Sunday, May 31, 2015

We are LIVE!

Our new site is live!  Visit us at www.guided-math-adventures.com, or same ole' URL!  We have a new look, but it's the same blog--just simpler and easy to navigate!


If you follow us with Google Friends Connect or google+, you will want to follow us on Facebook to stay current with our posts.

AND...

We have just announced our summer book study!  

Saturday, May 30, 2015

Coming Soon: A New Look!

Coming Soon!

We will have a brand-new look for our blog coming very soon! We will be located at the same place---www.guided-math-adventures.com but will be using WordPress instead of Blogger.

Below is a sneak peak of our simplified and easy to navigate site. Can't wait to get everything switched over!
If you are a follower with google+ or google FriendsConnect, you will want to follow us on facebook to stay current with our posts!


Thanks to all of our adventurers!

Monday, May 11, 2015

Math Playground:Math & Logic Games for Everyone!

Just a quick post today to share a site my kids have come to LOVE---Math Playground!  If you have seen or used this site before, you already know how wonderful it is. If you haven't, you will want to run on over to the Math Playground!

http://www.mathplayground.com/index.html

Here are just a FEW of my kids' favorites...

Number Bonds

Number Bonds is available in Make 10, 20, 30, and 40 versions!  We all know how important it is for students to have automaticity with making 10, and being fast is the name of this game.  I'm sure you will love playing this one as much as your kids--I do!



Kitten Match

Kitten Match allows kids to customize their kitten and play against three other kittens.  A sum flashes in the middle and the kids need to find two addends to equal the sum.  Fun, and it pays to be fast!



Cat Around Africa

Cat Around Africa is found in the Logic Games section of Math Playground.  Addicting!



Kangaroo Hop

Kangaroo Hop is a basic geometric shape/solid identification game.  It's a race for the finish!



Math Playground has games for as high as 7th grade, spanning a variety of concepts.  Your kids can pick and choose games to meet their needs.  I talk to my kids about picking a "good-fit" game, just like a good-fit book, because some of my kids want to pick the same game each time, and it may or may not be a game that is appropriate for their needs.  As with any game site, some games are better than others, but I am sure you will finds some great ones to introduce to your kids.

ALSO---Look for a post in the near future about our summer book study!  You will get a chance to vote for your favorite, and we will choose the book that gets the most votes.  Stop back soon!

All the best--

Tuesday, April 14, 2015

Makin' It Math Mid-Month Linky -- April

Welcome to this month's Makin' It Math mid-month linky!  If you are a blogger, feel free to join us by adding your link at the end of this post.  Check out the details here!

http://www.guided-math-adventures.com/p/makin-it-math-mid-month-linky.html
This month, I put together two sets of task cards for measurement and geometry.  I also updated my money task cards to include QR Codes. AND since I usually include at least one freebie in my make-it posts, I will be giving away three sets! If your name is drawn, you pick the set you like best!  Just enter the rafflecopter to win...


https://www.teacherspayteachers.com/Product/2nd-Grade-Measurement-Task-Cards-Measure-It-1796703


https://www.teacherspayteachers.com/Product/2nd-Grade-Geometry-Task-Cards-2-D-Shape-Task-Cards-Polygons-1807055


https://www.teacherspayteachers.com/Product/Money-Task-Cards-Show-Me-the-Money-Differentiated-Math-Center-Cards-522227

a Rafflecopter giveaway

We hope you will share your made-its by linking up below!

All the best--

Monday, April 6, 2015

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!

a Rafflecopter giveaway
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!

http://www.guided-math-adventures.com/2015/04/book-review-fluency-through-flexibility.html

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




Wednesday, April 1, 2015

Book Review: Fluency Through Flexibility: How to Build Number Sense (Numbers 0-20)

Good day from sunny Illinois! What wonderful weather we are having here for our spring break!

Today I come to you with a book review of an outstanding teacher resource written by one of my fellow math bloggers, Christina Tondevold, The Recovering Traditionalist.  Her new book is titled, Fluency Through Flexibility: How to Build Number Sense (Numbers 0-20), and it is perfect for new teachers and seasoned teachers alike.


Thank you to Christina for sending me a copy of her book and some wonderful materials to accompany the activities included.  Most of all, thanks to Christina for making such a positive contribution to our profession.

In reading the introduction, I especially appreciated the background Christina provides for what fluency means when it comes to students learning addition facts.  Fluency involves:

  • Efficiency - a speedy way to get the answer
  • Accuracy - getting the right answer
  • Flexibility - having another way to approach a problem when it can't be figured out

Christina goes on to stress the importance of flexibility.  If students are not yet able to recall a fact, they need to use what they do know to help make the problem easier.  This is something my second graders are able to do, yet it needs to be instilled in children through much exploration. An example of flexibility would be a student who cannot yet recall the sum of 8 + 9 but can use his/her current knowledge of number to create relationships between numbers.  He/she might choose to:

  • use doubles, "I know 8 + 8. That's 16.  9 is just one more than 8, so 8 + 9 is 17."
  • use tens, "Well, one more than 9 is ten, so I can move one from 8 to make a ten.  Then 10 + 7 is 17."
  • create landmark/benchmark or "friendly" addends, "I can think 8 + 10, and that's 18.  18 - 1 = 17."

When a student has flexibility, he/she is able to think in this way.  Without flexibility, Christina stresses, students will "revert back to counting on fingers."

Number sense is SO much more than simply memorizing basic facts.  This book will help you provide valuable experience for your students to explore numbers and discover relationships that lie within.  Activities are organized into four areas, and these areas coincide with what students who have good number sense understand.

They understand:
  • Spacial relationships - recognizing how many without counting (subitizing)
  • One and two more, one and two less - knowing which numbers are one and two less or more than a given number
  • Benchmark of 5 and 10 - knowing how numbers relate to 5 and 10
  • Part-Part-Whole - seeing numbers as being made up of two or more parts

Christina provides a detailed description of each of the above areas in her introduction, and goes on to give suggestions for using the activities included.

Various tools are also used with the activities and some can be downloaded or purchased on Christina's website, Mathematically Minded. Tools include subitizing cards, number paths, and the MathRack (rekenrek). It would be well worth your time to investigate Christina's rationale for using a number path vs. a number line for kindergarten and first grade students.  

What do I like about this book?
  • Christina's introduction that provides sound rationale for using the activities included
  • the variety of activities for use with students at different stages of development
  • suggestion for what to "Look For" when observing students work within an activity
  • suggestions for "Reuse" depending on how students are developing
  • the adaptations/extensions that can be made to activities based on student need 

How will I use this book? As a teacher who uses guided math, I can pull various activities from this book to use in small guided groups based on need, and the activities can also be done independently during station work.  I did not have Christina's book at the beginning of the year, so it will be a wonderful added resource as I help my new second graders develop fluency through flexibility.

What have I tried?  My second graders explored one of the part-part-whole activities, Number Search (Numbers 11 to 20).  I presented the activity one way with two game boards (one for each player) in plastic sleeves using dry erase markers.  Students wrote a sum in the center of the game board and each took turns circling addends to add to the sum while saying the combination aloud, "10 plus 3 equals 13."  The player with the most combinations circled was the winner.  Natural questions arose.  "Can we overlap?", "What about the other person who can see what you just circled?", "If the sum is 19, you can't hardly circle anything.", etc.  Their questions and suggestions led to some variations in game play that they created.  They tried using one game board with two colors of markers, and they definitely wanted to overlap.  Sums that yielded fewer combinations became games where three addends could be circled. The kids loved it! Number Search is also an activity I will be sending with the kids for at-home practice along with their math tool bags.


Do you like what you've read? Well, you can enter to win a copy of Fluency Through Flexibility, a MathRack, and Savvy Subitizing Cards--all donated by the author!  How do you earn the most entries into this giveaway? Share your thoughts about Christina's new book in a comment--What sparked your interest?, What do you like?, How could you use it?, etc.  Good luck!


a Rafflecopter giveaway
Keep in touch with Christina, her publications/materials, and professional development opportunities on her blog and website:

The Recovering Traditionalist
Mathematically Minded

Also--don't miss Christina's free webinar this coming Wednesday, April 8th.  Click here to register!

AND, in the spirit of giving, the Easter Bunny has arrived early with a FREEBIE for you! Feel free to download this fun jellybean math activity Courtney created to use with her kids this year--Jellybean Taste-Off: Jellybean Math Fun!  Simply click the pic to download!

https://drive.google.com/file/d/0B_1w1VapXOL_VWd3NkpuUEF2U0U/view?usp=sharing

Happy Easter to you and yours!




Saturday, March 14, 2015

Makin' it Math Mid-Month Linky -- March

Good day!  Thanks for stopping by for our Makin' it Math mid-month linky!
http://www.guided-math-adventures.com/p/makin-it-math-mid-month-linky.html

Wanted to share a few things that have been going on in the classroom and a few made-it to go with them...

First, we just had open house this past week and I asked my kids to reflect on their learning thus far this year with a "Glow & Grow". This is something that can be done any time during the school year.  Students simply write something they are able to do well after all of their hard work and help, and they write about something with continued effort is an area they will "grow"/improve. Loved to see some of the students' reflections about math!  Feel free to download a copy to use with your students.


Second, we explored fractions with pizzas this week.  I purchased Amy Lemons' Pizza Fractions and adapted it for my students.  We used all of the toppings and pizza template divided into fourths and added four toppings to cover one fourth, one half, three fourths, and the whole pizza.  Students began by choosing a topping to use on the whole.  Then a topping to use only on a fourth, on half, and finally three fourths.  Afterward, they completed the sheet shown below.  This really tested their understanding of equal-sized shares of a whole and how to represent fractions by adding toppings accordingly.  Not to mention, it was fun!  You can use the sheet I created with other pizza fraction activities, so snag it if you like.



Lastly, we explored fractions with foods (faux foods) this week in guided math groups.  Students are developing a solid understanding of fractions at the second grade level and LOVED using the foods.  I shared this made-it in a previous post, but I decided to share it again here.  So many possibilities for using these gems, so you will want to download them!

https://drive.google.com/file/d/0B_1w1VapXOL_Y0V6UGRaSmRoWU0/view?usp=sharing

Hope you find this month's made-it useful!  Have a blog and want to share your math-made its in a post? We would love to have you link up below!

All the best for the coming week--




Saturday, March 7, 2015

2nd Grade Masterpieces: Art with Fractions

Happy Saturday! I just wanted to share something my kids did this week that turned out fabulously.  Even though it was a last minute idea, the kids created some wonderful masterpieces, learned about fractions, and had a lot of fun.  So easy!

Every year we explore fractions by folding wholes into parts (halves, thirds, and fourths) and talk about how each part represents a share of the whole, begin to use the language of fractions (halves, thirds, and fourths), and learn that two halves make up one whole (thirds and fourths as well).  I decided to do this with my kids on Thursday and go a step further and use their folded wholes to create a piece of art.  Below are directions, if you are interested in trying this with your students... 

2nd Grade Fraction Masterpieces


Materials Needed:

  • 4.5" square pieces of black construction paper, 4 for each student
  • oil pastels
  • 11" OR 11.5" square pieces of black paper (for mounting squares--depending on how much space you ant between and bordering the folded squares.  I used 11" square pieces for mounting.

Step-by-Step Directions:

  1. Give each student four, 4.5" square black pieces of construction paper.  Have students set one sheet on the corner of their desks.  This piece will not get folded and represents a whole that has not been divided into parts.
  2. Have students fold the next piece from corner to corner (in half).  They may fold it to create two rectangular parts or two triangular parts.  Talks about the number of parts show after folding and opening the paper.  This piece represents a whole divided into two parts, into halves.
  3. Have students fold the next piece to create three parts.  You may want to mark this piece for students where the 1/3 fold will be and demonstrate folding.  Talk about the number of parts shown after folding and opening the paper.  This piece represents a whole divided into three parts, into thirds.
  4. Finally, have students fold the last piece to create four parts. They may fold it to create four square parts, four rectangular parts, or four triangular parts.  Talk about the number of parts shown after folding and opening the paper. This piece represents a whole divided into four parts, into fourths.
  5. Then students use the fold lines to help guide them in coloring the parts of each piece different colors.  Oils pastels work best because they do not smear like chalk pastels and the colors really pop on black paper. 

Mounting:

  • Fold each 11" or 11.5" square piece of black paper into fourths.  
  • Use double stick tape to mount each student's four pieces to the black paper, starting with the unfolded whole and ending with the whole divided into fourths.
  • The fold lines will help guide you in mounting the squares an equal distance apart (from the fold lines).

Display! 


AND, you will have engaged your students in an understanding of the following Common Core Standard for Mathematics:
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.

I can also see this same project done with wholes divided into more parts in addition to those shown (sixths and eighths).  If you decide to try this project, I would love to hear how it turned out and what your kids thought of the experience.

Can't wait for the kids to surprise their parents with their masterpieces at open house this coming week and listen to what they tell their parents. Anticipating a lot of wonderful math talk!

Enjoy the rest of your weekend and the week ahead---





Tuesday, March 3, 2015

Q&A with Sherry Parrish!

We are thrilled to have a wonderful Q&A for you today!  Sherry Parrish, the author of Number Talks, graciously agreed to do a question and answer session with our followers.  We hope you will take the time to absorb her thoughts and suggestion for using Number Talks in your classroom/building.  If you are not familiar with Sherry's outstanding book, or have just happened upon our blog today, feel free to visit our Number Talks Book Study Archive. Many thanks go out to Sherry!


What suggestions do you have for the implementation of number talks as a building?  Steps for beginning? Unforeseen obstacles? General suggestions?
One key element that determines whether or not the implementation of Number Talks is successful or not is the intentionality and purposefulness from the school’s administration. If the administration believes in the value and impact Number Talks can have upon their students and they make sure there are support systems in place, then I find the implementation of Number Talks is successful.  Placing an emphasis on Number Talks during grade-level meetings, vertical teaming, etc., helps build capacity in this area.  Share successes during faculty meetings, grade-level teams, etc.

I cannot emphasize enough the importance of starting small to allow students and teachers an opportunity to establish protocols for respectful conversations and the expectation that mathematics should make sense.  Beginning with dot cards for all grade levels, basic facts before moving into higher computation, etc., allows the routines of a Number Talk to be established.

It is also helpful to frame computation problems in a brief context so that the numbers can be anchored to specific situations.  For example, instead of posting 13 – 7 as a bare problem, we could frame it in a story such as I want to read 13 pages each night.  I have read 7 pages.  How many more pages do I need to read?  The context supports the reasoning and can also influence specific strategies.

Another critical area that is often overlooked is the importance of educating our parents and providing support for them as they look at mathematics from a different framework.  Invite parents to visit your classrooms or host a grade-level open house with a Number Talk demonstration.  Send out a podcast of a classroom Number Talk or tweet a link to a video clip with student strategies.  I have found that when parents see that their children can arrive at an answer faster than they can, they are sold!

Finally, the biggest misunderstanding I see with Number Talks is that educators believe they must directly teach the strategies in the Number Talk book. While my book lists numerous strategies for each operation, the strategies are there to provide a support for teachers so they can anticipate possible ideas that will arise during the Number Talk.  A Number Talk is designed to use purposeful problems that allow students to use numerical relationship to “invent” their own strategies. In fact, the strategies in my book were ones I learned from my students and not ones I taught them!

Do you ever use number talks with missing addends?
While you certainly could do this, I think a much better way to approach this is through subtraction.  If students understand that subtraction is about finding the distance between 2 quantities, then you typically see them add up to subtract.  For example, if my Number Talk problem was 50 – 26 and a student added up to find the difference, I could record this as 26 + ____ = 50.  This is a perfect way to address our standard that focuses on students using the relationship between operations.

I teach fifth grade, and I have not used number talks.  None of my colleagues before me have used number talks.  Where do I begin?
The higher up we go in grade levels, the stronger the likelihood of students saying, “no thank you,” to mathematics.  Many students enter the upper grades without confidence or reasoning; often their only access is memorized procedures that they do not understand.  For this reason, I suggest beginning with dot images that are found in the K-2 section of my book.  While your purposes for using these are not the same as a K-2 teacher, there are many benefits for using these as a starting point in the upper grades.
  • It is difficult to be threatened by a collection of dots! Students begin to relax and realize that mathematics is about making sense and reasoning.  Confidence begins to grow when students are successful.
  • Students begin to see there are multiple ways to arrive at the same answer.  This is such an important disposition to build with students, especially with those that have had difficulty memorizing one way.
  • Starting with something as simple as a dot card allows the teacher to begin building norms for productive discourse. 
The next transition in your Number Talks is to move into Talks that focus on basic facts.  I repeatedly hear from teachers all over the country that students don’t know their basic facts; yet, I find that we often resort to repeating the same skill and drill instruction with timed test while expecting different results.  By using either isolated “facts” or a Number Talk string around facts, we can provide a safe place to begin computation conversations while building strategies.  The same strategies that work for fact acquisition also work for larger computation problems - so time spent here is not wasted.

What projects/publications, if any, do you have in the works?
I am currently working on a new Number Talk book that focuses on fractions, decimals, and percents.  The manuscript is already complete, and we will begin videotaping in classrooms late March and into April. During the field testing of the fraction Number Talk strings, it has been rewarding to see how students are developing strong fractional reasoning.  The book and DVD should be released in spring, 2016, during the NCTM/NCSM conference in San Francisco.  

Thanks so much for stopping by today, and thanks again to Sherry Parrish!

All the best--

  

Sunday, March 1, 2015

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?" GraphingBoth are great for use as guided math workstations/centers!


https://drive.google.com/file/d/0B_1w1VapXOL_ckFqcGppbGkwVFk/view?usp=sharing

https://drive.google.com/file/d/0B_1w1VapXOL_SGZwMHZEdHp2RWs/view?usp=sharing
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...


Saturday, February 21, 2015

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!


https://drive.google.com/file/d/0B_1w1VapXOL_Z18xQjh2N2VuVlU/view?usp=sharing

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.

Four Leaf Fractions Board Game & Spinner


Flying High with Fractions Board Games & Spinners

https://docs.google.com/file/d/0B_1w1VapXOL_aERCRkhGT3ZYVVE/edit

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!

https://drive.google.com/file/d/0B_1w1VapXOL_cDlvY29GREdEWmM/view?usp=sharing

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!

Button

Happy hopping---