Picture Books…In Math?

It’s National Reading Month and, as you know, I love using picture books in my teaching. I love it so much that I’ve even included picture books in my math lessons! There are books made specifically to teach math, such as Scholastic’s Math Mystery Mini-Books and the MathStart series, but there are so many others that are great to use as well. Today I’d like to share with you some of my favorite picture books to use when teaching math, both those written specifically for this purpose, and those which were written just for fun.

Among the Odds & Evens by Priscilla Turner

This book is a nice introduction to even and odd numbers, of course, but it is actually much more than that. The story starts out with two letters, X and Y, crashing into a town of numbers. They notice the many differences between the odd and even numbers and get a little judgmental about the way the numbers get together and reproduce. By the end of the story though the letters have learned an important lesson about accepting people for who they are and how different isn’t necessarily wrong or bad.

A Remainder of One by Elinor J. Pinczes

This delightful story about a group of soldier bugs putting on a parade for their queen explains how sometimes numbers can’t be divided evenly and one or more are left over, or remain. The group of 25 bugs starts out in two lines, but poor Joe is left out. Each day they try forming one more line, but Joe is consistently left standing alone. It is only when they reach five lines that Joe is able to be part of the group and all march happily together.

Sir Cumference books by Cindy Neushwander

I first found these books when I was searching for a literature tie-in for my geometry unit. Geometry is my worst math area and I was trying to find things to liven it up and explain the concepts in a different way for both me and my students. My students and I both loved Sir Cumference, and the way Neushwander explains the math concepts made them easier for us all to understand. There’s even a book of classroom activities to help you creatively integrate the books into your lesson plans.

Gator Pie by Louise Mathews

This book is an old one (copyright 1979), but a good one. In it two alligators, Alvin and Alice, find a pie and decide to share it. Each time they prepare to cut the pie (first in half, then thirds, then fourths…), more gators arrive wanting a slice as well. Poor Alvin and Alice have to continually figure out how to cut a new number of even slices from a single pie. It’s a great introduction to fractions, and the illustrations show how the size of the individual pieces actually gets smaller as the denominator of the fraction gets larger. My students always laugh and laugh as we read the story, and it makes a great start to our factions unit.

The Berenstain Bears’ Trouble With Money by Stan & Jan Berenstain, “Smart” by Shel Silverstein, Alexander Who Used to be Rich Last Sunday by Judith Viorst

American money, especially our coins, is not easy to learn. My English language learners and I spend a lot of time practicing our skills with money, and we love to read stories as we do. We talk about how “smart” the boy really is in Shel Silverstein’s poem, learn along with Brother and Sister Bear as they spend their money, talk about money idioms, and then earn their own money; and sympathize with poor Alexander who has only bus tokens in his pocket. The stories are all funny, totally relatable to my students, and they provide a welcome break from all of the math and vocabulary practice that goes with this unit.

The Five-Dog Night by Eileen Christelow

Writing algebraic expressions is a difficult skill to master for all students, but especially English language learners. Not only do they have to figure out how to translate words into numbers and symbols, they have to try and understand the words first! This last book is a great way to introduce the concept with a fun story about a lonely old bachelor named Ezra and his neighbor Betty. Betty can’t understand why Ezra always says he doesn’t need blankets, but the pictures reveal the answer Betty won’t discover until the end of the book. After reading the story, the students and I work together to write an equation that will help Ezra determine how many dogs he’ll need each night to stay warm. It’s a fun exercise and helps to lower their anxiety about the work to come.

The truth is I could list many other picture books to use when teaching math, but I won’t. I encourage you to give some of these a try, and seek out others you and your students can enjoy together as well. Be sure and let me know what your own favorites are, or become! Happy teaching, everyone.

Multiplication Fact Practice and A Helpful Slides Add On

Multiplication Picking Apples Digital Task Cards
Multiplication and Division Picking Apples: Paper Version

The vast majority of my students through the years have needed basic math fact practice, especially with their times tables. The reason for this need varied from it was what they were learning that year, to interrupted education, to never learned them in the first place, etc. At the end of the day, the reason the students needed practice didn’t matter, the fact that they needed it did. Today I’d like to share with you two of my students’ favorite multiplication (can be adjusted for other operations, especially addition) games that can also be used as time fillers at the end of a class period. Then I’d like to tell you about another game that gets students up and moving, the digital task cards I created to replace it for distance learning, and the newest add-on that has me excited.

Shake ‘N Multiply
All this game requires is a few basic items that you likely have laying around the house already, and about two minutes of your time. You will need: an empty egg carton (I use the 12 cup version, but you could use 18), a couple of pom poms, and a marker. To make the game, open the egg carton and number the bottom of each cup 1-12. Drop in two pom poms, or other small objects. I like the pom poms because they are cheap and, more importantly, quiet, but you could use beans, marbleserasers, anything that will move around the carton. Close the lid and your game creation is finished.

To play the game put the students in pairs or groups (I do no more than four to a group to prevent boredom while waiting for their turn, pairs is my favorite way to play.), and give each set of students a prepared egg carton. The first player shakes the carton, opens the lid, and multiplies the two numbers the pom poms are on. If he/she is correct, he/she gets a point. The second player then closes the lid, shakes, and multiplies the two numbers indicated. Play continues in this manner until time is up. The player with the most points is the winner.

Since the cartons are free, pom poms are extremely cheap, and set up takes almost no time at all, I keep sets of these in my classroom year round. When there are five minutes left in class all I have to do is pass out the cartons and students can play. It’s a great academic time filler for the end of class, or a nice brain break for when we need a change of pace.

Toss ‘N Multiply
Requiring even fewer materials, and taking almost as little time to create, is my students’ other favorite fact practice game. All you need for Toss ‘N Multiply is a small soccer ball (the one I use is size 1.5, 6″), and a marker. The reason I use the soccer ball is that the clearly defined sections make it easy to label. Write the numbers 1-12 in the sections of the ball, repeating as many times as necessary. If you get a ball with black and white sections, simply use a silver marker on the black sections. Let the numbers dry (should only take a few seconds), and set up is complete.

To play, have students gather in a circle. You can choose to play as a whole class, or in groups of three to six students. Students must toss the ball under hand, and catch it with two hands. Toss the ball to a student, reminding him/her to catch with both hands. The student then looks and multiplies whatever two numbers his/her thumbs are on. There will be a couple of sections without numbers, due to the presence of logos and other advertising, but the student can always use a different finger if his/her thumb is on one of those sections. If the student is correct, he/she stays in the game. The ball is then tossed to another student who repeats the process. If a student answers incorrectly, he/she is out of the game and must sit down. The last student standing is the winner.

Again, this is the perfect game for filling time at the end of class, or a brain break during class. The ball takes up very little room at all, and other than having students stand in a circle, there is no prep work.

Picking Apples
This last activity does take a little more prep and time, but it is still a lot of fun. When we play Picking Apples, my students help me clear space by shoving all of the desks to each side of the room. We then have a starting line at one end, and a table for our apples at the other. I divide the students into two to four teams, and each team has a set of cards (we usually put them on a chair near the team’s starting area) and a bucket. At the opposite end of the room I place a table and hundreds of miniature apple erasers. When I start the game, the first person on each team grabs the top card, computes the answer to the problem shown (I have sets for multiplication and division as well as addition and subtraction), runs to the opposite side of the room, gathers the correct number of apples for the answer, and runs back to the team. If correct, he/she earns a point for his/her team. The second person then takes the bucket, grabs a new card, runs to the other end, dumps out the apples from person one, and gathers the correct number for his/her card. Play continues in this way until time is called. The team with the most points wins. When playing this game with more than two teams, I will appoint at least one student to be my fellow answer checker. Also, when the answer is a large number (such as 144), I do not take time to count all of the apples, I look, estimate, and ask the student to tell me verbally how many are there.

This year has brought new challenges to our lives; students are no longer all in the classroom together, and when they are in the classroom the sharing of materials is forbidden. Thus there is no Picking Apples game play this year. Instead I created digital task cards for students to practice with. Each card features a single problem written in the clouds, a basket to hold their apples, and an apple tree with over 150 apples on it (I copied and pasted the apple about 15 times, selected them all, aligned them to center and middle, and then copied and pasted the stacks to create “infinity” piles of apples in the tree.). On all of the sets except subtraction, the basket is actually a pile of baskets, so students can use groupings (such as repeated addition) to help them find the answer. These digital task cards allow students to safely use manipulatives to practice their basic math facts, 1-12 for multiplication and division, 1-20 for addition and subtraction.

Helpful Add On

When making these kinds of digital activities I always design my non-moving elements in PowerPoint and save them as image files. I then upload those images as the background of my Google Slides. In order to speed up the background insertion (these activities had between 146 and 202 slides each!), I’ve long used the add-on Slides Toolbox. I once again used Slides Toolbox, but I also needed to do something else: randomize the slides. In order to be sure I included all of the facts students needed to practice, I created the task cards in order. When using paper task cards this isn’t a problem, because I simply shuffle them before giving them to students. Digital task cards a little more tricky, and I needed a way to shuffle them so students would have to do more than count in sequence for the answers (multiplication is still in order because you may want to practice only certain facts). Thankfully, much as there’s an app for every situation, there’s an add-on for every situation today. I used every teacher’s best friend, Google, and found an add-on called Slides Randomizer. This add-on will randomize the order of your slides once, or every time you open the file. You can choose to have the first slide remain stationary or not, and you can initiate a randomization of slides anytime you choose. In order to reset slides, you must use the back or undo button, and they will not return to their original order when you close the file. I decided it was worth a try, and it worked great. It was incredibly easy to use, and took hardly any time at all to perform the randomization of the slides. The only thing I wished was that I could choose the number of slides at the beginning to keep in place, as my activity has a title slide, a directions slide, and a helpful tip about groupings slide. I realized later that I should have just built my deck without those slides, randomized it, turned the auto-randomization off, and then added those three slides last, but at least I know for next time.

I know most people don’t automatically put math instruction together with ESL, but I have actually done quite a bit of it over the years. There’s a lot of vocabulary in math, and it’s an important subject for every student. I hope your students enjoy these fact practice games as much as mine. Happy teaching, everyone!

Integer Fishing

As an ESL teacher I end up teaching all subjects. During my middle school days (ah, the good ol’ days) I had a self-contained classroom of newly arrived 7-9th graders. Those were some fun times, but also some tough times for this grammar guru. Don’t get me wrong, I love math, social studies, science…all of the subjects. Grammar is just the one that comes easiest to me. In the end I approached all of the subjects, especially math, the same way I approach grammar: with games! Integer fishing is one that I originally created using plastic eggs, dice, and white boards. With the arrival of Corona Virus, I knew that a digital version was needed. Enter Google Sheets with scripts and conditional formatting. Then I kept hearing about teachers at Microsoft schools who couldn’t use Google Apps, and I could relate (my college has Google for students and Microsoft for professors–try to figure out that combination!). Enter macro-enabled Excel. Today I’d like to share with you one of the games that I’ve made using these methods and give you a template with a macro-enabled button for “rolling” a number cube.

Before I get to the digital version of the game, let me tell you about the physical game. To make the game you’ll need several items: an egg carton (I used an 18 count), plastic eggs in two colors (one for positive and one for negative), a six-sided die, a positive/negative die, and a twenty-sided die. Write an integer between +20 and -20 on the bottom of each egg (put positive numbers on one color and negative numbers on another) and place in the container. When you’re ready to play, pass out one container, the dice, and a whiteboard & marker to each set of students (I usually have students play in pairs, but you could do up to four in a group). The first player rolls all three dice. The +/- and D20 dice tell the student the goal answer, this is the number he/she wants to be at when his/her turn is over. The D6 die tells the student how many eggs he/she must turn over. The student turns over eggs one at a time, adding the integers together as he/she goes (the whiteboard is very helpful for this purpose). The object is to have the final total be the same as the goal number the student started the turn with. After turning over the required number of eggs, the student’s score is the distance between the goal and the final total (so if the goal was -4 and the student’s eggs added up to +1, his/her score would be 5). The game starts out difficult, because other than knowing if an egg is positive or negative, the student does not know the values of each egg. As the rounds progress, students start to remember the value of different eggs and the students are able to use their knowledge of integers to help them.

Now I’d like to share with you how I created the digital version of the game, but first a look at how it is played:

For most of the creation process, the steps are the same in both Google Sheets and Microsoft Excel. When creating the activity I started by typing out the directions for students. I wanted it to be very clear how to play the game. I then created color-coded recording spaces for students to keep track of the game rounds (we used to use a white board for this). This was nothing more complicated than selecting the cells I wanted them to use for each purpose, filling the cells with a particular color, and then labeling the group. The real fun came when I started creating the fishing hole and the catch basket. The fishing hole was simple, I simply selected a group of cells, colored them blue, and set the text to be white and centered. The magic started with the catch basket.

I used a random number generator (Google) to get 12 numbers between -20 and +20. I typed one number into each cell, selected the cells, made the text a dark brown, and then colored the cells a dark brown. This essentially made the numbers invisible. My next step was to enter the conditional formatting. I described how to do this in detail in my blog post about mystery picture activities (there’s even a video). Just as a quick reminder, here are the steps to conditionally format cells based on the contents of another cell:

  1. select the cell you want to change
  2. click Format
  3. click Conditional Formatting
  4. under Format rules, Format cells if… choose “Custom formula is…”
  5. add the custom formula: =$[column of the cell you are referencing]$[row of the cell you are referencing]=””  (ie: =$A$3=”X”)
  6. choose the color you want the cell to turn (I chose white so as to reveal the brown letters)
  7. click done

Unfortunately, you have to format each cell individually, but it didn’t take me too long and the end result is worth it. When I finished, each blue cell in the fishing pond corresponded to each brown cell in the catch basket. When students make an X in a blue cell, the corresponding brown cell turns white, revealing the catch value.

The magic continued with the addition of the Catch Goal and Number of Casts buttons, but this is where I needed my husband (a software engineer) to help me. I do not program and to create the activities two different programming languages were required. Sheets required JavaScript and Excel required VBA. All I did in this process was to insert an image and label it, from there the expert took over. He inserted a script for Sheets and a macro for Excel. I’ll spare you the long explanation of how he made it all work (because I don’t understand it). The good news is that he did and says it wasn’t difficult (so if you do know how to program you could do it yourself).

The final result was the game that you saw demonstrated above. The demonstration video was made with the Google Sheets version, but the play is the same with the Excel version. The Google Sheets version is for sale in my Teachers pay Teachers store, but the frustration of being a Microsoft school continues for all. It turns out that macro-enabled files are not supported on the TpT platform and I was unable to upload the Excel version. But the GOOD news is that since the game was already made, I decided to use my blog to disseminate it–for free! And, because I feel the pain of not always being able to use Google Apps, I included a template as well. The template includes the macro-enabled dice roll button. To use it simply open the file, do a “save as” so you don’t mess up your template, and design your game. The Roll button will randomly generate numbers between one and six, just like a number cube. I hope you and your students enjoy the game as much as I and mine have. Happy gaming, everyone!