Subitize & Make Five with the (free!) Number Rack

Having great fun with a kindergarten group. Yesterday we thought about what makes 5. We did a little subitizing and made use of the Math Learning Center's free app, Number Rack, that is also available as an online application for those who don't have a mobile device. Since I was a portable classroom (working in the hallway), I used my iPad. The kindergarteners were so impressed...until I said it wasn't mine! Here's one of the activities we did:


First, I showed them my virtual Number Rack and explained that today we'd only be using the red beads.

I asked them how many red beads I had.

Then I changed the configuration and asked again.

And again. "How many red beads?"

And again. "How many red beads?"

And again. "How many red beads?"

Eventually most of them started laughing. "There's always FIVE BEADS!!!"  After they straightened me out, I explained the next step.

First, I would hide some red beads on the right side of the screen under a flap. I'd set it up like this, but they wouldn't see any red beads at all, at least at first...

Because I'd make it even trickier. I would cover the beads on the left with my hand, move my hand to flash them a REALLY QUICK glimpse of what was hiding, and then cover it up again. They'd have to tell me what was hiding on the main (left) part of the screen based on their quick view (subitizing.)

After they guessed, I'd show them what was there. Then they could try to figure out how many red beads were hiding on the right side of the screen and we'd check by pulling down the ? flap to check.

I learned a lot about students' number sense. Especially "Dan's." At first, I thought Dan had the concept of making five. When 2 beads were seen, he said that 3 were hidden. But then when 3 were shown, he said that 4 were hidden. When 4 were shown, he insisted that 5 were hidden. Later I worked with him individually using a 5 frame. We have a bit more work to do!

Try out the Number Rack. Do a little subitizing. And "make five" math! (Or make five math friends!)

Math Monday Blog Hop #76 (November 26, 2012)

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The Yearly Announcement...

As many of you hit the streets (cyber or otherwise) to shop, I'll take the opportunity to make the annual announcement. If you use the Amazon links on this site or enter through the Amazon portal on the right menu of my homepage, I give commissions (at no cost to you) to Grace and Hope, an incredible group who puts Chinese orphans into foster care. My son benefited tremendously from the three years he lived with his foster family. You can read more about our story here.  And you can find links to Math Toys, Gifts and Games and Math Related Children's Literature. Over the last several years, your orders have helped me to put two children into foster homes in China as well as to buy coats for orphaned children. On their behalf I thank you. Immensely!

Happy Thanksgiving...and may the holiday season begin! :)

P.S. If you order QUICK you could also get the 24 Penguins Before Christmas: A 365 Penguins Advent Calendar.

Math Monday Blog Hop #75 (Nov. 19, 2012)

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Oregon Trail Adventure: Quilt Wall Hangings

We're just finishing up our Oregon Trail Adventure class. Here students share their beautiful wall hangings, combining a hand-sewn quilt block of 4 with a drawing (on fabric) of a memorable moment on the trail. Feeling very proud of my students.

Read about other past lessons using quilts here.

Math Monday Blog Hop #74 (Nov. 12, 2012)

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The Most Important Grade in School

Have you ever considered which grade, K-12, is the most important? Take a look at this fascinating article, "Why Third Grade is So Important: The Matthew Effect," and see if you agree.

Admiring a Math Momma

This fall, I've been fortunate enough to have a mom participate in one of my student math clubs. Why fortunate? Like many of us, she grew up learning that there was only one way to solve each kind of problem. (How do I know the math environment in which she was raised? I went to the same school...!!) That environment put a temporary damper on her math education.  (And mine!) Yet the story doesn't end there...

During math club, as we explore different visual models and strategies, she jumps right in, enthusiastically wanting to learn more. She shares her "ah-ha" moments; rather than finding new ideas threatening, she embraces them and mulls them about in her mind, connecting concepts and strategies faster than I can teach them.

I've learned so much from her. About enthusiasm. About reserving skepticism. (I'm really good at that!) And about being a lifelong learner.

Thank you, Momma B! May each of us have the pleasure of working with a parent like you! You reignite my excitement for teaching math each time I see you.

May each of us continuously strive to find the math momma in ourselves. :)

Math Monday Blog Hop #73 (November 5, 2012)

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First Do No (Mathematical) Harm

The principle of "first do no harm" is a familiar one to medical personnel. Wikipedia sums it up in this way:

"given an existing problem, it may be better not to do something, or even to do nothing, than to risk causing more harm than good".

I've been contemplating the phrase in relation to math--specifically the teaching of math. In my job I am privileged to work with a wide variety of ages, abilities, grade levels, and teaching situations. I'm alternately awestruck by some students' mathematical thinking and downhearted to see some students--still quite young--who have already had their little mathematical minds messed up. Some of these kiddos, only a few years into their school careers, have decided that math isn't supposed to make sense. Math is just a confusing, random, jumble of rules that they cannot remember...or rules that they can't apply to situations outside the 25 identical problems given on the daily assignment in their textbook. It's painful to watch a child pull numbers out of the air, as he assumes that a random guess has as much likelihood of being correct as anything else he might figure out. As an esteemed colleague said, "Nothing makes sense after you've had your thinking taken away." I worry about these kiddos. A lot. And they're found everywhere. In every grade. And in every school situation: home, private, and public.

Here we read:

A related section from the Hippocratic Oath has been translated as

I will follow that system of regimen which, according to my ability and judgment, I consider for the benefit of my patients, and abstain from whatever is deleterious and mischievous. I will give no deadly medicine to any one if asked, nor suggest any such counsel...

 What if we applied it to the teaching of math?

I will teach in a way which, according to all that is currently know about learning mathematics, I consider for the benefit of my students, and abstain from whatever will prevent them from becoming the best mathematicians they can be. I will do nothing to mess up any mathematical minds (even if a fellow teacher, homeschooler, administrator, or standardized test points me toward unhealthy teaching practices), nor will I suggest any mathematical teaching strategies that may harm someone else's child.

In the homeschool world we hear a lot of debate about the practice of "unschooling"; I hesitate to even mention it because the concept means such different things to different people. But I will say this. It is far easier to introduce mathematics to a child who has never been taught formal math than it is to try to reintroduce a concept to a child who has had his thinking taken away.

First do no harm.

5 Favorite Fraction Books

It's no secret that I'm addicted to math-related children's books. Yet even within that genre, there are concepts that scream for my attention.

FRACTIONS!

Why fractions? They lend themselves to story. And the stories help to heal a bit of my wounded math self. As a 4th grader, I was one of a small group of kids in the accelerated math group. Our teacher told us to go ahead in the book, as fast as we wanted. I was SO PROUD. I flew. Until I crashed. Into the chapter on fractions. I was too embarrassed to tell her that I had no clue. None. Nada. Zilch. Not even 1/100th of an idea of how to do this new, intimidating stuff that masqueraded as math. So I stressed. Kept silent. And the rest of the class passed me.

Here are some books that help to heal the fraction-anxious 4th grader in me:

The Lion's Share: A Tale of Halving Cake and Eating It, Too

We enjoyed a great little exploration with fractions and doubling with Matthew McElligott's book, The Lion's Share: A Tale of Halving Cake and Eating It, Too (2009.) In the story, an ant is invited to the lion king's dinner party. At the party, the other animals demonstrate horrendous manners. When the king passes the cake, each animal takes half of the cake he is passed. So, the elephant take half of the original cake and passes on a half. The hippo takes half of that piece (a quarter) and passes the remains to the gorilla who takes another half (an eighth of the original), passing the remainder on to each animal until a mere morsel is given to the ant. The tiny creature, embarrassed because he doesn't have enough to share, tells the king that he'll return the next day with a special cake for the king. Each animal, wanting to outdo the next, agrees to bring double the amount of cakes to the king. So the ant will bring one, the beetle two, the frog four, and so on. Click to the entire lesson with visuals.

Little Numbers and Pictures That Show Just How Little They Are!

 

This out-of-print book can often be found inexpensive, used. Little Numbers and Pictures That Show Just How Little They Are! is a nice fraction/decimal book to use with 3rd-5th grade students because:

1. The "unit" is a dinosaur. Specifically, a seismosaurus. Kids need to understand that a "unit" can be flexible. In this book, everything is measured in terms of a dinosaur unit.

2. The book depicts increasingly smaller measurements. If a dinosaur is worth 1, then a dinosaur shrunk to 1/10 will fit in the front yard. It talks about various other tenths, like a dime being a tenth of a dollar. It shows both decimals and the fraction equivalent.

3. The numbers creatively get smaller, each time decreasing by powers of ten. For example... 1/10,000 is an ant. 1/1,000,000 is an amoeba. Some kids will be very intrigued by the exponents, which are also included.

4. The book is big (13 x 8") and good with crowds.

Picture Pie

The boys and I found a book that we absolutely love. Ed Emberley's Picture Pie is a circle drawing book. He shows you how to divide circles into fractional pie pieces to create designs, flowers, birds, animals, fish, clowns and a whole host of fun pictures. Click to the entire lesson with visuals. And a follow up lesson with creative writing. With the same lessons we also use Picture Pie Two.

The Wishing Club; a Story About Fractions

My opinion about The Wishing Club; a Story About Fractions by Donna Jo Napoli, totally changed. When I read it alone, I wasn't terribly excited. When I read it to my student, his enthusiasm was catching. In the book, siblings, ages 8, 8, (twins), 4, and 2, wish on a star. Over several nights they discover that their wishes are granted in fractions, determined by their ages: 8yos get 1/8, 4yo gets 1/4, 2yo gets 1/2. My student quickly understood the concept of fractions, exclaiming after the second page (which shows four 1/4ths make 1), "then one penny is 1/5th of a nickel!" In the story, the siblings put their wishes together to make one whole wish and get the wish that all of them want.

Disclosure: If you purchase books through my Amazon links, all commissions go toward foster care through Grace and Hope at no additional cost to you. I do not keep any money myself; I am hoping to be able to sponsor an additional child in foster care through commissions on this site. Thank you!

Math Monday Blog Hop #72 (Oct. 29, 2012)

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10 Ways to Mess Up a Child's Mathematical Mind

I don't know many people who went into elementary education or homeschooling because of their love for math. (I know a few of you are out there. You're weird. Outliers. Accept it with pride.) Teaching math can be challenging, particularly if we have our own math demons lurking in the closet. The following post is designed expressly for those who would like to ruin the mathematicians of the next generation. If that's not you, you can skip it...or read it with the humor intended.

10 Ways to Mess Up a Child's Mathematical Mind:

1. Teach her that there is only one way to solve a problem. Reinforce that by giving her assignments in which she learns a set of predetermined steps to solve a particular type of problem and then practices that sequence over and over and over. And over. Don't ask her if there are other ways to solve problems.

2. Teach him that math is a solitary process. Reinforce it by placing him alone in front of a computer or textbook without talking about a variety of math strategies that might be used to solve similar problems. (See #1!)

3. Teach her that math only exists between the pages of textbooks. Don't point out the math you use as you grocery shop, balance your checkbook, calculate miles/gallon, prepare dinner, or figure how long it is until her bedtime so you can watch Jersey Shore in peace.

4. Teach him to be fearful of math. This is easy. It helps to do #1-3 above. But it also helps to model your own fearful behavior. Say things like, "Math is hard for me." Or "I never liked math." Or "I was born without the math gene." According to Marilyn Burns (Math: Facing An American Phobia), you're in good company with 2/3rds of American adults being math phobic. You're already on the bandwagon. It's a popular place to be. Don't jump ship now!

5. Teach her that math is primarily a world of pencil and paper. Don't ask her to estimate or use mental math.

6. Teach him to avoid visual cues. Forget using manipulatives, sketches, or drawings.

7. Don't read any math-related children's literature. Don't play any math games.

8. Always emphasize the importance of fact memorization. Drill, drill, drill. And if she can't get it, drill some more.

9. Never look at what wrong answers have to teach us. That would just be wrong!

10. Teach her that math is boring. And scary. Reinforce with #1-9 above.

Want to add to my list? Comment with your own ways to mess with children's mathematical minds!

Math Monday Blog Hop #71 (Oct. 22, 2012)

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Math Monday Blog Hop # 70 (Oct. 15, 2012)

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New Math Monday Blog Button!!!

Here's a HUGE SHOUT OUT to Heather of Teaching My 3 who created this gorgeous button for the Math Monday Blog Hop. Thank you so much, Heather!!

Ironically, and without Heather's knowledge, I've been doing a lot of finger math this fall. The new picture couldn't be more perfect!

While you're blog hopping, check out Heather's big fall blog hop!!

Explore Units of Math -OR- What is One?

Nice video from TED-Ed. Description:

One bag of apples, one apple, one slice of apple -- which of these is one unit? Explore the basic unit of math (explained by a trip to the grocery store!) and discover the many meanings of one.

Math Monday Blog Hop #69 (Oct. 8, 2012)

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Math Monday Blog Hop #68 (Oct. 1, 2012)

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Homeschool Chicks Have Hatched!

The Homeschool Chicks website has hatched! Several of the bloggers from www.TeachingBlogAddict.com have come together in a brand spankin' new website for home educators. Each of the five of us will focus on a specialty area. We have a Fun Chick, Organized Chick (that's NOT me!), a How-To Chick and a Reading Chick. I'm the "Math Chick." (Never in my wildest dreams...) On the site you'll find a homeschool blogroll (we'd love to add yours!), pinboards, linky parties, and lots of freebies. Spread the news! And click the button below to come check us out.

Poison! Race to 100

Poison! Race to 100

In the upper grade Math Club we played Poison! Race to 100. Here are instructions to continue play at home:

Materials Needed:

• Base 10 manipulatives: 1 mat per child and a bunch of strips (10s) and units (1s) - those pictured can be purchased from The Math Learning Center.
• 2 Dice labeled 0-5 and 1-6

Directions
Each player gets a mat (red 100s grid shown above) as a playing board. Player #1 rolls the two dice, adds the numbers, and collects that many base ten pieces. The player can choose to keep those pieces, adding them to the playing board (the red mat), or roll again and collect additional pieces. BUT, if the dice rolls a 0 (POISON!) he loses everything in that turn.  (Once pieces are on the mat, they are safe.) Each time the player rolls, she must exchange base ten pieces from that turn so that she has the least number of pieces in her possession. So, for example, if in one roll she gets 8 and then in a second roll she gets 4, she must trade in 10 units for 1 strip (ten) with a total of 1 strip and 2 units. The same is true of the board. As pieces go into the safe zone/red board, they are exchanged for the smallest number of pieces.

As students play, they might consider:

• How much do you have?
• How many do you still need to reach 100?
• How many more/less do you have than the other players?
• Challenge: What is the probability of getting poisoned (a zero)?

Ruptured Eardrum

I'm out this week with a ruptured eardrum. Hope to be back soon. Carry on with math!

Math Monday Blog Hop #67 (Sept. 17, 2012)

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Subitizing - Try it Online!

Familiar with subitizing? Try some online subitizing exercises for yourself. Can you see how many dots there are...in a flash??

Math Monday Blog Hop #66 (Sept. 10, 2012)

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Students Who've Suffered Early Trauma - Dealing with Behavioral Issues

Over the last several years, I've worked with students who suffered early trauma, usually as infants. Contrary to what I used to think, trauma can involve many things other than abuse. Neglect, separation from birth mother, extended hospital stays, inadequate daycare...and many, many more things can contribute to a traumatic start, which can eventually lead to rather unappealing behaviors as students reach school age.

If you teach (or parent) a child with behavioral issues, take a moment to read "An Open Letter to Educators Who Work with Students Who Have Been Diagnosed with Reactive Attachment Disorder or Have Suffered Early Trauma." It's an excellent primer for those who are struggling with disruptive student behaviors.

Sometimes I shake my head. At myself. I thought I knew so much as a 22-year-old beginning teacher. And later as a beginning parent. Now, over twenty years later, I'm amazed and humbled as I consider all that I still have to learn.

Taking the Outside Temperature

I love this idea for learning about temperature, found on the Math Learning Center Blog. It could be done at home or at school. Students read the outdoor temperature each week, thinking about a range as they consider this poem:

Fahrenheit Weather

90 degrees is pretty hot.
70 degrees is pleasing.
50 degrees is getting cold,
and 32 degrees is freezing!

Look at the original post for detailed lesson instructions. You'll find a blackline classroom wall thermometer here if you'd like to add one to your room. I printed one on cardstock, slit the very bottom of the thermometer and added a thin strip of red tagboard to slide up and down for the temperature gauge. 

Math Monday Blog Hop #65 (Sept. 3, 2012)

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TBA Open House Week ~ Monday: Meet the Teacher!

Over at Teaching Blog Addict (TBA) they are having all kinds of link-ups to introduce some changes to the website. Bloggers (teachers and homeschoolers!) can link up to share:

Monday: Meet the Teacher- tell us all about you and your teaching style!
Tuesday: Classroom Photos
Wednesday: Handouts for Parents
Thursday: Bulletin Board Photos
Friday: FREEBIES!

Meet Me...

I'm Cindy. I first entered the classroom a little over 20 years ago as a high school English teacher. I looked too young for that setting (got asked for my hall pass!), so I found a job teaching middle school language arts, social studies, Spanish, drama, and more. That experience made me interested in learning more about self-contained classrooms, and I went back to get my Master's in Elementary Education. As an elementary teacher, I loved teaching literacy, became addicted to children's books, and then...wait...fell in love with teaching MATH. Over the years I've taught almost every grade level, preschool to graduate school. I do a lot of consulting, work with both classroom teachers and homeschool parents, and teach kids of all ages in a wide variety of both public and private settings. Oh...and I have 5 kids.

My style? LOL. Based on the description above, I'd say ECLECTIC. :) One of my hobbies? Collecting math-related children's books.

Who are YOU? Introduce yourself and join the blog hop! :)