Math Monday Blog Hop #55 (April 30, 2012)

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The Daily 5...Let Go, Let Grow

This post is for teachers and homeschoolers.

But it's mostly for me. :)

If you're a teacher, you may have have read the book The Daily Five: Fostering Literacy Independence in the Elementary Grades. If not, I highly recommend it.

If you're unfamiliar with the book (whether teacher or homeschooler!), here's what I consider the essence...and the part that I want to remember:

Each day, children should have the opportunity to participate in 5 daily literacy activities:

1. Reading to themselves.
2. Reading to someone else.
3. Listening to reading.
4. Work on writing.
5. Spelling/word work.

Whether I'm in a public school classroom or working with homeschool students, I sometimes forget what's important. Kids need daily, uninterrupted time to improve their literacy skills. They need to:

1. Read to themselves by choosing the books and other meaningful texts that they find interesting. I'm not likely to be that interested--or learn nearly as much--from a book that someone else demands I read. Why should I expect more from children?

2. Reading to someone else. I've never made this a huge priority. Now we're doing something called "brother reading." My 9yo reads a picture book to his brother, using his best animated voice. My 6yo "reads" the pictures in one of his favorite, well-loved stories, to his older brother.

3. Listening to reading. This is huge for me. In public school I read to my students a lot. At home, it's not unusual for us to spend up to an hour on the couch, snuggling with a pile of books. I'm convinced that this is one of the main reasons that my children all love to read. I've understood that the #1 predictor of school success lies in how much a child was read aloud to. I believe it.

4. Work on writing. As in reading, kids are most likely to enjoy writing and want to write more, if they can write about what interests them. They need daily, uninterrupted time to do that. And they need exposure to a wide variety of writing so they have access to new ideas, models and incentive for putting pen to paper.

5. Spelling/word work. I think #5 is highly overrated. (My thoughts. Not the authors'!) It's not unusual for it to get the most focus, whether at home or at school. Reality is that if children are abundantly exposed to #1-4, this largely takes care of itself; and it's easy to fill-in the few places where it doesn't.

Another big thing I got out of the book? If you expect a child to do something independently, you need to give the child a lot of time to practice, building up with incremental steps. I cannot expect my 6yo to sit down and read independently for 30 minutes. But he can certainly build up to that, by starting with 3 minutes and adding on a minute a day.

The funny thing about this book? It describes what a lot of kids will do naturally, if given the time. But the irony is that kids' time is so often filled with things that we (adults!) put on them that they don't have time to grow these abilities.

Let go, let grow.

My new mantra. :)

Math Monday Blog Hop #54 (April 23, 2012)

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Subitizing - Making Sense of Numbers

I'm in love.

With subitizing. Rhymes with oobitizing. (I always thought it rhymed with rub-itizing.)

Know what it is? If you're teaching, it's a great tool to add to your toolbox!

Ever since I read about it in Teaching Children Mathematics, I've been on a mission to learn more. Basically, it's the ability to instantly recognize a quantity. An example that frequently comes up: dice. Most adults see a number on a die and immediately recognize the number, without counting. We define two different types of subitizing:

Perceptual Subitizing - a number is instantly recognized, usually with quantities of 5 or less.

Conceptual Subitizing - recognizing small quantities within a number and combining to find a total. For example, you might see 7 dots as a combination of 3 dots and 4 dots.

You can see how the ability to subitize leads to all kinds of math skills. If you can instantly recognize a quantity, you can count faster, add/subtract/multiply/divide more easily and efficiently...the list goes on. It's a no-brainer that we want our kids to master this.

So I've been trying.

I started by placing objects on a peg board, showing a quick glance, and having the child replicate it on his own board. I also tried flashing quantities on a DIY counting rope.

More recently, I've been flashing quantities on a five frame. We used ducks after our lesson with Little Quack's Hide and Seek.

I've only done subitizing a handful of times (probably less than 5) this year. My little student showed a good grasp of numbers up to 5, but anything beyond that was pushing it. I thought. Shows how much I know.

Yesterday, I printed off some subitizing cards. (Went to a TON of effort. Smirk.) Googled "subitizing cards" and printed out cards from the first Google link. (Apparently, they go to a private school site, but I found the same ones linked here titled "subitizingcards.pdf.") They are FANTASTIC. Mostly because I didn't have to make them. But also because they fit neatly into a cardboard flap. I literally grabbed a piece of cardboard out of the recycling box and had a flap made in seconds. You'll see how it allows you to flash the dot pattern and then reveal the number after the child states an answer.

I apologize that the child's volume isn't more clear. I need to invest in an external mic. Listen carefully, however, and you'll hear the reasoning that went into his answers. You might think about when he used conceptual subitizing...or when he was able to instantly see smaller quantities within the number and add them together to get a total.



Although you certainly don't need to ask a child how he arrived at an answer, I found it very helpful to help assess my student's abilities. I was surprised that he knew so many number combinations. Formal addition is going to be an easy next step.

Now...go subitize! Here are some more links/resources to assist you:

Math Four
A terrific blog entry, Why Learning to Subitize is Important. (Thanks, to Tricia for the suggestion!)

Staff development with 1st grade teachers
In this YouTube Video, the facilitator guides teachers through steps that children might take in gaining number sense. It's 20 minutes but really gives you an education.

Math Coach's Corner
Donna has several posts about subitizing. She writes that subitizing is "foundational to the development of number sense." She links blacklines from John VanDeWalle's book with lots of subitizing cards. I'm printing these next. Also read her post describing different ways that kindergarten students saw a dot pattern.

Dr. Nicki's Guided Math Blog
Love Dr. Nicki's resources. She has several posts on using subitizing in the guided math setting.

Freebie! - Number Rack
Read about Math Learning Center's new free app, Number Rack. It could be easily used for subitizing, both online and on an iPad/iTouch. The entry also links you to a free activity/lesson book.

PDFs - Use with Subitizing
This site has a whole list of pdfs to print for subitizing with kids.

Math Monday Blog Hop #53 (April 16, 2012)

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Little Quack's Hide and Seek (book & lesson ideas)

Here's a simple storytelling activity to go with the book, Little Quack's Hide and Seek.

Momma Duck has five little ducklings. One by one they hide so Momma can come find them. Little Quack doesn't have enough time to find a hiding spot, so he hides right behind Momma, following her as she goes to find the other ducklings. As each duckling hides, you see a subtraction sentence at the bottom of the page using pictures of ducklings. (See below.)

I used a cookie cutter to make a duck template and cut 5 ducklings from felt. My DIY "felt board" is a piece of flannel sewn onto cardboard.

During the story, as each duckling hid, I hid a felt duckling behind the ? as shown above and asked the kids how many ducklings were hiding and how many were left. As Momma finds her ducklings, I added ducklings back to the felt board and we counted how many had been located and figured out how many were still hiding. I noticed that kids were subitizing (instantly recognizing quantities.) I placed the last duckling (who followed Momma when he couldn't find a hiding place) in the book, behind each picture of Momma duck. The kids thought this was absolutely hilarious!

This is a great book to get kids excited about telling their own math stories. Don't forget to sing Rubber Duckie and Six Little Ducks!

The activities involve several Kindergarten Common Core Standards:

K.CC.4. Understand the relationship between numbers and quantities; connect counting to cardinality.

K.OA.1. Represent addition and subtraction with objects, fingers, mental images, drawings¹, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

K.OA.5. Fluently add and subtract within 5.



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!

Plastic Eggs - Counting/Number Recognition Game

Don't put away your plastic eggs yet! Here's a super easy, fun, counting/number recognition game...

1. For each child, use a Sharpie to label an egg carton and a dozen plastic eggs with the numbers 1-12. (See example at right. When game is played, children will place eggs in the correct slot.)

2. Gather all the eggs into a big container and scatter them over a wide area like a yard, field, or gym. Give each child an egg carton to keep at a designated "base" such as a line on the gym or playground or a back porch at home.

3. When you say "go," each child must run out to the scattered eggs, pick up ONE egg, and bring it back to his/her egg carton, placing the egg in the hole with the corresponding number. When the egg has been placed, the child races back to the grass for another egg.

4. If a child picks up an egg that he already has (i.e. he brought a "5" back to his egg carton but he already has a "5"), he must return the extra egg to the playing field and get another one.

This could be a competition, but you could also say that friends could help one another if they fill their egg carton. My preKers (ages 4-6) played this today and loved it. They were TIRED by the time they finished.

Math Monday Blog Hop #52 (April 9, 2012)

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The Lion's Share - fractions and doubling

We enjoyed a great little exploration with fractions and doubling that you may want to do with your students. We used 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.

I read about half the book, stopping at the point where the ant was left with a crumb. (Warning: the insides of the front and back covers show some of the fractional pieces of cake so you may want to cover them up.) I gave each student a square piece of paper and made a list of all the animals on the board. I asked, "How much would each animal get?" and challenged them to show the fractional pieces of cake with the paper. In the midst of cutting "cake" a student laughed and said, "This is going to go all the way up to 1/128. I figured it out." He soon discovered it got even smaller! (1/512)

After figuring out the fractional pieces of cake, I finished the story and asked, "If each animal doubles the number of cakes he is bringing to the king, how many cakes will the king receive?" (Work shown at right. 511 cakes.)

So, now a final question for you all...

Do you see a relationship between the two results? (1/512 and 511) Explain.

Spoiler alert: see chart at the bottom of the page...


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 #51 (April 2, 2012) - Pinterest!

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