## Saturday, October 31, 2015

### The Benefits of Card Sorts in Math Class

I recently started using card sorts in my eighth grade math classroom.  Using card sorts has really had a very positive impact on my students.

Identify patterns
Card sorts require students to look for overarching patterns, making them great summarizers at the end of a lesson.  I recently had a jigsaw lesson where students each graphed a different function and then discussed patterns within the various families of functions.  After students had completed the jigsaw, I set each group up with a card sort (available here) where students sorted equations into four families: linear, quadratic, absolute value, and rational.  Based on the lesson, they were able to recognize the characteristics of the equations and then classify the functions.

Jumpstart Discussion
The card sort was very effective for jump-starting discussion.  Students consider one card at a time and pick a category.  If there was disagreement, they had to defend their decision with evidence from the characteristics of the equation.  In many groups a leader emerged, but I modeled for students the type of discussion that I wanted to see to ensure all students were engaged in the activity.  Very impressive results!

Hands-On Learning
Whenever possible, I try to incorporate hands-on learning activities.  There are countless benefits of engaging students in “doing” activities, as opposed to “listening” and “seeing” activities.  The process of having to think about each function, make a decision, willingly make a change if needed, and arrive at an end product is a much more effective process than having a direct instruction lesson in which I summarize and a couple of students participate verbally.

How do you use sort cards in your math class?  Do your students enjoy using them?

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## Tuesday, October 27, 2015

### Strategies and activities for teaching slope and rate of change

I am very excited to participate in Education with DocRunning’s Teacher Treats Blog Hop.  I am currently teaching slope and rate of change to my eighth grade students, so I’d love to share some strategies and activities that my students and I love.

1 – Undeniably Terrifying!
It’s true.  I have lived in New Hampshire all my life and I can’t ski.  I went on one ski trip as an eighth grader and all was going well until my friend convinced me to take on a very, very difficult trail.  Let’s just say I knew that as the ski lift climbed higher and higher up the mountain that I would not be skiing down.  Long story short, I held down the bar when we got to the top and convinced the employees to let us ride back down on the lift.  I love sharing this story with my eighth graders and I spare no detail.  Every year I have all eyes locked on me, total engagement, as I tell them about my personal experience.  The UNDEniably terrifying mountain that appeared to have UNDEfined slope.  When possible, I love to use personal anecdotes with my students.  I think it’s a great way to build relationships with students, and, in the very least, it wakes them right up!

2 – Soccer in Math?
My students in standard level eighth grade math struggle to understand the difference between zero and undefined slope.  I couple of years ago I drew some symbols on the front whiteboard and said aloud, “Imagine the 0 is a ball that someone is standing on.”  Somehow that simple statement has evolved into a demonstration of me standing on a soccer ball in front of my students.  (You might even find a vine somewhere floating around if you search crazy math teacher on soccer ball.)  The connection is that if I hold the ball over my head there is ZERO excitement.  If I stand on top of the ball I will UNDoubtably fall over (hopefully without injury).  As silly as this demonstration is, I believe it gives them a visual to associate with an otherwise abstract concept.

Another strategy that helps reinforce this topic is using the multiplication check.  I start by reminding students that we know 12/3=4 and 4*3=12.  So 0/3=0 because 0*3=0 (check in reverse).  However, 3/0 cannot equal 0 because 0*0 does not equal 3.  The answer must be undefined.

3 – Whiteboard Volunteers and Non-volunteers
My eighth graders love to write on my whiteboard.  Consider ditching the worksheet and inviting students to write on the front board.  I use this practice method for many different skills.  I invite 5 volunteers to front board.  Students at their desk each have a piece of paper that they are writing on.  For slope, I would read aloud two points and ask everyone to find the slope of the line that passes through the two points.  Students at their desks try the problem on their paper, while I can monitor the progress of students at the front board.  Everyone tries the same problem at the same time.  After everyone finishes the problem, we discuss anything tricky or interesting and then rotate to have five new volunteers come to board.  Some classes are more willing and eager to come to the board than others.  I refer to students who need some coaxing as “non-volunteers,” and require that all students come up to board at least once.  I try to be strategic when selecting groups of students so that I can differentiate based on readiness and help all students build confidence.

4 – Differentiating Instruction
I try to differentiate based on readiness and interest where possible.  One idea that I picked up at a conference years ago is the idea of differentiating by designing a “menu.”  I designed a slope menu that is sorted by appetizers, entrees, and desserts.  The appetizers have skill-based questions, entrees consist of higher order thinking conceptual tasks, and desserts are fun, hands-on applications.  Students are instructed to select at least one task from each part of the menu.  Each question is assigned a point value, and students are assigned a required total value they must complete.  They can choose any combination of problems they want as long as they reach the required minimum points value.  This is a fun twist on worksheet practice and it allows students to have choice regarding the type of practice they complete.  I further differentiate by encouraging my high flyers to focus on the higher order thinking questions and check in to make sure my struggling learners understand how to complete all of the skills-based problems.  Here are some sample problems:

Slope has great connections to the world around us, and it tends to bring out my creative side.  I would love for you to comment below with activities and strategies that you love to use when teaching slope and rate of change in your classroom.  Thanks for stopping by!

Stop by my TpT store for tons of awesome resources related to slope and rate of change!  This truly is one of my favorite topics.  :)

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## Sunday, October 18, 2015

### Tips and Tricks for Teaching Students How to Solve Linear Equations

My students arrive to eighth grade with a fairly strong knowledge of one- and two-step equations.  This year with the new seventh grade curriculum my standard math students are coming to me having never solved an equation with the variable on each side.  Within a couple of short weeks, we will review two-step equations, discuss equations that involve the Distributive Property and Combining Like Terms, solve many equations that have the variable on each side; including those with fractional coefficients and special solutions, and study word problems with scenarios modeled by linear equations.

Solving linear equations is an immensely important skill for middle and high school students to master.  It is imperative that students understand what they need to do and why they need to do it.  In this post, I would like to share some of the strategies and resources I use in my eighth grade math classes.

1 Socks and Shoes: Understanding “Reverse Order of Operations”
Whenever possible, I try to relate what we are doing in class to something students understand in their own lives.  Last week I compared equation solving to putting on socks and shoes.  In the morning when getting ready for the day, socks go on first, then shoes.  But at the end of the day, shoes come off first, then socks.  The same is true for equations.  Consider the equation 3x+1=-14.  When the x “got ready” using order of operations, it would have been multiplied by 3, then the 1 would have been added.  So to undo the operations, start by removing the 1 and then the 3.  I have used this analogy year after year and it has proven an effective strategy for my students.

2 Require Beautiful Work: Ban the “Baby Symbols”
I require very clear equation-balancing evidence – even for one-step equations.  I want students to understand why they can add/subtract/multiply/divide.  Very quickly we move from one-step review to solving equations with four or more steps.  I have found that students who are lazy about showing their work in the beginning of the unit tend to flounder when they have many more steps, variables, and numbers to keep track of.  I have also seen many more errors with integers and incorrect operations when the work is not clearly done out.  There are always some moans and groans, but I know that it makes a huge difference a week later.

When students are showing their beautiful work, I ban some of the symbols they may have used in the past.  I “joke” that we are “breaking up” with them and that it won’t be their last break up.  Eighth graders find it shocking that I bring in the idea of relationships and it captures their attention.  I do not allow students to use “x” for multiplication when solving.  It can get confused with the common variable, and parenthesis are a better way to communicate multiplication.  I do not allow the traditional “divided by” symbol either.  I urge my students to use the fraction bar to show their division.  I had a student tell me last week that he didn’t like the fraction bar because then he couldn’t tell whether it was a fraction or division.  Ahh!  I gave a couple of basic examples to show that they represent the same thing.  Finally, I do not allow students to divide by a fraction.  I require multiplication by the reciprocal.  I help students buy-in by demonstrating how it actually saves them time and work if they multiply directly within their organized steps.

3 Use a Discovery-Based Approach to Special Cases and Strategies

I am a big fan of balancing discovery-based learning and traditional practice.  Special cases can be challenging to understand.  I group “x=0” in with special cases because it often is confused with no solution.  To help students build meaning and understand no solution and all real numbers, I created discovery-based worksheets that lead students to the big ideas.  They learn, not just what to look for in order to identify the special solutions, but what it actually means for there to be a special solution to an equation.

I use a similar approach when teaching students about equations that involve fractions and decimals.  I created a discovery-based worksheet that walks students through how to clear out fractions and decimals from equations.  They learn how to select the factor they should multiply by on each side of the equation, and they clearly observe how much easier an equation can be to work with when taking the time to clear out the fractions or decimals from the start.

4 Practice in a Fun and Engaging Way
The best way for students to master linear equation solving is to do lots of practice.  But the practice does not need to be worksheet-based.  Here are some of the activities I use to help students learn to solve equations:

Holiday-Themed Partner Practice: My first few years of teaching, holidays would roll around and I would get so excited!  I wanted to acknowledge the holiday in my classroom, but I could never find anything mathematically meaningful.  That’s why I decided to create my line of holiday-themed partner stations!  Students travel in pairs as they each solve a different problem.  If they are correct, they will have the same answer as their partner.  Great self-checking activity.  Fun unscrambling component at the end, too!

·
Front Whiteboard Practice: My eighth graders love to write on my whiteboard.  I call five students up to board at a time.  Everyone else has paper and pencil out so they continue practicing even if the spotlight is not on them.  I read an equation aloud that everyone solves at the same time.  I switch up which students are at the front board so that everyone goes up 2-3 times.

Mini-Whiteboard Practice: I have a set of mini-whiteboards to use with my classes.  Students solve an equation on the board, then when I give the signal they all hold up the boards with their work and the answer so I get quick feedback on the level of understanding in the room and I can pinpoint students that I should check in with.

Task Cards: I love task cards!  My favorite strategy for task cards has been to leave them in a bin in the front of the room with the answer key posted nearby.  Each student takes one card, checks their answer, and replaces their card with a new one once they get it correct.  I have done this individually or in pairs.

Scavenger Hunt: I purchased a CSI-type scavenger hunt to use with my students.  I hid the “clues” around our Auditorium and we took a “field trip.”  Students loved getting out of the regular classroom setting, working at their own pace and in an unconventional way, and filling in the answers to the mystery during the process.  Thank you 21st Century Math Projects!

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## Saturday, October 3, 2015

### Games in the Secondary Math Classroom

For five years I taught eighth grade math in – what I like to refer to as – my pre-Teachers Pay Teachers era.  I had great relationships with students, delivered instruction in my own unique way, and facilitated student learning.  I worked really hard and considered myself a good teacher.  Then I was introduced to Teachers Pay Teachers.  I was completely in awe of all of the amazing resources being created by and shared with teachers around the country – even the world!  Suddenly my go-to methods for practicing math skills didn’t seem to have the “wow factor” I once thought they did.  Maybe you’ve heard it before.  You’ll definitely hear it again.  Teachers Pay Teachers inspired me to grow, to improve, to keep learning.  I have become a better teacher thanks to TpT.

I have always used games as a way to review math concepts.  However, TpT has challenged me to make them better: more meaningful, relevant, and attractive.  I feel great about the games we play in class.  My students are also more likely to buy in when the game has a polished look, clear instructions, and directly relates to the skills they have been learning in class.  I have refined many of my own games that are available at Free to Discover.  There are also some wonderful games from other sellers that I would like to highlight in this post.

Created by Amanda from Free to Discover.

Old Math Guy is a game I created that is modeled after the traditional card game “Old Maid.”  Students play as a group as they look for “matches.”  In the Graphing Inequalities edition, students try to match each inequality with its corresponding number line graph.  The Old Math Guy card provides added fun and excitement as students try to avoid getting stuck with it at the end of the game.  My eighth grade students love this!  I currently have two other editions available: Matching Linear Graphs to Equations in Slope Intercept Form and Matching Input and Output of Functions.  An updated look for my old math guys is coming soon thanks to Sarah Pecorino Illustration.

Trig Functions GO FISH – Grades 9-12
Created by Sandy from Weatherly.

When teaching secondary math concepts, Sandy believes in going beyond the “how” and teaching students the “why.”  Trig Functions GO FISH is a creative, engaging game that facilitates students’ understanding of trig functions.  According to her description:
“It is important that students in higher math classes commit certain concepts to memory. Games like this help them do just that, without resorting to boring flash cards or repetitious copy work.  Played like the game of “GO Fish,” this small group activity gives students an opportunity to review the six trigonometric functions and identify the equation, graph, domain, range and period of each.
They won’t even realize they are learning!”

Created by Brigid from Math Giraffe.

Visiting Brigid’s store, you will find that her activities provide a mix of fun and rigor.  Simplifying Rational Expressions Golf is a hands-on game that provides an awesome, interactive way for students to practice simplifying rational expressions.  According to her description: “This is a fun way to work through practice problems with rational expressions. Students "play" each hole on the course (5 hole-worksheet) by pulling a "driver" card, then an "iron" and then as many "putter" cards as necessary to sink the ball (get one right).  Each card has a rational expression that must be simplified. The golf worksheet has room for work, answers, and scores. A correct answer is 1 stroke. An incorrect answer lands your ball in the sand/water/etc. and forces you to add a stroke.”

I would love to hear about other games you have created or are you using in your secondary math classroom.  Please comment below to share your ideas!

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