Student Notebook Strategy Posters

This quick, easy idea is one that works well for student notebooks. When I work with students on strategies, I often create a classroom anchor chart for the wall. I like to record the name of the student who used the strategy, along with a title that clearly describes the strategy. Kids love to see their own names in print and when they're asked to name what happens in the strategy, they often delve into rich mathematical thinking and discussion to define exactly what it is that they've done.

To give students greater ownership in the process, I invite students to make their own posters to go in their math notebooks or journals. I give each child an 11" x 17" paper, folded near (but not on) the halfway mark and 3-hole punched on the left. This way, the poster can be folded and added to their math notebooks as permanent reference.

Today, we made posters for Addition Strategies. If you click on the photos, you can see that we depict and name a variety of strategies. You'll also notice that this exercise is appealing to the artists in the crowd.

Give (and Take!) Me a Great Addition Strategy

Exciting work continues in our summer math sessions!

Last week, my 10yo son and I started exploring strategies to help with multi-digit addition fluency. The "Give and Take"* strategy has given us inspiration and taken away some of our math anxiety. Here's how it works...

Let's say you're asked to add two, somewhat unfriendly, numbers.

97 + 78

Yuck. Not a great combination.

But what if you could do a little give-and-take to make it easier?

97 + 78 = 97 + (3 + 75) = (97 + 3) + 75 = 100 + 75 = 175

Which would you rather solve?

97 + 78

-OR-

100 + 75

The consensus was pretty clear around here!

How about:

443 + 289

What if we "take" 11 from 443 (443 - 11 = 432) and "give" it to 289 (289 + 11 = 300)? Is it easier to now add 432 + 300?

 My 10yo explains the strategy in his math journal, in the photos you see here.

So "witch" would you rather add? :)

After journaling, to solidify the concept, he made up his own problem:

270 + 665

He took/gave 30:

300 + 635 = 935

And today, he applied it to a story problem where he had to add 275 + 168. He took/gave 25 to end up with 300 + 143. He bubbled with excitement ("MOM!!!!!"), telling me how great the give/take strategy works!

I hope this gives you a little inspiration to take back to class!

P.S. This also works well with decimals!


*The Bridges Curriculum calls this the "Give and Take" strategy.

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.

Math Monday Blog Hop: Addition & Subtraction

Well that's one GIGANTIC topic...any and all ideas for teaching addition & subtraction! Post ideas below (no ads, please.)

Have a happy week...adding up all those blessings as you celebrate Thanksgiving.






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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.

Visual Models Make the Math!

I remember little of early elementary school math, so I find it rather remarkable that this stands out...

My elementary school math experience was primarily composed of rules or sequential steps to memorize. One rule: add by starting with a given number rather than starting with 1. So if we had 6 and wanted to add 3, we were supposed to start with 6, rather than starting at one.

I'm not sure how I missed the instruction (I did enjoy watching Stacey, the class clown, tie Jennifer's shoelaces to her chair...recall that much better than math class), but I couldn't add by starting with a given number.

Why? Here's my 7-year-old thinking:

Should I say 6 and then count 3 more on my fingers (say "6," then "7, 8, 9"), or should the 6 count as one of the 3 numbers I'm counting? (say "6, 7, 8"):

6...
7 (holds up 1 finger) 
8 (holds up 2nd finger)
9 (holds up 3rd finger)

-OR-

6 (holds up 1 finger) 
7 (holds up 2nd finger)
8 (holds up 3rd finger)

Can you follow my thinking? I was so worried about the steps that I forgot to consider what I was actually being asked to do, or what it meant to add two numbers. What if someone had given me visual support?:

A number line that shows I already have 6 hops and need to add 3 more hops:

A Number Rack to show that I have 6 beads and am adding 3 more:

Or Number Pieces to show that I have 6 units and add 3 more:

I don't think my teacher ever knew that I couldn't add by starting with a given number. After I missed a bunch of problems, I just gave up and put my fingers under my desk and counted, starting with 1. Because I was so busy with this inefficient addition method, I think I missed memorizing my addition facts. I don't think I mastered those until adulthood.

But I got straight-As in math through high school. I was a master math swindler.

Do you support math concepts with visual models? Do you have a story to tell about a kid like me? I'd love to read your comments. :)

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!)

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)?

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.

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.



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Math Myth: Borrowing is the Only Way

Subtitle: How I "Borrowed" Trouble and Have "Carried" It With Me...

I recently wrote an entry that included a link to a piece of research on "The Harmful Effects of Carrying and Borrowing." This has been on my mind a lot this past year. Here's why...

The math curriculum I use, Bridges in Mathematics, does a tremendous job at having kids explore various ways to solve problems. The way the lessons are set up, kids develop their own strategies, share their thinking with others, and refine their ideas as they become and more and more efficient at math. I was NOT taught this way and it's been amazing to watch my students develop strategies that are far superior (meaningful, more efficient, etc) than the algorithms I was forced to memorize.

This year I've been working with a 9-year-old. He's been able to use a variety of strategies to solve multi-digit addition and subtraction problems. Here's an example of one way that he solved a multi-digit subtraction problem. (Taken from a Bridges Grade 3 assessment.)

1349-675

1300-600 = 700
700+49 = 749
749-75 = 674

I asked him how he did the last step. He said:

750-75 = 675
675-1 = 674

The strategy shows number sense and comfort with place value. As a child I was told that the correct way to do this problem was by borrowing. It made no sense. No one bothered to familiarize me with place value and number sense to give the problem any context. I had no options except to follow the rules. So why, then, would I mess up this child's system by giving him rules?

I did, you know. Here's what happened...

After being exposed to a wide variety of strategies and showing marvelous strength in his own knowledge, I introduced the standard algorithm. Why? Standards specify that kids must know how to do the standard algorithm along with other strategies. So we did it.

It seriously messed him up. The harder I tried to teach him the standard algorithm, the less he maintained a grasp on the meaning he'd constructed for himself. I taught the standard algorithm using both manipulatives and numbers, so it wasn't like I taught it completely out of context. We looked at how the numbers had to be broken apart (carrying/borrowing) with the manipulatives.

But it made no sense to him.

So I abandoned the standard algorithm. Actually abandoned all multi-digit addition and subtraction for awhile because he seemed so defeated. I seriously thought I'd ruined the kid. When we came back to it, we did a lot of work with manipulatives and I let him do it HIS WAY. Lo and behold, it came back to him. Stronger now than before.

I do still occasionally show him the standard algorithm. But only after extensive time with the exploration of other strategies. And only after he seems very, very comfortable in his own methods. I have abandoned telling him to "do it this way." 

Cause "this way" may not be "his way." And "this way" may actually do more harm than good.

I'd love to hear about your experiences.

Exciting Freebie - Number Rack!

The Math Learning Center has an amazing new set of freebies. The Number Rack App can by downloaded from the iApp Store in iTunes -OR- used as a free Web application.

The moveable beads work with counting as well as addition and subtraction strategies. You can also download a free activity/lesson book to use along with it. I'm interested in trying it with subitizing.

This could be used at home or in the classroom with individual children or with a large group lesson. Read more about it here.

Part-Whole Math With a Plate!

At a conference last fall, I heard Kim Sutton mention something about using Zoo Pal Paper Plates to show parts and whole in math. She briefly described putting the parts in the ears and then showing the whole in the larger plate area. I'm not exactly sure how she uses the plates. But I wanted to experiment with the idea...

I couldn't find the zoo plates locally (Amazon link is below), but decided to try it with a plastic plate from a local one buck store. (My plate is sorta like this divided plastic picnic plate.) I've used this a couple different ways to explore the part-whole relationship in addition with my 5yo...

With Dice:
He tossed one die into each of the smaller compartments and put that many items (I used centimeter cubes) in each dish. He wrote down the two dice numbers in an addition number sentence. So if he rolled "2" and "3," he put 2 cubes in one small slot, 3 in the other small slot and wrote "2 + 3." He then moved all the cubes to the bigger area (the whole) to count the total and finish the number sentence (= 5.)

With Pre-Written Number Sentences & Penguin Pieces: 
I wrote several number sentences. (Photo above models 2+2.) If the sentence was 2 + 4, he counted out 2 marble penguins into the first small compartment and 4 marble penguins into the second small compartment. He then moved all the penguins into the larger compartment, counted the total and finished his number sentence.

This could easily be replicated at home or school. And could be used with subtraction, multiplication, division, fractions, decimals and more. Enjoy!

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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.

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?

Review: Math Dice Jr.

As of TODAY, my continuing education math workshops for teachers are done for the season. I'm very excited to get started with the school year a bit closer to home. Oh wait...in our home!

Last year, my youngest attended preschool two days a week. This year, at 5.5yo, we'll be doing some minimal kindergarten work. Recently, we were excited to receive a game that we can use as he begins learning more about MATH.


MathDice Jr. is designed to be used with ages 6 and up. At 5, my son is on the young side. To play, the rules say to roll the 12-sided Target Die and the five 6-sided Scoring Dice. All are large, chunky and bright...fun playing pieces for young children.

The Scoring Dice can be combined to make addition or subtraction problems that equal the target number. So, for example, in the picture below, you could use 6 + 2 to reach the target of 8. Since my son isn't ready for subtraction, we added another element...  If one of the colored Scoring Dice exactly equals the Target Dice, that dice can also be used to achieve a match. My son spent a lot of time counting the dots on each dice to see which matched the target. It was nice for counting practice.

The original instructions call for players to move one space on the track for each die used. Again, we played an easier version (our invention) to meet my son's developmental level. Player #1 (whomever rolled the dice that game), got the first opportunity to make the number, either through addition of several dice or by one-to-one correspondence, "matching" a dice to the target number. If he found a way to make the number, he called "Math Dice," showed his results, "captured" the dice he used (removing them from the play area) and moved one space on the track. Then, the next player in the circle could try to reach the target number from whatever dice remain. If he can match the target number, he also calls "Math Dice" and gets to move one space on the track. We continue around the circle until no possible combinations for the target number remain. Then the player who did not roll the last time gets to roll. Using this method, the play stays pretty balanced; no one is able to get far ahead of others on the track.

The first few times we played, I tried to let my 9yo son play using any operation (add, subtract, multiply, divide) to reach the target number. This left my younger son at a significant disadvantage. So I'd "help" him...again using any operation. But this meant my younger son got very little out of it. So I told everyone that for now, we'd only do one-to-one correspondence or addition. As my youngest learns more math, we'll add more operations...which will make it more of a family game. Right now it's mostly a counting game for the youngest.

The game itself comes with a nice little canvas game board and all pieces fit into a convenient drawstring bag. It was a nice compact game to carry along on a campout. No game markers come with the game but my boys have enjoyed picking out buttons (note the long button in the middle photo!) to use. On the MathDice webpage, you can pick up a pdf for a game board and some pretty cool looking game markers.

My opinion in a nutshell? This is an inexpensive, fun, educational game that could be used by teachers (a great math work station!) or by homeschoolers (a great math workbox!)


Disclosure: I received a free Math Dice Jr. game in exchange for a frank and unbiased review. Thank you to ThinkFun for the opportunity! I was not paid for this review, nor was I required to write a positive review. Frankly, I love the ThinkFun products I've had the opportunity to try...most of which I've purchased myself. :) If you purchase this product through my Amazon link at right, 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.

Addition Fact Games--Make Ten

We've been working on materials from Bridges, Grade 3, of The Math Learning Center. I want to share some fun activities, designed to promote fluency with addition facts.

One card game, "Make the Sum," comes with the MLC materials. Prior to receiving the materials, we played "Make Ten," a variation based on the MLC game using a deck of regular cards.

Materials Needed:
deck of cards, A = 1, then 2-9 cards (remove all other face cards)

Object:
To collect combinations of cards that make 10. Player with the most cards at the end of the game wins.

To play:
Shuffle the deck and lay face down on the table. Draw top card and lay face up on the playing field. Player #1 looks at the card and says which card he would like to draw in order to make 10. He draws a card. If he can make 10, he tells the other player which cards add up to 10 and takes those cards. If not, he adds his card to the field.

Player #2 then says which cards he would like to draw in order to make 10 using the cards already on the field. He draws and then either makes 10 or, if not, lays his card on the field and play goes back to Player #1. Combinations of more than two cards are desirable as the players with the most cards at the end of the game wins.

Here's a video demonstrating how to play the MLC game.



My student gained more skills practice in "Make 10" by using an on-line game (also recommended by MLC) called "Math Lines." This game is unbelievably addictive. It's embarrassing to admit, but I made my little student stand next to me and watch while I played because I wanted to see how many levels I could master. ;) He loves the game as well.

Farm addition is another game that provides practice in addition facts. We found it just as we finished My Little Farm.