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.

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:

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!

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

Amanda, Your passion for differentiating in math is evident. I can't wait to read about your next post on this topic.You have great ideas and techniques.

ReplyDeleteThanks for sharing.

Thanks Jean! I was really excited to write this one. :)

DeleteAmanda! I love the idea of having students complete progressively harder practice problems at the white board. Talk about accountability! I definitely will be trying this in my classroom later this week or early next week. Thanks for the tip.

ReplyDeleteIt's one of my favorite activities!

DeleteThanks for ll the great ideas. I have a similar pre-assessment process that includes problem ratings - very helpful. This year I am trying exit tickets for the first time. I really appreciate your insight on them.

ReplyDeleteCheers,

DocRunning

Awesome! Exit tickets can definitely provide valuable information when used correctly. :)

DeleteThank you for providing a timeline of differentiation in the math classroom! I thought it was very helpful how you started with the pre-assessment, went through a typical class activity like notetaking, and ended with the exit ticket. Very nicely written and informative.

ReplyDeleteI'm so glad you found these ideas helpful!

DeleteI have never liked the idea of pre-assessments because, like you said, kids don't like them and they are a time-suck. BUT, I think every once in awhile is good, and definitely would have helped me this year in Algebra 2 for the first unit, which I thought was review...turns out it wasn't and a pre-assessment would have given me the heads up. I think I might start doing Friday exit tickets to see what they actually learned from the week as well. Thank you, again, for the great tips!

ReplyDeleteI think Friday exit tickets are a great idea! Then you have the weekend to analyze the data and plan accordingly. :)

Delete