Math Quizzes as “Think-Alouds”

In my former life as a reading teacher, I made sure to incorporate a read-aloud each day. I picked an interesting novel, and I sat on a stool and read aloud for 15-20 minutes. Some people may have viewed this as a way to kill time.  It looked way too easy for all the students who were supposed to be preparing for the rigors of standardized testing.  I read from a book that someone else wrote, and the students usually just sat there and listened, only chiming in when I asked them to do so.  To the casual observer, I’m sure it didn’t look like much learning was taking place.

But there was tons of teaching and learning happening!  The read-aloud was actually a read aloud.jpgthink-aloud.

Throughout the text, I would stop and literally think out loud about what I was reading.  I would make inferences based on the text.  I would use context clues to think through the meanings of unfamiliar words.  I would make make observations that led to predictions.  I would make connections to other texts and to my own experiences.  I would accomplish many of the thinking tasks that I wanted my students to be doing in their independent reading time, or during our Guided Reading sessions.

And by listening to my out-loud thinking, my students couldn’t help but also think.

Sure, it looked different than a traditional reading worksheet, and I didn’t have written documentation to measure every student’s growth. But it just made sense to pause and take time out of our day to read aloud.  It gave students a break from the norm, and it showed them that their teacher was actually practicing the same thinking strategies that I asked them to use.  As the reader and the out-loud thinker, I felt vulnerable, because of course I would mispronounce a word or stumble through a sentence here or there. But I always got the sense that my students could relate to me much better, as they watched and listened to me model the ways to navigate through a new text.

Those experiences as a reading teacher have a big impact on the way I teach Math, especially when it comes time for my Math quizzes (or formative assessments, in educational-lingo).

But first, let me emphasize a major difference between teaching Math and teaching Reading: Math moves at about 100 miles per hour.  We’re constantly adding new layers that students are expected to master in a very short amount of time.  Lesson 1 leads to Lesson 2, which leads to Lesson 3, and so on.  If you didn’t master Lesson 3, you’re going to struggle with Lesson 4. And if you struggle with both of those, then you’re pretty much out of luck for the rest of the chapter.  Plus, next chapter, your struggles are bound to continue, but it will be exponentially worse, since you lack the prerequisite skills from the previous chapter!
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In Reading, you can move at a more leisurely pace, and students have multiple opportunities in different texts throughout the year to master each standard.  Sure, there are different genres, but as a former Reading teacher for 8 years,  I can tell you that in Reading, it’s much easier to spiral back around to previous standards several times throughout the year.

Don’t get me wrong.  I do think Reading is the most important subject.  It opens the gates of learning for every student.  Every other subject relies heavily on a student’s ability to read. But, it’s simply a different beast.

Again, realistically, Math is different.  We move at a breakneck pace.  Hurry up!  Pay attention!  Move along!  It’s time to start the next lesson!

And because of this fast pace, as we try to cram in the seemingly infinite number of standards in our very finite amount of time, we have to give many quizzes or “formative assessments” along the way to be sure that we haven’t lost anyone.  We have to constantly assess our students, to make sure no one falls through the cracks.

In fact, many of my colleagues understandably complain about the lack of instructional time in Math class, because we spend a great deal of our time quizzing our students to be sure that they have mastered a topic, that they have gained a solid foundation, so we can move on to the next topic.  But at the same time, we want them to hurry up, because we’re already falling behind!

How can we include a Warm Up for review or front-loading, plus check homework, and give a quiz, then teach a lesson, and manage to possibly throw in a …(wait for it)….fun activity on top it all?

My answer is simple: Use what we know about good reading instruction in Math class.  Use each quiz as an additional “think-aloud” learning opportunity.  Start them down the right track on each question by reading each question aloud, and use think-aloud techniques to support your students.

Because this isn’t just good reading instruction.  It’s good instruction. Period.

Our common 6th grade quizzes are all 5 questions long.  But when we give our students time to work independently, these 5 questions take a long time.  Sometimes it’s because students have trouble reading the text.  Sometimes it’s because a few perfectionists take a really long time.  Other times it’s because struggling students seize up and freeze when they don’t know what to do.  But no matter the reason, reading each quiz aloud and thinking through the problems together helps everyone.

It gives the perfectionist confidence that they have sufficiently responded.  It gives the struggling student a kick start (or a kick in the pants!) in the right direction.  It gives the 504 student the required read-aloud that’s dictated in their 504 plan. And, it gives me, the teacher, the peace of mind that I am helping my students, not just constantly testing them!

Think about this: How much true instructional time do you really have?  When you subtract the time it takes your students to get settled, the time for announcements,the time for interruptions, homework check, and quizzes, you lose at least half of your class time.  I usually wind up with only 20-25 of actual instruction time for introducing new topics each period.  That’s it!

Quizzes as think-alouds add to my instructional time, because I’m instructing during the quiz. Plus, the time that this saves allows me to have more instructional time after the quiz, too.  It’s a win-win!

Here is a screen capture of one ofquiz with notations.png my recent quizzes.  As I read through each question, I not only think out loud, but I also make notations of what I’m thinking.  You can see that it’s not pretty, but it’s a realistic look at how I want my students to think and work through each problem.

When I explain my strategy to my colleagues, and I show them examples of how much writing and talking I do during a quiz, I can tell that some of them question the validity of my students’ great results.  But, wouldn’t you rather give your students too much help, than not enough?

The students who would do fine without my help wind up working ahead anyway.  But the students who do need my help are receiving my assistance in real time, not later on when we’re trying to correct misunderstandings through remediation, after the damage is done and we’ve moved on to a new topic.

By thinking aloud and guiding students through their quizzes, I never arrive at the answer for them.  But I do read it aloud, think through the initial steps aloud, and even make notations on the displayed version of the quiz on my Promethean Board.

I do this because it’s just not realistic to expect a 12-year old to master a concept and be able to demonstrate that mastery independently after only 20 minutes of instruction and a quick homework check.  I do this because I want to help my students.  I do this because it’s my classroom, and I know that I want to set my students up for success, not failure.

And I do this because it’s not just good Reading instruction.  It’s good instruction.  Period.

 

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Making the tasks of Converting, Comparing, and Ordering Fractions and Decimals Fun!

Although we adults are pretty good at converting common fractions and decimals, it’s just not an activity that’s very relevant or interesting for a child.  If anything, converting to percents makes more sense, since this is how their grades are determined.  But fractions to decimals, and vice versa, just doesn’t seem important to most 12-year-olds.  So, I’ve put together a few items that will make this task much more fun and engaging.  After all, that’s half the battle when teaching Math!

First, a tip for new teachers: just make everything fraction to decimal by dividing.pnginto a decimal.  It’s much easier than trying to have students write fractions with common denominators or have them write a decimal as a fraction, then find a common denominator.  I make my students repeat the phrase,”To get a decimal, we divide,” on a daily basis during this unit.  The alliteration and repetition engrains the simple one-step conversion into their heads.

Second, take a few minutes to see which common fraction-to-decimCommon Fractions with Decimal and Percent Equivalents.pngal equivalents your students already know.  They often surprise themselves by generating their own lists, even if it just involves halves, quarters, and thirds.  I usually give my students a “cheat sheet” to place in their math binders.  Typically, most of my students don’t use it, but just knowing that it’s there gives them confidence.  You can click on this link to view the list of common fraction and decimal equivalents that I give my students.  It’s from FactMonster.com . It also includes percents, but you could always crop that out if you would like.

After my students have had time to practiceConverting Fractions to Decimals Sorting Activity.png this basic conversion, I have them complete a Fraction to Decimal sorting activity.  You can grab a free copy at my store!  Over 2,500 people have already downloaded it.  In this sorting activity, students cut out 16 sorting cards. Half of the fractions (or 0.5, if you’re following along) convert to terminating decimals, and half of the fractions convert to repeating decimals. Students must sort the cards and attach them on the chart, under the appropriate heading. Students are required to provide justifications for at least two questions in each category. I usually have my students work in pairs or small groups, to generate Math Talk conversations.  Sorting activities like this one are quick, fun, simple ways to help students establish the basic skills they need before taking on more complex tasks.

Next is one of my students’ favorites, the Fraction vs Decimal War card game!  The basic rule of the game is easy: Draw 2 cards, just like in the regular game of war. Determine which card has a greater value. The winner is the player whose card has the greatest value. You get 64 cards, with a widefraction-and-decimal-war-main-thumb variety of fractions and decimals, all in printable sheets. You don’t have to purchase or alter real playing cards. The game doesn’t get stale, because I have included several Joker cards with special conversion/comparison tasks for fractions and decimals. It doesn’t get better than this!

Just print the cards, have your students cut along the lines. Display the rule sheet, and you’re set!  You could always choose to laminate the cards and store them from year to year.

Your kids will love the game, and they will gain lots of extra practice comparing fractions and decimals. You can grab a copy at my store.

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Another fun teamwork activity for your whole group is the Human Number Line.  As the teacher, I randomly distribute either a fraction card or a decimal card to my students. The students look at their cards and decide where they belong on the number line, from 0 to 3. Should they move to the left or to the right? Is it closer to 0, 1,Human Number line main thumb.png 2, or 3? I encourage students with fractions to convert them to decimals, and even write the new form of their number right on their card.  I give each student a small piece of tape, and then dismiss them one row at a time to tape their cards on the board, in order.  The rest of the class has to stay silent, until I ask for suggestions about what my need to be adjusted.  Do any cards need to be flip flopped?  Is anything out of place?  They love finding errors, and keeping their attention is pretty easy. Everyone gets to participate. Students become good at justifying why a number is or is not in the correct position.  Even passive students are exposed to positive, articulate math conversations during this activity.

You may even choose to time your class with each repetition of the activity to see if you can set a new class record for fastest number line completion!

You can find this Human Number Line activity, as well as several other versions with integers, percents, and more at my store.

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Finally, if you’re looking for quiet, independent hidden-picture-math-convert-fractions-to-decimalsactivity for students to demonstrate their knowledge of converting fractions and decimals, you can check out the Hidden Picture Math – Converting Fractions to Decimals worksheet.  Students work to reveal the hidden picture by converting fractions to decimals and shading in their answers on the grid. This fun, simple worksheet includes directions for your students, including which colors to use. You will be able to grade/check these in mere seconds using the color key that I have provided. Head on over to my store to get your copy.

If you have other fun ways to get your students to convert, compare, and order fractions and decimals, please let me know in the comments 🙂

Subtracting Isn’t Always Last! Make Order of Operations Easier

A lot of times when I post a new blog entry, I’m thinking of new teachers, who could use some quick and easy advice that would simply make their day a little easier.  I’m always looking to get the most “bang for your buck”, to maximize the very short time we have students in our presence, actually paying attention, and staying engaged.

I’m not saying that I’ve got it all figured change-signout!  Even in this 16th year of my teaching career, I spend more time than ever changing my lessons, creating new activities, and searching out better ways of teaching, to make the biggest impact that I can, given my students’ abilities (wide-ranging) and my own energy (running on empty with a 1-1/2 year old and another on the way!).

These tweaks don’t have to be earth-moving, monumental changes.  Sometimes, a little, quick change can make a big impact on the way your students understand what you’re trying to convey.  These are the kinds of things that I try to share with new teachers at my school.

One quick and easy change that we can make as pemdasMath teachers is to simply write the PEMDAS order of operations steps like I have pictured here.

Put the M above the D, and the A above the S.

The reason for writing it this way is that many of my 6th graders arrive with the misconception that addition must come before subtraction, when using the order of operations.  And I get it.  I understand that they have been taught the “Please Excuse MDear Aunt Sally” line, and that Aunt comes before Sally.  And I understand that they have been seeing the abbreviation written down in a single horizontal line, like this: PEMDAS.

But when they are suddenly faced with relatively complicated expressions that include increasingly long number of steps, they often get to the last two steps and blow it!  It’s disheartening to them (and to us!) to see students navigate through parentheses, exponents, multiplying with new symbols besides the traditional “x”, and division with a fraction bar, only to have all their work negated by an insistence that adding comes before subtracting!

So, from Day 1, I require my students to write the steps like I have pictured above.  We even draw the arrow from right to left, so students remember that multiplying and dividing are equal in the eyes of Dear Aunt Sally, as are adding and subtracting, as long as you’re moving from left to right.

It’s a small change, but it can take away some of the headaches involved in teaching the Order of Operations.

If you’re looking for a fun way to practice using the order of operations, check out my last post on the Evaluating Expressions Number Cube Games.  And if you have other ways of reinforcing the order of operations, let me know in the comments!

Evaluating Expressions throughout the year with Number Cube Games

X’s, Y’s, Z’s?  What do those have to do with math?!football-number-cube-game

If you put yourself in the shoes of your sixth grade students, you might be wondering why in the world letters are suddenly appearing in Math class.  In fact, algebraic expressions might seem like a whole new language to you.

So to ease students into the evaluating expressions, which include variables, I introduce them to my Evaluating Expressions Number Cube games.

These quick, competitive games are designed to introduce students to the concept of replacing a variable with a value, and then evaluating the expression.  Instead of traditional x, y, or z variables, I use small pictures, like tiny footballs, pumpkins, or beach balls.  There are 9 seasonal varieties, each with a different theme.

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As you can see from the screenshot above, students roll number cubes or dice, and they replace the variable with the value that they rolled.  After evaluating their expressions, the student with the greatest value wins that round.  The player who wins the most rounds at the end of the game is the champion.

You can download a free copy of the September football version right here, as a thank-you for checking out my blog!

I always walk my students through a aunt-sallyfew sample rounds, so they understand the concept of replacing variables with the values they rolled.  I have found that my students also need a reminder of their Dear Old Aunt Sally (PEMDAS, Order of Operations).

Oftentimes students also need reminders about ways of showing multiplication, beyond the traditional x symbol, which we move away from in 6th grade, to avoid confusion between the variable x and the multiplication symbol x.

I also use this game as an opportunity to introduce my students to writifraction as division.pngng division problems as fractions.  Very few of my students have seen division problems written this way, but by playing the game several times throughout the year, they are able to recognize this new form, which they will see in middle school and beyond.

number-cube-game-displayed

There is both a front and a back to the game, but not all pairs of students will make it to the back each time.  And that’s ok.  We’re giving students the opportunity to play a game and be exposed to a fundamental algebraic concept, so any practice is better than no practice!  number cube game varieites.png

The monthly themes are as follows:

  • September – Football
  • October – Pumpkins
  • November – Turkeys
  • December – Snowmen
  • January – New Years
  • February – Candy Hearts
  • March – Shamrocks
  • April – Easter Eggs
  • May – Beach Balls

If you’re looking for a quick, easy way to create random groups for games or cooperative work, check out my post about the Team Maker website.

If you have other fun ways of introducing students to evaluating algebraic expressions beyond a traditional worksheet, let me know in the comments 🙂

 

 

 

 

Random Team Maker

A few weeks ago, I wrote about a handy tool called the Random Name Picker.  It’s especially helpful at the beginning of the school year, when not all students feel comfortable to volunteer on their own.  It also keeps the students on their toes, since they know their turn to talk might be coming up soon.

Similarly, the Team Maker tool from Chirag Mehta is a fantastic way to quickly arrange your students into random groups for cooperative learning.  You get to choose the number of groups, and this free website randomly places your students into teams.

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I really like using this site, because if given the option to choose their own groups, my students always tend to work with the same people.  With the Team Maker tool, students are exposed to new voices and new opportunities to cooperate and learn from each other.

I find that it’s also much faster to use this tool than to have students count off.  We all know that there’s always someone who forgets their number or who conveniently finds their way into the wrong group!

A nice feature with this site is that you can copy and paste a list of names that you already have saved, so you don’t have to type in the names each time you use the Team Maker.  I keep a simple text document (just use Notepad) with all my students’ names.  When I want to use the Team Maker, I just open the text document, use Ctrl+A to select all, Ctrl+C to copy the list, and then use Ctrl+V to paste the names into the Team Maker.team-maker-names

There are some fun options for team names, beyond just Team 1, Team, 2, etc.  You can use the drop-down list to select from Animals, Cars, Sports Teams, and many more themes, seen here.  You can even edit the names within the list, so if you select Cars, but your students aren’t familiar with a Bugatti, you can change it to Corvette, Mustang, or maybe even old rusty station wagon!

I recommend displaying the whole process on a Promethean Board or SmartBoard.  This way, students see that it truly is a random grouping, and no one is receiving special treatment.  They also like seeing the team names and when time allows, they generate some fun alternatives.  Plus, it’s really easy to display the names on the screen, so students can see their group name, instead of just hearing it.

You can choose the output format, including a small, scrollableteam-maker-output-format preview window, a whole new browser window, or a .csv file, which you can save in Excel.  I recommend  the New Window option, because you can see several teams at one time, and it’s a much cleaner, clearer look.

Just click the Generate Teams button, and your groups will appear in seconds.  This site is very fast, and it’s rare to ever experience a delay.

Here’s an example of what you will see if you use the New Windoteam-maker-teamsw option.  Apparently, the site’s creator was a big fan of the TV shows The Office and Mad Men, because the default names are all characters!  (Imagine a team with Don Draper and Michael Scott working together!)

If you have other random team/group maker sites or electronic tools that you enjoy, please share them in the comments!

 

Long Division That Doesn’t Stink!

As I wrote earlier, the dolts authors that wrote our textbook decided to start the year off with long division.  bart long division.jpg

Not a smart move!

After shuffling lessons around and avoiding it as long as possible, I finally decided to end our first unit with long division.  The Common Core Standard states that students must fluently divide multi-digit numbers using the standard algorithm.  The good news about that is that it’s the method that I learned as a kid back in the 1980’s, and it’s probably the way most of your students’ parents learned to divide.

This really nice, clear explanation fromlong division CoolMath4Kids.com walks students (and maybe teachers who grew up with another algorithm!) through the basics of long division.  The color-coded steps make it very easy to follow along.

Even though the Common Core Standards don’t explicitly state that students in grades 4 or 5 need to use the standard algorithm, I am very fortunate to be able to say that most students arrive in 6th grade with a familiarity and an understanding of this traditional algorithm.

And that makes things much, much easier!

However, it’s still necessary to review the steps for long division, since no one sat at home over the summer and practiced, and there are always a few new students who aren’t familiar with this traditional approach.

I actually make my students raise their right hands snorks.pngand repeat some sort of pledge that I make up on the spot.  I say that if they promise to follow along with a pencil and a piece of notebook paper, they don’t even have to open their textbooks.  This grabs their attention, and then I really hook them with this game, called Snorks, from KidsNumbers.com .

The Snorks website cheers on students as they walk through the steps of long division.  Every now and then, there’s an easy mental math division problem, but most of the problems require actual long division.  At first, I call on individual students to tell me what to do for each new step, but eventually I let the class call out the steps all together.  They really get into it!  Who knew long division could actually be exciting?!

For more advanced students, KidsMathTV.com has a Millionaire long division game.  There is a timer involved, so the students have to calculate really quickly.  Not everyone is going to be able to keep up the first time through, but it’s a fun game to offer students who are looking for a challenge.

millionaire Long division.png

So now that my students are engaged, what’s next?

I created this “Text Me” long division homework page, and
text me long division pic.pngmy students have done really well with it each year.  It’s set up so that students only write in the boxes that I’ve provided, so their work stays neat and organized.  The gimmick is that students are trying to find the missing digits in their friend’s phone number, so they can text the friend later.  Not only do students need to get the quotients correct, but they also need to provide the correct work, since some of the missing digits are found in the work area beneath the division bracket.  You can download the Text Me – Dividing Whole Numbers worksheet right here, as a thank-you for reading my blog!

You can also grab the Text Me worksheet as part of my “Long Division That Doesn’t Stink” bundle.  It includes a second teaching/homework sheet for dividing decimals by whole numbers and third sheet for dividing decimals by decimals.long division bundle.png

Each sheet includes around 8 problems, with plenty of space for students to show their work, and scaffolding is provided to make sure that students are guided through the entire process.

I’d love to hear what you think!  If you have other ways to get your students excited about long division, let me know if the comments.

Wordle Welcome Sign

If you’re looking for a quick way to decorate your classroom door, with a personalized, welcoming touch, I recommend heading over to Wordle’s website.  This site is an oldie but a goodie.

If you’re not familiar with Wordle, it’s a site that creates “word clouds”.  It’s basically a fun way to display a group of words, simply by adjusting the format and font, after you type or paste in a list of words.Wordle 1st variation

As a Math teacher, I’m sure there are other applications for this word cloud site, but I use it every year to create a quick Welcome sign, featuring all the names of my students.  Again, you can either type in their names or paste a list.  As I’ve written before, I highly recommend the book, The First Days of School.  In it, the authors emphasize the importance of making your students feel welcomed.  They state that you should always tell your students and clearly display for your students a warm welcome.  This is a fast, free, eye-catching way to accomplish this.  Students love finding their names in the word cloud.

I find that the Wordle site works better with Internet Explorer than Chrome, but your results may vary.  You need the latest version of Java installed.  It takes about 2 minutes, and you can grab it here, in case your version is out of date.  Because your results will vary, I recommend copying and pasting your list of names, because if the site won’t load in your browser, you can just open a different browser and paste in the list, in a matter of seconds.

After you type or paste in your student names, there are a few things to consider. First, any names that are repeated will appear larger than the rest, because the site displays the most common words larger than the rest.  You can get around this by simply using any confirmed nicknames, or by using variations such as JoeyL and JoeyZ.  Just click the Go button when you’re ready.Wordle type or paste.png

It’s very easy to experiment with the font style and the font/background colors.  Just use the menu at the top to choose from the difWordle color optionsferent options.  There are lots of fun fonts to try out.  You can also change the direction of the text until you find the one that you like best.  You don’t need to re-enter any of the text to make these adjustments.  It’s very easy to view the different layout options.  There’s even a “randomize” button that you can use if you’re feeling adventurous.

Here is another variation of the word cloud that I showed you at the top of this page:

Wordle 2nd variation.png

The names are the same, but I changed the font and the font/background colors.

Here is a third variation with a twist.  I pasted in the student names, but I also added the word “Welcome” three times.  The reason I included it three times is because of Wordle’s way of making the most popular words appear the largest.  Since it’s a welcome sign, I wanted “Welcome” to stand out.Wordle Welcome variation.png

It’s quick, it’s easy, and it’s a fun way to welcome your students to your classroom.  I had a few parents at Open House stop and mention how cool they thought the sign was, and several parents made a point to stop and find their child’s name.  Give it a try!