Multiplying Fractions on a Geoboard (w/ free app!)

It might be an understatement to say that my life changed the day I realized that you can visually represent fractions. I had a rather tortured early fraction experience. (Tummy ache every day of fourth grade if that tells you anything!) What I wouldn't have given for someone to tell me that "fractions" doesn't equate "memorizing steps that mean absolutely nothing to the average fourth grade brain!"

In this little video I show you one thing that I wish someone--anyone--had shown me as a fourth grader. The Geoboard App I use is from The Math Learning Center and is free, both online and as a mobile app.

Math Monday Blog Hop #97 (April 29, 3013)

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Math Game List for Teachers and Parents! (freebie)

A new PBS survey reveals that "although research shows that math skills at kindergarten entry can be an even stronger predictor of school achievement than reading skills" many parents feel uncomfortable supporting math at home. Let's turn this around!

We play a LOT of games at our house. It's one thing that a family with kids ranging in age from 7-23 can do. Together! Not surprisingly, many of our games just happen to include a wee bit o' math.

For the longest time I've been wanting a math game list to pass along to teachers, parents, and homeschoolers who are interested in enriching children's math experiences at home through simple card and board games. This list, which also includes a few game-like activities, could be used in a variety of ways:

• letter home to families at end of school year
• math center ideas for school or homeschool
• early-finishers list
• a checklist for summer fun

Permission granted to post the unaltered document on classroom webpages and to make photocopies to send home with families. Grab this freebie in my Teachers Notebook or Teachers Pay Teachers Store. Become a store follower to receive automatic notification when I update or add to the document.

Enjoy!

Thank you to My Cute Graphics for the darling graphic!

Update 6/3/13: this handout is also used in the new Vacation Workstation, a great way to encourage kids to play games during school breaks.

Math Monday Blog Hop #96 (April 22, 2013)

Happy Earth Day!!!





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Multiplication Strategies with Number Pieces App

Earlier this week, we started "Rethinking Multiplication Fact Memorization." Several people have asked me for examples of strategies that could be used to develop fact fluency. Here's a quick video using the online version of the new Number Pieces App (free) to get you thinking. Please leave a comment if you're interested in additional videos on multiplication strategies.

Math Monday Blog Hop #95 (April 15, 2013)

Stop by Rethinking Multiplication Fact Memorization and leave your thoughts. I've enjoyed your comments so far. And have a great week!




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Rethinking Multiplication Fact Memorization

My friend Tamara at Teaching with TLC asked a really great question. Specifically, she asked about a condition called dyscalculia, but more generally she questioned what to do if a child doesn't seem to be able to memorize multiplication facts, no matter what you try. To answer that, I'm going to tell a story...

I used to conduct math (teacher) trainings with "Julie." She was (is!) a phenomenal math teacher. But one day, while working with a group of 4th/5th grade teachers, the topic of multiplication table memorization came up. After a number of folks shared their ideas and perspectives--including their frustration with kids who just don't get it, Julie spoke, close to tears. She told us how she struggled throughout childhood with the fact that no matter what she did, she could not memorize multiplication facts. It became a huge point of anxiety. Yet mathematical thinking and strategies came naturally to her. She explained how at 40something, she still does not know her facts. BUT, her knowledge of math strategies is so great that she can compute quickly and easily.

As she spoke, I reflected on my own experience with memorizing facts. As a 4th grader, I was scholastically competitive. Surprising, I know. When the class multiplication chart went up, the race was on! I was eager to conquer the chart (and beat my classmates.) I memorized it quickly. To this day, if I need to recall a fact, I do this sing-songy thing in my head to find it. ("Nine times nine is eighty-one.") But here's the irony...  I didn't have a clue what I was doing--what multiplication meant. I was great at memorizing, but it was really no different than memorizing a random list of words, letters, or numbers. It carried absolutely no meaning. Yeah, I could use them to do higher level multiplication and division, but my knowledge of the gamut was pretty limited because I'd done nothing more than memorize, first the facts and later the larger algorithms.

My friend Julie, in the meantime, fully understood the mathematical thinking behind multiplication. She had a wide range of strategies to pull from in order to figure out facts. I meanwhile, had none.

Which brings us to the concept of fluency. The definition of fluency is "good command." I would wager that as kids, Julie had excellent command of multiplication facts while I had relatively little. Today, Julie uses strategies to compute facts just about as quickly as I can locate them with my little sing-songy memory.

When I teach multiplication, my goal is fluency, not instant recall. I want kids to command multiplication--by thoroughly understanding what it is and being able to express their understanding through a wide range of strategies.

That sing-songy voice occasionally fails me. Julie's strategies never do. Her toolbox is loaded; mine has one unreliable wrench. ;)

In Salman Khan's book, The One World School House: Education Reimagined, he quotes from Nobel Prize-winning Eric Kandel, a neuroscientist:

"For a memory to persist, the incoming information must be thoroughly and deeply processed. This is accomplished by attending to the information and associating it meaningfully and systematically with knowledge already well established in memory." 

In order for something to be memorized [well], it has to make contextual SENSE! 

For more thoughts on fluency, read "Teaching for Mastery of Multiplication."

P.S. I'm on the edge of my seat, waiting for the online version of Number Pieces to come out. When it's available, I'll show you some spectacular strategies for multiplication. (Even this 40something can add a few tools to the ole' toolbox!)

Love this Quote...on Ideal Teachers

"Ideal teachers are those who use themselves as bridges over which they invite their students to cross, then having facilitated their crossing, joyfully collapse, encouraging them to create bridges of their own." 

~Nikos Kazantzakis

Purpose for Writing Numbers...Checkbooks!

When my friend's fourth graders wondered why they need to learn how to write numbers, she made it practical, writing digits as they would for entries on checks.

This Play Checkbook set would be terrific for a math lesson with allowance...and what a great reason to practice writing numbers!

If your students want to say and write really big numbers, check out this fun activity at Math Cats. Kids can enter really BIG NUMBERS, say the number out loud, and then see the number written out in an effort to check their work.  Check out this example from E is for Explore! :)

Math Monday Blog Hop #94 (April 8, 2013)

It's April and poetry celebration month! You'll find several links below that celebrate math through poetry. Enjoy!




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Finding Area of Parallelograms with the Geoboard (App!)

We've been working on a free lesson from the Math Learning Center, "Area of Parallelograms." (See Supplement D9.) On a regular geoboard it took a lot of rubberband maneuvering to figure out how to change a rectangle into a non-rectangular parallelogram and keep the same area. We decided to use the (free) Geoboard App to make it easier. (Available in both online and app versions.)

To the above right, you can see the original rectangle.  Below you'll see the rubberband movement that resulted in a non-rectangular parallelogram. I took a photo and quickly scribbled down how my student calculated the total area. You'll notice that he combined the sides to calculate the area.

In my more recent math education (teaching!) it's been enlightening for me to use manipulatives like this to calculate area of shapes.

Here, you might calculate area by first seeing a triangle as a part of a larger rectangle. In the photo at left, you can see a rectangular area of 3 square unit. If you divide those 3 square units in half (with the orange rubberband), you're then left with 1.5 square units. (So 1.5 square units on each side of the parallelogram above.)

Who knew it was so easy to calculate area? :)

Ultimate Freebie Celebration!

Stock up on ink and paper.

Get your printer warmed up.

Practice finger exercises for clicking to download.

The ultimate freebie celebration begins tomorrow at Teaching Blog Addict with over 1,000 FREE items waiting for you to grab!

{CLICK HERE to begin on Friday at 7:00 am EST}

Personal Note from love2learn2day: 

In honor of Teaching Blog Addict, all the items in my Teacher's Notebook store will be on sale through the weekend, from Friday-Sunday. Celebrate! :)

All I Need to Know I Learned in Kindergarten (?)

All year, I've counted on my son's kindergarten papers for an ego boost. The "oh you're such a good mom because your son's invented spelling is so advanced" kind of moment.  The Invented- Spelling Fairy either has a good sense of humor, or knows that my ego needs a bit deflating.

A friend told me I should inquire to see if my teens can visit kindergarten to complete their education.

Cute fairy graphic by MyCuteGraphics.

Invented spelling by anonymous cute kid.

Math Monday Blog Hop #93 (April 1, 2013)

In honor of today, don't miss the Top 5 April Fool's Day Math Hoaxes of all Time! :)





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