Parent Function Poster Idea

Last week we were reviewing parent functions in my math models class.  After introducing and taking notes on different families of functions (linear, quadratic, square root, cubic and absolute value), it was time to dust off an old favorite to help cement it in their minds.

Adjusting the mini-poster idea from Ten Cheap Lessons, I had my students illustrate three parent functions (linear, quadratic and their choice of one other).  Their posters included the graph, equation, domain and range as well as 2 examples of other functions from that family (labelled as "babies," "kids" or simply "examples").  I'm a strong believer in the power of having students illustrate key ideas while creating their own examples to supplement them, and this idea was no different.

Above you can see a completed example.  I sketched something similar for my classes so they could easily see what I was asking for.  Below are directions they were given.

Versions of this mini-poster idea have been invaluable over the years.  Just recently I had my Algebra I students compare and contrast solving equations and solving inequalities.  It's a project that requires a minimum of supplies and preparation on your part: you just need unlined paper (color if possible, but it's not necessary) and markers or colored pencils to draw with.  You can also assign it as homework without worrying too much about whether your students will have what they need to do it (you can always provide some materials to those that do).

This should take students no more than one 45-55 minute class period to complete.  I counted it as a minor assessment (aka quiz) grade, but of course you should do whatever makes sense for you.

Have you used any variation on this theme?  Share it in the comments.

Equations vs. Inequalities Mini-Poster Project

The first chapter in my first book is entitled "The Mini-Poster," so it should be no surprise that it's a favorite that I constantly adapt to new topics.  This time around, I wanted to do a "six weeks" project to wrap up the grading period in Algebra I, where we've been working on solving equations and inequalities.

In this project, students make four mini-posters (one 8.5" by 11" page each) for four (technically seven) types of problems:

1. One-step equations and inequalities
2. Two-step equations and inequalities
3. Multi-step equations and inequalities
4. Special case for inequalities (when you have to flip the inequality sign)

Except for the last one, each poster is supposed to have what is essentially the same problem worked out the same way, but one is an equation and the other an inequality (with the sign of their choosing).  The difference is that the inequality has the particular sign and needs to be graphed on the number line.

By forcing them to do the mirror-image problems, the message is explicit: you solve both problems with the same steps.  Along with reviewing all of the problems, the purpose of this project is indeed to draw the clear connection between solving the two types of problems.  I told students to keep the title and "how to solve" sections the same as what's on the directions, but to change the examples (helpfully outlined in boxes) to their own

Regular readers will probably note that this isn't all that different from the Linear Equation Formula Book project I shared last week; indeed, one student that I have in both classes made the same connection fairly quickly.  That's because it's not really all that different.  But that's okay.


Download a PDF of the project directions here:

Equations vs. Inequalities Mini-Poster Project

Here are some of my earlier mini-poster ideas for you to draw from:

• Project Idea: Independent vs. Dependent Variables - the original (I feel like this constitutes a "classic" at this point)
• 2 More Mini-Poster Ideas
• Project Idea: Linear Functions Mini-Poster

Updated Linear Equation Project Idea

One of the lesson ideas I recently rediscovered was a project I dubbed the "Linear Equation Formula Book".  Student get to prove they can do the types of problems we've been focusing on throughout the unit in a way that doesn't seem like an assessment.

First, the kids create a "book" by folding two pieces of paper together (hamburger style).  On each page, they'll write a title, a formula/steps to follow, and include their own completed example.


On my guide I include completed examples of each page and type of problem we've been focusing on:

1. Finding slope between two points
2. Rewriting equations into slope-intercept form
3. Finding an equation using point-slope form
4. Graphing from slope-intercept form
5. Finding x and y-intercepts
6. Finding the slope of parallel and perpendicular lines
7. Graphing linear inequalities
   

My students really had to just worry about using their own example--the title and formula/steps (explained in the way I usually break it down) could be the same.  While some students missed the point and just copied the whole thing verbatim, most did it right (or did so when it was returned to them to fix).

I like this as an effective review (or a fun alternative assessment in and of itself) because students have to demonstrate that they can successfully do each of these types of problem.  Either way, the book can stay with the students as a fun, accessible study guide for future state or end-of-year exams.

Download a PDF of my project directions below.  This is designed to take about two 45-55 minute class periods at most.

Linear Equation Formula Book (new fall 2011 version)

Here's are two alternate versions you can also draw ideas from:

Linear Equation Formula Book (2009 version)
Project Idea: Using Formulas to Find Area, Perimeter and Circumference

History Week, Day 5: Constitutional Expert Project

In December of my second year of teaching, I was absolutely despondent. My classes were not going very well and I wasn't very happy with myself as a teacher. Desperate to create the kind of exciting, student-centered classroom I had always dreamed of having, I went to my TFA advisor and asked for guidance. With her help, I created what is still the most ambitious project I've ever asked students to do.

It's called the Constitutional Expert Project, which asked students to "focus on either: one of the amendments we studied, the entire Bill of Rights, or the principles of the U.S. Constitution (popular sovereignty, federalism, checks and balances or separation of powers)." I wrote about introducing this project at the time:

It was grander in scale than anything I had thus far tried, and required me to really sell it to them at the beginning in a way I had never successfully done before...

I dressed up like a waiter and arrived Wednesday in character as head waiter of DeRosa's New Jersey Diner, where the options are endless and there's plenty of "food" (knowledge) available for any budget. Based on what they knew coming in about what we had been doing the past week, they would pick from different sets of assignments--pictures, songs/raps, writing their own amendment, skits, surveys, letters to the editor, PSAs, etc.

It is a highly differentiated project that's meant to incorporate many learning styles. After introducing the basic premise of the project, each student completed the "wallet check" diagnostic to see what they could "afford" (which types of assignments they could choose from). There's a graphic organizer and rubric included to keep them on task and show them how they will be graded.

Here's a small sample of what my students came up with:



There were also puppet shows, skits, new proposed amendments and opinion pieces. Needless to say, it was exciting to witness both the creation of their projects and their presentations.

I have to give a lot of credit to materials I found in my TFA curriculum and examples of projects my TFA advisor gave me. As with just about everything good I've done in the classroom, this was the product of many other people's good ideas. Of course, I comfort myself in the fact that most good teachers "beg, borrow and steal" to create their best lessons.

Constitutional Expert Project [MS Word]

Solving Quadratic Equations by Graphing Mini-Project

Here's a simple, tiny alternative assessment for solving quadratic equations by graphing:

Finding Zeros Mini-Poster Project

1. Graph one quadratic function that has two zeros (create one or use one we did in class).
2. Show how to find the zeros using a table.
3. Show how to find them using the graphing calculator’s “zero” function.
• Buttons to press
• What to do when it says “Left bound?” “Right bound?” and “Guess?”
4. Mark the zeros on your graph clearly.

Alternately, you could ask students to graph three equations: graphs with one, two or no zeros. I also stress that solutions, zeros, x-intercepts and roots are all different words for the same thing, and you could have them work it into the title of their posters.

This project can be scaled up or down (a huge poster vs. a single piece of graph paper) and easily incorporated into a larger unit on the various methods for solving quadratic equations.

As always, share your related ideas in the comments!

Quick Adding and Subtracting Integers Review

Here's a short informal assessment that I've used for years when we've studied adding and subtracting integers. This is one of those little things that gives us (and them) headaches throughout the year. Whether we're solving equations or simplifying expressions, there's no way around needing to know these simple rules. I hope you find this helpful!

Adding and Subtracting Integers Review

Basics of Quadratic Functions Project Idea

Up until recently, my Algebra I students had faced an uninterrupted string of quizzes each Friday--something like five weeks in a row. I usually mix things up a little more than that, so this project was a long time coming.

This is a poster project that covers the some of the basic vocabulary of quadratic functions:

• vertex
• axis of symmetry
• minimum and maximum
• domain and range

Students make 2 graphs of 2 quadratic functions, one that opens upward and one downward. They label the parts, then explain the significance of "a" in ax²+bx+c and how to find the axis of symmetry and vertex using the function.

Last year, I did a similar poster project about parent functions that you could also use. If you're wondering about transformations of quadratic functions, I covered that this week and am continuing that this week. That topic might also be well suited to a poster project as well!

Download Basics of Quadratics Poster Project

These posters can be any size, but are designed to be simple and scalable. If you like this idea, it's a remix of Idea #1 from my book Ten Cheap Lessons: Easy, Engaging Ideas for Every Secondary Classroom. There's more great inspiration inside!

Project Idea: Straightforward Example Posters

This past week in Algebra II, we studied the Law of Sines. It took longer than I anticipated for students to really start to "get it". Nevertheless, due to sporadic attendance and what I saw as varying levels of mastery by Thursday, I decided students weren't ready for a quiz quite yet.

I instead gave students a project that would give some a chance to demonstrate their mastery of the material and allow students who were still struggling a chance to finally figure everything out. Thus it is both a teaching tool and an alternative assessment.

I found a set of 15-20 problems that I would have included on a quiz and put them onto a handout with dead simple directions:

Directions: Pick two of the problems below. You will complete two posters.

1. Solving a triangle. Find the missing angles and side lengths. Show the Law of Sines, all of your work, and the correct answer (of course)!
2. Area of any triangle. Show the area formula and explain how to know which sides and angle you have to use. Show your work and the correct answer.

EXTRA CREDIT: Complete the remaining problems on a separate paper.

This project can be adapted to just about any topic, especially ones where completing any single problem requires a lot of time and effort to complete. Students complete just one or two examples of problems you've been studying, showing all of the work and any formulas, rules or procedures you've taught them.

When you hang these posters around the room and school, you and your students can refer to them for help whenever necessary. Their presence also serves to build your classroom culture by both making your room more warm and inviting and giving your students a sense of pride and accomplishment.

This kind of straightforward example poster is also one of the ideas for using the word wall in the secondary classroom from my book Ten Cheap Lessons.

Project Idea: Transformations of Exponential and Logarithmic Functions

I assumed when I started teaching Algebra II that since the students were older and more mature that I wouldn't need to do a lot of the kinds of engaging lessons I always needed for my Algebra I students. I wasn't wrong, but I wasn't completely right either. It's all a matter of degrees.

I still need to engage my older students with innovative lessons, projects and games. In this case, we'd been studying transformations of exponential and logarithmic functions for two weeks, so I decided to use a final project as a final assessment.

The project was quite straightforward: Choose either exponential or logarithmic functions and make 1-5 posters of the five transformations we studied in class. I did ask them to show examples and to include something to make it easy to understand and memorable, but otherwise it was open ended. The five transformations are:

1. Vertical translation
2. Horizontal translation
3. Vertical stretch or compression
4. Horizontal stretch or compression
5. Reflection

Each transformation has two possibilities, which really means there are ten in all. As usual, I didn't have poster board, so I made do with some large paper I found in our supply closet. Here's what they came up with:

This project is an adaptation of Idea #1: The Mini-Poster from my book Ten Cheap Lessons: Easy, Engaging Ideas for Every Secondary Classroom.

Linear Equations Formula Book

In October, I wrapped up a unit on basic geometry by having students create a formula book. Each page of their booklet contained a title, formula and completed example. I recycled this project for last week's unit on parallel and perpendicular lines. I figured it would be a good quick assessment of this week and key things we needed to spiral back to that we studied before winter break.

The book would be little more than two unlined pages folded in half together (I used colored copy paper). Besides a cover, there would be 5-6 pages:

1. Slope Formula
2. Changing Equations into Slope-Intercept Form
3. Point-Slope Formula
4. Parallel & Perpendicular Lines
5. Parallel & Perpendicular Lines Through a Point
6. (extra credit) Finding slope from a graph, graphing from slope-intercept form, etc.

I gave students a chance to prepare by giving them the 5 example problems as homework the night before. As expected, very few students completed the homework, but those who did had a far easier time. This project could be completed in less than two 55-minute periods, and the handout is designed to be printed as a double-sided 1/2 page (print two copies, turn one to the opposite orientation, and print 1->2 sided).

Linear Functions Formula Book (PDF format)

Alternative Assessment Idea: New Version of "Students Become the Teacher"

Last week I replaced my usual weekly quiz with a new version of an idea I shared both here on the website (Slope-Intercept Project, Teacher for a Day) and in my book Ten Cheap Lessons, (Idea #8 "Students Become the Teacher"). In my new school there is less of a focus on teaching to the test, so I use very few multiple choice questions on my assessments. This was a central part of the original version of the lesson, requiring quite a bit of reflection and revision.

I've been very impressed by the progress of my classes this year, and I think their fundamental skills coming in are far beyond what I was expecting given the reputation and results of the school districts here. So I've been giving a lot more open-ended problems, which gives me a much better picture of where students are as we progress. It also means I had to scrap much of the original idea and create a framework to guide students in creating a much different kind of quiz.

The purpose of this kind of assessment is two-fold:

1. Student create a quiz with an answer key, proving they can answer questions about whatever it is you've been studying.
2. It promotes higher order thinking as students determine what type of questions to include, what they might look like, and the relative level of difficulty involved. This is especially true if they have to write word problems.

In addition, students may realize that being the teacher isn't the easiest job in the world (even if you don't explicitly mention that part). That's good for your classroom culture.

I decided to use this in both my Algebra I and II classes (for different topics of course), and to give students a clear rubric in the form of a checklist. The list tells them:

• How many of each type of problem to include
• In Algebra I, I asked students to include some negative numbers, fractions and decimals to insure a higher level of difficulty on their quiz (those kind of basics are things we struggle with constantly)
• To include a complete, correct answer key, directions, and a heading as any assessment must have
• An extra credit question (as teachers like me are known to provide frequently)
  

What I had thought about providing, but didn't, was an example of a completed quiz as a model. I did give a few examples of what each problem might look like, and strategies for coming up with problems, but neglecting a complete model left many students lost. The class period wasn't long enough to complete the assignment either. This made the turn in rate really low, and is purely my fault.

On the other hand, I've learned over the past month that my students want a more traditional, straightforward approach in my teaching. This is mostly due to a complete lack of stability in the math department at my school--they've had eight different teachers over the course of 2 years, with varying degrees of effectiveness in their respective tenures. In Texas, I often had to use the kinds of alternative strategies I share because my students didn't get the material the first time around. Now, my students tend to get more of the material in less time, and appear to have an insatiable appetite for challenging material. It's a very interesting dynamic to deal with.

In any case, here's the two versions of the checklist via Google Docs. They are designed to fit two to a (landscape-oriented) page to save paper. The back of each half page would be a good place to put a full sample quiz or examples of appropriate questions.

You Make the Quiz (Algebra I version)
You Make the Quiz (Algebra II version)

Math & Website Design: Reflections and Best Practices

Reflections
If you read my last post, about my final week of summer school, you might have noticed that we didn't get a whole lot done over the course of the week. I briefly mentioned some "complications" that made my straightforward plans into a fiasco. I am writing about these separately from my recap of the week that was, both to help me sort out my thoughts on the course and serve as a guide to other teachers who may want to do something similar.

The first problem was that on Tuesday and Thursday, Mystudiyo was working only sporadically or not at all for several hours both days. Even when it was working, a major user interface flaw made sure that more than one student lost all of their work from Friday and Monday: if you don't type in something in the "question" field, everything else you type is lost when you click "Submit Question". Since most students were writing long word problems, they used the optional, supplemental text box instead. No one, myself included, knew what was going on until it was too late, because there is no error message to alert students that the questions weren't saved! On most websites, when you fail to fill in a form correctly, you are immediately brought back to the form and alerted as to what you failed to fill out correctly (believe me, my students are now well aware of that truth).

In addition, students started to forget usernames and passwords. Some had forgotten even the email addresses we had created back in the first week. I spent entire periods walking students through the "Forgot Password?" process on Synthasite, MyStudiyo, and their email accounts. Of course, the fact that the websites were buggy or not functioning didn't help matters.

There was one last problem, one that made sure nothing would go to plan last week, and that was poor attendance. Almost every student missed at least one day last week, compounding the above problems. As a result, I pushed the individualized math problems to the bottom of the agenda, and didn't hold it against students if they didn't have the time to get to them. I suppose I lowered my standards and perhaps that's why I feel so guilty.

I didn't anticipate or plan for any of this--indeed, if for some reason we weren't able to get online at all, I wouldn't have been ready. I am happy with the websites that the students produced, but I'm nonetheless disappointed in myself and wondering whether my course was a failure in both design and execution.

As per usual, I gave my students an end-of-course survey on the last day of class. Most of the responses leaned positive, but this student's concerns are the one that has resonated with me:

He tought us how to build a website so that it can help us with our own math...but he could have gave us math problems to figure out and the questions that we didnt know...thats what our website could have been based on

I liked being able to use the computer to make a website...But i didnt like the lack of math that we got to do...or learn...maybe next time the same amount of time that we spend on the computer we can spend doing math...but this was just summer academy so overall it was good...plus the subjsct of this math class was to mak a websitebut still a little math wont hurt

I might have a trouble in his math class...because its hard for me to understand they way he teaches

I can't remember any student telling me at the end of the year that they didn't understand the way I taught. That's arguably the most important skill I bring to the table: the ability to break down concepts in a way students can relate to and understand. The fact that this very bright student feels they were let down is extremely troubling.

Best Practices
If you want to try website design as a course or perhaps a project, this is what I've learned from the process:

1. Know exactly what you want them to do. Figure out what online resources they'll use well ahead of time, decide what the final website should include, and provide clear, concise steps for them to follow. You can do this either by publishing it online, as I did with my class blog, or by providing printed directions and rubrics.
   
2. Tie in your subject matter from the beginning. You could easily build a web design course where students make a site about whatever they want, but there's so much potential for long term learning if they create a thorough subject-area resource that can be used in class. I waited too long to refocus on math, and my students suffered.
   
3. Differentiate. This might mean that every student works on a different topic but follows the same basic outline for their website. It might also mean that the website can be one option from a list of possible products for a end-of-unit, semester or year project. As much as students should have some scaffolding to follow, you must allow some flexibility within the structure to let student creativity and brilliance shine through. For example, I required at least one video on their website, but gave students the option of finding an appropriate video online or creating one themselves.
4. Don't get sidetracked. There's no shortage of great web resources that students could use to create amazing content for their websites, but there's only so much time available for any such project. I spent days having students play around with Dvolver Moviemaker, Bubblr!, Make Believe Comix and Sketchcast; meanwhile, they couldn't navigate their new email accounts or the sites that we actually did use on our websites. Decide what kind of creative content would be most appropriate and meaningful for your goals and spend most of your time on those.
5. Plan for worst case scenario. Be prepared for Internet outages and non-functional computers. There should be a strong "offline" component for any project like this. Also, remembering multiple usernames and passwords is difficult, so you must decide if that is absolutely necessary for your purposes. In my case, I wanted to use multiple websites that required registration, so having permanent email accounts was necessary. Based on the nature of your prospective project, you might choose disposable email or a teacher-controlled system.

If you have designed or plan to design a course like this, I'd like to share your insights as well. Please email me (teachforeverATgmailDOTcom) or leave a comment. Thanks!

Math & Website Design Week 3: Final Results

Today was the last day of our Summer Academy, and this week I tried to reconcile the math and website design facets of my course. As I mentioned last week, I wanted tie more actual math problems into the class into the limited time we had left. Things didn't go exactly as I had hoped, but I'm happy with the results and I think the permanence of this project will have positive effects far into the future.

On Monday, students tried to complete their Mystudiyo-built quizzes, which were then easily embedded into their websites (hosted at Synthasite). I also put together and distributed packets of 10-15 problems drawn from Barron's MCAS in Math that were individualized for their respective topics. I urged them to use their websites and the skills they had been practicing to find additional online resources to help them.

Then on Tuesday, students were still trying to complete their quizzes, although there were some complications that I'll talk about in a future article. Only a handful of students got the chance to jump into their math packets at all.

We visited Northeastern University on Wednesday. For many, this was the first exposure to the concept of college as a possible future, not to mention their first visit to a college campus. Our school is young but committed to building a stronger culture of achievement and success, and this is a great building block to that end.

When we returned to campus on Thursday, students were given this Final Presentation rubric, which contains a website checklist and the questions I would be asking during their presentations on Friday. I also made sure to clarify how to not only save but publish their websites, so I created the slideshow below using screen caps (edited with IfranView) and Photobucket. It should be helpful for any teachers trying to use Synthasite with their students.

Finally, it was the last day of (summer) school! I had the chance to see a few of my students' websites earlier, but this was my first chance to see everyone's completed projects. I was very impressed at what they came up with:

• A & J's World of Geometry ***
  
• Da Ladi Hawk's Graph Help***
  
• Jonathan’s Word Problems Site
• Josh’s Math Website
• Maira’s word problems site
• MCAS math prep
  
• Mean, Median, Mode and Range ***
  
• My Geometry Site ***
  
• Patricia’s Order of Operations website ***
  
• Algebra and Wonderful Algebra
  
• Quadratic Formula
  
• Slope and Linear Equations
  
• Star’s Volume Formulas ***
  

The sites marked with stars (***) are the best of the bunch IMHO. Jonathan's site and Maira's site were special achievements because both are ELL and were thoroughly committed to improving their English language skills. Overall I think this experiment was a tremendous success, and it has given me a lot of ideas and inspiration for the coming school year.

More About This Project

1. Watch my Math & Website Design course unfold as it happens! [First post about the project]
2. Math & Website Design: Creating the Websites
3. Math & Website Design Week 2: Experiments and Progress
4. Mr. D's Math & Website Design Class Blog [The site will remain online as a useful math resource and of course a testament to our hard work.]
5. Final Presentation rubric [via Google Docs]
   

Coming this weekend: End of summer student survey results and my reflections on best practices and pitfalls to avoid.

Graph BINGO Review Game

Last Friday was the last day before Spring Break, so I had to pull out all the stops to keep my students engaged and maybe, just maybe, actually teach them something. We needed to wrap up our review of Objective 1 & 2, incorporating a lot of different ideas and tying them together:

• linear equations and inequalities
• what is an isn't a function
• quadratic functions
  
• parent functions
• connecting word problems to graphs
• identifying all of the above visually

So I decided we'd play BINGO, using a board made up entirely of graphs. There are plenty of resources available online to create bingo cards for free, but I couldn't find one that did what I wanted it to do (the closest was this picture bingo card maker at ESLactivities.com). I was cutting and pasting from the PDF files to a Word document, not creating individual image files, so I had to make it myself.


All of the graphs were pulled from TAKS released tests from Grade 8, 9, 10 and 11 and the 9th grade TAKS Study Guide. The graphs are informally grouped together, and I manually moved graphs and columns around to create 20 different cards.

The game is played like regular bingo, 5 in a row across, down or diagonally with a "free" space in the middle. The call sheet contains each graph and a verbal descriptions of it. I wrote each description on my document camera (the 21st century overhead projector) and repeated it verbally as well, and then students worked alone or in groups of 2-3 to identify the correct graph.

Instead of yelling out "BINGO!" students yelled "GRAPH!" and I verified their results. We were able to play 2 games in 45 minutes. I guided students as much as possible through the first game, but then left them on their own for the second. They enjoyed it, were engaged (even with Spring Break looming) and most importantly had a clear grasp of the material.

I used highlighters as markers, which means the boards couldn't be reused. This was a pain, but better than the alternative. I've done different versions of bingo in class for years, and no matter what I used for markers--actual bingo chips, pinto beans, candy--students would throw them at each other, steal them and create a huge mess. By having them work in small groups, there were enough cards left over that I only needed to print the 20 for each class.

GRAPH bingo call sheet

20 GRAPH bingo cards

For more games and good ideas, check out my book!

2 More Mini-Poster Ideas

In my book I discuss mini-posters, where students create a "poster" on a standard 8.5" x 11" piece of unlined paper. Recently I used this idea in two new ways:

4 Questions, 4 Mini-Posters

After a week of classwork on percents, proportions, reading charts and probability, I wanted to use an alternative assessment (I have been working under a no multiple-choice test policy since our most recent benchmark). We have a state test prep workbook that has multiple-choice questions on each objective we need to cover, but obviously I like to use this sparingly. It is not always as aligned as I might like it to be and often the scope and level of the problems is just plain overkill.

That being said, it's still useful in bits. So I asked students to make a mini-poster for each of the four topics we covered, drawing questions from the pages in the test prep workbook. So they would have four questions, four correct answers, and most importantly, the work involved in solving the four problems. While I did ask them to put some effort into making it look presentable (so we can hang them up), the 4 mini-posters were graded solely on showing the work (or writing an explanation) and the right answer.

To keep grading simple, each question was worth 15 points for the correct answer and 10 points for showing the work (although I could understand if you wanted to flip that ratio). I also then looked at the posters as a whole and took off a few points if they didn't really follow the directions (i.e. they put all 4 questions on one paper or put little to no effort into making it legible or poster-y).

Overall it gave me just as good of a picture as any traditional assessment I would have given, while allowing them the time to really analyze the problems and get help on difficult problems.

Parent Functions

Mini-posters are also useful for vocabulary that needs to be memorized, because it forces the student to visit and revisit the definition and to create visuals and examples that illustrate it. On our January benchmark, students had no idea what the linear parent function was, because we hadn't yet discussed it in class (I wanted to save it for later in the year since we would couple it with the quadratic parent function). This is one of those rare Algebra items that requires no work, just memorization like they do more frequently in history or biology.

So first we defined the two parent functions we focus on in our course: linear and quadratic. We wrote the equations (y=x and y=x², respectively) and sketched the graphs. I explained that linear functions made a straight line graph and had no exponent higher than 1, and that quadratic equations made a U-shaped graph and had x² as the highest exponent in its equation.

On the poster, I asked them to illustrate this, as well as an additional example from each family of functions--the babies. The parents are the most basic functions that we compare the others to, I explained, and all of the others are "babies". Besides the definition, students are asked to identify which family a given function belongs to, so this is crucial.

So their poster has two parents and two babies. I'm concerned that maybe I should have left the babies out so as not to distract them from the definition of a parent function, but I think this was simple enough that there was little confusion. I just hope my students don't go home and tell their parents, "today in Algebra, Mr. D told us to make babies."