Fractions, fractions, fractions

One of the most dreaded concepts by students--and some teachers, fractions is a key piece to better understanding how numbers work.

This post is to share some different resources that might help you as you plan for your fractions instruction.  I have tried to locate a variety: games, enrichment, tasks, and problem-solving.  Please let me know if there is something else you are searching for.  I will be happy to help in the quest.

Let me know if you have questions.  Please share this post with a friend who might find it useful.

E-toolkit:  Our EM ConnectEd component has a great fraction piece to it.  It is worth your time to explore all of the things it can do!  

Battleship Numberline:  Fun practice for 3rd graders on putting numbers on a number line

Slide to the Top:  This game has students place various fractions on a number line.  Can be played with fractions, decimals, or percents.

Dig It:  more practice with locating fractions on a number line.

Fraction Feud:  Students reason about numbers to make fractions bigger or smaller than each other.

Melvin's Make a Match:  a fractions matching game

Greedy Algorithm:  students work to figure out how the algorithm works

Fraction Jigsaw: jigsaw that includes practice of equivalence and addition and subtraction of fractions.

A variety of primary fraction tasks:  these are probably most appropriate for 3rd grade

Ben's game:  Good problem solving activity

Sweettart Hearts:  This 3 act task focuses on 3.NF.1 and 4.NF.4.  3 act tasks give context to problem solving and should be presented in a way which allows students to really explore the problem before solving it.  This notebook file has all of the questions, videos, and links in it.

Do the Dew:  Another 3 act task--this one involves unit fractions and simple addition.  3 act tasks give context to problem solving and should be presented in a way which allows students to really explore the problem before solving it. This notebook file has all of the questions, videos, and links in it.

The apple:  This 3 act tasks focuses on 4.NF.4.  3 act tasks give context to problem solving and should be presented in a way which allows students to really explore the problem before solving it.  This notebook file has all of the questions, videos, and links in it.

Engage New York has some good materials to supplement our Everyday Math study of fractions.  These links just take you to a grade level's page.

Grade 3

Grade 4

Grade 5

Do you have any great resources to share? Please feel free to share below in the comments

Rethinking Our Instruction

This TED talk by Dan Meyer has been driving a lot of my learning and thinking lately.  While I worked hard to change my instruction to make it more meaningful for my students, I had not reached the level that he is talking about.  I wish I had.  His discussion and meaningfulness about his instruction inspires me.

I have found some resources from Graham Fletcher which are motivating me to change my instruction.  Would you like to take some steps to change the way your math class works?  Let me know!  I would love to work together for change.

Using Number Bonds

As I am working with students to build number sense and fact fluency, I find more than a few who can become pretty good with their basic facts. For example, a group of firsties I was working with on facts within 10 were becoming quite adept at getting the correct answer quickly and efficiently.  I was so pleased!

But then--we tried a new game.  A game where I gave a target number and they had to look at their cards to see if they had two that could make the target.  I was dismayed to see that there was a significant hole in their fluency.  This skill was really hard for them.  We had used number bonds to break apart numbers, we had played the pennies under the cup game, we had discussed decomposing numbers...but when asked to do it in a new context, these guys had a tough time.

So, I began teaching the concept from this angle.  Starting with the number and breaking it apart and identifying the addends.  We had done it during the beginning of our fact work, but it apparently needed some extra practice.  We are continuing to work on this through games and story problems. I am hoping to see it all making a difference!

Have you tried giving your kiddos a target and asking them to come up with a fact that will get it?  I'd be interested to hear your results.

Number bonds are a great visual to use when teaching decomposition of numbers or part-part-whole.  I have created number bond mats where the kids lay manipulatives out so they can better see the number's decomposition,

You often see number bonds in use for primary grades, but they work well for helping older kids grasp the concepts of expanded form, fractions, multiplication, and division, too!  Consider using them to help cement the idea of part-part-whole.

I created a snowflake number bond page that you can use if you wish.  Share with someone that you think might benefit.

For the Holidays

It's that time of year again....we are busy, our students are busy, and we still have a lot of work to do.  :)

Attached are two holiday SMART documents.  You are welcome to use them in your room as you wish.  Maybe you take a page or two a day...maybe there is only one page that interests you....maybe you want to save them for those final days before break....whatever you choose, I hope you find some use of them.

Each contains a couple logic puzzles.  I like to give kids little manipulatives to help them solve the puzzle, so I made a doc for you that you can print and use if you wish.

Have a great December!  I love being in the classrooms--let me know if you could use anything!

K-2 Holiday SMART

K-2 Logic puzzle images

3-5 Holiday SMART

3-5 Logic puzzle images

Timed Tests...How can we measure automaticity?

A common discussion I have with teachers centers around the idea of measuring fluency in our students.

Fluency is much more than automaticity. That is part of the eventual goal, but it is not necessarily the most important goal. In fact, while fluency is a part of every grade level's standards, 2nd and 3rd grades are the only grades where "instant recall" or "knowing from memory" (automaticity) is mentioned.  Both of these grade levels ask for this piece to be mastered by the end of the school year.  In grades K-1, students are focusing on the fluency piece which builds students'  number sense.

We need to seek out ways to measure this "knowing from memory" other than timed tests.  Jo Baeler, a professor at Stanford and a leading researcher in mathematics instruction wrote this interesting article for the NCTM in April 2014.

So...how can we measure instant recall without giving timed tests?  I know they are easy to administer--I gave them, too, for many years, but I eventually found that the students who excelled on timed tests were the same kids who picked up on their facts easily no matter what practice we used.  

There are a number of ideas that I think we could try.  
*Observation in the classroom is an easy example.  Watch your students as you work in small group, during minilessons, or when they are playing games.  Do they know their facts in these situations?  
*The use of games and student data from games can help demonstrate instant recall.  *Consider using a fact exit slip before leaving for a special....you could present a fact and students would write the answer on the slip or on a dry erase board before leaving the room.  You could use this data over time to help show instant recall of facts.  
*Have your students self-assess:  provide them with a list of 10 facts and have them complete them and mark the ones that they knew automatically.  
*Take a few minutes of transition and have the students roll two dice or draw two cards, write down the numbers, and perform the operation they are currently working on.  They just keep rolling and computing until you tell them to stop.  (In this scenario,  you could differentiate the problems by giving specific dice or cards to the child)  When they are done, they turn in a list of facts that they completed.  
There are many alternatives, and you are all so creative. Besides, you know what works best for your kids.

The thing is... this goal of instant recall is for the end of the year.  We don't need to begin measuring the instant recall until later in the year in 2nd and 3rd grade.  We should be working to immerse our students in the facts that best fit their needs.  Our books lay out a plan for fact acquisition.  Many of your students will move according to this rate.  Games and activities would build off of only the facts that have been instructed.  If doubles haven't been taught yet, the students would only be working on facts which have been covered in the classroom.  If we begin measuring the automaticity of these facts too early, we just beat kids into believing that they aren't good at math.  We need to work to show them different ways to build their fluency throughout the year, and saving our worries about instant recall until the end of the year. This will allow our students to interact with the numbers and patterns in a more meaningful way, and hopefully, lead to the acquisition of these facts.

Many teachers use Xtramath to help build this automaticity; while this program does have a timed piece to it, I don't believe that the time factor is as negative as it is in a timed test or another program like RocketMath.  As mentioned above, many children just gain anxiety about their facts from these timed situations.  

Most importantly, we want our students to feel good about math and their skills.  I was doing a math running record the other day on a student, and I asked him if he liked math.  His response was, "No, I'm not good at it."  Yet, when we completed his running record, he had used very high-level strategies to determine all of his answers.  He was not automatic about all of the answers, but it was impressive the ways he had learned to acquire the answers.  That, to me, is more important than the instant recall. I told him how good he was with math, and he was surprised to hear that.  :(

I have read multiple articles comparing math fluency to reading fluency.  We would not expect students to read or work beyond their level in reading.  Why do we do that in math--pushing them into facts before they have mastered others?  Would we rather have a student who can comprehend or one who can read all the words but has no idea what they mean? I believe we need to revisit our beliefs about math fact fluency and look to make our instruction match what the research shows.

So--as we work to build our students' fluency in facts--here is another activity you can use this month for individual practice.  By using different dice and menus, you can differentiate it for each student.  I shared this with a friend a couple of years ago, and her students liked it so much that she created one for many different times of the year.   

What do you think about this?  Do you have other ways to informally assess this standard?

Games That Cover Key Concepts

Calculation Nation is part of the NCTM's Illuminations site.  The games on Calculation Nation allow students to compete virtually with other students around the world to practice key concepts of the upper grades: fractions, geometry, and factors and multiples to name a few.

Here are some ways I think these games could be used in the classroom.

1) Set up accounts for all of your students to play as they wish.

2) Set up a class account and then play on the SMARTBoard as a class to practice key concepts.  

3) Have students sign in as a guest to play the concept that practices an important key concept.

Playing these games on the SMARTBoard to start or finish a lesson could lead to some great number talks and problem solving discussions.  

Share your ideas with others.  Have you tried these games before?  Which ones work?  Which need special preparation?

Share this post with a friend.

Parent Involvement

With conferences around the corner, you might want to provide your students' parents with resources that will help them when working with their children at home.

For each grade, I created a sheet which highlights some of the goals for that grade level  as well as ways parents can help their children to sharpen their skills without just offering more worksheets and math problems at home.

I am also resharing the parent page that you were given at the beginning of the year that has QR code links for parents to use to help them better different concepts and algorithms of each grade. If you haven't had a chance to share this yet, now might be a good time.

Both of these handouts might be a good resource to share with  parents at conferences next week.

Kindergarten At Home                  Kindergarten QR Codes

1st Grade At Home                       1st Grade QR Codes

2nd Grade At Home                      2nd Grade QR Codes

3rd Grade At Home                       3rd Grade QR Codes

4th Grade At Home                       4th Grade QR Codes

5th Grade At Home                       5th Grade QR Codes

Let me know if there is anything else you are looking for!