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Math Journaling: Why I Love It!



Welcome back for my final Math Monday of the summer!  If this is your first time stopping by, be sure to check out the previous posts in this series:




Now, if you didn't already know, Math Journaling is my JAM!  It may be my favorite thing that goes on my my classroom, no matter the grade level!  My goal for today is to provide you with big picture rationales and objectives, as well as explain some of the smaller details to help you implement math journaling in your own classrooms.

BIG PICTURE: Top 5 Reasons to Start Math Journals

1.    It doesn’t matter what math program you use in your school, because math journals are a wonderful addition to ANY math program from grades K-12. 


2.    It is an open-ended and therefore, naturally differentiated assessment


3.    It shifts the instructional focus from computation to problem solving and real-life application


4.    It creates a documented portfolio-like record of student growth and progress


5.    Teachers gain insight into children’s abilities, opinions, understandings, and misconceptions


6.    Provides students practice with putting their knowledge into writing (integrating curriculum!)

SELECTING THE RIGHT PROMPTS

The value of math journals is highly dependent upon the kinds of prompts you select.  After many failed attempts at trying to explain these types of prompts and discuss their pros and cons, I decided to put the information into a table for easier navigation. (Click on the image below to view as a PDF)



I use open-ended prompts in my own classroom.  The most important piece to remember is that each type of prompt will provide you with information.  You need to determine your instructional needs, and select the type of prompt that will best match them.

IMPLEMENTING & BUILDING INDEPENDENCE

This section is mostly to help those of you looking to implement open-ended, math journal prompts in your classroom. It is no secret that implementing this kind of work requires a lot of explicit instruction and modeling before we can expect our students to work independently. Much of this is because our students have not been exposed to this kind of mathematical thinking. Most students think of math as a series operations they must compute to find the correct answer to a number sentences or word problem. Initially, math journaling can be very uncomfortable for students who struggle to expand their definition of “math” or “math work.” Often, these mental barriers need to be broken down before the real thinking can even begin. 

Here are the highlights of how I implemented math journals in second grade this year. I started off the year doing the journal prompts as a whole group. I put the prompt on the top of chart paper or our smart board and allowed students to share their ideas while I wrote them down.  This way, my students could see a variety of ideas and understand that there were multiple "right answers," as this can often be difficult for them to understand.


From there, I had them jot a few of the ideas from the whole group discussion into their journals to document the discussion (pictures and/or words, as many aren't writing yet). I made sure to leave the chart paper/smart board document up to alleviate any anxieties that students may have had about trying this for the first time. I also wrote the different ideas in different colors so students could better identify their own idea (“mine was the red one!”) or that of their friend.

Also, I should mention that I start math journaling by reviewing things they may have learned from the year before. When I taught first grade, these prompts might include: "What do you know about they number 5?" "What do you know about patterns?" or "What do you know about shapes?" Sometimes using information they already know to introduce a new format of learning can prove VERY beneficial!


Once they tried this a few times and it seemed comfortable and confident in the process, we tried it individually, but all at the same time. This way I was still available to support them, as opposed to already running math groups and being unavailable. When they seemed to not need teacher support anymore (usually 3-5 times), that was when it became part of math centers. Students were then responsible for journaling independently while I taught a separate group of students in a small math group. An added bonus this year: Math Journaling kept my students engaged and quiet while I completed all of my beginning of the year math assessments!

One final plug for using  open-ended journal prompts:  The work is never finished.  Since there are an infinite number of answers, your fast finishers can never say "I'm Done!"  All of your students can work the entire time at their level, and you never have to worry about creating additional work!

Below are links to my series of Common Core Aligned Math Journal Prompts below if you are looking for a place to get started, or to enhance what is already happening in your classroom.  They are currently available for grades K-4!  






Thanks for stopping by!

Teaching Place Value


It's Monday again, so it's time to talk math!  If you have missed the last two posts in this series, be sure to check them out:


I am excited to explore place value this week!  At it's core, place value is understanding groups of 10.  This is a big jump for many students.  We are asking them to shift from counting with one-to-one correspondence to counting groups.  We are asking them to understand that ten ones are the same as one group of ten.  That's a HUGE jump!  

Another huge jump with understanding place value is that students need to shift from understanding the digits 0-9 representing a specific number to the idea that depending on their position within a number, they can can represent different amounts (e.g. the "8" in 81 has a different value than the "8" in 18.)



CREATE A MEANINGFUL INTRODUCTION:

One of my favorite introductions to the regrouping process is an activity from Kathy Richardson called Zib!  It's AMAZING and really helps reinforce the counting and regrouping process.  Here's the gist of how it works:
  1. Explain to students that you will be making groups of four.  The only thing is, you can't say the word "FOUR."  You can allow students to make up a new word that means "four," or if you are like me, make it easy on yourself and just call it Zib! (read: I can't ever remember what they name it, and later I become completely tongue-tied and ruin the entire lesson, so it's better that I just pick one name and stick with it!)
  2. Give students some unifix cubes and piece of paper with a clear line dividing the paper in two (or if you're really fancy, make each side a different color- I swear it helps!) 
  3. Tell students that each time you say "plus one," they should place one unifix cube on the right side of their board (or name the color if you've created a two-color board).
  4. With each new unified cube, the students must tell you how many ones they have and how many zibs (e.g. I have zero zibs and three ones).  Once they reach four cubes, the students must put their unifix cubes together to create one zib.  Then, place that zib on the left side of their board.  They would name this one zib, zero ones.
  5. Have students continue with this pattern until they reach 3 zibs and 3 ones (no need to introduce the hundreds place just yet!)  

In your next lesson you can revisit Zibs by subtracting one each time.  This time start with 3 zibs and 3 ones.  Students will likely be able to remove one at a time until there are no more single cubes left on the right side of the board.  The next time you say "subtract one," watch watch for what your students do.  Some will instinctively break apart a zib into four cubes and place them on the ones side.  However, some students might break off a single cube from an existing zib and leave it there.  This is where you will need to check in:  "If you take one away from a zib, is it still a zib?"  Help students recognize that only zibs are allowed on the left side of the board, and see if they can figure out what to do with the remaining three cubes.  Remember to have your students name the number of zibs and ones every time!

Once your students become familiar with adding and subtracting one cube at a time, venture into adding and subtracting larger digits.  For more ideas (and how to regroup beyond two places) see Kathy Richardson's Developing Number Concepts Book 3!  She's a genius!


REINFORCING WITH TEN FRAMES

I am determined to find as many ways to incorporate ten-frames in my classroom as possible!  Here are a few ways I've used them in the past, but I would love to hear from you how you've used them in your classroom:

1.  Taking Attendance (or lunch count)

A brilliant teacher-friend of mine showed me this idea.  The "IN/OUT" board in my classroom is one place I found to incorporate ten-frames.  Every morning when students walk in, they take their name magnet from "AT HOME" and move it to our "AT SCHOOL."  The ten frame structure helps us instantly recognize how many students are in school that day (and helps me keep track of who is where during the day!)



2.   Tracking Days In School

I done this in two ways (and sometimes both at the same time).  The first is using the traditional place value pocket chart.  I use ten frames instead of straws.  I find this naturally helps students recognize how many more days are needed to create another group of ten.



I also like to represent all 180 days with ten frames on one poster.  This helps students count by tens to see how many days we have been in school, and how many we have left.  It also helps with our countdown at the end of the year!


3.  Ten Frame Playing Cards

A few years ago I switched out all of my playing cards with ten-frame cards.  They are a great way to constantly reinforce groups of ten!  I use these to play a variety of games (some listed below).  You can grab a FREE set by clicking [HERE].



FAVORITE TOOLS FOR THE CLASSROOM

Ten Frame Dice
These are one of my favorite new products on the market.  I purchased mine from Lakeshore Learning.  They are great for reinforcing tens and ones, as well as developing skills in counting, comparing, addition and subtraction!


Rek-en-Reks
I LOVE Rek-en-Reks!  I especially love how they support students compose and decompose numbers 11-20 (or ten and "some more").  Like ten-frame cards, Rek-en-Reks visually cue students into recognizing groups of 5 and 10.  Student versions can be purchased, or easily made with some cardboard, pipe cleaners and plastic beads.


Ten Frame & Hundred Chart Stamps
I wasn't sure about these stamps at first (I'm always a skeptic when I pay for my classroom out of pocket!)  I bought ONE set to see if it would support a few students who struggle with fine motor and visual/spatial skills, and was immediately impressed. Those students were using them to organize their thinking and show their work in their math journals.  I had to buy a few more, and made them readily available to all of my students during math centers.


Place Value Dice
I have found SO MANY uses for these dice!  Whether it's teaching standard/written/expanded form, comparing large numbers, or multi-digit addition and subtraction, these are my go-to tool! I love that there are six of each die too, so it's perfect for small group instruction!



FAVORITE PLACE VALUE CENTERS

Race to 50 & Race to 500
Race to 50- This game introduces the idea of gathering "ones" and exchanging them for "tens" until you reach 50 (or 5 "tens).  It is a great, hands-on approach to help students see a ten frame fill up, and knowing that means they have completed one group of "ten."  You can find this game [HERE]


Race to 500- This game is an extension of Race to 50.  It allows your students to explore place value further, and instead of trading "ones" for "tens," they exerience trading "tens" for "hundreds." You can find this game [HERE]

Standard/Written/Expanded Form
Fun dice make even the most mundane task fun!  My students love this center, and really get to develop an understanding of the relationship between standard form, expanded form and written form.  I originally included a word bank at the top for my English Language Learners, but quickly realized that it would benefit my entire class.  You can grab this FREEBIE [HERE].


Make it Big
This game strengthens the understanding of place value by forcing students to understanding that a digit's value changes depending on its place.  Each student gets to flip 3 cards, but ONE at a time.  With each flip, they must decide whether they want to place that digit in the hundreds place, tens place, or ones place (and they cannot change it once it's played!)  Students will realize that if they first draw a two, it is best to probably put that digit in the "ones" place, as it will hold little value in the "hundreds" place.  It is a mix of skill and luck, and one of my favorite 2-player games for place value.

You can find the 3-Digit version [HERE] and the 2-Digit version [HERE]


Roll, Build, & Write
I love this center because it asks students to build their own numbers, and then represent those numbers in expanded form and standard form.  It is a great way to reinforce the connection between the digit and its value!

You can find the 3-Digit version [HERE] and the 2-Digit version [HERE]


Ten More
For first graders this game works as a great introduction to adding ten to a number.  For my second graders struggling to mentally add 10 to any number, this game is a great intervention!  Simply add the two dice (5 + 3 = 8) and that is how many "tens" you have.  Then add ten more! (80 + 10 = 90)  The student would then cover up any 90 on the board with their counter.  The first to 5 in a row wins!

You can find the 0-120 version [HERE] and the 0-100 version [HERE]


Missing Pieces
Just take a 100 or 120 chart and remove a good chunk of the numbers (differentiate by how many in each row/column).  It helps encourage students to recognize patterns within the chart to fill in the missing pieces.  In the photo below, I used a 0-119 chart, which begins at the bottom right and works its way upward.  I personally like this version better because the numbers go up, as they increase.  However, I know that many curriculums require the use of the traditional 100 chart, so I have made both available!

You can find the 0-119 and 1-120 version [HERE] or the 0-99 and 1-100 version [HERE]


Hundred Chart Puzzles
This one couldn't be easier to make on your own!  Just print out a 100 chart and cut it up into pieces (differentiate by how small your pieces are, and how many columns and rows they cover).  It's a great way to let students manipulate the 100 chart and recognize patterns!


ONE More/Less & TEN More/Less
I love these little pieces of a hundred chart!  This is a great tool to support number sense and understanding of place value.  Being able to identify the "neighbors" of any number is an important skill and this is a great way to visually represent the concept!

You can find the 0-120 version [HERE] and the 0-100 version [HERE]


Base Ten Cards
I love using these cards to play memory or go fish!  The best part is that it's naturally self-correcting!  If there are any mis-matches at the end of the game, students have to back through their pairs to identify where the misunderstanding took place!

You can find the 3-Digit version [HERE] and the 2-Digit version [HERE]


Roll Ten More/Ten Less
My math specialist at my previous school introduced me to this idea!  Roll a die and let that determine how many ones place of your teen number.  In the photo below, I rolled a 9, so my number became 19.  Students can then practice adding and subtracting groups of ten from that number!  (Again, fun dice can make any activity a blast!)

You can find this game [HERE] and [HERE]



I have/Who Has
Looking for a game for a small group?  I Have/Who Has is always a great one, because everyone has to constantly be engaged for it to work!  There are NO taking turns.  You have to be alert enough to realize when it's your turn!  Win/Win for the teacher!  Like the Base-Ten Cards above, this game is naturally self-correcting... another WIN!



You can find the 3-Digit version [HERE] and the 2-Digit version [HERE]

RESOURCES

I have bundled up these games and activities into 2 resources for you!  One focuses on numbers 0-100, while the other moves into 3-Digit numbers and works with a 1-120 chart.  You can grab them by clicking on the images below!




These are some of my favorite tools and centers to teach place value, but I would love to hear from YOU!  What are some of your favorite ways to teach place value?

Thank you for stopping by!  Don't forget to swing by next week when we take a look at Math Journals!

Math Word Walls


Do you have a Math Word Wall in your classroom?  Have you thought about having one, but not sure where to begin?  Well, today I'm going to show you how I have used Math Word Walls in my classroom, and some tips for how to make them an effective reference tool in your classroom!

I LOVE my math word wall now, but it hasn't always been that way.  A few years ago I tore down my math wall.  Hate is a strong word, so I will say that I thoroughly disliked it!  Why?  Well, it's a bit embarrassing.  My old math word wall cards were adorable!  They used really cute clip art and fun fonts.  However, over time I cam to the realization that I only had them up because I liked them (insert gasp and dreaded feeling of being a horrible teacher!)  To my students, these cards were probably very distracting and were not helping them learn and remember the vocabulary.

I started working on a new math wall with my student's needs in the front of my mind.  I teach in an inclusion setting, with a high population of ELLs, so I really wanted to make the vocabulary as accessible as possible!

This was my Math Word Wall this past year in second grade:


It has accomplished all of my Math Word Wall goals!
  • Clean and Easy-To-Read Lettering
  • Include Visual aides
  • Colorful (if it's going to be up on my wall all year, it needs to be pleasing to the eye!)
  • Concise definitions when needed
  • Allow the words themselves to carry a visual when possible (see Fractions, Even, Odd, Equation...)


I now love my math wall and it has become a great focus wall and point of reference for my students.    Mind you, this is how it looked at the end of the year.  It looked nothing like this at the beginning!

Just like our ELA word wall, we start the year off empty (it doesn't make sense to put up a bunch of words that mean nothing to them yet!)  Even though I would love our classroom to look finished on the first day of school, it's important to introduce things slowly, and give students ownership over the information that goes up in their classroom.


Each time we came across a new term in a lesson, I pulled out a new math card.  Since my math word wall is on a magnetic white board, I use magnetic tape (or cut up the magnetic business card stickers from Staples) to hold them up.  This also means that I place them on our Meeting Area easel during the introduction, and later move them to their permanent place on the Math Word Wall.

I like to keep my words organized, and this year I decided to organize them by Common Core strand. This created a natural "categorization" to help my students easily navigate the wall.  I tried labeling them for you in the photo above (the strands aren't actually present on my math wall).


I have taught 3 different grade levels in the past 3 years, so I created a new Math Word Wall with each move to include all of the necessary Common Core vocabulary for Grades 1-3.  After some requests, I also made sets for Kindergarten and 4th Grade (Don't worry 5th Grade teachers! Your are in the works and should be posted soon!) 

You can grab a set for yourself [HERE] or by clicking on the image below:


This past year I noticed that many of my students were getting up during math time to go look at the math wall.  Some would bring their journals and stand in front of it, checking for understanding, or just looking for proper spelling.  Then an idea hit me.  Why not make individual cards for students?


The idea was a hit with my kiddos. The students who wanted them kept them at their table spots, or in their math folders.  They decided not to include EVERY single term, but only the cards that they had trouble remembering, or wanted to practice.  You can find these Individual Math Word Walls [HERE] or by clicking on the image below:


I am now obsessed with BOTH versions of these word walls, and am so excited to finally be sharing them with you!  Be sure to come by next time (after July 4th) to take a closer look at teaching Place Value! Thanks for stopping by!