# Different Forms of Linear Equations Card Set with Seven Variations of Use

In order for my students to practice changing forms of linear equations, I created a set of cards that they can use multiple ways.   For each equation, there are four cards:   a version of the equation in y=mx+b form, a version of the equation in x=kx+d form, a version of the equation in standard form, and a scaled up version of the standard form.

I love card sets because I can use them so many ways.   I can use them when I first teach the lesson one way.   I can then use them again a different way for additional practice or as a quick review leading up to a quiz or a test.   I can also use them as part of a differentiated instructional piece of a lesson to work with students who still haven’t mastered the concept.   Finally, I can bring them back out in a month in yet another way as a quick refresher.   (In Make It Stick, the author articulates the power of revisiting a concept after some time has lapsed in order to “make it stick”).

Option 1 – Card Sort

Students work in table groups or in pairs to sort the cards.    They need to match the four different forms of the same equation.

Option 2 – Rummy

Students use the cards to play Rummy.  Students play in pairs or triads.   Each player is dealt six cards.   A single card is face up and the remaining cards are face down in a draw pile.   The player to the left of the dealer begins play.   He or she takes the top card in the draw pile or takes the top face-up card in the discard pile.  The player may lay down any matched sets he or she has face up.  A player may add any one or two cards from his or her hand to a matched set already laying face up on the table.   If he or she does not play any matched sets, he or she must play a card in the discard pile (it can’t be the same card he or she drew from the face up discard pile).  Matches consist of cards that are different forms of the same equation.    The first player to play all of his or her cards is the winner.

Option 3 – Odd One Out

Remove one equation card from the set.    This leaves one equation with only 3 equations.   Since the game play involves making matched pairs, the remaining equation  is the “Odd One Out”    Students play in groups of 3 or 4.   The cards are dealt out.    Players look at their cards and lay down their matches (in pairs).    When it is a player’s turn, he or she draws a card from another player and tries to make matches with the cards in his or her hand.   At the end of the game, the player with the Odd One Out card loses the game.    Of the remaining players, the one with the most matches is the winner.  (This is essentially Old Maid with equations.)

Option 4 – Concentration

Students work with a partner or play individually.   All the cards are laid face down.   The player turns over two cards.   If the two cards represent the same equation, it is a match and the player keeps them.   If they do not represent the same equation, the player turns them face down again.   If two players are playing, the next player takes a turn   The player with the most matches at the end of the game is the winner.

Option 5 – Spoons

You need a set of teaspoons in addition to the cards.   You should have one fewer spoon than the number of players.   Put the spoons in small circle in the middle of the table.   Deal four cards to each player   Each player tries to make four of a kind.   The dealer takes a card off the top of the deck, removes one of his/her cards and passes it facedown to the left.   Each player discards to the person on his/her left.   The last player discards into the trash pile.   This continues until someone gets four of kind and takes a spoon from the center.   Once the player with four of a kind takes a spoon, anyone can take a spoon.   The player without a spoon gets a letter in the word SPOON.    When a player has spelled SPOON, he or she is out of the game.  If the cards run out, reshuffle the trash pile and continue play.

I didn’t have enough spoons on hand, so we played spoons with forks.    Spoons took a far amount of time today, but the students had fun and liked the game.  This option is probably best for a review activity rather than on the first day of instruction.

Each student is given a card of a particular form.   I direct them to change it into a different form (e.g., they are given a card in standard form and I tell them to change it to slope intercept form).   They solve the problem and then do a Quiz Quiz Trade.  Quiz Quiz Trade is a cooperative learning structure.   The first partner quizzes the second partner to turn his/her equation into a different form.    If he or she struggles, the first partner can give him or her a hint.   If he or she continues to struggle, the first partner can give a second tip.  If he or she continues to struggle, the first partner can tell the second partner how to solve the problem (Tip Tip Tell).   Partners then reverse the process and repeat.   Finally, they trade cards and find new partners.   I have students continue for whatever amount of time I want to allocate to the task.

Option 7 – Concept Attainment Cards

When I make the card activity, I use a different color of card stock for each set.   With this activity, I give each group a set of cards that is all the same color for the desired concept (all the pink cards are in slope intercept form) and a different color for the non-examples (purple cards with equations in standard form or in x=kx+d form).   Students then have to look at the examples and non-examples in order to define the concept illustrated by the examples.

Option 8 – Give One Get One

Students line up in two lines, facing each other.   I give each student in one line a card with an equation in a specified form of an equation (e.g., everyone in the first line has a card in y=mx+b form).   I give each student in the second line a card with an equation in a different form (e.g., everyone in the second line has a card with an equation in x=ky+d form).   I then tell everyone to transform their equation into another form (e.g., standard form).   When they have done so, they step forward into the space between the lines.   They trade cards and solve the other card, discuss their solutions, check each other’s work, and then step back into the lines.    When all the partners are done, one line passes their card down and the other line passes it up.   The second line shifts up by one (the person at the head of the line goes to the end of it and everyone moves forward) and the first line shifts down by one.   Now everyone has a new problem and a new partner.   I repeat the process for whatever amount of time I want to allocate to the task.

You can download the  rewriting-equations-card-sort  file by clicking on the highlighted text.

# Angle Card Sets – Exploring Angle Relationships and Solving Equations with 3 Activities and 5 Variations

I wanted to create an activity that I could use to reteach and review angle relationships with some of my students who did not yet show mastery on these concepts.    I decided to create a card set that I can use multiple ways.    Each card has a picture of angles on a point.   They each include adjacent angles, vertical angles, complementary angles, and supplementary angles (with the exception of one card, which does not have complementary angles).   They also each include unknown angle measures.    This allows me to use the cards for five different purposes:  identifying adjacent angles, identifying vertical angles, identifying complementary angles, identifying supplementary angles, and using angle relationships to solve equations.

I can use the activity multiple ways for each concept.

Activity 1 – Give One, Get One

Students form two lines.   Each student has a card.  I direct them to do a task (identify adjacent angles, identify vertical angles, identify complementary angles, identify supplementary angles, or solve for the unknown angle value)   Each student completes the task on his or her card and then steps forward.   When both partners have stepped forward, they discuss their respective cards/solutions.   When they are done, they step back into the line.    When all pairs have returned to their starting position, one of the two lines shifts (down or up) by one so that they have a new partner.   The cards are then shifted so that they also have a new problem.   This repeats until the allotted time for the activity is complete (usually about 5 minutes).

For this task, I have students use dry erase markers to identify the angles.

Variation 1 – Find complementary angles

Variation 2 – Find supplementary angles

Variation 3 – Find adjacent angles

Variation 4- Find vertical angles

Variation 5 – Find the missing angle measures

Activity 2 – Quiz, Quiz, Trade

Students solve their card.    They then find a partner.   They ask their partner to solve the card (find the angle pair or solve for the missing angle measure).   If the partner has difficulty, they may give a tip (hint).   If the partner still has difficulty, they may give another tip (hint).   If the partner still needs help, they show the partner how to do the problem.   (Tip-tip-tell).   The second member of the pair then quizzes the first partner with his or her card.   After the pair is done, they find new partners.

Variation 1 – Find complementary angles

Variation 2 – Find supplementary angles

Variation 3 – Find adjacent angles

Variation 4- Find vertical angles

Variation 5 – Find the missing angle measures

Activity 3 – War

Students each turn over a card.   They find the missing angle measure.   This requires them to use angle relationships to write an equation to find the missing angle measure.   They then solve the equation and use the value of the variable to find the missing angle measure.   The student who has the card with the greater angle measure wins the cards in that round.   The student with the most cards when I call time is the winner of the game.

For this card set, I used images from an EngageNY lesson to create the cards.

# Necessity Is The Mother Of Invention – #ILookLikeAnEngineer

Necessity is the mother of invention.   Unfortunately, the “necessity” can be all too easily forgotten as an essential component in education.    I teach what I teach, in part, out of necessity but it is my necessity not that of my students.   I need to teach the curriculum that I teach because it aligns with the standards set forth by the state but it is not a burning necessity for my students no matter how many times I tell them the essential questions and how they will use it in the future.   Knowing something only becomes a burning necessity in the mind of an eleven year old when they see a need to know it so they can do something they want right now.

So how do we create that need to know?   I think we give kids real problems that they really want to solve.   It’s not something that I can do every day, but I try really hard to find time and space to do it every year.   To do this, I  compact lessons and I accelerate where I can.   This year, I managed to squeeze out almost a month at the end of the year to do an engineering project with my students.

Request For Proposal

Students were presented with a Request For Proposal (RFP) from a fake toy company.    The proposal indicated that this fake toy company was seeking to expand market share to include more girls in their customer base for motorized toys.    The toy company wanted those bidding on the contract to conduct market research and build a toy to meet that need.    The toy company indicated that the toy must meet one of three different criteria:  travel 3 m in 3 s, climb 1 m at a 15 degree slope in 2 s, or climb 1 m at a 30 degree slope.

Creating a Team and Conducting Market Research

Students were assigned teams and formed mini-companies that would bid on the RFP.   They created a team name, logo, and slogan.   Then, they conducted customer surveys with both adults and children in the target age range.    They analyzed the data and determined the type of toy the customer was seeking.

Building Technical Knowledge

During the same time-frame, students built knowledge of how gear trains work.   They began by building gears on a frame and exploring relationships between the rotations of the gears and the number of teeth on the gears (gear ratios, teeth ratios).   Next, they added a motor and wheels so that they could calculate the rate on a 3 m course and measure the rim force on the wheel.   They repeated this process with gear ratios ranging from 1:3 up to 225:1.   As they did this, they were building important skill in construction as well as an understanding of the different kinds of performance they might expect from different kinds of gear ratios.    From there, they measured rim force on the tooth of a gear connected to the motor.    They did so for different sized gears and then learned how to calculate torque.    With this knowledge, they could explain why certain gear ratios would not move and why certain gear ratios would be well-suited to climbing.   At this point, they had built sufficient knowledge to answer the first stages of that burning question of how to build a toy that would meet each of the criteria.

Making a Prototype

Each team began construction of a basic prototype to meet their desired criteria.   This amounted to attaching the motor and the desired gear train along with the wheels on the frame structure.   Students then tested their motorized frame to see if it met the criteria.   Once they had a basic working prototype, they started constructing a body to give the toy the desired aesthetics.    As they constructed the body, they continued to test the toy to make sure the additional weight did not place them out of compliance with the criteria in the RFP.    They repeated tests multiple times and used median values in order to eliminate outlier trials resulting from poor testing technique.

Sealing the Deal – Writing a Written Proposal and Giving an Oral Presentation

When the toy was completed, each team wrote a written report in response to the RFP and prepared an oral presentation.   The final stage of the project required each team to present their toy to a panel of judges representing the fake toy company.   I recruited 3 engineers and a soon-to-be lawyer to represent both the technical and business interests of the company for the panel of judges.   (I am lucky enough to have Sandia National Laboratories nearby and willing to provide this kind of support to encourage excellence in math and science.)   The judges selected a winning team based on the presentation and a demonstration of the toy.   (The winning team members each got a gift card to Cold Stone Creamery).

While this last stage is not “math”, it is very much a part of what engineers do and I wanted my students to appreciate the importance of being able to communicate effectively as an engineer.  Reading, writing, and speaking are just as much essential skills for an engineer as are math and science mastery

Why It Mattered

• Students got to experience the engineering process, which is so much more powerful than hearing about it.
• Girls had to learn how to make something and how to make it work.   It’s not that they are any less adept, but many of them are much less experienced.   This results in a certain amount of hesitancy, initially,   Having to make it work pushes them past this hesitancy and they discover just how good they are at it.    Giving girls this experience and confidence is important in leveling the playing field when it comes to engineering.
• Students used the math that they have learned this year to do something real that mattered to them (finding unit rates, conducting surveys, making data representations, analyzing data to make decisions, finding medians, using equations to calculate torque, measuring radii).
• Students had to find ways to work together – teams could not shift part way through the month long project.
• Students who lacked confidence as speakers learned that public speaking is a learned skill and that you get better at it with practice.   (I made each team do a dry run of their presentation in front of their classmates and get feedback the day before the final presentations.  They took the feedback and were so much better the second day.)

Gallery of Toys

Presentations

# Fearless – Introducing Mathematical Proof

“Ugh.   It is the worst class ever.   It is so hard.”  I heard those words expressed in almost identical fashion twice, roughly 5 years apart when I was a student.    The first time, I overheard them in the hall spoken by a student a year older than me.   He was taking about his experience learning how to do a proof in his geometry class.    The second time, I was in college and a couple of upperclassmen were talking about their experience with proofs in Linear Algebra.   Both times, I went into the class with a bit of a knot in my stomach, expecting the worst.    I don’t know if it was because my brain just works that way or if it was because I was lucky enough to have some really good teachers, but I thought proofs were kind of fun.    (Strange – I know.)

As I thought about introducing my 6th graders to proofs, I wanted to make sure they didn’t walk away with the same sentiment that some of my classmates expressed so many years ago.    I thought a lot about how to go about it.    It’s been so long since I learned it, that I don’t really remember what my teachers did.   My course doesn’t use a single textbook so I couldn’t fall back on textbook lesson plans.   So, I ended up thinking about it and just trying some things.    I decided to go forward with a gradual release model in mind.

Prequel

I introduced my students to most of the properties that we are using now in our proofs during a unit last fall.   They are familiar with them and can use them, but don’t always remember which property is which.

Modeling a Proof

I began by modeling a proof with the whole class.   I felt like they needed to see a proof before they could do one, but I didn’t want them to just sit there and watch me, so I modified things a little bit.  The goal was to find a simplified, equivalent expression and use properties to justify the process.   I set up the original expression and the first step in the proof and then asked the class what property justified the step I had just done.  I then called on volunteers to provide the justification (property) for the step.   I repeated that process with each successive step.    However, each volunteer had to be a new voice.   I would not return to any one until everyone in the room had offered a justification.    I wanted every voice heard, but I also wanted to respect the fact that some of the students were going to take a little longer to venture a toe into this particular pond.

Collaborative Proof

The next proof, I modified my approach a little bit.   I did the proof with the whole class again.   However, this time I had students suggest each successive step and provide the property justifying the step.    Just as I had done in the previous proof, I took volunteers but did not return to a particular volunteer for another contribution until everyone in the room had offered input.     I thought this would be a way to chunk the process of a proof into manageable pieces so that it would not seem so intimidating.    The idea of coming up with a single step in the process is a little less overwhelming than looking at that blank table that has to be completely filled.

Partner Proof

By the time that we got to the third proof, I felt like most of the students had at least a place to start.  Some of them were still on shaky ground, though.    I decided that the next logical step was to have them complete the proof with a partner.    (My seating assignment is such that I have a student who is stronger in this particular strand sitting next to a student who is not quite as strong.    This enables students  who have less mastery to have access to the thinking of the students with a stronger grasp of the material through the small group discussions and partner work that they do.)  In this scheme, Partner 1 provides a step and justification, Partner 2 provides the next step and justification, Partner 1 provides the following step and so on.

I think this worked really well.    Both students were engaged, both students felt responsible/accountable, both students had a support system if they got stuck.   Every pair was able to successfully complete the proof.    They also had some great discussion about the “next step” in the proof.   This brought out the idea that there is more than a single solution path.   This led to a nice discussion of which solution path is more efficient and the question of whether efficiency matters.

Practice Makes Perfect?

Over the course of a week, we worked through the process of generating equivalent expressions.   Each day, the initial expressions were a little more complex.   Each day, we spent a little bit of time working with proofs.   The proofs weren’t the whole focus of the lesson, just a piece of it.   This revisiting of proofs each day gave students practice with proofs.   I think equally important though is the time they had to just live with it, the time to mull over the process without even realizing they were doing it.

As I watched students progress over the course of the week, the students who continued to struggle a little bit were struggling with identifying the property rather than figuring out the next step.   To help them, I created a set of cards on the different properties that we were using.    Each property had three cards:   the name of the property, a verbal description of the property, an algebraic expression illustrating the property.   I used the cards in several different activities over the course of a few days.    Each review activity took five minutes or less.

One day, I used the cards for a Quiz-Quiz-Trade entry activity.   I had more cards than students so I used  all the algebraic expression cards and some of the verbal description cards.   I left the cards with the names of the properties out of circulation for this activity.    The students each looked at their card and determined the property.    Next, students found a partner (they move around the room to do this which incorporates a little movement into the period, which  Marzano has shown to be an important engagement strategy).   In each pairing, Student 1 shows his/her card.   Student 2 identifies the property.   If he or she can’t, they use a Tip-Tip-Tell strategy.   That is, Student 1 gives a tip (clue) and Student 2 tries again.   If he or she still can’t identify the property, Student 1 gives a second tip (clue) and Student 2 tries again.   If he or she still can’t identify the property, Student 1 tells him/her what the property is.    The pairing then reverses rolls and repeats.   Finally, they trade cards and find new partners.   I only continue the activity for about two minutes and challenge students to see how many pairings they can complete in the allowed time.     The time limit keeps the engagement level high (Marzano) and allows me to do a quick review of important information without taking too much time.

Properties Card Sort

Students worked collaboratively with their table group to sort the cards.    They had to match the property name, the verbal description, and the algebraic expression representing the property for each different property.   I had them lay the cards out in rows so that I could quickly walk around the room and see how they were doing.   I like using this kind of formative assessment because it is a quick, easy way to find the gaps that I need to address.

You can download a copy of the Property Card Sort by clicking on the text below the picture or by going to the Resources page.

Next Steps

My next step will be to have students complete a proof that is fill-in-the blank.   I will provide some of the steps and some of the justifications.   Students will have to fill in the missing steps or justifications.

# Which Bicycle Shop Should I Use –A Lesson Introducing Proportional Relationships in Tables, Graphs, and Equations

“I’m thinking about purchasing a custom-made bicycle. Bicycle City charges \$160 plus \$80 per day that it takes to make the bicycle. Bike Town charges \$120 per day to make the bicycle. For what number of days will the charge be the same at both bicycle shops?”

I introduced the lesson with this question (taken from the NY Institute for Learning). We began with our usual process of making sense of the problem (What do you notice? What do you wonder? What is the question? What do you know?). Then, students set to work on the task individually.

Once everyone had solved the problem, I had three different students present their solutions (one who had used a table, one who had used a graph, and one who had used equations) to the class using the document camera. This gave us the chance to talk about how you find the solution using different solution paths.

At that point, I told students that a proportional relationship was one in which you could multiply the x value by a constant and get the y value. I asked them to figure out whether either bike shop’s pricing was proportional and how they saw that in their particular solution. This gave us the opportunity to discuss how they see the constant rate of change in each representation. It also gave students the chance to discover that a proportional relationship goes through the origin for themselves.

We wrapped up the lesson by completing a foldable summarizing the characteristics of a proportional relationship and how to see them in a table, graph, and equation. You can download the foldable by clicking on the link.

Proportional Relationships

The lesson is designed to give a whole-part-whole understanding of the concept. This is particularly important with students who are at the extremes on the conceptual/sequential dimension of cognitive style. I have several twice-exceptional students who are at one end of this spectrum or the other. I struggled with how to help them succeed for the entire first semester. I started building in the use of a whole-part-whole structure and the use of graphic organizers for note-taking more after reading Twice-Exceptional Gifted Children by Beverly Trail, EdD. It has had a pretty big impact for these students (test scores moved from the 50-60% range to the 98% range on the last test). I don’t know if that will continue to hold, but with that kind of improvement, I am going to keep incorporating this technique and find out.

The way that the foldable is designed, students can compare and contrast how one sees a proportional relationship in a graph, table, and equation by looking across the foldable.   The can also compare and contrast an example of relationship that is proportional and a relationship that is not proportional by looking down a column.   Marzano’s research shows that the use of comparing and contrasting can result in significant gains in student learning.

I also incorporated the use of color in the completion of the foldable to highlight the important points. This was not as intentional as it should have been. Early in the day, we worked through the foldable summarizing the ideas in the lesson. As the day progressed, I thought it would be a good idea to have kids highlight the key points in each representation (constant rate of change and going through the origin). By fourth period, I finally refined it so that kids used one color to highlight the rate of change and a different color to highlight that the relation goes through the origin. This seemed to really bring out the idea across representations, so I will do it this way from the start the next time I teach this lesson.

# Equation Stations

I spent much of this week focused on solving equations and inequalities.   I started out the week reviewing how to solve one-step equations, moved on to solving one-step inequalities (linking one-step equations and graphing inequalities) and then spent the remainder of the week solving two-step equations.  I really liked the fact that we kept coming back  in all these scenarios to the same big idea of isolating the variable.

The first thing that struck me was how good my students were at solving the equations intuitively but how haphazard their work was.   I know that this will not serve them well as the problems become more complex, so I embedded  a fair amount of focus on getting them to use a more structured approach to the task.

Day One and Day Two were quite frankly on the boring, dry side.   Students took notes and then practiced the process.   I had them work in partners using Kagan’s Showdown Cooperative Learning Structure so that they would have some discourse, even if it wasn’t on a rich task.   Students had to analyze each others’ work and discuss/resolve discrepancies.   I spent my time circulating and working with kids individually to improve the “organization” of their work.   Naturally, I met with a certain amount of resistance.   From their perspective, they could get the right answer so that should be good enough, right?   Alas, to their dismay, it was not.  As they saw from the daily feedback on their entry cards, I was holding pretty firmly to my expectation on how they must show their work.

Day Three and Day Four were all about two-step equations.   I had students start out by taking Cornell notes on two-step equations.   I used color-coding to make the process more visual since a large percentage of my students are visual learners.

Two-step equation notes with color

Next, I demonstrated how to use algebra tiles to model a two-step equation.   Then, they had to correctly solve two two-step equations before moving on to work in equation stations.

I structured the stations so that there was work developing some conceptual understanding in the early stations and then more abstract work as they progressed.   I also structured them so that there was a gradual release.   In early work with a concept, students worked with a partner, then worked individually with a teacher check, and then worked individually with a self-check mechanism.

Using the stations allowed me to incorporate some movement into the class period, which is always good.   It’s hard to sit still for 6 1/2 hours when you are eleven or twelve.   The stations also allowed me to differentiate instruction.   Each student was working at his or her own pace, at his or her own level of understanding.

Station 1:  Algebra Tiles

Two-step equations with algebra tiles

Students had three tw0-step equations to solve using algebra tiles.   The use of the algebra tiles gave them a concrete representation for an abstract concept and helped to build some conceptual understanding of the process.

Station 2:  Two-step equation puzzles

Two step equation puzzles

Students worked with a partner to build a set of puzzles.   Each puzzle had a two-step equation problem.   Students had to put the pieces in the correct order to complete the puzzle.   Each color was a different puzzle.   When students thought they had all the puzzles correctly put together, I would check and tell them “OK, you’ve got it go on to the next station” or “No, you have a mistake in the pink puzzle”.   I was intentional about not telling them what the mistake was.   This forced students to compare and contrast (a Marzano high-yield strategy) and analyze their work to find the error.

A pdf file of four of the puzzles is below.  I print each puzzle in a different color piece of card stock.   Then, cut the steps apart.   Mix up the steps and paperclip them together.   Four puzzles go into a single ziploc bag as a task.

TwoStepEquationsPuzzles

Station 3:   Problems with a teacher-check

Problems with a teacher check

Students had to correctly, independently solve three problems.   I would check their work as they progressed through the problems.   If their were errors, I worked with them 1:1.   For each problem where there was an error, they had to do an additional problem.   They did not exit this station until they had correctly and independently solved three problems.

Station 4:  Two-step equation fortune tellers

Self-checking two-step equation fortune tellers

Students worked independently at this station.   They had to solve all of the problems on the fortune teller.   The use of the fortune teller allowed them to self-check their work.   While the check mechanism in solving two-step equations should ensure that they know when they make an error, I have found that a lot of kids who make a mistake in their solution seem to also make a mistake in their check mechanism.  So, the fortune teller provides a secondary check mechanism.

A pdf of the two step equation fortune teller is below.

TwoStep Equation Fortune Teller

On Day Four, I continued to focus on two-step equations.   I wanted to increase the difficulty level of the problems (incorporating negative numbers and fractions) and bring in some more problem-solving.   I began by playing the Employee Lounge puzzle in MIT’s Education Arcade Lure of the Labyrinth game with the class.   Students had to decide what actions to take in the game.   Since they have been playing the game since the beginning of the year, there were many thoughts on the best moves.   As we played the game,  we discussed the equations necessary to solve the problem, de-privatizing the thinking and linking the math we were doing in class to the math they were doing in the game.

After some game play, I had students solve two two-step equation incorporating rational numbers.   After successfully doing so, they moved on to a second day of stations.   Students returned to whichever station at which they had been working the previous day (I keep track of this using an index card system).   I also added several new stations for those students who were progressing more rapidly through the stations.

Station 5:   Combining Like Terms Pyramid

Combining Like Terms Pyramid

Students had to combine terms from adjacent bricks to fill the brick above.   When they reached the peak, they had to compare their final expression with their partners as a checking mechanism.   If there was a discrepancy, they had to go back and find the errors and fix them before moving to the next station.

A friend gave me this activity and I would like to credit the source.   However, I’m not sure where she got it.  I recreated it and the files are attached below.  I used the “Easy” version for this station.   Later, I will bring out the challenge version for those students who are ready for additional challenge

Combine Like Terms Reach the Peak Easy

Combine Like Terms Reach the Peak Challenge

Station 6 – Combining Like Terms Uno

This would have been the final station of the day, but no one got quite that far.   I didn’t really expect that they would, but had it ready as a “just in case” station.   We will use it later in the spring when we come back to these ideas again.

As I look back on the week, I see some changes I want to make for next year.

1.  I want to pull the Lure of the Labyrinth game play forward to the first day of the sequence.   The initial problems in the game play are one-step equations and would lead nicely into the lesson.   It also turns the sequence back to a place where the students are figuring out how to do things in the first part of the lesson, which is what I would much rather have.   I think a lesson in which they work with an idea first and then I help them bring their ideas together and formalize them gives them a lot more ‘sense-making” and a much deeper understanding of the material.
2. I want to find a way to make the solving/graphing inequalities lesson a little more interesting.   Students grasped the concept well, so it was “successful”.   It was just boring and math should not be boring.  I also think I need to bring in more problem-solving here.
3. I would like to develop/find some foldables relating to these topics to use as part of a summary at the end of the lesson.   I think they are a nice way to bring things together and are a good study tool as kids prepare for quizzes and tests.