Ratio Scavenger Hunt and Online Ratio Games

We just started a new chapter in our Go Math textbooks, and the good news is that it starts out really easy.

The bad news is it starts out a little too easy.  So easy that it gets dull really quickly.

According to the Common Core standard 6.RP.A.1 , students must understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.  The most logical (and the most common) way to introduce the concept of a ratio is to use drawings or models.

To introduce the concept, I always have my students compete in the Ratio Scavenger Hunt. I allow the students to work on their own or in pairs as they search for ratios around the
room. For example, what’s the ratio of kids to desks? What’s the ratio of girls to boys? Kids will understand ratios when they finish this 10 min introduction.  Almost 9,000 people have downloaded the scavenger hunt.  Visit the link above to get your free copy today!

After our Scavenger Hunt, instead of spending all class period just drawing models or building them, I searched for online ratio activities that would be fun for my sixth graders.  I wanted to keep them engaged and interested, and I wanted them to be able to “level up” to more challenging ratio model activities.

As I wrote earlier, I make online study guides for my students.  I’m including a copy of my current chapter study guide here, if you’d like to download it and check it out.  Today, I let my student check out all of the 4.1 games, and they loved them!

At SoftSchools.com , students can model ratios in the Ratios Coloring game .  Students are receive a prompt, and they can select the appropriate colors to draw the given ratio.  They have to follow the rule that the order of the ratio matters!  Students are also introduced to equivalent ratios.  For example, they may be prompted to model 5:1 , but they may need to color the equivalent ratio of 10 red stars and 2 green stars in to advance to the next round.

Over at IXL.com , students are presented with a ratio model, and they need to identify the ratio being modeled.  I like this site because it is the reverse of the ratio coloring game shown above, plus it shows students how to write ratios with a colon, instead of just using the word “to”.  This site also provides students with both part-to-whole and part-to-part ratios.  Unfortunately, students are limited to 20 questions per day on IXL, unless they have an account, but 20 questions is plenty of practice.

Their favorite site of the day was Ratio Rumble, at MathSnacks.com . It reminded me a lot of Candy Crush or Bejeweled, both of which my students enjoy.  Students get to select an avatar and follow the ratio “recipe” to make a “potion”.  Each ratio is comparing one color of potion to another color, so essentially, students are modeling ratios.  The game is really addicting!

As students level up, the recipes get progressively more complex, so students get an extra challenge that they’re actually excited about, instead of having it just feel like more work.

Be sure to check out the other ratio and rate games on our ratio and rate study guide!  And if you have other fun ways of introducing ratios, let me know in the comments.

Here’s a quick tip for teachers young and old: Ask, “Who doesn’t…?”

What I mean by that is when you’re addressing the whole class, trying to figure out if you have passed out enough papers, or asking if everyone has turned in their work, don’t ask, “Does everyone have one?” or “Is everybody finished?” because you’re setting yourself up for a loud, rowdy class.

In each of these examples, you are going to get a lot of kids shouting, “Yes!” and you’ll miss the real information you’re looking for.

There are many times when experienced teachers are trying to calm the class down and transition into a new topic, and instead they just rile everybody up!

It’s a very small, easy change, but when we ask these questions multiple times a day for 180 days a year, it adds up to either a lot of clarity or a lot of confusion.

To make things even clearer and calmer, I often don’t even ask for a verbal response.  When I’m passing out my daily warm ups, I always say, “Raise your hand if you didn’t get one.”  This keeps the room quiet, and no one gets distracted by their neighbor calling out information that really only matters to me and that one student.

Try it tomorrow.  Ask, “Who doesn’t…?” and you’ll have classroom that’s a little bit calmer and quieter.

Free Teacher Tech: Online Stopwatches

After a brain break or at the end of a game or partner activity, students need to learn to reel themselves back in.  They need to self-monitor and prepare themselves to mentally get back into a quiet, focused learning mode.

Having a visible timer on your SmartBoard or Promethean Board is an excellent way to keep track of how much time your students have left to enjoy their break.

Your students won’t be taken by surprise when you tell them that the activity or break has reached its end.

I highly recommend that you visit Online-Stopwatch.com .  This site has been a favorite site of mine since I first started using my Promethean Board.

It’s free, and it even offers a Classroom Timers section, with several fun, interesting ways to keep track of the time students have left.

I make a folder in the bookmarks bar in Chrome, and I keep several of my favorite online stopwatches bookmarked there.

There are traditional timers, such as a simple digital stopwatch, an hourglass, or a circle countdown.

But there are also many surprisingly interesting countdown timers, such as a car race, a swimming race, and even a hilarious, agonizingly slow snail race.

Sometimes I find my early finisher students actually watching the timers instead of chatting with their friends!

A word of advice: stay away from the dynamite timer, and be sure to mute your speakers if you use the fireworks timer.  The former doesn’t show great judgment on your part, and the latter can be startling when the pop of the fireworks is heard.  There are plenty of other fun timers that do the job with none of the potential headaches.

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 think-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!

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 of 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.

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 into 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-decimal 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 practice 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 wide 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.

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, 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.

Finally, if you’re looking for quiet, independent activity 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 out!  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 Math 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?!

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.

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 few 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 writing 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.

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!

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 🙂