Wednesday, February 15, 2012

Differentiating Math!!!


The beauty of differentiating math instruction is that there is not one single strategy or approach to meeting the needs of your students. I've had several e-mails asking how I teach and differentiate math in my classroom- some specifically relating to how I use the Investigations series. To be completely honest with y'all, I rarely open up an Investigations teaching manual and don't use Investigations student workbooks {we had the choice to order them or not}. I know some school districts make you use your adopted math series/workbooks on a daily basis, but I am fortunate enough to have permission to supplement like crazy to teach the standards. With this being said, there are many fabulous games/ anchor activities my students love playing from Investigations {Five in a Row, Counters in a Cup, Roll and Record, etc} and some of the units have awesome ideas that align to our standards- geometry and measurement are two of my favorites! I supplement my lessons with these, but I'm not a textbook teacher. I truly enjoy finding resources from all over the place & of course, making my own!!! I'm also blessed to have the support and guidance of an amazing math coach who goes out of her way to provide my grade level with awesome lesson ideas!!

One of the most recent standards I taught was how to identify what is 1 more/less and 10 more/less than any given number up to 100. The first thing I did before teaching this skill was preassess to find the basic level of understanding for each individual child. Let me tell you, I LOVE some clicker assessments!! It amazes me how you get instant data/graphs on individual students, as well as your entire class. However, the old fashion paper and pencil way also works, too!! Once I have the preassessment results, I map out my leveled groups. I typically have 3 leveled groups.

Tier 1 (needs a lot of support/remediation with grade level standard): involves hands-on, scaffolded tasks, manipulatives are used so they can "see" what they are doing, a parapro or teacher heavily facilitates this group.

Tier 2 (progressing towards the grade level standard): hands-on task, mostly independent with some teacher facilitation, manipulatives offered if needed, involves some higher order thinking questions or activities.   

 Tier 3 (mastered grade level standard and needs a challenge): hands-on task that involves taking the standard to a higher level of thinking, often involves creating, designing, comparing/contrasting, investigating, sorting, etc

I think it's important to stay away from giving the challenge group *Tier 3* more work, but rather work that engages them to really "think deep". I personally believe that the activity in this group should also center around the grade level standard. I'm constantly referring to Bloom's Taxonomy when planning out  activities for these smarties.  

My {Start to Finish} Math Lesson Breakdown
Day 3 of teaching -1, +1, -10, +10

Calendar/Math Journal
After calendar{I use a simple one on my SMARTboard}, I go right into math journal time. I love it when a prompt aligns to the standard I am teaching that day, but I also use ones that review previously taught standards just as much in order to keep skills fresh. 

Below is the math journal prompt I used for this lesson- Day 3~ Number Neighbors. This lil' prompt alone is differentiated because students pick their own number and show/explain their own thinking to figuring out the problem. I have used prompts at the beginning and end of a lesson. I prefer to use them at the beginning right now. They are a nice problem solving warm up!! I give my kiddos about 5-10 minutes to work out the problem & then we share our work using our document camera that projects the  journals on the SMARTboard.
 
You can click the picture to download the number neighbor journal prompt. If you like it, I sell sets of these cut/paste prompts in my TpT store! Check out what my sweet customers are saying about them!! I almost have a complete year of prompts...spring ones will be posted soon!! Most of them contain more prompts on a page, but these were big ones!! 

**math journal time saving tip**
Cut all of the prompts out, paper clip them together, and store in a big ziploc bag. Put a prompt on your students' desk each morning for them to glue into their math journal {spiral notebook) as a part of the morning routine. When it is time for math, the kids open their math journal & are ready to problem solve. Saves tons of time!! 

Whole Group
For this particular lesson, the math journal prompt lead us into a great discussion about the essential question shown below. The essential question is just the standard in a question format. It was the first slide in my whole group SMARTboard activity. 99.9% of the time I begin a lesson by looking at the EQ, highlighting the important vocabulary, and making sure my students know the standard we are working on- takes usually no more than 5 minutes.

Then I get my students "hooked" with a fun & engaging activity. The purpose of this is to get them super excited about what we are learning!! For this lesson, I had the students put together their very own 99's chart puzzle {You could also use a 100's chart.}. I differentiated this activity by making the puzzles range from 4-15 pieces. I also whited out numbers to make it more challenging for some!! Yes, I made 22 different puzzles for this lesson, but it was so much fun!!! I put each puzzle in a big ziploc bag {labeled with students' names} with a white piece of paper inside for them to glue the puzzle on. If you wanted to simplify this, you could pair your kids up to put a puzzle together. The reason I wanted each child to create one was so they could use it as their tool for the rest of the lesson. However, I encouraged students to collaborate and help each other put the puzzles together. They also had completed 99's charts available to use as a guide. You could really see who "mentally" knew how to put together a chart and who needed support, as well as who was using the number neighbor standard to help them and who was not. Hello, formative assessment!!

Here's the slide where I introduced the "hook activity"!
Working together to help put their puzzles together!!
Completed 99's chart puzzle!!! YEAH!!

After everyone had their chart put together, we discussed the patterns we noticed in the 99's chart (really focusing on -1, +1, -10, and +10 patterns). Then we played a little game to review the skill as a whole class. I made this pitiful SMARTboard lesson. I have NO talent what.so.ever making SB's cute. BUT it focused on the standard & that's what matters the most, right?!?! To play the game the students had to press the number generator to get a random number, find that number on the number grid and represent it with  base ten blocks on the place value mat. Then they rolled the number neighbor die {-1, +1, +10, -10} and changed the number to show what they rolled on the chart & with the base tens. While we were working on the SMARTboard, the kids were also at their desks using base tens/place value mats, a 99's chart, and marker boards to show their work. That way everyone was interacting with the game whether they are at the board or not. During this time, we would have lots of "think, pair, share" time to explain our thinking, restate the standard, answer the eq, etc. in mixed ability groups {my desks are arranged in groups of 4-5}.

After we played the game for 25 minutes or so, I showed the students the results from our clicker preassessment and formative clicker assessment from the day before this lesson (same test to measure growth). 
Having students be a part of seeing their growth and knowing where they need to improve is HUGE at my school!! What's funny is my kids love seeing these graphs!!

Differentiated Groups
Now it's time to get into our differentiated groups! The last slide in my SMARTboard lesson explained the groups' tasks. As you can see, I use different colored stars to give each group a name.

I put a colored star sticker on each child's desk so they quickly know what group they're in. It's super easy to say, "purple stars over here", "green stars at the front table", etc. Star colors change all the time ( every 2-3 days based on progress = flexible grouping). My students know they are in a group that is going to help them understand the standard better.

Here's what my loves were doing in each group....

Tier 1 {green stars}- This group continues to play the SMARTboard game with me at the front table using base ten blocks/place value mat and marker boards to show their work. We focus on -1 and +1 first and then practice -10 and +10.

Tier 2 {purple stars}- I noticed this group of students had mastered identifying what was -1 and +1 than a number, but they has some difficulty with -10 and +10. They played a game called 10 more and 10 less roll. All you need to play this game are number cards & dice labeled -10 and +10. You can buy blank dice to label {here}. 

Click on the picture to download the game.
Tier 3 {orange stars}- This group made their own number puzzle flipbooks. I gave the students blank flipbooks and number grids to make their puzzles. They glued the puzzle on the front flap and had to create an answer key underneath it. Once they were done, they had a friend try to solve their puzzles! I wish I had a picture of a completed one....bummer!! They were so cool. I will see if I saved one in my classroom tomorrow & post a pic of it!!


I had a parapro facilitate the orange and purple star groups. If you don't have a parapro, I recommend trying to get a parent volunteer if possible ( I know in some cases that is hard to find). 

The groups lasted about 20-25 minutes. If students were not finished with their work, they continued working on it the following day.

Whole Group Summarizing Time
To summarize this lesson, I went right back to the essential question slide and discussed with the kiddos what they were doing in their groups to help them understand/answer the essential question. We talked a lot about the strategies they used to identify the number neighbors.

Lastly, I gave each student a "ticket out the door"..aka..slip of paper with a problem on it. This was very similiar to their math journal prompt. They gave me their "tickets" as they were lining up to go to the restroom. This was another great (and quick) formative assessment to see who was or was not understanding the standard on an independent level.

Whew! I wrote a book. Sorry!! If you made it this far, I love ya!! I really hope this crazy long post helps you see how I differentiate a math lesson from beginning to end in my classroom. Please let me know if you have any questions in the comment section & I will answer them in a Q & A follow up post!! 

Here are a couple more printables/games to go with teaching how to identify number neighbors. Just click on the pictures to download!!

1 more and 1 less roll

Number Neighbor Roll
Frame by Fancy Dog Studio

One of my goals this summer is to start creating differentiated math units for all of the first grade common core math standards! I can't wait to get started on them!!

Right now, I'm working on Dr. Seuss themed math and literacy centers that would be perfect for your first graders to celebrate Dr. Seuss' birthday while also practicing important first grade skills. I hope to have this packet posted by the 20thish!!

Happy Thursday!!!

P.S. I apologize for the poor quality of the pics...all I had was my phone on me for most of them!!