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Fractions

Use This Free Resource if You are Teaching Fractions

Have you seen this great new website tool for teaching and assessing mathematics for elementary students?  On iknowit There are multiple lessons included about various math topics all from the makers of Super Teacher Worksheets!  One of my favorite lessons is the one about 3rd grade fractions.  What I like about the fraction lesson/assessment is that it focuses on equal parts.  This gives children the chance to really think about what equal parts look like.  Sometimes the idea that fractions are equal parts can become a misconception to students.

 

There are also different types of general fraction questions such as what fraction is shaded or what fraction was taken etc.

There are questions using the written words halves and quarters instead of only the numbers.  These are words that students struggle with seeing and using.

I also like that the program gives students automatic feedback to let them know if they were correct or incorrect.  If students are incorrect, the program gives students an explanation to tell them why they were incorrect. The little robot is animated and jumps around each time students get a question correct.  He has a different animation for each question.

You can even take a quick grade with this program because the program shows students their total score when they complete an assessment.  Teachers can easily use the score for their grade book.

The best part is that it is free!  FREE! Yes, absolutely FREE!  (At the time of the writing, the website is free, but eventually this website will charge for membership.)

Try it out and enjoy!

Have You Heard About this Great New Math Practice Site?

Screen Shot 2016-08-25 at 8.41.54 PMTell everyone you know about this great new free animated website iknowit.com that helps elementary kids practice math skills by playing games.  This site will remain FREE for at least the next year while improvements and more lessons are added.  Iknowit was built by the makers of Super Teacher Worksheets and Modern Chalkboard, a SMART board lesson site.

The lessons give children immediate feedback so that they know if they have answered each question correctly or incorrectly.  There are drill lessons for basic math facts–addition, subtraction, multiplication, and division.  These lessons are timed.   Then there are lessons based on progress in which students answer a certain amount of questions.  Right now the lesson topics include addition, multiplication, division, time, money, fractions, and there are many more to come!

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In the future as a teacher, you can log in and set up a class roster.  You will be able to assign lessons, monitor student scores, and track their progress.  You will also be able to adjust the number of hints children are allowed to have on each problem.  Teachers will be able to set the amount of time students practice drills and set the number of questions a student must answer for a lesson.

Because this small business was set up by teachers, they value teacher’s and student’s constructive feedback as they venture forward with improvements to this site.  You can follow them on Facebook, Instagram, or Twitter to give your input.  Just imagine a website built with your feedback in mind

Use This Strategy to Easily Multiply Large Numbers and Fractions

You know the guys who easily multiply in their head who leave you picking your jaw up off of the floor?  Well, these folks have special strategies.  I am going to teach you one of these so that you can teach your students!

FirstSlide1, let’s look at this example with fractions.  If you double ½ you get one.  Instead of going through all of the steps it takes to multiply fractions, why not simply double the fraction and multiply?  In the case of one half or any other fraction with an even denominator, this process is simple.  ½ becomes 1.  Then multiplying by 1 is super simple.

In the case of a denominator such as ¼,  in the second example, you can double the number twice and halve the other number until you find a factor that is easy to multiply.  ¼ doubled becomes ½ and ½ doubled becomes 1.  As long as the other factor is easy to halve, this works great!

This may be done with mixed numbers as well.  As long as one of the numbers is even, you can double the other.

Now let’s look at examples with whole numbers.  Again, double one factor and halve the other.  Hmmmm 6 x 24. I don’t know that in my head, but I do know that I can easily double 6 to 12 and halve 24 to 12.  Wow!  I do know 12 x 12! 144!

I will skip the next two examples (12 x15 and 25 x 16) because these are self-explanatory.

Let’s look at 6 x 32.  If we double 6 and halve 32, we get 12 x 16.  Still not an easy fact.  Ok, I will try to double and halve again, and I get 24 x 8.  Hmm, again I don’t know that one.  Let’s try another time.  We get 48 x 4.  Whew!  Still difficult.  One more time.   Ok, 96 x 2.  To solve this problem, I will use a combination of strategies.  First I know that 96 is 4 away from 100.  If I have two groups of 4 away from 100, then I know that I will be 8 away from 200 because 96 is almost 100.  If I take 8 away from 200, this gives me 192.  Teach children through number talks etc. to think flexibly about numbers and ways to solve problems.  By teaching children these strategies, you will become stronger at solving math problems in your head as well!

How to Use Clocks to Teach Fractions

I just recently revisited one of my favorite lessons due to teacher request.  I used to teach in a Title I school last year, but now teach in a more affluent area.  I found myself teaching differently with the new set of students.  Still, this lesson is one of my favorites, and helped 100% of students answer one of our practice standardized test questions (we are taking the ACT Aspire this year).  First, I copy clocks on three different colors of paper for the students.  Students get 3 different colored clocks each.Screen Shot 2016-02-19 at 11.27.05 PM

I pose questions to get the students to think about how we would cut the clocks into halves, fourths, and thirds.  I found with the new group of students they had more intuition to think about how to divide the clock–reasoning about a clock face containing 60 minutes.  Next, I questioned them about how we could divide the clocks into halves.  This was easy for students.  They knew we could split the clock into 30 minutes for each half.ClockFractionHalfHour

Because halves relate well to fourths, through discussion I had students break their next clock into fourths.  Sometimes there is a misconception when students break a clock into quarters or fourths because there are four quarters in a dollar.  Students want to start their sections dividing on the four.  This didn’t happen in this case however.  Students knew that they could split the circle on the 3, 6, 9, and 12.FractionClockFourths

Next, I had students divide a clock to make thirds.  This is always more of a challenge to students because thirds are not multiples of twos.  I allow students to have a little group discussion at this point among themselves because they are unsure of how to divide the clock into thirds.  When I remind them that the clock face contains 60 minutes, suddenly, they realize that they can divide the 60 minutes on the clock face into three parts on the clock face into equal 20 minute sections.  Some also realize that they can take the 12 numbers and divide them into 3 equal parts which places four number sections in each part. The kids say, “Oh! It’s like a peace sign!”

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From here, I have students  do a worksheet which asks them questions about fractional parts of a clock.  For example, what is 2/4 of an hour? ¾ of an hour? ⅔?  And we explore how the size of the whole affects the size of the fraction when times smaller than a whole are used.  Read here if you want to know more about this lesson.

If you want materials for this lesson, go here:

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Free Fraction Cards for Tonight Only!!!

I just finished these fraction cards per request to go with a Decimal Wall Number Line I have in my TPT store.  The cards include halves, fourths, thirds, fifths, sixths, eighths, tenths, and hundredths.  They are free for tonight only.  They are pointy so that they can precisely point to a number on the Decimal Number Line.  Just click the picture to be taken to the freebie.

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Below is a sample of the Decimal Number Line that I made the cards to match…

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Simplify Fractions Using These

I must have found this idea on Pinterest somewhere…I would give credit if I remembered where, but it works so well!  I love it–Factoring Rainbows!  About 2 weeks ago I used this with the fifth graders who were struggling with simplifying fractions.  Using this trick really helped them.  Below you can see how it works.

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There is a rainbow for both the numerator and the denominator.   The rainbows always start with 1 and the number itself on the first arch.  Then each arch underneath progresses with the next largest factor.  With the 15 rainbow, 2 was not a factor, so I skipped to 3.  Three and 5 are factor pairs.  I could then try the factor of 4, but the only other number that could be a factor would be 4 itself.   I know 4 x 4 is 16, so that won’t make 15.  Then I could move on to a factor of 5, but I know that 5 has already been used.  When the factors repeat in the rainbow, then I know I have found all of the factors.  To simplify fractions, circle the largest common number in both rainbows  (GCF) and divide both the numerator and denominator by the largest common factor.

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Here is another example above.  I factored both the numerator–16 and the denominator–18.  I started the factor rainbow of 16 with an arch having the factor pair 1 and 16.  Then I moved on to an arch with the factor pair 2 and 8.  Three won’t equally divide into 16, so 3 is skipped.  Next, I know 4 and 4 will multiply to make 16.  Because these numbers repeat, I know the 16 factor rainbow is complete.  The factor rainbow of 18 begins with the first arch’s factor pair 1 and 18.  Next 2 and 9 are a factor pair, followed by 3 and 6.  Then, I ask myself if 4 would be a factor.  What about 5? Nope.  So that brings me back to 6.  I know that I have found all of the factor pairs because I have reached a repeating factor–6.  Then I circle the greatest common factor of 2 and divide the numerator and denominator by 2.

FactorRainbow3If a fraction is already simplified, the fraction rainbows will help show this, too.  The only thing that will be different is that the largest common factor will be a 1.  Dividing by 1 doesn’t change the numerator or denominator obviously so the fraction is already simplified.

I hope using fraction rainbows will help your students as well.

How Can Your Students Learn About Clock Fractions?

Oh, my gosh!! I have wanted to post about this forever, but when I taught the lesson, I didn’t think to take pictures.  Well, here arose the opportunity when a 5th grade teacher wanted me to do this lesson with her class.

First it was all out WAR with the copy machine when I shrunk a larger clock face to smaller clocks to make this original.  I wanted to have smaller faces so I could give them several and not waste paper.  Plus I wanted to use colored paper.  I shrunk the larger face to about 60% on the copier.  Fifty percent was too small.  I wanted the faces to be large enough for the kids to still be able to easily see the tiny marks around the sides of the clock.

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I copied a class set of these on 3 different colors of paper.

 

First we discussed how many minutes were included in one hour on the clock face…Sixty of course.  Then I had the kids tell me how many minutes were in half of a clock face or half an hour…too easy…30 minutes!  Each time we found a fraction on the clock face, I had students label it with the fraction and with the amount of time.

ClockFractionHalfHour

Next, I asked them how many minutes were in a fourth of a clock face.  To see what kids knew, I didn’t allow them to raise their hand or blurt out.  I really wanted to know what each child thought.  I had them write the minutes they thought were in a fourth on the back of the clock face and then cover it with their hand–so no cheating ;).  This gave me a quick assessment of the class.  Before students drew lines on the clock face for fourths, we discussed where to draw these lines so there were equal pieces.  Fifteen minutes are in ¼ so students drew a line from the center to the 12,3,6, and 9.  Then they snip, snip, snipped on the lines to make pull apart fraction pieces.

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Now, for one that doesn’t work out quite so nicely–thirds.  How can you split up 60minutes into 3 even sections?Hmmm…students gave me answers ranging from 10 to 60 when they did secret answers on the back of the pink clock face.  I wrote down the ranges of answers that students gave me on the board.  We weeded out the wrong answers as a class by justifying why the wrong answers couldn’t be right–this way the mathematical practices were involved.  Several students, however, were easily able to tell me 20 minutes and reasoned that 3 sections of 20 minutes would be able to fit in the clock face.  We discussed again where to cut the clock face so that the sections would be equal.

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Below are all of the clock faces together….I LOVE, LOVE, LOVE colored paper

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Then I started posing problems to the kids, so they could use their clock pieces as manipulatives.  The picture below shows what the kids had on their desk when I asked them to show me how many minutes 2/4 of an hour was–EASY 30 minutes.

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How many minutes is ¾ of an hour?  Just look at the clock pieces to see how many.  Below is a simple sheet I gave students to do as guided practice to make sure they were following along while we discussed their clock faces.

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Yes, I do quick smileys (although usually with a pen) on every single one students get right as I walk around the room.  I do this for two reasons.  1.  It gives students a boost if I ask them to fix something.  They don’t feel defeated because they got so many right and only a few were wrong.  2.  This saves me time from grading papers later because I can tell which ones I have already checked.

To make students think outside the box, I also changed the size of the whole.  For example, students had to find ⅔ of 45 minutes.  This tripped up most students who were used to figuring out ⅔ of 60 minutes/the whole circle.  Hmmm…if I think about 45 minutes in thirds, I can use three of the fourths pieces.  Now these fourths pieces turn into thirds because three of them now make the whole of 45 minutes.  If two of them are chosen then that makes ⅔.

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Finally, students will tuck their fraction clock pieces away behind fraction notes in their journals for safe keeping.  We taped envelopes down in journals for this.  Most kids are able to do this on their own, however, some are not as self sufficient as one would hope in 5th grade.

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A little more about this lesson… I gave each student a large white sheet with the three clocks (my original copy shown way above) for them to figure out other fractions of a clock such as twelfths or fifths.  Students also did two word problems following the easy guided practice sheet.  Those are not pictured.  Here is the FractionClockConversions guided practice sheet shown above.

Updated 2-19-2016:  Here are the detailed lessons for sale on TPT for $3.  These include lesson plans, small printable clock faces, worksheet practice, and word problem practice.

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My Favorite Fraction Tools

I wanted to share with you these new tools that I ordered for this year.  I knew that we would be studying a lot of fractions, and we only had the linear models for a class set.  Normally, when introducing fractions I start out with whole sheets of colored paper and have students cut them apart into halves, thirds, fourths, and so on.  Then students can lay these pieces of paper on each other to find equivalent fractions.  While this has value for students understanding that fractions are parts of a whole (piece of paper), students tend not to cut them out perfectly, so their equivalence investigation is a bit skewed.  Because of this I move to manipulatives for the equivalence investigation, but again, I only had tools that were linear models…so here is what I ordered…  Foamy fraction squares!

 

What is even better than the fact that they are brightly colored and quiet?

They are exactly the same size as a base ten block!  This makes teaching decimal equivalents so much easier!  I know the shadow makes the base ten block look larger but, they really are the same size.

 See!

Students can easily see that one-half equals five-tenths, one-fifth equals two tenths, and one tenth equals ten hundredths.

I ordered a class set of these from EAI education here.  I promise I make no money from telling you about these, but they make teaching fractions so much easier.  Every teacher who has used them loves them!

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