love the way they're all engaged and challenged by this and they're starting to see the connections. At first, one student said "But there's no x!" so I had to explain to her that x represents the unknown number, which in this case is our input number. I saw the light bulb go on and she quickly wrote and solved the equation.

Next, I think I'll let them take turns being the rule makers as the book suggests. I didn't do that with the first lesson, but when I let them build their own patterns for each other to solve they really loved that. It gives them some ownership and, as I firmly believe, if you can teach something it really shows that you understand it. I plan on using this lesson for another day or two and then moving on to patterns with two steps. Stay tuned!

Check out the rest of my series on From Patterns to Algebra here:

From Patterns to Algebra (Part 1)
From Patterns to Algebra (Part 3)
From Patterns to Algebra (Part 4)
From Patterns to Algebra (Part 5)

From Patterns to Algebra - How students connect patterns, tables, equations and graphs

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I recently discovered the book From Patterns to Algebra by Dr. Ruth Beatty and Dr. Catherine D. Bruce and thought it was perfect for my students to give them the hands-on and visual connections to linear equations and support their algebraic thinking.  As they say in the introduction, "Mathematics has been called 'the science of patterns'."  The lessons presented in the book are meant to be followed in the given sequence.   The first chapter of the book, which is where I am now with my students, has them playing "Guess My Rule" and pattern building.  I chose to purchase the DVD with the book which gave me access to video vingettes and Smart notebook files for each lesson.

In the first lesson, "Guess My Rule", I asked students to give me a random number between 2 and 9 (1 and 10 make it too easy), and then apply the rule I'm thinking of and write the answer.  As they figure out what the rule is (what I'm multiplying their input numbers by), they write it down on their whiteboards.  When I think everyone has figured it out, I take one more random number and have everyone write down the output number on their whiteboards to check.  Some of my students lack multiplication fact fluency, so this is good practice for them.  As the authors advise, don't have the input numbers in order because that leads to students looking for additive rules instead of multiplicative rules.

In the next lesson, I displayed various patterns with 'position number' cards underneath each iteration of the pattern.  The students must again figure out what the rule is.  The first day we did the patterns, I heard one student say "This is hard!"  I told her that once she sees how the first one is done, she will think they're a lot easier than she originally thought.  They were all overthinking it!  Once everyone figured out the rule and wrote it on their whiteboards, I had them draw what position number 4 would look like.  One student (the same student who thought this was hard) expressed the rule additively instead of multiplicatively at first (for the first example below she said you're adding 3 each time).  I asked her to try to see what the position number was being multiplied by instead of how the pattern was changing each time.

After doing the patterns for a few days, today I had them create the first 3 positions of their own patterns with color tiles.  After I checked their patterns, I had them rotate to someone else's pattern, write down the rule on the whiteboard, then try to build the 4th position themselves.  They really liked this activity!  I loved how engaged everyone was with creating their own patterns and figuring out each other's patterns.  Here's some of the patterns they created:

The lessons coming up next deal with composite rules.  I think this will be more difficult for my students because they have to see the two steps being done (multiplication and addition) instead of just one (multiplication).  I hope I'm pleasantly surprised and they pick this up very quickly.  I'll keep you updated on our progress!

Check out the rest of my series on From Patterns to Algebra here:

From Patterns to Algebra (Part 2)
From Patterns to Algebra (Part 3)
From Patterns to Algebra (Part 4)
From Patterns to Algebra (Part 5)

Expressions and Combining Like Terms ... "Can I Take Your Order?"

In keeping with my new school year resolution to introduce new topics with real world situations, I start out teaching combining like terms by telling my class we're going on a pretend class trip - after going to see a play, we're going to stop at McDonald's for lunch.  Instead of waiting to get there to place our orders, I'm going to call in the orders ahead of time as soon as we get back on the bus.  This is where I really grab my students' attention - I pass out 9 magnets to each student with pictures of McDonald's food and drink items (I made these magnets a few years ago with the magnetic paper [affiliate link] that you can run through a printer).  They can choose 2-5 items that they want to order.  I have each student make their decision and then stick their magnets on the whiteboard in the front of the room, circle them with a dry erase marker, and write their name next to their circle.  Then I grab my cell phone and pretend to call in the order to McDonald's, naming EVERY.SINGLE.ITEM separately, faking being out of breath from having to say so many items!  Then I ask them if that's how I should have done it, or is there a better way?  Right away they all have an answer for me, although they don't all know exactly how to put it into words.  Basically, they tell me I should have counted up how many of each item I wanted to order, so we go through all their orders and count up how many burgers, chicken nuggets, fries, salads, sodas, chocolate milks, milkshakes, ice creams, and apple pies we all ordered.  Then I make my call again the easier way.  Then I segue into my combining like terms lesson...

I have a SmartBoard notebook file set up with infinitely cloned color tiles (in the rectangle on the left), which I drag out across the screen.  I have my students practice writing an expression to represent the color tiles by combining like terms (colors in this case).  For example, the expression we wrote for the color tiles shown here was 2R + 2B + 1Y + 3G.  We only do one together as a whole class, then I have my students come up and take turns dragging out the color tiles for the rest of the class to write an expression.
Then I move on to defining parts of a variable expression and making sure they understand that terms must have the same exact variable raised to the exact same power in order to be considered "like".  I give them several sample expressions and they practice naming the terms, coefficients, constants, and like terms.  We end this day with two games of Kahoot! to practice identifying the parts of an expression, one regular Kahoot! and then a ghost mode round of the same Kahoot! game.  They love trying to beat their ghosts!
Next I have them practice actually combining the like terms - I teach them several strategies to do this.  I demonstrate using shapes or colors to group the similar or like terms.  Each student can come up to the board to drag the shapes over the terms to show which terms are alike.  Then they have to write the final expression with the like terms combined.  I start out using only positive terms, and once they have the hang of combining these, I throw in negative terms - you should hear the moans and groans!
For more practice with identifying like terms, I created a card sort in the Desmos Activity Builder (love this!).  I used an idea from Cathy Yenca's "Becoming an "Expert" blog post of displaying the teacher dashboard on my SmartBoard in the anonymous mode until I found my first "expert".  Then I let them know which set of cards was theirs.  After they had all green cards, they moved on to the second screen which asks them to combine the terms they identified as like on the first screen.

After that, we did a Combining Like Terms scavenger hunt.  As soon as they walked into the classroom and saw the QR codes hanging around the room they cheered!  They love doing these scavenger hunts!  I love watching them moving around the room so focused on their work.
The last activity I do before the study guide and quiz is centers.  One center had a (boring) worksheet on which they had to identify parts of an expression.  The second center was an iPad app called DigitWhiz [update 10/2026: sadly, this app is no longer available] which has several combining like terms activities. At the third center, they had Combining Like Terms Sort Cards - they had to first decide how to sort them and then combine each set of like terms.

 
They had their quiz on expressions and combining like terms on Friday - most of them did really well!  The biggest issue most of them have is not recognizing that a subtraction sign indicates the number following it is negative.  I remind them to change the subtraction to addition by "adding a line, changing the sign", but some forget to do this.  I'm hoping this will improve as we move into solving equations.
One topic I am skipping this year is expressions and equations that require distribution.  Teaching resource classes means I go at a slower pace than the general ed classes, so unless I leave out certain topics, I will never be able to get to every topic in the 8th grade curriculum.  It's always difficult for me to decide what to leave out and every year I feel like I leave out something different.  I chose to skip distribution this year because it's always so frustrating for my students (and me!).  Now it's on to one-step equations...

Teaching Integer Operations Activities and Strategies

I love teaching integers! I think it's probably my favorite concept to teach. I've already blogged about the Wii activity I did with my LLD class to introduce real-life integer situations, so I thought I'd write this post about the rest of the activities and strategies I use to teach integer operations.

Since this is my LLD class, I really take my time to ensure my students understand each operation before moving on to the next. I try to give them as many tools and strategies as possible to help them feel successful.

Addition with Chips

I spend a few days on integer addition. One integer addition strategy that many teachers use with students is two-sided chip manipulatives. When I started teaching, this was my go-to activity for integer operations.

Then I discovered the Interactive Integers iPad app, which I've blogged about previously. Unfortunately, our tech people were re-imaging all of the iPads, so they were not available to use. I had to fall back on the two-sided chips.

I knew from previous experience with my OCR classes that my LLD class would have a hard time remembering which color was positive and which was negative, so I wrote + and − on each side with a Sharpie.

I begin by demonstrating on the SmartBoard using an infinite cloner for the chips so I can drag out as many as needed, just like the app. We discuss what a “zero pair” is and first relate it to money:

“If I had $1, but owed my friend $1, how much money would I have left? Right, $0!”

I repeat this a few times with different amounts. Then I go around the room asking each student what their favorite number is. For example, if they tell me 7, I say, “So positive 7 and negative 7 equal...?” and wait for them to answer 0. I repeat this with each student.

Now it's their turn. I write an integer addition problem on the SmartBoard and have students write it on their individual whiteboards. Then I give them chips and ask them to set up or model the problem before attempting to remove any zero pairs.

I'm a real stickler for having them set up their chips neatly and lining up the chips under the correct number on their whiteboards. Once I know they can model the problems correctly, I have them start the “game.”

“Can you make a move and take away a zero pair?”

Once they do that, I ask, “Can you still make a move, or is your turn over?” They like thinking of this as a game. Once they cannot make any more moves, they count the remaining chips to find the final answer.

Addition with a Number Line

Then we move to the number-line method. I explain that most students end up liking this method better. It's one they can use anywhere because, as long as they have scrap paper, they can draw their own number line.

I even show them that if there is a coordinate plane somewhere on a test, they can use the x-axis as a number line. All of my students' desks have these stick-on number lines from Nasco.

On the SmartBoard, I use a template with “start” and “move” boxes and a number line.

I give students communicators with the same number line and plenty of empty space at the top for them to write the problem. I have them draw a dot at the start number, then use the move number to travel the correct number of spaces in the correct direction.

I remind them that negative means move left and positive means move right, just as negative numbers are located to the left and positive numbers are located to the right on a number line. Most students pick up on this strategy very quickly.

Subtraction

Once we finish addition, I tell students that I do not like subtraction, so we're going to change subtraction problems into addition problems. That allows us to use either of the two addition strategies we just learned.

I use the slogan “add a line, change the sign” to teach them how to do this.

After students work with subtraction for a day, I give them a mix of addition and subtraction problems. They must pay attention to the operation and determine whether they need to change subtraction into addition before using one of the strategies.

This is where I see the most difficulty. Students may forget to change subtraction to addition, change the operation but forget to change the sign of the second number, or attempt to use “add a line, change the sign” on an addition problem.

I make sure to give them plenty of practice so they become comfortable switching between addition and subtraction. For my LLD students, I kept the operations separate on the integer-operations quiz and clearly indicated which problems were addition, which were subtraction, and when they should use “add a line, change the sign.”

One way I provide practice with integer addition and subtraction is through a friendly game of bingo. Students love the friendly competition and don't mind doing the work when it's fun.

I use BingoBaker.com to create my online bingo games. I also blogged about Bingo a few years ago.

Multiplication and Division

On to the easy part! I explain the rules for multiplication and division and tell students that they can use a basic four-function calculator for the fact part, but they must use the sign rules to determine whether the answer is positive or negative.

I emphasize that for addition and subtraction, they should use the number line rather than the calculator. For multiplication and division, they cannot use the number line and should either solve the fact mentally or use the calculator.

I still saw a few students try to use the number line for multiplication and division or the calculator for addition and subtraction, but not too many!

Integer Operations Centers

On Wednesday, we completed centers for review. This is my favorite day! The centers included:

1. Integer Operations Cubes
2. Integer Operations Notes and Puzzle
3. Math Practice iPad App

Students had about 10 minutes at each center. Partners worked together on the cubes and puzzle, while students worked independently on the app.

Integer Operations Quiz

While students worked on the study guide Thursday and took the quiz Friday, I left the integer-operation rules on the board for them to reference.

Now that the unit is over, I will allow my students to use scientific calculators so they can use the negative button to complete calculations. Integers are such a big part of the eighth-grade curriculum, so I want students to understand that working with negative numbers is not the same as working only with positive numbers.

At the same time, I'm realistic. Even if students correctly learn the procedures for solving equations, they may still get an incorrect answer if they make a mistake with the integer operations. Calculator use is also included in each of their IEPs.

Looking for Integer Operations Activities?

These hands-on resources give students extra practice with adding, subtracting, multiplying, and dividing integers.

View Integer Operations Cubes View Integer Notes and Puzzle

"Pre-Reflecting"??

One of the new practices I have this school year comes from the ideas I got from my summer reading.  Before I begin a new topic this year, I am "pre-reflecting" (not sure if that's a real word or if I just made it up).  I am more cognizant of the prerequisite skills my students need coming into each topic and thinking about how I can incorporate more real world applications to help my students better relate to and understand how it applies to their lives.  Sometimes, with math topics as abstract as they can be at times, this is difficult.

George Couros quotes Chicago-area teacher Josh Stumpenhorst in his book The Innovator's Mindset: “Innovative teaching is constant evolution to make things better for student learning.”  George rephrases this as “What is best for this learner?”  The students in my resource classes come to me with all ability levels, so this is a question I am constantly asking myself about each and every one of my students every day.

Most "reflections" are done post-lesson, looking back at what went wrong or right.  I'm calling this "pre-reflection" because I'm looking ahead at what I can do to make the lessons I'm teaching this week better for my students before I even teach them.  I'm rethinking activities I have used in the past and modifying them to fit my new teaching/learning model.  In the past I have used a lot of technology, but after being a part of the amazing #IMMOOC group the past few weeks, I realized innovation is not all about the tech that you use.

I’m defining innovation as a way of thinking that creates something new and better. Innovation can come from either "invention" (something totally new) or "iteration" (a change of something that already exists), but if it does not meet the idea of "new and better," it is not innovative.   - George Couros

So innovative doesn't necessarily mean I have to throw tech at it.  It just has to be a change that makes it better than it was before.  My goal is to get my students from point A to point B and sometimes I don't need tech to do that.  I've incorporated more hands on materials this year to help my learners.  As Katie Martin said during last night's #IMMOOC live session, "You can't measure innovation but you can measure student outcomes".  I've narrowed down and fine-tuned my list of go-to tech apps this year and I'm only using the ones that really help my students understand the concepts better and improve their learning outcomes.

Innovation is something new and better.  This blog started out as me writing about all of our 'tech adventures in a middle school math class', but this year is a turning point for this blog, hopefully new and better.  I was even thinking of changing the name of it but couldn't come up with a good title.  George says "change is an opportunity to do something amazing".  I hope I'm making my students math experience this year at least somewhat amazing and memorable.

My new approach to "Do Nows"

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“Do Nows,” “bell ringers,” “warm ups”... whatever you call them, I've been wanting to change my daily routine for a few years now. But up until this year, my Do Nows always consisted of a quick review of what we learned the day before. While there's nothing wrong with this approach, and I occasionally still revert to it, what I've been wanting to do is use this time to focus on improving my students' number sense and mental math abilities.

It's something I've always wanted to work on with them but could never find the time while trying to “cover” (my math supervisor hates that term!) the required curriculum. This summer, after reading a lot about building number sense and daily routines, I decided the perfect place to build this practice into our daily routine was to steal the time from the Do Now time.

My Favorite Number Sense Resources

My three favorite resources for these new routines are Jessica Shumway's Number Sense Routines, Sherry Parrish's Number Talks, and a PDF I discovered online from San Diego City Schools entitled “Middle Level Mathematics Routine Bank.”

Number Sense Routines

Number Talks

Number of the Day

The second week of school I started out with the “Number of the Day” routine from the “Middle Level Mathematics Routine Bank.” I gave my students a random number and they had to write down three different ways to express that number. At first, they looked at me like I had two heads—they had no idea what I was asking them to do. So I gave them a few examples.

Unfortunately, most of them wrote down the super easy “+1” or “×1” expressions, so I had to include in the directions that they could not use 1 as one of their numbers. The next day I gave them the stipulation that each of the three ways had to use a different operation. Gradually throughout that week I expanded the task so they had to use multiple operations in their expressions. I was very proud of one student who thought outside the box and was using exponents and parentheses!

Mental Math and Counting Around the Room

I started out the third week of school with what I thought was a fairly easy routine—using mental math to add 10 to a random number, such as 37 or 148. While most of my students found this easy, there were a few students for whom this was quite a challenge. I gave those students a hundreds chart and showed them that adding 10 just means moving down one row on the chart. After a few days, they began to understand this concept.

So after the two-problem Do Now of adding 10 to a number, we did a “Count Around the Room” activity (Shumway calls it “Count Around the Circle” in her book). They actually loved this and never wanted to stop! I ended up going around the room twice each day. Each day that week and the next I upped the ante and increased the number they were counting by to 20, 30, 40, and 50. Some days we would count forwards, and some days we would count backwards. The trickiest turns were the ones that required them to jump across a century (197 to 207, for example), but they improved on this as time went on.

Multiplication Strategies and Number Talks

The next week I changed it up and we multiplied a random number by 10, 20, 30, 40, and 50. We discussed strategies for doing these calculations mentally. I had explained to them that I wanted them to improve their number sense and be able to take apart numbers and put them back together again, so this was the perfect activity to demonstrate how that works.

We had “Number Talks” about all the different strategies they had used. This brought us into the following week's Do Nows, in which I taught them how to use the area model for multiplication so they were breaking numbers into their hundreds, tens, and ones, multiplying using our mental math strategies from the previous weeks, and putting the numbers back together again. That week I also showed them how to use the partial products method instead of the traditional multiplication algorithm. At one point we had five or six ways recorded on the board for solving one problem—being the math geek that I am, I was super excited!

Building Confidence Without Calculators

What frustrates me is that after a few weeks of Do Nows consisting of “Counting Around the Room” by 30s or multiplying a number by 20 successfully, when my students are faced with the same type of problem in the content we are currently learning, they automatically reach for the calculator for these problems. They are super dependent on their calculators, so trying to break them of this habit is going to be difficult.

I try to anticipate when they are going to reach for the calculator and head them off at the pass! Hopefully after another month or so of doing these types of Do Nows, they will gain more confidence and realize that they don't need the calculator for these mental math problems.