## Differentiation 1.1

How timely that Doc Running is hosting a blog hop focused on differentiation!  I recently started a series of blog posts on differentiation because it is a topic I am super passionate about.  This post will provide the nitty gritty details about differentiating based on readiness.  Check out the introductory post here.

As I’ve said before, most differentiation resources fail to provide specific examples for how differentiation practices can apply in a math classroom.  I’ve spent countless hours reading and thinking about how to make it all work.  I’ve also been very lucky to work with talented teachers who have shared some of their best practices with me.  The ideas included in this post are a collection of ideas I have found and/or created throughout my years of teaching.  I decided to start with 5 basic ideas for differentiation today.  These are a great place to start.  I sorted out 5 more intense ideas to save for next time.  Specific.  Concrete.  5 Try-one-today kind of ideas. Enjoy!

Pre-Assessment
Pre-assessing students at the start of unit can result in some moans and groans.  “But we just took a test!”  And they’re right.  I don’t pre-assess before every unit because it can be a time-suck if not used properly.  I choose 2-3 units that involve a lot of review and/or few unique topics and I pre-assess my students on their prior knowledge.  8th grade topics that I have pre-assessed in the past include equation solving, Pythagorean Theorem, and exponent rules.  These pre-assessment results can really help me in all my decision-making throughout the unit.  The results help me to decide how to best implement some of the following practices that I’ll describe.

Teacher Tip:  Take 5-10 minutes to have students self-correct.  This will save an hour or two of your time.  Remember this is something “extra.”  Take your time back!  Once they self-correct, all you need to do is a quick scan and sort.
Pile 1 – Uh oh!  Minimal retention evident.  May need extra help.  (None or practically none right.)
Pile 2 – Ok, they just need some review.  (Half-ish right.)
Pile 3 – Whoa!  100% (or close) before we even start the unit.  They need a challenge.

Note: I also have a pre-assessment for all 8th grade standards and one for all 7th grade standards available for sale in my store.  These are great for measuring growth on a larger scale.

Options for Notes
Note-taking differs for each teacher and classroom.  Some of you may use foldables.  Perhaps your students have interactive notebooks or you have implemented a flipped classroom.  Maybe you take it old school and have students write on lined paper as they copy your examples from the board (like my accelerated classes).  I’m going to focus on what I do in my standard math classes.  I think this general idea can be implemented no matter what your method for note-taking is.

A huge part of differentiation in my classroom centers around choice.  A great way to differentiate note-taking for students is to allow them to work at the level that is appropriate for them.  Some students may be ready to hand-write and organize their own notes on lined paper.  Other students may require more of a graphic organizer to help them decipher the notes later on.  Still others may have needs that require the completed notes to be given to them.  Students all have different needs so you differentiate by readiness by making some small changes to your routines.

The majority of your students will likely do the same thing... whatever that is.  For me, it is filling in skeletal notes and/or graphic organizers.  Then to help your students who need more assistance with note-taking for a medical, emotional, or other issue, provide additional scaffolding.  You can give them completely filled in notes if appropriate (or indicated on IEP).  You can fill-in for a student parts that require a lot of writing or are super important to emphasize.  On some occasions, I have given students copies of filled-in notes at the end of class… especially if I’m concerned they may not have gotten all the information down that they needed to.

To challenge students who take exceptional notes, consider offering them the opportunity to hand-write and organize their own notes on lined paper.  (This always seems like an upgrade to me because that’s what my students in accelerated math do.)  For students who have already mastered the topic (which you know from your pre-test and/or teacher observations) give them the notes, then send them off to practice independently.  (Okay, maybe I’m wandering into my “challenging" suggestions.  More on this later).  The point is, with very minimal planning, you can ensure every student is taking notes – and learning - at just the right level of challenge.

Build Confidence with Specific Problems
Once you get to know your students and you develop a general awareness of their math ability and their confidence, you can build student confidence by being strategic with which practice problems you give them.  Here are some ways that I do this in my classroom:

Human number lines, like my free Negative Exponents Activity, engage students in moving around the classroom and, in this case, line themselves up from smallest to greatest value.  Some of the cards are super basic.  Others are much more challenging.  I do not just pass these out at random, but it does look random.  Ahead of time, I line up the cards from easy on top to difficult on the bottom.  Then when I walk around I give each student a card from the top, middle, or bottom.  I have found that this encourages struggling learners to participate even if they may have otherwise been intimidated and also advanced learners are (usually) excited to take on the challenge.

One of my favorite ways to have students practice math problems (like equation solving or exponent rules) is to have students come up to whiteboard 4-5 students at a time.  I ask for volunteers to come up, and I explain that everyone will go up to board at least once and the problems get harder as we go.  Most of the time, many hands will shoot up right at the beginning once I’ve made those little disclaimers.  And, of course, there are those students who want to go up every time.  Students at their desks, try the practice problems, too, but they don’t have the pressure of everyone watching.  J  Well, I call students up in groups with similar ability.  I avoid tricky cases for students who are still trying to master the task.  The tricky cases are better to be completed at their desks so they don’t need to be embarrassed if they are not sure what to do.  Sometimes I will even say “Whoa! This is really good one!”  (They know me well enough to know that means it’s a tough one.)  Then I know who is excited to take on the challenge at the front board.

Before we start graphing linear functions, I like to do a jigsaw activity where students graph linear, absolute value, and quadratic functions – all by making a table.  Students make their graph (which matches their partner’s graph).  Then they get together with another group that has the same function family.  They look for attributes that make the function look the way it does.  Once they have some ideas, they move to a new group and they learn about the other functions, too.  To differentiate - I bet you guessed it – I give the linear functions to struggling students and quadratic functions to my high flyers.  (I try to make sure I have at least one or two confident students with a linear function so that the group discussions move in a good direction.)

Vary the Complexity of a Task
Very similar to the previous suggestions, you can also vary the complexity of a specific task.  One example that immediately jumps out is from the Juice Box Project that my students complete.  Students work in small groups to design and build a “juice box” that has a set volume, minimizes surface area, and markets well to parents and children.  Students do all of the planning, calculations, scale drawings, etc before they actually build a juice box out of oaktag.  Students have wild, wonderful dreams when they sketch out their initial ideas.  I tend to steer my lowest students toward rectangular prisms.  I allow only my strongest students to make a cone or sphere because they require a ridiculous amount of patience.  Then there are my high-flyers… I’ve seen everything from a hexagonal prism to a multi-part composite figure that looks like a turtle.

During our unit on slope and rate of change, I give students a “Slope Menu.”  There are the appetizers, entrees, and desserts.  The appetizers are the skills (just a warm up).  The entrees are the concepts (getting to the meat of the big ideas).  Finally, the desserts are the fun stuff and applications.  I require students to do at least one problem from each section, but the rest of their selections are up to them.  I can encourage some students who need to either stick with more of the entrees if they’re ready for the challenge or hang around the appetizers section if they need the extra practice.  I took this idea away from a conference featuring Rick Wormeli.

Exit Tickets & Remediation
My fifth and final differentiation strategy for today is another tool that helps you to identify students needing extra practice.  Exit tickets are great for quickly checking which students are getting it and which ones are missing the mark.  I am very lucky that at my school we have a period dedicated (at least every other day) to remediation and extension activities.  Sometimes I quickly check in with each student who missed problems on the exit ticket.  Other times I run a review session for a group of students – especially if we are nearing the end of the unit or approaching a quiz.  The exit ticket itself usually has 2-4 review problems based on what we have been working on throughout the week.  I don’t include what we learned that day because they haven’t had time to fully process and practice the skill yet.  The extra help period is a great way to give more time to those who need it.  Sometimes a little extra attention can make a big difference.

If you have any questions about these strategies, please feel free to leave a comment below or send me an email.  The activities mentioned in this post are all lessons I’ve used in my classroom.  Most are not in my store yet, but make sure you’re following me on TpT to get notifications about my new products.

Continue the series here:

Also, be sure that you are subscribed to my blog to receive a free math resource and to stay updated on this differentiation series and other ideas.  Thank you!

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Be sure to check out these other amazing ideas from some of my secondary math blogger-friends!

## Differentiation 1.0

As I was trying to organize my storage space, I came across boxes of books from college.  I read a ton of education-related books while I was at Emmanuel College… some required, but most I just found really interesting.  I remember learning about differentiated education for the first time in Dr. Merritt’s course and I became so in love with the idea I read everything I could get my hands on.  The best resource I have come across for an introduction to differentiation is Carol Ann Tomlinson’s How to Differentiate Instruction in Mixed-Ability Classrooms.  It’s an excellent quick read and a great place to begin!

According to Tomlinson, there are three different reasons to differentiate for students: readiness, interest, and learning profile (2001).  Readiness refers to the level a student is working at on a particular topic.  Differentiating based on interest often involves choice so that students can demonstrate their knowledge by doing something that they love.  And learning profile refers to the way in which students prefer to intake information.

Have you ever noticed that there are rarely examples of differentiation in books and articles that can actually apply to math?  Ugh.  So frustrating when you’re getting started!  Today I’ll provide a super brief introduction, but be sure to follow these posts so that you can get specific and realistic strategies to implement in your middle or high school classroom this year!

Whenever you’re taking on something new in the classroom, it’s a good idea to take one step at a time.  Starting with learning profile can mean engaging in effective practices like presenting material in an auditory manner with visuals and a hands-on component.  By doing this you are meeting the needs of many students, which is what differentiation is all about.

Differentiating by interest can be achieved by offering choices.  As students wrap up their study of solving linear equations, I always end the unit with a differentiated project.  Students are given 6 choices of assignments and are able to choose which one they like the best.  When I created this project, I tried to base the choices on Gardner’s multiple intelligences.  Students could take on a challenging open-ended math problem, write a song or poem, reflect on their learning, and demonstrate their knowledge in any way, really.  Note: This project was always completed in conjuncture with a unit test.
Then, of course, there’s readiness.  This is something I consider everyday when planning my lessons.  Phase One: Plan the main lesson and create or find any resources needed.  Phase Two: Think about your struggling learners and make any modifications needed to help these students achieve success.  Phase Three: Consider your high-flyers and early-finishers.  What else can they do to be challenged?

I have SO much more to share, but I’ll save some more for next time.  Remember to take one step at a time and start by differentiating one lesson, project, homework assignment, etc.  Be sure you have subscribed to my blog so that you don’t miss a thing!

Tomlinson, C. A. (2001). How to Differentiate Instruction in Mixed-Ability Classrooms. 2nd Edition. Association for Supervision and Curriculum Development.

*Quote from page 5 of text.

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## Reviewing Integers

I always start off my eighth grade classes with a review of integers.  Fluency in integer operations is SO important for pretty much every other skill that students will learn in eighth grade.

INTRO
My favorite way to open up our integer review involves a document camera, projector, and some basic round manipulatives with a different color on each side.  My set is represented with yellow for positive and red for negative.  I write out a few basic problems that can be easily modeled using the chips then call on students to help with the modeling.  For example:
-3+5
I call on 4 different students to help me with each example:

Student 2: Add 5 yellow chips.

Student 3: Match up the 3 pairs.  Each pair equals 0 because 1+(-1)=0.  Remove the pairs.

Student 4: The result is 2 because there are two yellow chips left.

SHARE A STORY
To help students remember the rules for multiplying and dividing integers, I share this story (a version of this told to me by a colleague):
If you want to be friends with someone and they want to be friends with you, that’s a good thing!  (positive x positive = positive)
If you don’t want to be friends with someone and they don’t want to be friends with you, that’s no big deal.  Go your separate ways.  (negative x negative = positive)
If you want to be friends with someone but they don’t want to be friends with you, that’s a negative thing.  (positive x negative = negative)
If you do not want to be friends with someone but they do want to be friends with you, this can be annoying.  (negative x positive = negative)

Here’s another version:
If a good thing happens to a good character, we’re happy.
If a good thing happens to a bad character, we don’t like this.

FLASH CARDS
I also give students time to practice, practice, practice using flashcards.  Each pair gets a pile of flashcards and one partner starts as the flasher.  The other begins by computing the answers.  (The answers are all written on the back.)  After about 3 minutes, I have them switch roles.  I love this independent time for two reasons.
A)     They are getting actual practice and everyone is engaged.
B)     I do this during the first week of school so this gives me time to walk around practice names and get to know my students.

BACK TO SCHOOL
I also have a fun “All About Me with Integers” activity that works well within the first week of school.  Students answer questions about themselves, then use a key to translate the letters into integers, then add them all together.  You will get to know your students on a personal level and also begin to develop an understanding of how much information about integers they retained.