Jeans Pocket Recycling = Add/Subtract Game for Any Target Number

I recently did this activity (revived from an old post) with a handful of first graders who needed a little extra support in adding/subtracting within 5. Across the board, they all said, "This is FUN!" With that endorsement, here's an idea for adding/subtracting with any target number. All you need is an old jeans pocket and some change.

I cut a pocket from a pair of jeans in the ragbag. We used the pocket for lessons at a variety of levels...

Add/Subtract Within 5:

I showed my 4yo five coins. I told him that I would hide some of the coins in the pocket while he shut his eyes. When he opened them I asked, "How many pennies are in my pocket?" While I was thrilled that he got the first one right, I quickly realized that it may have been a fluke. He needed more support to understand how many coins were hiding.

I made a little 5-frame. We put all five pennies in the frame and counted them. After I hid some, he used the 5-frame to help him figure out how many coins were missing.

Once understanding is more solid, continue without the five frame.







Add/Subtract Within 100:

I told my 7yo that his coins totaled $1. I put some of the money outside and some of the money inside the pocket. He counted the coins he could see and then told me how much money he thought he'd find inside the pocket. He then emptied the pocket and counted the change. I'll upgrade to dollar bills as he needs a bit more of a challenge.

Mental Math Game: I Have, You Need

In the context of our curriculum, Bridges Second Edition, we've been introduced to a quick, easy new game: I Have, You Need. The premise is simple and can be played with a pair of students or with an entire class.

1. Set a target number.
2. Call out "I have ________ (a number)."
3. Someone responds with "You need __________ (a number)."

I quickly do this with the entire class. Here are some examples:

Numbers to 100
Teacher: I have 22. (point to a student)
Student: You need 78.

Numbers to 10
Teacher: I have 7.
Student: You need 3.

Fractions to 1
Teacher: I have 4/8.
Student: You need 4/8. (Or 1/2.)

Decimals (as we're doing now!)
Teacher: I have 0.15
Student: You need 0.85.

Students can also pose problems for one other, taking turns with the questions/answers.

This has become a wonderful, quick tool to assess fluency. To provide students additional practice in mental math, try using the free, online game, Numberbond. Choose a target number of 5, 10, 100, or set your own number.

Flies Make Fabulous Math Manipulatives!

Reposting to enjoy during the Halloween season... Plastic flies are readily available at this time of year!

Since our study this week included insects, I thought it might be fun to do a little math "on the fly." Turns out that plastic flies are the perfect math manipulative. They're quiet. (No buzz. Honest.) Cheap. (Bought mine at the dollar store.) Fit great in a kid's hand. Are big enough to find if they "fly" to the floor. (Although we didn't really have trouble with flying flies...) And the math exploration possibilities are endless. (I saw the idea for counting flies here, but I extended it.) Flies would make great manipulatives for probability or fraction work with older kids. But this week was at the kindergarten level.

1. Practice writing numbers:
I made a sheet with the numbers I wanted my kids to practice. I gave each child 5 flies to spill out of the hand and onto the desktop.  Children then traced the number of "dead flies" (ones that landed on their backs) in one color and number of "live flies" (upright) in another color.

2. Practice addition bonds:
I set a target number and gave the child that number of flies to spill onto a desktop. We started with 5 flies. I made a worksheet to record a fly addition sentence: Dead Flies + Live Flies = How Many Flies Altogether? I put the paper in a page protector so we could change the target number. The picture matches the type of flies I found, but I think you could use it with any plastic fly. As long as kids record the upright flies in one column and the upside down flies in the other column, they're good to go. I mean fly!

On the first day, one little guy looked at the column of sums and remarked, "It always equals FIVE!"

Click on the picture for a free Google Doc download. Since I can't see how many people download, you'd make my day if you'd leave a comment saying you grabbed a copy! :)

This little activity would make a great Math Station or Work Box.

Related Kindergarten Standards:

K.CC.3. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).
K.CC.4. Understand the relationship between numbers and quantities; connect counting to cardinality.
K.CC.5. Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.
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.2. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
K.OA.3. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
K.OA.5. Fluently add and subtract within 5.

Kids Create Subitizing Cards

My sweet kinders love to subitize. In case you're unfamiliar with subitizing, look at some of my past blog posts. Basically, we're working on developing number sense through instant recognition of quantities. I downloaded a free set of subitizing cards that have a variety of dot combinations. For example, if I flash them (just for a moment) this card:

...and ask them "how many?" they may say "7, because I saw a 4 and a 3 and that makes 7." Or they might say "I saw a 2 and a 2 and a 3 and I counted them [in my head] and that makes 7."

Today we switched things up a bit. Imagine their delight when I told them they were going to make their own subitizing cards! Here's how:

1. I gave each child a 5"x8" index card with a line penciled lightly down the center. I asked them to find the LEFT side. A student suggested that they lay a Cuisenaire Rod on that side to help them remember. 

2. I told them that they were going to make quantities with dot stickers. (Dot markers would also have been fabulous.)

Guidelines:

• Use two colors.
• Build any number from 4-7 (later I added 8.)

They then placed dots on the left side of their index cards.

3. Each child practiced writing his number on an individual whiteboard and showed me before writing the number on the right hand side of the card in his BEST handwriting. (This prevented a few backward numbers and a few dot miscounts.)

4. When the cards were done, we tried flashing their cards to a grandma who came to pick up her grandson. The kids were SO PROUD when they flashed the dots on the left and Grandma was able to figure out the number, hidden on the right side of their cards! We'll continue to use the kid-produced cards, making more with higher quantities.

This was a huge success for us! Hope you enjoy it. (I'd love to hear about how it goes with your kids!)

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!)

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.

Subitizing: Counting Rope & Speedy Pictures Game

I've been intrigued with the concept of subitizing or "instantly seeing the quantity" ever since reading about it in a recent issues of Teaching Children Mathematics. I've started using our DIY counting rope to flash quantities in front of my 5yo. Want to join us? If you're a homeschooler, just make a counting rope and pull a small number of beads to one end. Then hold up the rope for a brief look (long enough to see the beads but not long enough to count each bead individually.) Teachers could put the counting rope under a document camera or lay game chips on an overhead for a similar experience.

Then, extend learning with this "Speedy Pictures" game.  You can choose to flash a visual representation of a number using fingers, dice, rekenrek, eggs, or number discs. The flash time may be increased or decreased, according to student needs. Students get a moment or two to see the quantity--but not count one by one--before being asked to enter a total. This activity would make a great computer-based Math Station.

Make-It-Yourself-Math...Counting Rope

At the Northwest Math conference I felt very privileged to sit in on several Kim Sutton workshops. If you've seen her, you know how amazing she is. If you haven't, I highly recommend checking into her work at Creative Mathematics.

In one of her workshops, she briefly held up a "Counting Rope." I thought it a very nifty math manipulative and received permission from Kim to make a video showing how to make your own. This is an incredible visual model for demonstrating addition, subtraction, counting and more!

If you like the video, I encourage you to comment here or on YouTube, showing your appreciation to Kim for allowing me to pass on this information. And look for Kim's book, Do The Math (scroll down on this page), for activities using the counting rope. Enjoy!

Quick Image Math - Fluency in Basic Addition

Interested in helping your students (at home or school) become fluent in basic addition? I just read a fabulous article on the topic in the Sept. 2011 issue of the National Council of Teachers of Mathematics (NCTM) magazine, Teaching Children Mathematics.

In the article, author Gina Kling asks "what exactly does fluency mean, and how might fluency differ from having instant recall of each and every basic fact?" Great question. And one with which many teachers and parents struggle.

NCTM defines computational fluency as efficient, accurate and flexible ways of computing. Kling writes, "Traditionally, learning basic facts has focused on rote memorization of isolated facts, typically through the use of flash cards, repeated drilling, and timed testing. However, ...drill alone does not develop mastery of single-digit combinations."

The article goes on to describe strategies that fluent students use and suggests several ways that teachers might help students to become more fluent. She talks about ten frames and games. But the concept that jumped out at me was subitizing.

Subitizing is "instantly seeing the quantity." Kling suggests using quick images to show students a representation of a number "with the expectation that they will retain a mental picture of what they saw and then use that image in some way." The key? "...to flash the image quickly enough so that students [can] not rely on counting to determine their answer."

I decided to try it this morning. I put pegs into a mat, gave a 5yo a quick image, and asked him to then replicate the number of pegs in his own mat. The mathematical thinking is apparent in the video below as he decomposes the number four, seeing it as "these two and these two make four." As you can see in the video, he doesn't count the numbers. He knows that it is four because he recognizes 4 as a double of 2 or 2+2=4. Note that we've done no formal work with addition; I've never heard him say,"two plus two makes four."

In the representation at right I asked, "How do you know it's 5?"

"Because 2 of these  and 2 of these [he pointed at two on one side, then two on the opposite side] and 1 of this [pointed to middle] makes 5."

It's quite exciting to see his mathematical reasoning.

We're on our way to learning basic facts. I'd like to try other methods using subitizing. The author suggests one could flash a pattern of dots (think of 5 or 10 frames) or a certain construction of unifix cubes. Watching my boys this morning, it'd actually make a great partner game in a math station at school or in a workbox at home. Each student could make a quick image "puzzle", give their partner a quick peek, challenge the partner to replicate it and then check the work by explaining the mathematical thinking involved. For instance, each child could have a five frame, put pennies on it (anywhere from 0-5) and have the partner try to replicate it after a quick peek. What an engaging way to develop fluency! As I was jumping around the web I noticed that DreamBox Learning has a whole category of games/activities for quick images. (I registered--free--and could immediately access.) Also, while this 5 Frame exercise isn't presented as a quick image, it's also a great resource for fluency practice.

P.S. Want to check out something similar for bigger people? Check out "What's Your Number Sense?" on Mathwire and go take the Panamath Test and check your own Number Sense! It's fascinating!

P.P.S. Just found a couple links:
What is Subitizing and Why Teach It?
Where Will You Land? A Game Focusing on Subitizing
Subitizing: What Is It? Why Teach It?

Milk Cap Math: MADS Elimination

Here is another milk cap math game for basic +/-/x/division practice. My 15yo daughter thought of the name, MADS Elimination. (Thanks!)

The object?

M: multiply
A: add
D: divide
S: subtract

...in order to eliminate all milk caps on the playing field. (Before you go completely MADs!)

You'll need:

• two sets of 10 milk caps (any color), numbered 1-10
• two, 1-6 dice

To play the game, each player forms a line of milk caps, 1-10. Players take turns rolling the dice. When dice are rolled, the player may choose to multiply, add, divide, or subtract. So, for example:

Dice rolled: 3 and 5

I can:

M: 3 x 5 (won't work since my caps are 1-10)
A: 3 + 5 = 8
D: 5 / 3 = 2.5 (won't work)
S: 5 - 3 = 2

So I could eliminate either the 2 or the 8 cap. If the cap(s) has already been eliminated, I lose my turn. The first player to eliminate all caps, wins.

You can make this a little easier (preschool) by using 6 caps (1-6) and one die (1-6) and removing caps from the table as you roll each number.

You can make this a little harder by using bigger numbers (on the caps) or having the option of rolling multiple dice. For example, you could roll three, 1-6 dice, and make a number sentence using all three numbers. (You could also use dice with different numbers: 0-5, 4-9, etc.)

Example using 3 dice:

I roll: 1,3,4

I could do any number of combinations...I won't list them all, but for example:

3 - 1 + 4

1 x 4 - 3   (You could even talk about order of operations here.)

4 - 1 + 3

Lots and lots of possibilities for this game!

Running out of math caps yet?? ;)

This is another great math workbox game! ;)

Milk Cap Math: Magic Square Game

Here's another idea for Milk Cap Math...

[As a side note, when I went to find my milk caps, they were gone. I finally located them under the piano in my 4yo's "house." Apparently, they are good for a lot more than MATH!]

Milk Cap Math Magic Square Game

You'll need:
*9 milk caps, any colors, numbered 1-9.

To play:
Place numbers in a 3 cap by 3 cap square as shown. Rearrange numbers so that the sum of any 3 caps (diagonal, column and row) equals 15.

You can play this Magic Square Game online to get the idea, but I recommend using milk caps (or something similar) to manipulate the numbers. When you manually move the numbers, you are able to experiment with different combinations in a way that just isn't possible with the online game.

Thank you SO MUCH to reader, musicalmary, for alerting me to the connection to the book, Ben Franklin and His Magic Squares! We just happen to be studying Ben Franklin right now in history, so this is perfect!!!

This would be another great math workbox!

Sleeping Queens Game (Gift Idea #2)

My 8yo son received an inexpensive card game, Sleeping Queens, for his birthday. He'd play it every day if we would. (His 4yo brother is also able to play with adult supervision.)

The object of the game is to collect queen cards or points. Various character cards--king, knight, dragon, sleeping potion, wand, jester--cause a variety of actions. Although the game feels like pure entertainment, it includes a mathematical component; you can discard (a good thing!) three or more number cards that make an addition equation. For example, if you have cards numbered 2, 3, and 5, you can discard them if you notice that 2+3=5.

As a fascinating side note, the game was invented by a 6yo girl who lay awake one night, dreaming up the rules for the game.

The box says for ages 8 and up, 2-5 players, about 20 minutes/game.

LilDude says he highly recommends it! It would make a great math workbox.

Tri-Ominoes (Addition/Subtraction Game)

Tri-Ominoes, a game played similar to dominoes, provides addition and subtraction practice. When players lay a piece, they must add the three numbers on the triominoe as well as keep track of their total points. Since the game is played until someone reaches 400, it provides a lot of practice in adding and subtracting. (The subtracting comes in when a player must draw a triominoe...a loss of 5 points for each that must be drawn.) Bonus points are awarded for unique configurations of triangles, such as completing a hexagon.

We bought this game this weekend and kids ages 7-14 as well as adults have been playing and enjoying it ever since. :)