Unifix Cubes: The Elevation of a Common Math Tool

When updating my hands-one algebra product over spring break, I was reminded of a great tip for organizing a common math tool many of us use.  Several summers ago, Courtney and I attended and in-district 3-day workshop with Angela Andrews.  Angela is an expert in early math and offered an abundance of useful information and strategies. 

Just want to share a great tip Angela gave us for organizing a math tool many of us use with students, Unifix cubes (or linking cubes).  Angela suggested not only putting Unifix cubes in groups of ten (which many of us already do), but she also suggested using two different colors to show groups of five (see picture below).  The reason for this is quite simple, yet powerful.  

As students progress in their understanding of number, the tools must progress with them.  When Unifix cubes are separated and stored in a tub all mixed together, students who want to use them for modeling must count them one-by-one.  For example, a second grader may choose Unifix cubes to represent a "situation", but when he/she has to count them individually he/she is reverting back to an earlier stage of development. By organizing cubes in groups of five (two different colors) to make up ten, that second grade student can easily see five and add on. In this way, when he/she wants to show a value such as 12, using Unifix cubes/linking cubes, the use of this tool becomes much more appropriate and efficient.  

Organize cubes into groups of ten with two different colors (5 of one and 5 of another).  This will eliminate one-to-one counting of cubes that may not be desired and requires students to use their understanding of 5 and 10.

Here's a great missing addend activity that was shared in the same workshop! Students work in partners.  All that is needed is a group of ten Unifix cubes organized as shown above.  One partner holds the ten Unifix cubes behind his/her back.  Then he/she makes a break and shows his/her partner one group while keeping the other group behind his/her back.  The other partner must then tell how many cubes are hidden. He/she must also "prove" it by counting up or back or by stating what he/she knows. 

 

A student might respond, "I see six, and I know there are ten altogether.  I need four more to make ten with six, so four are hiding."

I hope you find these suggestions useful!
 

Here is the product that I was updating when  reminded of this organizational system I use with my Unifix cubes.  This early algebra hands-on math center requires modeling of known addends to help figure out the missing addend/s.  Unifix cubes, or ten frames, can be used as show below. 

Like what you see?  Enter to win one of two copies of Out of this World Algebra for your students!

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AND don't forget--If you haven't already checked out my book review of Fluency Through Flexibility and entered the giveaway of the materials shown below, click on the pic to do so!

Good luck, and all the best for a wonderful week--

Read Across America Math Fun!

Good day to you!  Just wanted to share some goodies with you for celebrating Read Across America.  Please feel free to download my Celebrating Read Across America Math Games and "Which Dr. Seuss book is your favorite?" Graphing.  Both are great for use as guided math workstations/centers!

The graphing activity comes with blank pages for choosing your own titles, and various graphing sheets are included as well. Enjoy!

ALSO--we would like to announce that we will be posting Sherry Parrish's Q&A this coming Wednesday.  We hope you will stop back to read her thoughts and suggestions about using number talks.

Until Wednesday...

Fly on the Math Teacher's Wall -- February Hop -- Fractions!!

Welcome to another wonderful math blog hop!  This blog hop is devoted to fractions and will not disappoint--so after reading this post, take a hop around to see what goodies you will find from some amazing math bloggers!

Each of our Fly on the Math Teacher's Wall hops are devoted to squashing teacher and/or student misconceptions.  I am not really discussing a misconception, but I would like to focus on some key ideas I feel most important in helping my students develop a solid foundation in fractions that will be built upon as they progress from year to year. If students understand these key ideas, hopefully some future misconceptions can be avoided.

The following is the second grade Common Core Standard for fractions:

CCSS.Math.Content.2.G.A.3
Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

There are several key ideas for understanding:

• A whole represents all of something (1 whole).
• A fraction represents part of a whole (for introductory understanding, this is important--as we know, a fraction can represent any number of equal parts--as with improper fractions, but students also need to understand when working with improper fractions that an improper fraction is greater than one whole.  This understanding will be developed in later years for my students.)
• A fraction represents part of a whole that has been divided into EQUAL parts (for my students this understanding is developed with the use of circles and rectangles, not equal sized parts of a set)

How do I help my students develop a working understanding of each of the above ideas?

We begin our explorations by identifying objects that are in the form of a whole and those that are not.  We examine items around the classroom that are and are not whole (an unsharpened pencil vs. a sharpened pencil, a unopened Kleenex box vs. a box that is part full, etc), and I also bring in various items (cookies, bottles of soda, fruits, etc.) in whole and part form.  Items are sorted into two categories.  The group of items that are not whole are then labeled as fractions.

To help students understand that a fraction represents part of a whole that has been divided into equal parts, we explore wholes that have been divided into equal and unequal parts.  A lesson about equal sharing is done.  Students seem to understand the concept of equal parts when it is related to sharing the whole of something with a friend.  Posing various sharing scenarios with items divided into equal and unequal parts is helpful.  My kids love when I choose students to share my pizza and candy bar with. I divide both unequally, share with volunteers, and then ask my students if my sharing is fair.  This naturally leads to a discussion of how my sharing is not fair because the parts I shared were not equal.  I then ask students how the items CAN be shared equally.  They, of course, can always tell me.  We continue our explorations by cutting out circles and rectangles.  We fold the shapes to create equal parts, cut them out and create models.

Only after students have a solid understanding of these three ideas do we move on to the concepts outlined in the standard.  Guided math groups are easily formed based on what I have observed in our initial explorations.  In small groups I am able to further develop some students' understandings of the key concepts before moving on, work more with some students on partitioning wholes, and challenge those who already have understanding beyond the second grade standard.

UPDATE: Totally forgot to post these little gems that I use in guided math groups.  So simple to make and use. How could I have forgotten? Enjoy!

Fraction Mats

Providing multiple opportunities for independent practice is always important, so this is done in rotations while I am meeting with guided groups.  Options for practice are differentiated.  Please feel free to download a few of my activities for independent practice.

Pizza Parts: Fraction Models Task Cards

Pizza Parts: Comparing Fractions Task Cards

Four Leaf Fractions Board Game & Spinner

Flying High with Fractions Board Games & Spinners

I have also made up some fraction foods you might be interested in using.  Foods are labeled and unlabeled.  These can be used in guided groups and for independent practice. I especially like to use the parts that are labled--in this way students can see that 3/4 is equal to 3, 1/4 pieces.  If you download this freebie, please take some time to share how you plan to use them by leaving a comment. Would love to hear your ideas!

Hope you have found something you can use with your students!

Please take the time to hop around to all of the participating bloggers.  Your next stop is Brandi from The Research Based Classroom!

Happy hopping---

Makin' It Math Mid-Month Linky -- Money, Money, Money!

Glad you stopped by! Welcome to our Makin' It Math Mid-Month Linky--a linky dedicated solely to math made-its.  If you are interested in linking up your math made-its, check out the details by clicking the logo below.  We would love to have you join us! 

Our kids have been working a lot with money in the past few weeks, and are quickly becoming money masters!  We thought we would give you an inside look at our explorations and share some made-its.

Our money explorations began with a simple pretest.  Students were asked to name each coin, tell the value of each coin, and count a small selection of coins (if able).  Students were pulled to do the assessment individually with real coins while other students were engaged in math game play.  This quick assessment made it easy to group students based on need.  Four groups were formed and guided instruction of small groups began.

Small Guided Math Groups

The following have been key in our small guided groups:

• the use of coins that students can touch/feel and manipulate
• mastery of coin identification and values before moving on to counting (some groups moved on sooner than others and students who showed mastery quickly were worked into a different group)
• a gradual progression in coin counting (mastery of counting like coins and adding coins from least to greatest--pennies and nickels; pennies, nickels, and dimes; pennies, nickels, dimes, and quarters)
• multiple opportunities to count random groups of coins and write the total value using numbers and symbols (students would count a collection of coins for the group two times and the other students in the group would agree/disagree, recount to check accuracy, and discuss order in which coins were counted)
• acceptance and discussion of multiple ways of counting (including discussion of counting on coins to create landmark tens for ease of counting remainder of coins)
• self and peer-evaluation and justifying of thinking
• use of the open number line to illustrate how coins were counted
• lots and lots of practice 

Students carefully counted in their heads as their peer counted aloud.  Students then agreed or disagreed and gave proof.  Discussions of how coins were counted (order) happened here as well.

Students showed their thinking with an open number line.

Students evaluated their peers and provided justification for their thinking.  The students on the left drew faces to provide evaluation for their fellow classmates as they worked their way from desk to desk around the room.

 Students showed multiple ways to represent a dollar.

Independent Practice

The following are a few independent practice opportunities we  provided for students to work on while meeting with guided math groups (differentiated based on each group's needs and all designed for practice of money skills).  Please feel free to download any you can use.  Some were created this year and others we have used for several years.

Math Journals:

Coins in My Pocket Journal Prompts - These prompts can easily be differentiated.  My kids use half-sized notebook journals and simply cut and paste the prompts and solve.

"Show What You Know" independent tasks (premade/teacher created activity sheets, roam the room activities, Scoot activities, What's a Word Worth?, etc.) that can be used as assessment:

I don't find too many premade activity sheets that I like, but I inherited an OLD version of this workbook years ago. I think it's one of those for parents to use at home, not sure. It's great!  It follows a logical progression of practice from like coins to pennies and nickels, pennies/nickels/dimes, etc.  It also has some great problem solving sheets.  I pick and choose the sheets to use based on student need and place them in folders labeled A, B, and or C.  Cups of coins are always made available for use with these activity sheets.

What's a Word Worth? -- I'm sure you have seen or used something like this before.  Students can use any word list and the coin key to figure out what each word is worth.  I have three different sheets made and labeled A,B, and C so students practice with the coins they can count independently.  

Counting Coins Scoot:  Stop back to download soon!

Games:

Bank It! Board Game -  This game can be played after students have learned to count pennies, nickels, dimes, and quarters.  It requires addition and subtraction of coins. My kids love this! Games like these are easy to send home for at-home practice. 

You may also like my This Little Piggy! Money Fun games on TpT.


Workstations (task cards, money bag activities, etc.):

Money Bags!: Coin Tasks - This differentiated workstation is used with bags of coins (fill with coins appropriate to student need).

You may also like my Show Me the Money! task cards on TpT.

Assessment

Ongoing assessment is easily done in guided groups.  Much is assessed through observation.  Courtney and I also created a performance task that we use to assess students' levels of mastery.  Please feel free to download, Suzy's Piggy Bank.  If you use this task, we would love to hear your comments and thoughts about how it went.  Feel free to email us anytime!

Please share your thoughts and ideas in a comment OR link your blog post up with us!

All the best--

An InLinkz Link-up

A Hundred Days Smarter & Number Talks Chapter 4 to Come Tomorrow...

Hello!  Today I come to you with news of a delay.  I got up to do my Number Talks Chapter 4 post this a.m. and discovered I had left the book on my desk at school.  SO, I will have to ask you to stop back tomorrow night to read my discussion of Chapter 4.  My apologies!

BUT you just might be interest in my A Hundred Days Smarter math workstations for celebrating the 100th day of school.

I updated the stations I did last year and added one.  I would like to share them with you!  Simply click the pic below to download your copy.  They will be used as workstations while I work with guided math groups.

Our 100th day is next Monday!  If yours has past, hope you had fun! If yours is still to come, hope these can be of use.  Enjoy!

Please look for my Number Talks discussion of Chapter 4 to be posted tomorrow evening! To read past book study posts, visit the book study archive.

Smiles,

It's a New Year!!

It's a NEW YEAR--a Happy New Year to you!!

It's that time of year--time to celebrate and look ahead...

To help you celebrate a new year, I have created a couple of FREEBIES for you.  Enjoy my Winter Walk-About problem solving activity and Winter Friends math games.  Simply click each pic to download!

Update:  Please redownload my Winter Friends math games, as there was an error on the "In the meadow..." game board. Sorry for the error!

AND just wanted to share a few of our blogging plans for the year ahead...

• share new-found knowledge (for example, book studies)
• provide a closer-look into our work with students in guided math groups
• add read and reflect sheets for use with math mentor texts (see Resources on navigation bar)
• continue to network with fellow math bloggers

We look forward to another great year with you!

To start it off, please feel free to join us as we participate in a new book study of, Number Talks by Sherry Parrish, sponsored by The Elementary Math Maniac.  We will do our best to keep up!  See the schedule below.

All the best to you and yours for a fabulous new year!

You Better HOP Around!: Fly on the Math Teacher's Wall--A Math Blog Hop!

Welcome to another wonderful math blog hop!  This blog hop is devoted to place value and will not disappoint--so after reading this post, take a hop around to see what goodies you will find!

Place value--a huge topic, and such an important concept for ALL ages!

As a second grade teacher, place value is at the heart of much of our explorations in math throughout the year.  Since I cannot possibly put everything I feel to be important about place value into this post, I will focus on some MUSTs in helping my students understand place value and build a solid foundation for what will follow.

THE POWER OF 10!
We as teachers know the power of 10 in our number system and how an understanding of 10 is a ESSENTIAL for building an understanding of hundreds, thousands, and so on.  I make a point of mentioning the power of 10 to my students DAILY! Any chance I get, I recite the words, "Ha--the POWER of 10!" in a sinister witch-like cackle.  They always chime in afterward! :0)  In the beginning of the year, it's a mixed bag as far as students' understanding that 237 has 23 tens and that 23 tens is the same as 230.  I like to use various prompts for students to agree or disagree with that require their use of 10.  Here is a picture of our Bright Ideas board and the first math prompt I gave this year (the board is used for all content areas). You can see the diversity of understanding with some thumbs being in the middle to show an inability to decide.  Prompts such as these bring with them wonderful discussions and students must justify their thinking.

PLACE VALUE TOOLS!
When I say tools, I mean beans, linking cubes, straws, ten frames, base ten tools, place value arrows, place value discs, an open number line, etc.  Representing numbers in multiple ways is a MUST!

At the same time, I feel it is also important for students to understand the power of different tools as well as their limitations.  An example--from the very first day of school, we do Daily Math (includes a number of the day) as a large group (this eventually leads to work in guided math rotations).  We begin with two digit numbers and eventually progress to three digit numbers.  In the beginning we use ten frame tools (small individual ten frames) to represent numbers.  The ten frame is a familiar tool used in kindergarten and first grade, so this is a great place to begin.  As we venture into representing greater numbers, students begin to understand the limitation of using ten frames for representing and drawing ten frame models.  The tools become less efficient/appropriate in this way, so a different tool is introduced (base ten tools).  We talk about each tool, their benefits and drawbacks.  We NEVER say a tool is BAD---or that it is WRONG to use a particular tool, but I feel it is important for students to understand the differences between tools and their effectiveness/applications.  Furthermore, I never begin using a tool with students, such as base ten tools or place value discs, unless they have a conceptual understanding of each disc's value.

Tools are ALWAYS readily available for students to use during guide math rotations--they never need to ask for permission.  Tools are also housed in our guided math area for easy access during small guided math groups. Please enjoy the following freebie tools that are posted under Workstations & Games on our navigation bar.  In addition, I have shared an open number line post from our other blog, Hoots N' Hollers, that you may be interested in. Enjoy!

Ten Frame Tools
Place Value Arrows

Place Value Discs

A Powerful Tool: The Open Number Line 

PLEASE NOTE: Courtney will be sharing a new place value tool she has just added to her classroom. Look for her post about Digiblocks in the near future!  

TALK IT!
When I say "talk it" I mean constantly talking about numbers as a composition of digits that have value.  When we add 36 and 45, we are adding 3 tens and 4 tens--6 ones and 5 ones.  We talk it!  This eventually leads to reciting our addition of place values or composing/decomposing when mentally adding .  As a kid, this is one thing that was never done, at least to my recollection.  The algorithm was the focus, and an understanding of place value and talking about digits and their values was not at the forefront. Undoubtedly, there were those that understood what was going on when using addition and subtraction algorithms at a young age, but for those of us who struggled there was a lack of conceptual understanding beyond the steps we took to solve.

One thing I require in all place value game play is the use of callouts so that students are continually focusing on the value of each digit in a number. Feel free to download this fun place value game that my students play--More, Less, or Trade?.  Hope your kids enjoy it as much as mine have over the years!

INDEPENDENT PRACTICE!
I provide LOTS of independent place value practice for my students during guided math rotations.  Workstation games and activities are cycled throughout the year.  Place value cube activities are one of their favorites.  I have included a link where you can learn about the use of place value cubes and download directions for making your own.  There are so many possibilities for using these little buggers!

Directions for Making Place Value Cubes

I hope you have found something that will be of use to you as you help your students develop a strong foundation.

BEFORE YOU HOP ALONG...

Feel free to sign up for the following giveaways!

The Number Line by Jeff Frykholm, Ph.D.

If you haven't already, read about using an open number line in my blog post referenced above.  Then enter to win!

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Place Value Cube Activities Pack

Enter to win some great place value cube activities that can be used in guided math groups and as workstations/centers.

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Now, HOP ALONG!!  Please take the time to visit Susan at The Math Spot!

A thank you also goes out to Brandi from The Research Based Classroom for organizing another AWESOME blog hop!

Smiles,

Makin' It Math! -- Mid-Month Linky -- {October 15}

Welcome! Thanks for stopping by for our brand-new monthly linky---Makin' It Math!  It's a linky dedicated solely to math made-its.  To learn more about the linky and how you can participate, click here!

I have been busy with several things...

Place Value Cubes

I have been making some new sets of place value cubes to start using with my kids this week.  They are so easy to make and are a fabulous tool for independent practice use while meeting with guided math groups. The best part is that you can customize them for your students' needs.  Feel free to download my free directions for making the cubes!  You can make up your own activities, or you may like the ones I have listed in my TpT store.

Low-Prep Halloween Math Games

I shared this made-it in our previous post, but this is my newest math made-it. I just finished putting a Halloween spin on some math games I have used in past years. These games are perfect for my kids' independent practice needs right now.  Thanks to Krista Wallden for her spookly clipart--so much FUN! You can check out the games in my TpT store, but you can also enter to win one of three two copies!  Good luck to you!



a Rafflecopter giveaway

Using Tens: Ten Frame Fact Cards

These ten frame fact cards really help some of my kids visualize the using ten strategy of addition before transitioning to the use of fact cards with just numbers.  Download a free copy here!

We hope you will consider joining us by linking up your math-made its!

Good day!

An InLinkz Link-up

Loved that Lesson Linky and Some Other Goodies...

This is the first time linking up with Meg from The Teacher Studio for Loved That Lesson--a wonderful linky opportunity to share those lessons we love.

One of the lessons I love to do with my kids at the beginning of each new school year relates to being mathematicians.  We always start by reading and defining the word mathematician, which is usually a new one for them.  Then we begin to think like mathematicians and ask ourselves what we do when we doing math.  This year my kids came up with a FANTABULOUS list of ideas given the simple prompt, We are MATHEMATICIANS! We...  Ideas were recorded on the SmartBoard and a door display was created to remain up all year long.  These can readily be seen for easy reference.

I was so pleased with their thinking!

We are mathematicians! We... 

• think.
• try different ways.
• have fun with math.
• work together.
• use tools.
• learn more every day.
• never give up.
• sometimes make mistakes.
• check and re-check.
• have really smart brains.
• are problem solvers.
• ask questions.
• need tons of education.
• study math.
• get stuck.
• use our brains.
• have good test scores. 

I also loved the construction paper self-portraits they made!

To read about more "loved" lessons, stop on over to The Teacher Studio!

I also wanted to share a few goodies that may be of interest to you...

Teaching Math by Hart TpT 1000 Followers Giveaway

Fly on over to Teaching Math By Hart for a wonderful giveaway opportunity and help Kim celebrate 1000 TpT followers! 

Low-Prep Halloween Math Games

I just finished putting a Halloween spin on some math games I have used in past years. These games are perfect for my kids' independent practice needs right now.  Thanks to Krista Wallden for her wonderful clipart--so FUN! You can check out the games in my TpT store, but you can also enter to win one of three two copies!  Good luck to you!

a Rafflecopter giveaway

New Linky on the Horizon!

Lastly, we have a new monthly linky on the horizon that will kick-off this week--Makin' It Math!  We hope it will bring along with it some wonderful math resources for many.  Stop back this Wednesday!

Wishing you the best for a wonderful week!