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My geometry students need practice with proving triangles congruent using SSS, SAS, ASA, HL, SAA, and they also need practice applying these congruence shortcuts to figures in which the parts don't necessarily "line up," or in figures requiring them

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This worksheet is designed to replace a lecture on the topic of special right triangles: it walks the kids through the 45-45-90 (isosceles right triangle) and 30-60-90 (half an equilateral triangle) shortcuts.
I start out class with a 15-minute

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Let's face it: Geometric Proofs are very difficult for students, and they're very difficult for teachers to teach, because there is so much information required to get across (such as knowing that the idea that 3 = 3 is the "reflexive property of

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In the past, when I taught students the properties of parallelograms, I always felt that I was telling students things they could see and measure, and then when the assessment rolled around, I found out that I would have been better off having the

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No matter what course I teach at the high school level, it seems students need a review of how to add, subtract, multiply, divide, and compare fractions. This worksheet has a summary of each operation with examples. It includes fraction problems

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My Geometry students struggle with the isosceles right triangle (45-45-90) and 30-60-90 special right triangle shortcuts. The purpose of this activity is to give the students enough practice so that they see the connection directly. I've found

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In the past, when I taught students the properties of trapezoids and kites, I always felt that I was telling students things they could see and measure, and then when the assessment rolled around, I found out that I would have been better off having

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After teaching my students about scatterplots, correlation, and the line of best fit, I take a day for them to do a hands-on lab, in which they measure their height (in inches) and their forearm length (from the tip of their elbow, to the bony point

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One of the most challenging concepts for Algebra students is understanding the distinction between a relation and a function. This worksheet is my best shot: it provides them with an analogy of "Joey's Restaurant," where each customer (who is

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My algebra students struggle with seeing the connections between a rate of change and slope, so this worksheet is designed to help them see those connections. It includes examples of problems in which they compute a unit rate, and it also has them

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Venn diagrams are always enjoyable to teach, because I tell the kids they can "color for credit," when they color in portions of the Venn diagram corresponding to a description.
I wrote this worksheet to help my students begin to visualize and make

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This worksheet is designed to give students an introduction to the concept of correlation, and it has them problem-solve with a problem requiring a scatterplot.
I use this activity within cooperative groups, and I circulate to make sure they are

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Once I've covered basic probability and statistical measures, I like to have students work with conditional probability, which can often go hand-in-hand with tree diagrams. I created this worksheet for my Algebra 1 students, and I find that it is

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Venn diagrams are always enjoyable to teach, because I tell the kids they can "color for credit," when they color in portions of the Venn diagram corresponding to a description. This worksheet includes notation for the intersection, union, and the

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My geometry students need practice with proving triangles congruent using SSS, SAS, ASA, HL, SAA, and they also need practice applying these congruence shortcuts to figures in which the parts don't necessarily "line up," or in figures requiring them

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TEACHING EXPERIENCE

I've been teaching math full-time in public high schools since 1989. In the past five years, I have taught Algebra 1 (regular and accelerated), Geometry, Algebra 2, Honors Algebra 2, and IB Math SL. (Formerly "Math Methods"). My side job is teaching an ACT/SAT preparation course.

MY TEACHING STYLE

I believe that students master content over time. I think the longer they are in contact with a concept, the better they will internalize the material. I therefore include a lot of "spiral review" in my lessons whenever possible. I no longer "lecture" my students with notes: as a matter of fact, notes are optional, as I have found that if students just pay attention to a 15-20 minute mini-lesson each day, they are much better engaged with the material and most of the "information" can just be included on the worksheet where they need it.

HONORS/AWARDS/SHINING TEACHER MOMENT

I have been a National Board Certified Teacher since 2002. My first student teacher is now a professor of Education and has served on the board of NCTM. (I can't claim any credit for his accomplishments, as they are his own, but it's fun to tell people about him!)

MY OWN EDUCATIONAL HISTORY

When I was in elementary school, I was literally the last kid to learn how to carry in 2nd grade, the very last kid in 3rd grade to learn how to borrow, and in 4th grade, I was one of the last 5 kids to learn to do long division. I thought at the time that most math facts were just memorization, and I have a really hard time just memorizing facts and information: flash cards were just a nightmare for me. I still struggle at times with memorization of information that others seem simply to soak up. In 5th grade, I had a wonderful teacher, Mrs. Baker, at Spring Hill Elementary School in McLean, Virginia. I don't know what happened exactly that year, but fractions and geometric constructions just made sense, and for the first time in my life, another kid actually copied off of my math paper! While I don't condone that, at that time, I was very proud of myself, as nothing like that had ever happened before. From that point on, I was one year ahead in math. During my senior year of high school in calculus, I got really psyched that I could integrate a function whose integral was the arctangent function to estimate pi. I wanted to write a computer program to estimate pi to dozens of digits by making millions of "rectangles" under the curve and adding up their areas. I saved up money cutting lawns and delivering newspapers to purchase my very own Apple ][+ computer, and I set about learning BASIC so I could estimate pi. The program did exactly what it was supposed to do, but because of round-off error, I think I was able to estimate pi accurate to about 3 decimal places. It was a bit disappointing, but the experience was so exciting, I went on to pursue electrical engineering. I attended the University of Virginia for my B.S. in Electrical Engineering. I have an M.S. in Electrical Engineering from Stanford, but to help pay for tuition, I worked as a teaching assistant, and realized that teaching was really what I should be doing. I switched majors to earn my Masters in Education at Stanford, and I have been teaching math in public high schools ever since. My favorite mathematical activities today are playing sudoku, writing excel spreadsheets to do things such as calculate 2^100, and trying to find an algorithm to pick stocks from the S&P 500 to outperform the overall market.

ADDITIONAL BIOGRAPHICAL INFORMATION

I love to run on the trails near my home in Colorado. I did the 2009 Denver marathon with a time of 4:27:03, which is just a tad over a 10-minute mile pace. I have two children, ages 7 and 10, and currently reside in Colorado. With two dogs, my wife and I are pretty busy!

GRADES

3^{rd}, 4^{th}, 5^{th}, 6^{th}, 7^{th}, 8^{th}, 9^{th}, 10^{th}, 11^{th}, 12^{th}, Homeschool

SUBJECTS

Math, Algebra, Applied Math, Basic Operations, Calculus, Fractions, Geometry, Graphing, Numbers, PreCalculus, Trigonometry, Other (Math), Arts & Music, Accounting, Anatomy, Statistics, Word Problems, Algebra 2, Mental Math