Firefighter Math

Have you ever wondered what mathematics firefighters use in their job?  How much is actually what we teach in the classroom?  It turns out we teach the foundation in several math classes but we don't supply the application of the topics.

After checking into the math that police officers use, I wondered what math firefighters used.  Low and behold, I found an online self-paced course for firefighter math.  It covers math that a fire fighter is going to need in the general sense such as ratios and proportion and then provides a fire fighting application with several practice problems.

Each topic is set up with a general introduction, examples, followed by practice problems. These practice problems are online multiple choice problems with immediate feedback.  I like the clear explanations you are given if you are correct.  I tried a couple and when I was wrong, the program told me I was incorrect, try again.  I did learn a fair bit.

This is set up nicely so I could use it in my geometry class to show how volume of cylinders has a real life application by having students work their way through the hose section.  It looks easy to assign the sections to students as needed.

It appears this is the only real site that discusses firefighting math but I found a great article on Fire and Math that talks about the use of natural logs and Fourier's law of heat transfer in arson investigation. This 6 page article is great because it explains natural logs and Fourier's law of heat transfer before providing specific examples.

This site has a 400 page document that talks about all the factors on fires.  It has detailed information on the factors and talks about mathematical modeling and computer modeling for Fire Dynamics.  There are so many more factors than I ever realized. This would make a good basis for a project.

Have fun exploring these sites.

SLO's

My district finally got around to doing Student Learning Objectives or SLO's.  Until the professional learning opportunity where they taught us about SLO's, I was under the impression that an SLO was like an IEP for each student. 

It turns out I was wrong.  Its simply a plan to teach a specific standard or part of standard.  I choose the what, how, when, and do it.  You set a goal for improvement and it gives you some real data.

I chose my Algebra II class for my first SLO. I looked at simple factoring from the standards and created my plan of action.   I found a nice pretest I gave my students and the majority of them freaked out and didn't do well at all.  Most had a zero percent but that means the only place they can go is up. 

My plan started students off with a sheet to learn the diamond factoring.  I taught it, passed out worksheets and when I moved on to simple factoring using that, I had them use the Diamond factoring app to practice throughout the unit.  At each step, they saw a video to introduce each step, followed by "I do, We do, You do."  They practiced using IXL.  Finally I gave them a set of practice problems. 

The post test is this week.  I told them they could take it any day this week.  So far half the class has taken it and the results ranged from 50 to 100% which shows real growth.  I'm happy with having to use the SLO.

Before this, I didn't know how to write a unit that would help me focus on the best way to instruct my students.  Usually, I've had administrators who had us make pacing guides for the whole year.  This never really gave me the focus I needed.  I also had someone who decided we should look at the previous year's state test, analyze that and use it to teach but that didn't always give the students a good mathematical background. 

I really feel as thought I hit a milestone in my teaching and I know how to prepare properly.  I love it when I made a breakthrough in my teaching.

Math Journals

  I am rethinking the idea of journals after reading about a teacher who has students write about all sorts of things from warm-ups to homework problems.

It used to be a math journal was only used for students to journal their thoughts and to summarize their learning.  In the last few years, the use of journals has changed.


Now journals can be used to:
1.  Take interactive notes.

2. Work their guided practice problems through.

3. Self-reflection.

4. Answer open ended questions.

5. Explain their thinking.

6. Share their answers on  homework problems.

According to  one document , journals serve several purposes.  They help
1. Increase student awareness of how they learn and remember.

2. Provide a record of student thinking.

3. To help students see that writing is a way of learning.

4. Provide a context for recalling previous learning and summarize current learning.

5. Provide a record of the challenges students face when learning new material.

Journal entries can be student or teacher directed.  Student directed journaling can involve their explaining how they feel, what they think, what they need to practice.  Teacher directed journaling covers material where the teacher asks the students to explain how a strategy works,  how to solve a problem, explain how to do something, explain an error in a problem, construct and model an answer for a problem, and support a point of view on why a certain way of doing something might be the best way.

One source recommends the teacher create an example journal filled with examples of what the students are expected to put in their journals.  This example journal is a quick way for students to check to see if they are doing things correctly.  Even though this suggestion is geared for elementary students, I can see using it in the middle school and high school for ELL learners.

I like the idea for creating an example journal for my classes because it becomes part of the I do, We do, You do method of teaching and it would help me plan what I'm doing in my class ahead of time.  I bet I could have students write down their answers to any scavenger hunt and comment on what parts they had trouble with.  It would provide another assessment.

Difference of Squares

Today I introduced factoring the difference of squares using the same drawing I use for multiplying binomials.  This was actually one of the best ways I've ever used to provide visually why it works the way it does.

I started by drawing a representation of 4X^2 -16 so they could see the two parts that existed.  I asked what is this drawing missing. The students noticed there was no x's in the drawing.  I asked them why would there be nothing showing.  After a bit of thinking and guessing they finally came up with the idea that the missing elements were opposites of each other.

So in a different color, I added in the missing x's.  One set of four is positive, one set is negative.  We drew in the missing parts to this square.  It was great because this is the first time students could connect the drawing with the equation and add in the missing parts. 
The final step in the process of drawing was to add the lengths of the side.  The 4x^2 was easy because it is 2x due to 2 x's.  The numbers were  4 and -4

It was so easy for them to see all.  I just realized, I should have cut the x's in half so I had 8 positive and 8 negative values.  I'll change that the next time I do it.

In Algebra I, I introduced multiplying binomials whose result is the difference of squares.  I drew the boxes, filled in the values and showed how the x values cancel each other out by erasing those area.  I loved the way the students kind of went "Oh."  When they did their guided practice, most of them just whizzed through the whole set and if they made a mistake, they had no trouble understanding why.

This method is going to show up in my box of teaching tools.  Tomorrow, I'm going to be using the same idea to help my Algebra I learn the pattern for binomials squared.  Yes!

Completing the Square

May I start off with the fact that I hate teaching the topic of completing the square.  I always have and I always will.  If all else fails, I run the equation through the quadratic formula, find the half way point, run that number through the formula and I have the three points I need for a rough graph.  Now, I carry a graphing app on my phone and I graph the equation, read it, and write the equation from the graph.  Unfortunately, I have to teach it as part of the curriculum.

So before I can teach completing the square I need to make sure that students at least know there are perfect squares as that is part of the form.  So then the question becomes, what is the best way to introduce the topic to high schoolers.  The Math = Love blog provides a great introductory activity to help students visualize the process.

This is the first time I've seen an activity that uses manipulatives to introduce the topic .  I have a whole set of Algebra tiles in my classroom for my students to use.  I see how this activity could be used to teach perfect squares and difference of squares.  Two uses out of one activity.

This file has a complete 5 page lesson plan that uses the idea from the hands on activity used to introduce the topic.  It comes with warm-up, the lesson, a think-pair-share, and practice problems.  It does a good job of connecting the visual with the process.  The directions are clear and it is ready to use.

 This final link is perfect because it uses the box method to show students how to complete the square.  This is great because the box method is one of the methods I use to teach students how to multiply binomials.   I love how its used rather than relying on the standard formula of taking half of the middle term, square it, and add to both sides. 

Due to these sites, I have a new way of teaching completing the square that I believe will be more effective than the way I've taught it in the past. 

Literal Equations

My students have such a problem with literal equations, especially when they have to rewrite them.  It might be because I do not give them enough practice in rewriting the equations themselves.

I am guilty of teaching formulas and literal equations in only one way and I don't teach them to find different things.  In Geometry, I had them find the area only.  I did not ask them to find the base given the area.

CPalms has a nice lesson plans with everything needed to introduce the topic.  I like the way it includes the necessary materials to accompany the lesson.

One way I've taught this type of thing is with sticky notes on the board that I could physically move around.  I write the variable on the sticky note, put it on the board as an equation, then move it around step by step.  I've passed out a ton of sticky notes to the kids to use on their white boards to go through the same process.

Hands on High School Math recommends using cards such as 3 x 5 cards cut in half with variables and operations written on them.  So you could create R x T = D using one card for each term.  Then they can rearrange the cards to form the new equations such as D/R = T.  I like the idea of using cards better because I can laminate them for future use.  This is much better than using sticky notes.

The Math = Love site suggests a scavenger hunt as a way to practice rewriting literal equations.  I enjoy the way she has it set up although I've been known to set one up using QR codes.  The only thing I missed in the examples was the statement on rewriting it to find x or y.  This is important.  I think I'll do one with the standard equations such as I = PRT or A=LxW.

I would add one thing to this and that is give students some numbers to use in the various equations to get answers.  My students are not good at going from the literal formulas to substituting values in for real answers.  I'm hoping by adding this in, my students might be able to transfer their knowledge.

Better Lesson has a nice fully developed lesson from a brainstorming introduction, to a guided notes and practice, a partner activity and a closing activity that includes an exit ticket.  I like that this has the power point presentation for the guided notes, the worksheets for the practice activity and a do now or warm-up at the beginning.  I like the way the lesson is fully developed and ready to go.  I plan to try this.

These resources when integrated will provide a nice unit for literal equations.  I will be teaching it in about two weeks.

Math Identity

  The March issue of the National Council of Teachers of Mathematics for Middle School Teachers magazine has a really nice article on developing math identity.  I wasn't sure what math identity is in this context because it was not something they talked about when I was in teachers training.

Apparently math identity is a the frame around knowledge, skills, habits, attitudes, beliefs, and relationships students need to successfully learn math.

It is suggested that their mathematical identity is connected with all their other identities.  Consequently, teachers have the ability to shape a student's mathematical identity.  One way to do that is to support a flexible mindset. 

Have students work in groups so there each member has a particular role, give them group type activities so that no students dominate the interactions.  Next, have students keep a math journal which could include warm-ups or bell ringers, classwork, open ended reflections and problems, and possibly homework.  In addition, the teacher needs to communicate expectations that every student will learn mathematics and contribute to the mathematical learning of others.

It is important to focus on their abilities rather than their deficits. It is also important to help students learn to believe in themselves as thinkers and problem solvers.  This means focusing on their skills and talents rather than learning the algorithm.  As part of this, students need to know it is possible to have more than one correct way to do any problem. 

There are four major things that they say we as teachers must do.

1. Give all the students a chance to write or talk to a partner before anyone answers a questions publicly.  This would be a great time to use silent conversation where two people share one piece of paper and carry on the conversation by writing it out.

2. Set routines so students can develop ideas privately and share to a small group before presenting to everyone else.  Think, pair, share would be a great starting point to have this happen.  So have them work in pairs, then in groups of four before sharing to the class.

3. Have the students either individually or as a group give a rating to indicate with hands or fingers, where they stand in terms of moving on.

4. Have the students set goals for the class.

Four easy things to help students develop a flexible mindset and a strong mathematical identity.  This article has helped me see where I need to go in my teaching.  I'm happy I found it.