number sense in secondary education

Usually, when I think of building number sense, I think about primary math education.  I know, though, number sense is something we all must work on all the time!  I'm curating ideas for secondary math and building number sense.

1. Knowing how precisely a high school freshman can estimate the number of objects in a group gives you a good idea of how well he has done in math as far back as kindergarten, researchers at Johns Hopkins University found.  This Science Daily article is quite interesting.


2. This is a go-to book for ideas: Building Powerful Numeracy for Middle and High School Students, written by Harris and published by Heinemann.  


3. This site says it's a community for number string design!


4. The state of Texas has a well-developed academic competition developed by the University of Texas - one of which is number sense.  Practice tests are available online here.
   


5. The San Francisco Unified School District Math Department has put together a page full of resources on number talks. Check it out!


6. Fawn Nguyen put together this set of 90-number talks for middle schoolers — enough for a full school year if you do this routine every other day.

What tools, routines, or materials do you use to build number sense in secondary students? How often do you work on number sense? How important is it in your math program?

Spiral Review Hit or Miss

I just read Julie's blog about the bombed tests and the need for review.   I understand completely!

We have 90 minute classes - plenty of time you say to build in spiral review!  But!  ... we meet only every other day and we have to teach the whole year before May 6 to be prepared for the state test.  We have been pushing our students like mad with very little time to stop, regroup, fill in gaps, review.  So my spiral review has been hit or miss.  Some days we have reviewed key concepts in our warm-up.  More often than not, though, our warm-up reminds students of the previous lesson or two ... but doesn't really go deep into reviewing.

I used the day before Spring Break as a spiral review day.  I created stations - each one addressing a standard from the past.  I gave varying points to the stations - students had to earn a 100 by working stations, checking them, reworking them.  That went well.  It was also telling - I could see which standards were still giving them fits (writing equations of lines - no matter what information was given  is our Achilles's heel).

Then after spring break, I made a class set of a textbook "end of course" review ... 9 pages, 50 problems.  Each day we are just doing one page ... 4 - 6 problems.  Because the textbook provides a chart matching standards to problems, I can tell at a glance which standards are weak.  We just did the first page - 6 problems.  Problems 4 and 5 were the pits - only half of my students could get them correct.

So ... on our next class day, I will spend just 5 minutes going over those 2 problems.  I thought about asking students to jot down their answers, then use "4 corners" to dialog about the problems.  Students will go to the corner of their choice - and discuss why they chose that answer.  Each corner will have to explain their thinking.  I'm hoping that dialog will help us clarify misunderstandings.

Then I'll pull a few problems like these to on our homework this week.  I'm hoping that by consistently completing a few problems a day, analyzing the results, going back over the weakest of the concepts will provide the spiraling we need in our last few weeks heading into testing.

This next week our PLC will meet to decide what other review measures we can put in place.  We will have 3 class days before the "big" test to review as well.   I'll report back with the strategies we decide to put in place.

(Not sure how it is with others who are reading this blog, but our students have to pass the state test to graduate.  In fact they have to pass 3 years of math, science, history, reading, and writing to get a diploma.  Each test is 4 hours.  So my freshmen are headed into a season of 5 days of 4 hour tests that affect their graduation status.  I'm all for accountability but this seems a bit ridiculous!)

homework - again

Grading homework is not for me!  How could I possibly keep up?

The school I am in doesn't want us to grade homework ... or at least they don't want it to adversely affect the grades of students who have mastered the concepts.

I'm OK with not grading and with homework not adversely affecting grades.

So ... is homework a non-issue?  Should I even assign it?  What is the value of homework?  This is my dilemma.

We have 90 minute classes - every other day.  I love the 90 minutes ... I don't like the every other day.  I am certain that my students encounter a neuralizer (http://meninblackneuralizer.com/) in between our classes.  I know my students are capable; they don't all have short term memory dysfunction;  and yet, several struggle to remember concepts from day to day.  Our curriculum is tight; we are required to teach new concepts in each lesson; there is little time for review.

So ... I envision 15 minutes of homework ... maybe 10 problems as the "perfect" solution.  It seems to me that a little practice in between classes would be beneficial.  And to no one's surprise, the students getting A's and B's are doing that little bit of practice consistently.  But the students who need the extra practice, for whom the extra effort could make a difference between failing and passing - those are the students who don't do homework.

I've tried various incentives.   Exact homework problems show up on quizzes - and completed homework can be used as notes on quizzes.  If homework is completed, students may retake quizzes and tests for up to 70 points.  I've tried consequences.  I record whether or not homework is complete in my gradebook - so that parents can see the pattern of work completed.  I've assigned students detention to work on homework.  But in the end, homework is not valued by students; the effort seems all mine to make sure it is done; and the students who might benefit the most are the most difficult to convince to do the work.

Is homework necessary?

Stations - work in progress

I'm so glad that the topic this week is stations.  I don't use them enough ... so I want to get more ideas.

In tomorrow's lesson, students are going to complete 4 activities.  We are wrapping up a unit; there is no new information being presented tomorrow.  It would have been the perfect day for stations ... but currently in my head I don't have the activities set up that way.   Students will ...

• Take a quiz on data collection and quadratics.  I'll provide the data ... they will analyze.
• Complete a practice activity on transforming quadratics.  I have a set of equations - they will describe the changes as compared to the quadratic parent function.
• Complete an activity in which they analyze a parabola within a particular context (our unit is on characteristics of quadratics)
• Finish the study guide for the test (we've done half of the study guide).

The day would have worked in stations ... but instead of trying to revamp this lesson, I will plan stations for Friday.  (We are on an A/B day schedule ... so Monday/Tuesday is the outline above; Wednesday/Thursday is the test).  While the work above is plain ol' practice, students will get to work with partners; I'll also post answer keys in the front of the room so that I am free to roam and help.  Students know my one rule is to check work with the keys without a pencil in hand.  For my teens there is too much temptation to change answers :)

Friday is our last day before spring break (whew - so ready!).  Students will be completing a spiral review that day.  Topics will include solving equations; something to do with lines (maybe writing equations; maybe analyzing linear functions in context); and systems of equations.  

As I'm reading the posts on stations, I'm thinking about how I could best pull together the activities for Friday.  I'll definitely be cutting up some already prepared worksheet type activities!  I hope to also use a computer station (Manga High).  I may also have an algebra tiles station.

This is the beginning of Friday's stations ...

Catching Up!

Helping students catch up in math is an ongoing effort.  On some days I think I am making a good dent in the process, and on other days I know I am fighting a losing battle.

As noted in other posts, I am in a new position, new state, new school, new curriculum ... and I've been out of the classroom for a while.  I'm delighted to be teaching again but whew!  I feel like I've been placed between a rock and hard place ... all the time!

I teach algebra to 9th graders.  I have students who came prepared to tackle the work, but I have some in every class that do not have competency in basic math skills.  We work on an A/B schedule, so students have math every other day for 90 minutes.  Sounds awesome but it is challenging to build momentum.  Our curriculum is laid out for us with very little wiggle room.  Many units require a new concept every class day; many units do not have a single day for review.  I am required to test on the same day as my team ... no matter what my formative data indicates.  And there is an expectation that there will be no more than 10% failing.  Early in the year I had as many as 20% failing - which was upsetting to me since in past years I have had very successful students.  I've whittled that down to 10% but I'm still not pleased.

Since we don't have much class time for catching up students who are behind, I use before school, lunch, and after school regularly.  Classes don't begin until 9; our contract day begins at 8:15; so I invite students to meet with me any morning that they can.  I usually have anywhere from 2 to 12 students each morning.  I often have a couple of students working in my room at lunch.  And after school I have a few.  I have a tight schedule after school so I don't encourage tutoring then.

In class, I am using a spiral warm-up to build retention and purposeful practice.  In our new lessons, I am talking less, and making sure students practice more.  I'm devising ways for work to be self-checking so that I am freed up to work with students around the room.  As students complete sections of work, they check with my keys, make corrections, and continue.  If they have errors or questions, I can assist them ... and I also encourage peer assistance.  We work most often in pairs.

Students keep a notebook; the Algebra team publishes a study guide for every unit test.  The study guide mirrors the test well so if students can do the review, they are ready for the test.

My frustration is that I am doing all I know to do; and I'm trying to learn as many different ways to meet students' needs as possible.  My failing students don't indicate that they sense any responsibility for studying or practicing in-between classes.  I believe both teacher and student have to accept responsibility when students are failing.  I'm struggling with how to inspire a bit of urgency on their part.

I look forward to reading the ideas shared online this week!

Anchor Charts

I've been creating anchor charts to go with each unit.  The charts hang around the room, hopefully reminding students of specific skills, steps, or formats.  Two of the most recent charts are pictured here.

Other charts are in this prezi.

the observed lesson

I was observed a few weeks ago.  I've been teaching a long time so I wasn't particularly nervous - instead I was curious about what my new school, new administrator would value.  He visited a high energy class ... my largest class ... 28 students.  It was Tuesday - the day after a school holiday.  I was pleased with the choice of class and the choice of lesson.

We had been studying systems of equations.  We had studied solving systems by graphing and by substitution. The lesson for the day was on solving systems in context ... yea for word problems!  One other key event was that all of our 9th graders had just been issued laptops.  They had had them for only 2 - 3 days prior to this lesson.

My outline:

• Check homework ... collect data via Google Forms, "Which problems did you miss?"
• Knowledge Check (aka quiz) ... just 2 plain solve by substitution problems
• Warm-Up ... translate words into algebraic symbols using Super Teacher Tools Speed Quiz
• Guided Notes ... just two problems emphasizing steps to success 
• Define Variables
• Write equations
• Solve system
• Interpret Solution
• Partner Practice ... 3 levels of differentiation
• Ticket Out of the Door ... online using Today's Meet, "What did you find more difficult, setting up the equations, or solving them using substitution?"

I wanted to highlight these school expectations:   formative assessment, differentiation, and high level of engagement.  I also felt the need to at least attempt the use of the laptops although we had had little time for practice.  That was the one thing I had asked my administrator to note - the laptops were new, we were still establishing a routine for their use.

I decided to use the newly assigned laptops for formative assessment.  I chose easy, easy online tools that required little set up from me.  They also required little prior practice from students.  I have a teacher website - I created an outline of the lesson there and posted the links students would use.  That way, students only had to go to my website to get to the short online activities.  There was no hassle with typing in long URLs.  And the data I collected was both quantitative and qualitative ... useful, too!

Students practiced with partners of similar abilities.  I color coded our practice problems.  There was a poster on the board with flaps - color coded to match the problems - where students could check their work.  I hole-punched their paper as they correctly completed problems - their goal - four hole punches.

I was free to be working the room, asking pertinent questions, talking to students about what I noticed in their work, and encouraging them to stick with the tasks at hand.  This kept my few rascals on task ... and students were engaged in the work.  They were successful too!

Our appraisal system is a complicated set of rubrics.  I was pleased with the outcome ... felt like my students demonstrated good success that day and that I was able to demonstrate key school expectations.

Here is the lesson plan:

Observation Lesson Plan by Beth Ferguson

If you are interested in any of the materials, leave a comment.  I'm glad to share.

Homework: Bane or Bliss!?!

Clearly "Bane" at my house!  I look forward to reading this week's posts on homework.  Homework has been a challenge this year and I don't know yet how best to handle it.  I just know ... I don't want to grade it!


So current status:

We give a very small amount of homework with each lesson.  Students have class every other day.  So 2 to 12 problems in 48 hours seems very small.

1. The homework we give is generally practice over that day's lesson.
2. We don't grade homework at all.  I provide solutions; students check their own work; and I typically answer any questions they might have which is most often very few.
3. I do record if homework was completed - but there are no points or percentage assigned to it.
4. The catch ... if we give a Knowledge Check at the beginning of class, completed homework counts 30% of the quiz.  Yes, that means if students get all correct solutions on the Knowledge Check but do not complete the homework, I record a 70 for their quiz.

When we started this requirement it sounded like a good idea.  The 30% was meant to spur students to complete the homework.  It has worked with some students - but not enough.  And of course the A student who really doesn't need the extra practice is penalized if they don't do the work; and the struggling students are the ones who resist doing homework the most - and they miss out on the "free" 30%.

OK ... so differentiation ... I've tried assigning "extra" problems and asking students to choose a subset of the assignment.  The element of choice is welcomed by my students.  But since we create all of our own materials, creating extra problems is not always profitable for me.  Occasionally I assign practice from the textbooks.  We very rarely use the books in class.  The plain problems match our curriculum, but much of the work in context does not.

So, bottom line, I have not done an adequate job of differentiating homework.  Hence ... I'm eager to hear what my online colleagues are doing!

Positive results from stomach bug

 I wasn't feeling well today.  My students were especially well-behaved when I shared that I didn't feel good and needed their help!  I love that about them!  One student was out of his seat - I called his name - reminded him that moving about the room was not one of the choices I gave.  He said, "I won't argue with you this time since you don't feel good."  I laughed.  I said, "I really wish you would demonstrate respect just because I'm your teacher - not just because I don't feel good."  It's a good-natured, high energy class.

So ... today I was supposed to teach the Laws of Exponents.  Since I didn't have my usual energy, and my stomach hurt ... I told students that I would give them a quick run-down on 5 Laws.  Then I would give them several choices.  I did just that ... I went through the 5 Laws of Exponents with just an example or two of each.  Students listened, and followed along.  Then they completed the required practice.

Their choices after the quick lesson and practice included ...

• Watching videos from our textbook publisher to go over the laws again
• Playing Manga High games that provide practice with exponents
• Playing a Monomial War game in partners 
• Reviewing the skill using their workbook

It was fascinating to watch which students chose specific activities.  I was surprised at the number of students who asked for their workbooks.  I had a few students choose the videos.  And many students chose either the monomial war game or the Manga High games.  All students worked 30 - 40 minutes independently and with partners on practice!  It was a positive day!

Since I teach on an A/B day schedule, I plan to use the same set-up tomorrow ... even though right now my stomach is better and I'm feeling like the bug has departed!

I'd love to structure lessons with less of my direct instruction and more choices for student practice!

Here is the Monomial War Activity and Answers used by several teachers in our school.  I don't know the original author of the activity:

Monomial War Problems by Beth Ferguson

Monomial War Answers by Beth Ferguson

Exploring Manga High!

I've been reading with interest the discussions around Khan Academy.  I don't assign the Khan videos.  I do post links to Khan videos that highlight particular skills for students who were absent or want/need more practice.  This past week I posted a set of videos (some from Khan, some from other sources) plus a practice set or two from Khan for students who failed the last test.  The idea is that students will review the skills and practice before retaking the test.  I'll let you know how it goes.  One of our math coaches recommended a training in our district on flipping a classroom.  She said I would learn why it is much better for me to create my own videos than to use Khan.  Not sure when I'll get to pause for the training but the teaser info was interesting!

The online practice site that I am exploring the most right now is Manga High.  It's a free site, with tutorials and practice.  Students earn points and medals for their practice.  The teacher can assign specific "games" as challenges and set a proficiency level. I uploaded my students' names just last week.  My A day students used Manga High in class for the first time on Friday.  So it is too early to report any significant findings.  We were starting our unit on polynomials.  Since adding and subtracting polynomials is a review of combining like terms from the fall I wanted students to engage in something other than our routine practice.  All of my ninth graders were just issued laptops 2 weeks ago ... so almost every student could practice online.  It was amazingly quiet in the room ... the talking was about math ... and students were celebrating the high scorers.  Naturally I was pleased with that for sure!  But will students practice on their own time?  Will they go to that program when they feel like they are missing a key piece of instruction?  I don't know yet!

X Marks the Spot!

This past week I had the opportunity to attend our district's just in time math workshop.  The focus of the day was quadratics ... primarily factoring.  The goal was to introduce teachers to multiple ways to present factoring.  Since I have been out of the classroom a while, I found the presentation refreshing!

In the next few weeks, we will teach polynomials, and then attributes of quadratics.  I plan to introduce factoring using those attributes ... as we examine the x-intercepts ... demonstrating how those roots are solutions to the equations.  Obviously this limits us to very specific graphs ... ones that integer roots that are easy to see on a graph.

Then as we begin to pursue factoring in earnest, we will use "flashback" to illustrate the inverse relationships between multiplying and factoring.

1. We will use x puzzles to build number sense ... numbers that multiply to equal one number while adding to equal another number.  I found these puzzles online (Sum and Product Pre-Factoring Puzzles) ... I plan to use the x puzzles even before we get to multiplying polynomials ... just as puzzles!  I hope that just exploring them as puzzles before we get to factoring will reduce anxiety in factoring.
2. Algebra Tiles will help to demonstrate the area model of multiplication.  We'll use the tiles for factoring as well.  I plan to use the ones at Illuminations for online practice.
3. From there we will use the "box method" (an array) to multiply and then to work backwards to factor.

One method I don't plan to use that was presented at the workshop is the "Kick It" or "Kick Back" method. It seemed contrived - a bit of math magic.  If you want to read more about it, check out this blog post!

I noticed that Julie at I Speak Math has a template for X-Box Factoring ... I plan to borrow it to slip into our dry-erase sleeves as we practice!

I'm looking forward to our new unit ... first a few Laws of Exponents, and then ... polynomials!

Math Games

Last night I listened in to the Global Math conference on games for the classroom.  I was intrigued and admittedly a bit intimidated.  Games are not my forte ... especially not online games.  I realize in this area I am behind the times!  I am a digital immigrant ... and doing fairly well with various productivity tools.  But I haven't spent much time with gaming.  Last night someone mentioned the Factor Game ... I have played that but had forgotten about it.  In going to the site today, I see that Illuminations has added a number of games at their Calculation Nation site.  Since all of our students are being issued laptops this week, I'm thinking about giving students the opportunity to earn a little extra credit if they will play these games and write a review of them for me.  

I am exploring Manga High as another option for online game playing.  I'm not familiar with the games there enough to comment on them yet.  But I am hoping they can serve as a tool for review of basic algebra skills. 

I am familiar with a few math games that are not computerized like Set and Equate.   I used to play Set with students often.  (The students I worked with didn't enjoy the Equate game!)  I am in a different environment now and there is so little down time so I haven't explored Set with my current students.  In reviewing the game today, I discovered there is a daily Set puzzle online ... might have to strain my brain a bit with this!

An interesting coincident today ... checked my email for my daily news from NCTM ... and yes, there is an article about games!  (Do you subscribe to the NCTM Smartbrief news service??  I highly recommend it).  The article today is about Girls and Games: What's the Attraction!

“When we asked them about springs and levers, they had no understanding of why they were important in the real world,” Van Voorhis said. “But when we were able to situate those kinds of tools in a real-world context, where they were solving a problem that was directed towards social good, we saw the engagement numbers pop.”  girls were talking about physics or game play 76 percent of the time and were only off topic 5 percent of the time."

Embedded in the article about girls and games is a link from April 2012 entitled, What’s the Secret Sauce to a Great Educational Game?  The article highlights the game, Zombie Division.  Their research is summarized in this sentence, "The results were clear: The children who had played the intrinsically-rewarding game learned more math."

It's time for me to catch up!  Looks like there is some gaming in my future!

Solving systems concretely

We have learned to graph systems ... and we learned to build tables to solve them!  Before delving into substitution and elimination full force, we took a day to explore ... Lizards and Beetles, Motorcycles, Cars, and Wheels, Circles, Triangles, Squares ... with marshmallows, toothpicks, and Algebra Tiles!

Our exploration of puzzles ... systems of equations embedded ... concrete materials excites some students, frustrates others.  It is interesting to watch ninth graders reaction to puzzles.  It's clear that I have not presented enough of them throughout the year.  Their lack of confidence and hesitation were obvious.  And tiles, oh my!  I don't know if it is the way I present them ... or just the fact that we don't practice with them enough ... but students don't enjoy working with them!  One young lady ... a conscientious A student .... shook her head ... "I just don't get algebra tiles.  Can I please just do the math??"

Across the room the attention to math dissolves in guffaws and giggles as one boy swipes his marshmallow-y finger through a girl's hair.  She shrieks.  Sad to say, in those few minutes (maybe just seconds) of silliness, students recommended she cut the marshmallow out of her hair!  YIKES ... we had a quick lesson in melting sugar.  

I digress ... 

How are legs on beetles, wheels on cars, shapes, tiles relevant to students ... they are not.  But interestingly enough, students participated in solving the puzzles with enthusiasm albeit a lack of confidence.  And hopefully the illustration of concrete visuals with symbolic explanation will help lay the foundation for our next steps in solving with substitution and elimination.

Favorites from 2012

Well - 2012 was a big year for me!

1.  I completed 30 years in education - the last 12 in administration.
2.  I moved across states to live close to my sons, their wives, and their children.
3.  I decided to continue teaching ... went back into a high school classroom ... teaching 9th grade algebra!

The retiring, the leaving dear teachers, students and parents, the selling of a house, the buying of another, the move ... and then oh my ... putting together a resume for 30 years of experience, finding work records from the 70s ... well these were challenging tasks!  All along the way, the excitement of a new adventure, a twist in my life journey fueled my energy ... enthusiasm has been high!

Adapting to the culture shift in high school has been interesting to say the least.

What I have so thoroughly enjoyed in this teaching adventure is finding an amazing community of math teachers online that share the good, bad, and ugly ... I am learning so much from them!  I have always considered myself a leader in education and not a novice with technology.  I facilitate university classes online and enjoy working with teachers across our  nation.  But I had no idea of the networking available among bloggers!  I have been blogging for a while - reflective posts, inspirational writing.  I had a few followers.  Quite definitely, my math blogs have been read much more than any of my previous writings!  I am so excited to share my thoughts and work ... and benefit greatly from the posts of others.  The teaching of Algebra has changed some in the last 15 years!  The emphasis is different.  The expectations a bit different.  The changes keep me searching, thinking and planning!  The online math community has been my primary source for professional learning!

I have a long list of math blogs in my Google Reader.  And I appreciate every author!  Early in the summer, when I learned I would teach Algebra, I found Dan Meyer's site first.  Just amazing!  And then I participated in the Math Blogging Initiative as a way to get started in writing about my work.  I find that I return over and over again to a specific few blogs ... especially these compilations ... these are rich with humor, passion, and ideas!

• MS Sunday Fundays
• Made 4 Math Mondays
• My Favorite Friday

These sites inspire me to keep learning and growing!

In the future I hope to participate more in the Global Math conferences.  I listened in on one ... it was great!  Hopefully I can arrange my schedule to catch up with the next ones!

Whew!  Can't imagine what 2013 will hold!

Systems Puzzle Problems!

I'm working on my systems unit tonight ...

I love the list of systems problems that are posted at Finding Ways to Nguyen Students Over.

I also like the puzzles problems posted at I Hope This Old Train Breaks Down.

I am compiling a list of animals, heads, legs problems ... as well as a set of wheels (cars, bikes, trikes) problems for systems.

I have a few real-world problems - cell phones, etc.

If you know of a great source ... or have a favorite problem to share, please comment!  I'll post my compilation in a few days!

lobbying for double block!

Second semester starts Monday.  We have reviewed data.  There are several students who were not successful - more than I thought should fail.

I am unhappy with this fact.

I have always believed that as teachers we must own our data.

I don't know what more I can do.

By that I don't mean that I think I'm a perfect teacher ... I can keep working on my planning and presentation skills.  I can keep working on the relationships I am building with students.  I can keep chipping away at the lack of interest in math, the thought that math isn't important, and/or the idea that students can't do math!

There is one thing that I think would make a huge difference.

Our school is set up on an A/B day schedule.  Most students receive algebra instruction every other day for 90 minutes.  There are a few select classes of "double block" algebra.  

My thought ... more, many more 9th graders need, must have double block algebra!  Algebra is the foundation of high school math.  Just barely getting by isn't going to work!  Every year, these students who lack prerequisite skills and interest in math are going to fall further and further behind!

Yes, it's costly to set up "double block" classes.  But it is worth it!!!

I saw this picture on an opinion piece in the NY Times online ... entitled "Is Algebra Necessary."  My answer - yes!  But let's don't let our students drown!

A Double Dose of Algebra is a must read for those organizing and scheduling early high school math classes!

How many minutes of algebra instruction is available for your students?

file folder mini projects

I haven't done any projects this year ... many reasons why ... but it's time now to offer my students an opportunity to show me what they know in some other way than our usual tests.

My students need choices!  I'm hoping they will get excited about these four mini-projects!  Students need to choose only one.  One project is a review of graphing; a second project combines problem solving with graphing; a third combines art design with graphing; and the fourth invites students to write creatively.

Students will complete their work (maximum 2 pages) and affix their work inside file folders.  (I might choose to use 12 x 18 construction paper instead of file folders).

If you are interested in seeing the projects, post a comment.  I'll email them.  I created two of them; one I found online and made a few revisions.  The fourth one I borrowed from Amy.

Lesson Planning - Systems of Equations 2

I love to see what materials and strategies other teachers use to teach math.  So before each unit I scour the Internet looking for great ideas.  Often, I find ideas that I can massage into useful activities for my students.

In preparing to teach systems of equations I did one of those Internet searches.  Here are some of my favorite finds ...

Unit 6 - wow!  Dan, blogger at The Exponential Curve, has an amazing set of math materials in his "Box" widget!  Unit 6 is a full unit on systems!  Great resource!

I Can Do This! System of Equations on the Ohio Department of Education website has several activities - I especially like the Lost at Sea problem!

Do These Systems Meet Your Expectations is published through the NSA site.  It has a carnival theme.  In addition it has a graphing lines foldable - a great addition.

Whose Line is it Anyway is also published through the NSA site.  It has a savings and summer job theme.  Several good problems are included.

Farmer's Market on the School Improvement in Maryland website includes a thorough problem solving task with additional problems in context!

This Flip Book from Math Tales from the Spring is a good organizer for our unit on systems!

2 sites that are perfect for posting on your class website to help students who want additional resources as they study systems include:

• Regents Exam Prep Center (notice that they have a nice summary activity for triads to complete!)


• BBC Bitesize

There are more I'm sure!  If  you have had good success in teaching systems of equations, what worked for you??  Please share!

Related articles

• Year 9 Equations homework (nsmaths.wordpress.com)


• Bringing maths to life with cross-curricular appeal (guardian.co.uk)


• Using Excel for Problem Solving (http://fawnnguyen.com/)

Lesson Planning - Systems of Equations

I enjoyed spending a few minutes planning ahead today ... we start with systems of equations in January.  Unfortunately, students struggled greatly with their test on linear equations.  I am building in a review to support students as we add new knowledge.  One tool for our review is Julie's graphic organizer on functions and graphing linear equations.

I plan to start our first lesson on systems with a typical puzzle problem ... chickens, cows, heads, legs!

Ol McDonald's Farm

Then we will take a few notes ... using a simple foldable.
Review Graphing Linear Equations Notes


Last, students will complete a partner practice.  Each partner will solve a system by graphing.  The work is self-checking; the solutions to the systems will match if their work is correct.
Partner Activity - Graphing Systems

I'm looking for a way to include pictures of intersections to aid understanding for my visual learners.  I welcome your ideas!

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my students speak ...

I asked students to provide some feedback on our algebra class – anonymously.  It is interesting that across six classes, the thoughts are very similar.  I will review these ideas before our second semester begins …

 What is one thing you like about math or about our class?

• It’s easy


• I like trying to learn


• My friends are in the class


• Helps you learn about most things in life like money


• Using the calculator


• When I understand the material


• I like how you can put math in everyday words


• It’s fun to learn


• The low degree of difficulty


• It will help me in the future


• Classmates are funny


• I like that we have plenty of time to take our tests


• I like that we learn well


• I like the posters with notes that you hang around the class


• The notes you give us


• The active activities


• We get rewarded


• I like the way we do reviews


• I like how the next topic fits in with the one we just learned


• I like coming to morning tutorials


• I like that we sit in groups and take notes

 What is one thing you don’t like about math or about our class?

• The class is somewhat slow


• It’s not helpful


• It’s too long


• It’s hard


• It’s confusing


• I don’t like having to write out everything


• I don’t understand it


• I don’t like when the teacher goes to fast


• Some people are annoying


• After you first teach us something, you expect us to know it


• The math can get super boring


• When I am trying to understand, I can get distracted


• I can’t remember how to do a lot of the material until after a long time of struggling


• Algebra is mostly pointless


• Not being able to sit with who you want


• Our class is noisy


• A lot of people cheat in our class


• Our classroom is cold


• I don’t like quiet individual work


• We don’t get a lot done


• I don’t like that problems have tons of steps to get to the solutions


• We go too fast


• None of my friends are in the class

What can I do to help you learn Algebra better?

• Use peers to help one another


• By being fun


• Take more time with the problems


• Help me understand the questions


• Do more activities


• Keep me on task


• Use more engaging activities


• Nothing more than you are already doing


• Explain more clearly


• Provide food/candy


• Use more visual learning


• Go slower/explain more


• Move faster – class is boring because you go too slowly


• Keep having tutorials in the morning


• Use pictures when you can


• Use better activities


• Do more homework in class so we can ask questions about it

 What can you do to help you learn Algebra better?

• Try harder


• Focus


• Study more


• Take the teacher’s advice


• Attend tutorials


• Pay attention in class


• Listen when you are talking


• Stay focused and care more


• Start doing homework


• Not be lazy

Hmmm ... how best to use these thoughts??

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• So, how did I do? Getting feedback from students in end-of-year evaluations (missaliceleung.wordpress.com)