Launch a Lesson on Parts of Circles with a Thinking Task

When introducing parts of a circle, it can be tempting to jump straight into definitions and diagrams. But students learn best when they first connect new ideas to something they already know. A thinking task creates the space for exploration, reasoning, and discovery before you step in with formal instruction. Here’s how you can structure a lesson on parts of a circle using this approach.

Launch: Review of basic geometry terms
Start by putting students in small groups at vertical non-permanent surfaces. Give them a partially completed table with three columns: term, diagram, and notation. Helpful terms would be angle, line segment, line, and ray — familiar vocabulary from earlier geometry work that will be used in the parts of circles.

Some rows of the table are filled in, while others are blank. For example, a diagram might be given but not the term, or notation provided but no diagram. Students must work together and use their reasoning skills to complete the missing pieces.

This thinking task is not yet about circles, but it primes students to recognize how these basic building blocks can appear in different contexts. More importantly, it gives them practice using precise mathematical language and notation before introducing circle-specific vocabulary.

Part 2: Exploring the parts of a circle
Once students have refreshed their knowledge, introduce the new content: the parts of a circle. Provide clear definitions terms and instead of just telling students to copy these down, give them blank circles and ask them to draw each part themselves. For example, after reading the definition of a secant, they must sketch it and label it correctly. This pushes them to think carefully about placement and relationships, and when done at VNPS in groups, students can see and compare different interpretations in real time.

 
Part 3: Guided notes for consolidation
After the group exploration, provide a structured set of guided notes. The format mirrors the opening table: definition, diagram, and notation. This time, however, you provide the definitions and leave either the diagram or the notation blank. Some rows might include a diagram so students must add the notation, while others give the notation and require them to sketch the diagram. This mix reinforces independence while still giving support.

 
Part 4: Practice for mastery
To wrap up the lesson, offer varied practice that asks students to apply what they’ve learned:

• Identify the circle part when given a diagram with notation
• Draw the diagram when given notation
• Match terms to their definitions

These practice tasks provide the necessary repetition, but in different formats so the work feels meaningful rather than rote.

Why this approach works
This structure mirrors the flow of deep learning:

• Start with what students know
• Explore new concepts through discovery
• Consolidate with notes
• Reinforce with practice

The thinking task at the beginning sets the tone; students are reasoning, talking, and making connections from the very first minute. By the time they reach formal notes and practice, the vocabulary feels earned rather than imposed.

If you’d like a complete version of this lesson with the thinking task, guided notes, and practice pages you can grab it at the link below.  It’s designed for group work at VNPS or independent practice, and it includes all the diagrams and notation you need.

CLICK HERE TO GRAB THE RESOURCE

Deepen Understanding of Quadrilaterals by Using Card Sorts - and a Free Quadrilateral Foldable Booklet!

When teaching quadrilaterals, it’s tempting to jump straight into properties and classifications. But before students can truly master those concepts, they need a solid grasp of the parts of quadrilaterals and key vocabulary terms. Without this foundation, understanding properties like parallel sides or congruent angles becomes much harder.

That’s why starting with a card sort focused on the parts of quadrilaterals and essential vocabulary is helpful for students. Pair it with a quadrilateral foldable booklet (available for download below) that clearly defines and illustrates the five main quadrilaterals for even better understanding.

Why Focus on Parts and Vocabulary First?

Students often know the names of shapes like parallelograms, rectangles, and trapezoids, but they might not be confident identifying parts like vertices, adjacent/opposite sides, diagonals, adjacent/opposite angles, or distinguishing terms like “congruent” or “parallel.” Clarifying this language upfront helps students:

•Understand and communicate geometric concepts accurately
•Follow along when learning about shape properties and proofs
•Build a foundation for higher-level reasoning and problem solving

The Card Sort: A Perfect Tool to Teach Parts and Vocabulary

The card sort activity breaks down quadrilateral parts and key terms into manageable pieces. Students sort cards labeled with terms such as:

•Vertex
•Adjacent sides
•Opposite side
•Adjacent angles
•Opposite angles
•Diagonals
•Parallel sides
•Congruent sides

Alongside visual diagrams and definitions, this hands-on approach:

•Engages students kinesthetically and visually
•Encourages peer discussion and explanation
•Reveals gaps in understanding early so you can address them

By the end of the card sort, students will feel confident with the vocabulary they’ll need to tackle properties and classifications.

How the Quadrilateral Foldable Booklet Supports Learning

Once students have solidified their vocabulary and understanding of parts, the quadrilateral booklet provides a clear, concise reference with:

•Definitions for the five key quadrilaterals: parallelogram, rectangle, square, rhombus, and trapezoid
•Diagrams highlighting important features of each shape

This simple, foldable booklet can be assembled quickly and used throughout your unit as a handy study guide or review tool.

Why This Approach Works

•Builds a strong conceptual foundation before introducing complex properties
•Promotes active learning and vocabulary mastery
•Helps students articulate their reasoning with precise terms
•Supports differentiated learning through visual and tactile materials

Download Your Free Quadrilateral Poof Book Today!



Ready to reinforce your geometry lessons with a focus on vocabulary and parts? Grab the card sort activity HERE and set your students up for success.

Free Math Posters for Your Classroom – Grab Them on Facebook!

 Hey teachers!

Looking for a quick, clear way to reinforce the Properties of Equality with your students? I’ve put together a set of eye-catching, printable posters that are perfect for your math classroom — and you can grab them FREE over on my Facebook page!

These posters cover:

• Reflexive Property

• Symmetric Property

• Transitive Property

• Substitution Property

• Addition and Multiplication Properties of Equality
  … and more!

They're designed to be simple, bold, and classroom-ready. Whether you're introducing the concepts or just need a visual reminder on the wall, these posters are an easy win.

➡️ How to Get Them:

1. Head to my Facebook post here

2. Comment the word “posters”

3. Watch your Messenger — the download link will come straight to you!

✔️ Quick
✔️ Free
✔️ Classroom-ready
✔️ Works great for digital or print

Don’t forget to follow the page so you don’t miss future freebies and classroom resources.

See you on Facebook!

Deriving the Quadratic Formula

Deriving the quadratic formula is probably one of the most challenging tasks an Algebra 2 student will have to complete during the year, and without a doubt, one of the most frustrating!

When the day arrives to derive the formula, I tend to make a big deal out of how difficult the day is going to be, how frustrated they will become, and how proud and excited I will be if they don't give up; how proud THEY will be if they come close to the end.  I also give out TONS of encouragement and of course lots of help.

I let students go mostly on their own, with some guided notes to help as they struggle through the class period, and I wander around helping students as they are working and discussing the task with their peers.

Each year, I continue to be amazed as they take on this difficult task, trudge through it, hurt their brains and continue on!  Each year, among and beyond the frustration, there are high fives, congratulations and proud moments of accomplishments!  

**The guided notes with entrance and exit tickets that I use with students are available to fans of my FB page "The e Elephant Loves Math" for FREE (for a limited time only), and can also be found in my TpT store.

Inverse Functions

When I taught inverse functions last year, I really wanted students to have a context to apply them to.  In the past, I just taught them the steps to write inverse functions and the concept was definitely lost on them.
So I came up with this little exploration activity to help them see how inverse functions are related to each other.  It's all based on a fictional trip to Europe where students convert money and temperatures.
You can find the activity at my TpT store by clicking on the image.

Zombies and Exponential Functions

While searching for a "fun" and engaging task or activity to introduce linear vs. exponential functions, I found this blog post from Learning with Tape about a zombie outbreak!  AWESOME!  I couldn't resist trying this out in my class.  I teach a remedial class called Algebra AB, which is the first semester of Algebra 1 over the entire year.  I was leery of this activity and knew that I needed to have a very structured activity that held each student accountable for the thinking and processing involved to fully comprehend the basic main goal: to understand that a linear function will have an adding pattern, or increase/decrease at a constant rate and that an exponential function will have a multiplicative pattern and why their graphs are shaped the way that they are. So after much thought, the help of the original idea from Learning with Tape and some zombie clip art I came up with this lesson plan, that involves a fun zombie simulation, an extension activity and an exit ticket.  Students were very engaged and loved the activity!  Success!

Verb Dice (Conjugating Verbs in Spanish)

I purchased some "Cool Cubes" this year and have been putting them to good use.  The students were really excited about them at first and I think the first time I used them we just wrote vocabulary words on them,  rolled them, then said the word in Spanish and English.  Needless to say, they became "NOT Cool Cubes" after that.  The next time we used them to conjugate verbs and they moved back up a notch on the coolness factor.  Anyway, we used them again today to practice the present progressive.  I like them because it gives students a variety of choices for subject pronoun, verb matches.  They like them, because, well, they are big foam dice!  You don't need cool cubes to do this activity, and in fact, until this year I have just been using two dice with a "key" on the board.  They use one die to tell them what they subject is and the other for the verb.  For example, 1): yo 2): tú, etc and then on the other die 1) comer 2) hablar etc.  They roll the dice and conjugate verbs and use them in sentences.  Roll a 1 and a 2 and say (or write) "Yo estoy hablando (en la clase de español)".  It's a fun alternative to a blah worksheet and the students seem to enjoy it.  If you would like to try it out in your class and don't have cool cubes or dice I've included everything you need to give it a try in your class.  Just click on the image and get what you need!  We used these today with the present progressive tense, but you can use them for any tense!  You might try laminating them and using a hot glue gun to glue them together (at least, that's what I would do!)  I also included a blank cube so you can write whatever you want!  Again, I would laminate first, then you can write, erase, reuse! Your own cool cubes! How cool!

Tener and Tener que

My Spanish 1 students are learning to use the verb "tener" and "tener que" in the present tense.  Every year I see sentences like "Tengo que la clase de arte." and my ears hurt inside my head. :)  To try and combat this very common error, I helped students write sentences using both tener and tener que and then had them draw and color pictures of their sentences.  It seemed to be helpful, I didn't see any "I have to art class." sentences.  If you'd like a copy of the template I used, click on the image below!

Spanish Reflexive Verbs

We are learning about reflexive verbs in Spanish.  This can be a somewhat odd concept for English speakers as we do not necessarily have reflexive verbs in English.  We have been doing several practice activities and I want to try and help students write sentences that have all of the pieces they need.  We worked through a fun sentence unscramble activity and then did some drawing and independent sentence writing.  I think they're beginning to grasp the concept! I'm including the sentence drawing activity we did here, click HERE to get a copy.  If you'd like to check out the sentence unscramble activity we did, click on the image for more details!

Factoring the GCF in Polynomials

AHHH, polynomials!  You've got to love 'em.  We've been working our way through parabolas and quadratics in my Algebra 2 class and in preparation for solving quadratics we are learning how to factor.  Of course, we started by factoring the GCF from polynomial expressions.  I created a few tic-tac-toe game boards for factoring the GCF to give the students a more fun way to practice and thought I'd share them with you all!  Click on the image to get the game boards!  Enjoy!

Pilgrim Hat Clipart Freebie!

My poor, little, neglected blog... school started and I fell off the face of the blogosphere.  So, here's a freebie to say "Welcome Back" to my little blog!  Click the image to get this pilgrim hat clipart set.

FREE FRAMES

Free frames!  Enough said. (click the image to download)

Clipart Freebie

There was a request to "whip up" some chocolate frosting and a graham cracker, so that is what I did...it's up for grabs

Click on the image to get it!

The Three Little Pigs Clip Art and a Freebie

The other day I posted on Facebook that I had developed a clip art addiction...I was referring to the purchasing of.  However, it has escalated into a full blown time consumption!  I created this "Three Little Pigs" clip art set just recently and thought that I would share a freebie with you all.  So click here to get a little pig for free!  You can view the entire set at my TpT store by clicking on the image below.

Have a Huffing, Puffing Day!  (and I won't blow your house down...)

Chevron Pattern FREE STUFF!

As promised, the chevron paper has been put to use.  You can grab up these inspirational, full of color, chevron patterned, printable pennant banners at my TpT store totally FREE!!!!  Dream, Believe, Achieve!!

Click on the images for an English or Spanish version of the banner.

Chevron Pattern Paper

I think I may have found a new love (sorry polka dots), HELLO CHEVRON PATTERN!  Apparently chevron is all the rage these days...who knows?!  SOOO, I made some digital paper with the chevron pattern and, of course, I'll be sharing some with you all!  Stay tuned to see what I do with this fun patterned paper!

Click HERE to get free blue chevron pattern digital paper.
Click the image below to get the entire package at my TpT store!  Enjoy!

More...could it be...POLKA DOTS!?

I just finished creating my polka dot themed back to school pack for my Spanish class!  Oh, so much work with polka dots...not sure if I like them anymore...well, wait, YES, I still do!  To celebrate the completion of this monumental task (which I initially thought would be quick and easy), I'm sharing  2012-2013 "at a glance" Spanish calendars, with, of course, a polka dot nuance.  So click HERE to get these calendars.  Click on the images below to view the "super polka dot" Spanish Back to School Packet at my TpT store.

Enjoy!

Polka Dots Part Two and more FREE Stuff

Look what I can do with POLKA DOTS!
I teach Spanish, so I made signs for each of the four language processes in both Spanish and English, with polka dots of course!
I thought I'd share some of the things I've been making with my polka dot digital papers (if you missed that post click here for free paper).  These are just some of the many things I have in store with my polka dots galore madness!   Click HERE to get the letters to make a polka dot "read" sign and click HERE for the Spanish version.
Click the images to get the whole set in either language...

Polka Dots Galore and FREE Stuff

I've been working on some things for my classroom for next year and needed some black and white digital papers.  I couldn't really find much so I went about creating my own.  In the process, I ended up creating a ton of colorful papers, and whodathunk I LOVE polka dots!?  What?!  So anyway, I thought I'd share the love and offer up some polka dot goodness.  Click here to get some pink polka dot digital paper FREE.  Click the image below to get the whole set of 16 digital papers (polka dots and stripes) at my TpT store.  Enjoy!

Math Foldable Book on Angle Pairs

This little book is a 6 top tab book about angle pairs that I have the students create in class..  Students draw pictures and write what they know about each type of angle pair.  They are also required to include an example of a problem involving the angle type.