Math Monday Blog Hop

Since both classrooms and homeschools are winding down for the summer, I'm taking a little Math Monday Blog Hop break. Think about what you'd like to post on the hop as we get closer to fall and starting back to school. Meanwhile, I hope to bring you more of my favorite math books for summer reading. I'll also be updating the big book list of Math in Children's Literature throughout the summer months. Check back soon! :)

Pattern Block Lessons K-5, Free (Meet CCSS!)

I can't believe this is free! Some of my favorite lessons from Bridges in Mathematics have been compiled as "Pattern Block Lessons." The combination of lessons are designed to help meet the Common Core State Standards in grade bands K-2 and 3-5. Download the pdfs here.

Lessons include games, activities, literature connections, and all the necessary instructions and blackline masters. All you need is pattern blocks. Perfect for classrooms and homeschools. Enjoy!

P.S. They also have tons of other items listed there! Check out the Bridges Breakouts!!

Math Monday Blog Hop #58 (May 21, 2012)

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Bedtime Math

Have you seen Bedtime Math? A friend just alerted me to this site where a problem is posted every day for kids to do at bedtime. You'll find 3 levels: preschool, K-2nd, and 2nd-up. Homeschoolers could add a math moment to their bedtime routines. Classroom teachers might want to alert parents who could develop this "math habit" with their kids all summer...or you could use it now as a "wake-up" routine at school.  Check it out! :)

Math Monday Blog Hop #57 (May 14, 2012)

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Math Monday Blog Hop #56 (May 7, 2012)

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Upper Level Math Instruction...Unnecessary???

I hope you take a minute to watch this video, "Why Math Instruction is Unnecessary." An excerpt from the written summary:

John is a teacher of math and a homeschooling parent who offers a radical-sounding proposal: that we cease to require math instruction in middle and high school.

If math education was done well...REALLY WELL...in the lower grades, we'd have a bunch of kids who are mathematically fluent. If then, they liked math (which they might, if they were taught well!), and wanted to enter a career in which higher levels of math are required, they'd have the necessary foundation to move ahead. And, if they didn't want to enter a math-oriented career, they'd have what they needed to enter society with the skills necessary to thrive.

What do you think?

Calendar Pattern: Fractions & Music

Each month we do a calendar pattern from Bridges in Mathematics. After doing patterns for several years, the proficiency level is high; we've seen and worked through a lot of complex problems. So this month I proposed a new challenge: make a calendar that includes 2-3 patterns. After reading about Teaching Fractions Through Music, I suggested that the pattern include music, looking at fractions in notes and/or rests.

The student-generated calendar included the following (easy) pattern(s):

• rest, rest, note, note
• color: red, blue, green

In order to create the more difficult pattern of fractional note/rest values, a chart was used showing rests with values of 1/1 to 1/32 and notes with values of 1/1 to 1/32.

The pattern on the calendar used two rests going down the value chart starting at 1/1, followed by two notes going up the value chart starting at 1/32.

As we went through the month, we analyzed what had to happen from day to day in order to change the value of the rest or note. In doing so, we explored a lot about fractions. To make it easier, we looked at a visual model using tile.

The first change was easy. From Day 1 to day 2, the value went from 1/1 to 1/2; to achieve that change, you simply divide by 2. Other days were harder. From Day 13 to Day 14, for example, the value went from 1/32 to 1/16. At first I heard, "divide it by 2!" But when we looked at the visual model, we could see that 1/32 divided by 2 would not result in 1/16. But multiplying by 2 would.

As we went, a couple generalizations emerged:

• when you divide a fraction the denominator gets bigger but the number gets smaller.
• when you multiply a fraction the denominator gets smaller but the number gets bigger.

Big grins. We continued to check our work against the visual model. It helped everyone...including me. Fractions cause me huge math anxiety. (It takes every brave bone in me to post this!)  I was only taught fraction rules. Each time I teach fractions, I feel like I'm trying to undo what was done to me. It's thrilling to see the visual models increase kids' understanding.

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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Press Here - A Book to Impress!

Have you read Press Here by Herve Tullet? It presses my funny bone!

It's a ridiculously simple concept...  You just do what the book says. For instance:

You see a yellow dot. The text says, "PRESS HERE and turn the page." When you turn the page you see two yellow dots. Now it reads, "Great! Now press the yellow dot again." Next page: "Perfect. Rub the dot on the left... gently."

The book continues to tell you exactly what to do on each page. The picture on the next page changes, just as if the book did what you said. It will tell you to tap a dot five times...and lo and behold there are five dots on the next page. It might say to tip the book to the left. On the next page, all the dots are clustered on one side as if your actions made the dots move.

We have read this book OVER and OVER and OVER and OVER.

My 5-year-old (without prompting) even made his own version of the book. It's a natural, humorous way to teach things like basic counting, direction/position (left and right), colors and more. My 9-year-old enjoyed it every big as much as my 5-year-old. Oh, who am I kidding? I probably liked it the most. (And I'm not telling my age!)

This is a must-read. Use it as a model for kids to write their own books. Or just enjoy it. Over and over again.

P.S. The Amazon page has a lot more information, including 100 customer reviews (impressive!...for a book that came out 6 months ago!!) and a video trailer. See to believe!

Extreme Makeover: Schoolroom Edition!

A while back I asked for some schoolroom advice. I wish I'd taken an even earlier photo, because this room had old carpeting in it, but you can still see the basic change:

We removed the warped, twisted beams that were bolted to the ceiling. Updated the lighting and popcorn ceiling. Painted.

I was stumped over how to handle the brick. I liked it better once the room had been updated, but I still needed shelving and storage in this longish/narrow room. So we added built in bookshelves/cabinets with drawers under what used to be a free standing hearth.

Here's a little room tour...

The wall to the immediate left (behind the recliner) holds the clocks. We have one clock for each of the places in which our kids were born. This is great for calculating elapsed time! We often talk about what's currently happening in Korea and China while looking at the clocks. [Clocks are from Ikea. Labels were ordered through Office Depot.]

Directly beneath the window you'll see a magazine rack that holds some of our library books. [I purchased the rack, used, at a secondhand store that was going out of business.] To the left of the rack is a Large Magic Wall (magnetic) from The Math Learning Center.

Looking straight at the fireplace, you'll see our reading couch on the left with a map above it. We agonized over what to get to hang things on the walls. After painting, my husband insisted, "NO MORE BLUE TACKY STUFF!!!" I couldn't blame him. We had teeny pieces of the stuff stuck all over the walls from years and years of hanging papers. We finally decided on map/tack strips (can't remember the name or where we got them) and the wire for artwork from Ikea. This picture gives you the idea.

The train table is used for rotating toys/projects/themes. I like to swap out Legos, Playmobil, etc.

Now the newest addition...

If you sneak a peek behind the couch, you'll see our schoolwork. I first saw the plan here. We decided to get two of these Expedit Shelves because I could separate them if I ever decide to rearrange. Two Itso Bins from Target (Clear Qtr Bin Itso See-Through) fit perfectly on each shelf. I put a throw rug back there to make a cozy reading corner. It's been there since yesterday and so far it's been the source of constant bickering. I pointed out that it has lines; it can be divided in HALF. They don't seem to be particularly interested in fractions when it comes to sharing space.

On the right wall you'll see all the usual classroom items: 100s grid, pocket charts (mostly garage sale finds!), whiteboard (Costco), more of the map racks and art wire, a DIY cookie sheet/magnetic board, and a Calendar Grid Pocket Chart on the far right. I bought the table/chairs years ago from a preschool that was closing. When I use the space for larger classes, I often clear the area and have kids sit on the floor.

Oh, and btw...  We spend a lot of our day in this room. But it isn't unusual to find us sitting at the kitchen table either. This certainly isn't necessary. But it does make it SO. MUCH. EASIER. TO. FIND. THINGS.  It didn't used to be so hard to lay my hands on what I needed. Life is a bit busier these days. Hopefully this organization will save me some time.

I hope you've enjoyed this little tour. I LOVE peeking in on other learning spaces! :)

Homeschool room, Homeschool classroom