A new puzzle to consider

Recently, a friend introduced me to this game/puzzle, and I wanted to be sure to share it with you.  It might be a great thing to use your PTO money or ask a generous parent to pick up for the class.

The only problem I really have with this game is its name: Genius Star.  I hate for that to cause students to believe they aren't capable of solving it, or vice-versa, that if they are able to solve it, it makes them a genius! 

This puzzle explores spatial relationships which for so many of our students can be a challenge.  It also offers students the opportunity to distinguish pieces they should prioritize as well as a trial in perseverance!

Here's how it works:

Roll the die that come with the game:

Lay the little white triangles onto the corresponding triangles on the board:

Now, I usually solve these on my own, and I don't recommend that it becomes a racing game, but students then take the 11 game pieces and place them on the board to cover in the star.

Students can compare their solutions to see what they did the same or different.

Students can also reflect on what made the puzzle challenging or easy. 

The box comes with two black trays to solve the puzzle on, but you could maybe get more than one game so that more students could work to solve. I find it quite fun, and it highlights the spatial skills of math.  The company makes other similar games that will show up when you follow the above link to this game.

Students can solve the puzzle in pairs and discuss their findings, they can investigate the dice and the regions of the board that each one covers, they could create their own puzzle numbers that they think are unsolvable and ask classmates to prove them wrong, they could create fractional questions about the puzzle or its pieces, or you could use two solutions for the same numbers as a same/different discussion. It seems to me like there are a lot of ways that this little puzzle could be used!

Let me know in the comments if you have found or find other ways to use this puzzle in the classroom!

Building Conceptual Understanding of Fractions

In 3rd, 4th, and 5th grades, fractions dominate much of our instructional time, and it is important that we work to help our students gain a firm grasp on the concepts of fractions. Going deep now will help them down the road as they use fractions in more complicated mathematical situations.

A reminder of the progression of fractions in elementary school by Graham Fletcher allows us to remember how important our models are:



Sometimes I'm afraid that teachers steer clear of fraction exploration because they are uncomfortable with them themselves.  Imagine all of the learning that could occur if we went out of our own comfort zone with our students?  

I have shared Fraction resources before in this blog.  I have also shared an exploration or two.  Here are some more resources that might help your students (and you) to make more sense of fractions.

When and when not to give the answer:  This Marilyn Burns' post offers an opportunity for your students to build their own understanding of fractions.

Fractions, Decimals, & Percentages:  A number talk which begins with fraction addition.

Exploring Fractions:  An article from nrich.maths.org which offers links to rich tasks that develop a deep understanding of fractions.

Illustrative Mathematics also has some resources that will help you better understand the horizontal progression of fraction skills.

Maybe you find one or two ideas above to help you stretch during your fractions unit--that's great!  Don't try to change everything all at once. As always, let me know if there is something I can do to help!

Unit fraction computation exploration

What is 1/2 - 1/3?
How about 1/2 * 1/3?

What is 1/5 - 1/6?
How about 1/5 * 1/6?

What pattern do you see in the fractions above? 

Will this work for all unit fractions?  Why?  

Are there other fractions it will work for? 

Is there a pattern when you increase the common numerator? (i.e. 2/7-2/8?)

DIfferentiating with Fractions

Differentiation can be a challenge. And a lot of work.  Over time, however, I have learned that it doesn't mean that I have to have 3 or 4 different lessons over different content.  In fact, we are encouraged to extend the lesson rather than teach a different lesson.  Below is an example of what I did with Mrs. Bainbridge's fraction kite idea.

I love to color and have lots of those cool design books. I took those design books and used them to design my kites.  The simpler kite ( top design) is made up of 100 equal pieces, and the students had to use 6 different colors.  The more complicated kite did not have equal pieces.  Using the smaller size as a unit, the kite had 650 pieces.  Students then had to use at least 4 different colors for their design, and then had to count and convert the big pieces into small pieces.

Here are examples of what the grids looked like:

The students received a kite shape already made out of these patterns, and they were told how many equal parts there were.  The kids had fun, and it was an appropriate challenge for those kids who needed it.  When the students were done writing their fractions under the kite, they had to check their work by adding the numerators of each fraction to be sure it equaled the appropriate denominator (100 or 650).  Maybe you make kites, or maybe you decide to make holiday ornaments or something else that matters to your class--the idea stays the same.

I have also used Mary from Pitner's Potpourri idea.  We looked at Ed Emberley's Picture Pie and created our own picture pie.  Differentiation was natural on this one.  Certain kids were told they must use 4ths and 8ths in a certain number of colors while others just used 4ths.  The artwork created was fun and beautiful!



Building Fraction Understanding

In a recent webinar by Graham Fletcher, he discussed the enigma of fractions for a student.  He had what I believed to be a great perception. Just like we teach kids to subitize whole numbers, we could dispel the notion that fractions are difficult by having kids learn to subitize fractions.   And, just as we have students subitize whole numbers in many different ways--through dominoes, fingers, dice, tally marks...we should present fractions in many different ways in order for them to be able to better understand their meaning.

The SMART document that I made stems from Graham's idea, but I also made it with Number Talks in mind.  I think these images could bring up some good math discussions and justifications of fractions.  It is made with images that are easy enough for 1st grade, and some that would be relevant in a 5th grade class.

If you decide not to use the image as a number talk, you might print out a page of the SMART document and have it be a collaborative activity for kids to decide.  

No matter how you use the pages in this doc, it would probably be good to print out the image so that students could cut the pieces apart so that they could prove their thinking to themselves and others by manipulating the pieces of the image.

Sample image from Fractions SMART doc. Click to download document.

Do you have other ideas on how you could use the pages in this document?  Feel free to share below.

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