Quadratic Functions INB


When I was trolling Pinterest this past summer, I kept seeing cool interactive notebook pages for elementary school that used paint chips.  They looked so creative and colorful.  I’ve had that idea in the back of my mind for awhile and have been waiting for inspiration.

Inspiration has hit.  This is my idea for an interactive notebook page for characteristics of parabolas.  This would work for 3 or 4 color paint chips.

Characteristics of Parabolas Interactive Notebook Page - quadratic function inb page

On the paint chip, students can write the three different forms of a quadratic equation (factored form, general form, and standard form).

Characteristics of Parabolas Interactive Notebook Page - quadratic function inb page

Off to the side, students can write why the form is helpful.  I like to do this so that students learn that all of the versions are helpful.  

Characteristics of Parabolas Interactive Notebook Page - quadratic function inb page

At the bottom of the page, I drew a diagram with helpful information off to the side.

Characteristics of Parabolas Interactive Notebook Page - quadratic function inb page

I hope this gives you some ideas for your interactive notebooks!


Note:  If you don’t want to get paint chips from the hardware store, there is a free printable from Erin Holleran on TpT.

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Create a 3D Pyramid

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In Geometry, students have such a hard time visualizing the different parts of 3-dimensional shapes.  My students always had a particularly hard time with pyramids.  This cool trick really helps - and all you need is an envelope.

How to Create a 3D Pyramid Out of an Envelope

First, you need an envelope.  You want the smaller kind, not the long type.

How to Create a 3D Pyramid Out of an Envelope - great for helping Geometry students visualize

Fold the envelope in half one direction, then the other direction.  You're trying to create a nice crease along the middle.

How to Create a 3D Pyramid Out of an Envelope - great for helping Geometry students visualize

Fold the envelope so that the sticky side is facing out.

How to Create a 3D Pyramid Out of an Envelope - great for helping Geometry students visualize

Cut along the edge of the flap.

How to Create a 3D Pyramid Out of an Envelope - great for helping Geometry students visualize

Throw the top part away.  Open the fold and make sure everything is cut nicely.

How to Create a 3D Pyramid Out of an Envelope - great for helping Geometry students visualize

Fold the points down to the middle crease.

How to Create a 3D Pyramid Out of an Envelope - great for helping Geometry students visualize

Open up the folds.  Carefully pinch the middle and tuck one side inside of the other.

How to Create a 3D Pyramid Out of an Envelope - great for helping Geometry students visualize

You should be left with a pyramid.

How to Create a 3D Pyramid Out of an Envelope - great for helping Geometry students visualize

Now that the pyramid is folded, open it back up so that you can label all the faces.  Label each side like the pictures below.

How to Create a 3D Pyramid Out of an Envelope - great for helping Geometry students visualize

How to Create a 3D Pyramid Out of an Envelope - great for helping Geometry students visualize

When it's folded back up, all the parts of the pyramid are labeled!

How to Create a 3D Pyramid Out of an Envelope - great for helping Geometry students visualize


One of the things I really like about this pyramid is that it can be folded an unfolded as needed.  Students can keep it in an interactive notebook or in a pocket of a binder.

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Math Misconceptions: Base and Height of Triangles

Today I'm linking up with Scaffolded Math and Science to share math misconceptions and how we fix them!

Even high school geometry students have misconceptions in math!  Teachers can help students find the base and height of triangles so that they use the area formulas correctly.

When teaching geometry, I (wrongly!) assume that students remember what they have previously learned.  I know that students learn how to find the area of parallelograms and triangles in middle school, so I assume that I don’t need to teach it in as much depth.

WRONG!

I have found that students often make mistakes when finding the height of a parallelogram or triangle.

In this example, students will often make one of two common mistakes.  Either they use 15 as the base and get frustrated that they can’t find the height or they try to use 10 and 8 as the base and height.  

Correcting Math Misconceptions - finding the base and height of triangles in geometry

However, I have to constantly remind my students that the base and the height are always perpendicular to each other.  To solve this problem, I have them mark the perpendicular parts with a highlighter and circle the right angle marking.

Correcting Math Misconceptions - finding the base and height of triangles in geometry

Marking diagrams with a highlighter is also helpful for me to quickly find where students make mistakes.  In this example, there are two ways students could solve the problem.  When they mark the diagram, I can see if they are having trouble finding the base and height or if they just made an arithmetic error.

Correcting Math Misconceptions - finding the base and height of triangles in geometry

Correcting Math Misconceptions - finding the base and height of triangles in geometry

This problem is tricky for students because they want to use 20 and 30 as the base and height.  Since a parallelogram is “kind of like a rectangle” in the student’s mind, they think it is ok.  However, when a perpendicular line is drawn, they can see that 30 cannot be used.  This problem is actually trickier than it first appears!

Correcting Math Misconceptions - finding the base and height of triangles in geometry

I like using this technique because they can even use it on standardized tests.  Tests don’t allow highlighters, but students can draw on their booklet darkly with their pencil.


The examples in this post are from my Area of Rectangles, Parallelograms, and Triangles Lesson and my Area and Perimeter Task Cards.

area-of-triangle           area-perimeter

Check out tips for below for other math misconceptions!

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Tips to Help Students Focus

As a student, it was always increasingly difficult for me to concentrate and focus in the spring.  I was always SO ready for the school year to end and spent most of my time chatting and daydreaming.  I reached out to some friends and asked for their tips that they use to help their students focus.

I have trouble getting my students to focus on their learning, especially in the spring!  These tips and ideas are perfect for teachers to help kids get back on track.  I need to add these to my classroom management toolkit!

I help my students focus by playing music. Depending on your school's policies, you can use Pandora. Just make sure you choose the setting that allows you to avoid any explicit language... I didn't know about this setting, and a song came on that had very vulgar language. My students had never seen me run to the computer so fast! I thought I had chosen a station that didn't have this...ummm, apparently not! A lot of teachers also play classical music, and the students appear to like this a lot (surprisingly)! 

Keep things interesting! Lots of activities, fast pace... Never give them a chance to get "lost".

I work on a lot on teaching them how to learn. It's all about process in my classroom, and because I break things down in steps, it's easier for them to focus on each one.

I keep some of my lights off; I have three rows and try to only use two at any time. I also ask them to put their phones face down on their desks and close their computers before giving very important directions.

To help my middle school students focus, I did three things: 
A) I bought several yoga balls and let students sit on them; they could bounce a little bit but their feet had to be on the ground the whole time as I did not want kids falling off or rolling all over the classroom. 
B) I let students get up and walk around the room quietly if they said it would help them focus more. Both boys and girls loved using the yoga balls but it was the boys who wanted to walk around the room. Since my middle school classes were small--the most I had was ten students--walking around in the back or around the perimeter was not an issue. I knew from reading education articles that boys often need to move around due to their energy levels and also that it helps kids with ADHD. I was happy to let them walk around but made it clear they could not disturb other students when they did. What was interesting was that the boys themselves knew when they needed to get up and move, and their behavior during these times was fine. 
C) When students had independent or shared reading to do, I let them sit wherever they wanted. I had a table in the back of the room that some students liked to work at and others liked to sit on the floor. My feeling was that if students felt comfortable, they would be better able to concentrate on the work they had to do. When I was a student, it was hard for me to sit in those hard chairs for any length of time so I wasn't about to force my students to do something I couldn't do myself!

I tell my students what parts of the brain help them focus with tangible benefits and which parts work against their focus and takeaways. That's all it takes! They love it! 

For me, the most effective way to re-gain the focus of a student is to just lay my hand on his/her desk while I continue on with the lesson.

My general philosophy: student learning is positively correlated to student engagement. My first goal is to get students engaged in the Algebra topic. Prepare yourself to be horrified… I don’t require students to raise their hands to answer my questions. I don’t wince when two or three students answer at once. In fact, I encourage it and try to reaffirm all the correct answers I heard. Now, if a student has something creative to say, a hand needs to be raised so that I know to share the floor; that, I enforce. 
A wise friend shared with me, “Unless the pain of change is less than the pain of staying the same, change will never happen.” I want my students to change, to transform from their sluggard, uninterested, UNFOCUSED state, and become involved in Algebra. The thought of raising a hand to just participate can be a hindrance to my goal (a goal the student and I may not share). You might say -- What about thinking time? A quick student may answer all the questions and set the lesson pace faster than the majority of the class can handle. Absolutely true; there are times that thinking time must be secured for the group. At least 25% of my class questions follow this model: “I want to see 10 (5,7,8) people who know before I hear the answer. What is ….(the actual question)?” Students begin to signal me, and I acknowledge that I see them by counting up to the target number. True, students often signal with a quick up and down with their hand, but the less motivated just give a perceptible wave and eye contact. No one is required to keep their hand in the air while we wait for all to think. Once the target is met, I repeat the question and let all respond (or I may try to ferret out a bluffer by choosing a student that signaled). 
This is by far one of my more common sense focusing strategies, not nearly as impressive as other tools I use. However, I too often see this rule in classrooms: “Raise your hand to speak.” The heart of this old rule is respect for the classroom structure, respect for the speaker who has the floor at the moment, remembrance that you are one of many in this group which requires some order for all to move forward. The classroom has evolved. Lose the “Raise your hand” rule and weave the heart of the message into new rules like “Support the learning momentum of the classroom.”

Sometimes I play Pandora. I was surprised how much quieter the loud classes are with a little music to listen to while they work.

Be interactive. Let students show their work on the board, or at the document camera. Ask lots of questions. Walk around the room. Help individual students at your desk. Monitor and adjust. 

I've tried many different things but what has worked the best for me is the 5 second countdown to get their attention. By 1 nothing is in their hand, eyes are one me, talking has stopped. As for staying focused during a task I try and make the task engaging and meaningful. I teach science and so I do a lot of hands-on learning and inquiry investigations using technology. 

I have done many different things to help my students focus. Sometimes I do whole-class brain breaks and other times I put a statement on the board and have students walk to one side of the room if it's true, the other side if it's false. Usually getting my students moving for a minute or two really helps!
I also let students stand in the back of the room, sit at my desk, or play with play-dough as long as they are working.

I try different types of teaching styles. I'll do whole group instruction, small group instruction, hands on activities, and then we might even watch a brain pop or Bill Nye. I try to do at least three different ways to get the content across and make sure that I got them in one of those ways!
JFlowers     

Turn off the lights. Put on some music. Let the students decompress after lunch. It calms them down and helps them to focus. 
A quiet, safe, respectful environment works wonders.
Other than that, it is to put the agenda on the board with examples of the expectations. Projects always have 3 or 4 examples for each grade along with a rubric for the students to know what I’m looking for and what is expected.

If it is a long unit test or standardized test, I'm not afraid to hand out a jolly rancher or lemondrop :) 
Becca    

Hand grips! I know, I know it seems silly, but it works WONDERS for the students that need to be moving. Cheaper than an exercise bike, and less distracting than those yoga balls. 

Focusing in my classroom came easily when I introduced Interactive Notebooks. With a 42 minutes class period there was no time to goof off and we had to be "balls to the wall" from bell to bell. Students quickly saw the value in creating their own resource one page at a time and knew that if they stayed on top of things then they would succeed.

I have very small class sizes (average about 10 students per class), so it's not difficult with such a small number of students. I find that communicating what needs to be accomplished each day and keeping them engaged with interactive notes and activities naturally do the trick.
Tyra Bauer    


How do you help your students focus?

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