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.

Option 6 – QuizQuizTrade

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.

img_1758angle-relationship-cards  .

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.


A Quest – Story, Problem-Solving, & An Award-Winning Video Game

“On a dark and stormy night…..”    So begins an incredible quest to save a lost pet.    Along the way, the protagonist must disguise herself as a monster in order to infiltrate the enemy stronghold.   She must solve a myriad of problems along the way in order to elude detection.    The farther she goes, the more challenging things become.     The stakes are high.      Time is running short.

This engaging story is at the heart of Lure of the Labyrinth, an award-winning video game developed by MIT’s Education Arcade.    The game addresses a fairly wide array of middle school math concepts (ratios, expressions, equations, integers, area and perimeter, linear relationships and slope).    It does so in a way that engages students in open-ended problem solving that enables them to construct a deep understanding of these concepts.    As is true of most video games, it adapts to match the player’s skill.     The game also incorporates a messaging system among players within a single team (a team consists of a subset of the students within the same class) that encourages mathematical discourse.    The game utilizes research-based techniques and is completely free.       The site also has teacher resources complete with fully developed lessons.

Lure of the Labyrinth is my all-time favorite video game.

  1. The game is engaging.   Its use of story is powerful to both boys and girls, but I think is especially powerful in drawing girls into the game and into mathematics.     Story is powerful for girls, I think.
  2. The problems that students encounter are very rich. They have multiple entry points and the level of cognitive demand grows to match the player’s problem-solving.   (This is not a skill-based game.)
  3. Progress in the game requires students to move beyond their comfort zone, to grow.
  4. The messaging capability in the game allows students to engage in mathematical discourse even when they are in physically separate spaces. Kids playing at home can discuss the math with each other as they play.
    1. The messaging capability is designed in such a way that students can only communicate with members of their own team (the teacher decides who is on what team when setting up the accounts).
    2. The teacher can see all of the messages. This ensures that the messages are appropriate (the teacher can block a student’s messaging capability if that student steps out of bounds).
    3. Because the teacher can read the messages, there is a documented window into student thinking.
  5. The messaging actually seems to develop perseverance in the face of challenge. To explain what I mean by this, I think the best thing is to tell a story about a couple of students.   I had assigned playing the game for homework one night.    A student was playing the game and got stuck.   He sent a message to his teammates asking for help.   They didn’t happen to be playing at that particular moment.    He kept at the problem while he was waiting to hear from someone.   Suddenly, his messaging changed.   He said things like “Wait, don’t tell me.”   “I think I’ve got it.”   He did get it, on his own.   Knowing there was support out there from another kid helped him to persevere and to eventually conquer the problem himself.
  6. The game gives an engaging context that can then be used to build lessons.   I have tried some of the lessons presented on the site and have built some of my own.   I’ve been really happy with how well they worked.


To use the game, I begin with game-play.   I usually start them with the game on the same day that I give a pre-assessment (I have to know what students know for their IEPs) for the year.   It is something they can begin as they finish the pre-assessment without requiring instruction or disrupting other students.   I then have them play the game a second day in the lab.    This time in the lab together is really important.   It gets them over the initial hump starting the game because they can talk to each other (there are no directions, students have to explore and discover how things work).    After they’ve had some time together, I can assign playing the game for homework (they’re favorite homework ever).   Once they have played the game a little bit, I can pull up one of the puzzles and we can play it together as a class.   As we play the puzzle, I have students direct the play and talk about their strategies.   This serves as a launch into a lesson on the concept addressed in the puzzle.

You can find the game here



Building Academic Vocabulary Review Games Part Two

I like to use games to review concepts and skills.     They are highly engaging (as documented in Marzano’s The Highly Engaged Classroom ).   They promote student discourse.   As students play, they are constantly evaluating opposing players’ work because they are competitive and want to win.   They are generally fast-paced and can build a lot of review into a little bit of time.

In my last post ,  I shared a set of cards and directions for using them to play several different games (Draw Me and a couple of versions of Charades).    In order to add a little more variety to my vocabulary review, I have also created a version of Taboo.   Students play in table groups.   A “talker” is designated (I will do this by seat position within the group).   The talker tries to get the team to say the name of the word at the top of the card.   However, the talker can not use any of the words below the line.   You can download the set of cards by clicking Taboo


Table groups will compete against each other to identify the most vocabulary words.    I will have them  play for a specified amount of time.   The group that identifies the most words in the game will be the winner (and will each get a piece of candy).

Building Academic Vocabulary – Review Games Part 1

I’m not sure if there is a kid alive who doesn’t like to play games.   Granted, they like some games better than others.   Given the choice of a game or not a game, though, they always seem to choose a game.   Marzano uses that fact as a key component in his recommended systematic approach to building academic vocabulary in Building Academic Vocabulary .


As I said in my last post, I have been working to incorporate more instruction in academic vocabulary but need to do more regular review of the vocabulary.  To that end, I spent the last few days building a set of cards I can use in a couple of different games.  (You can download the cards by clicking on Charades )  I normally spend the last five to ten minutes of  class every day for some kind of review or as some kind of differentiated instruction.   These vocabulary games will go into that rotation.


Draw Me 

This is essentially a variation of Pictionary.   Students will work in table groups.  One student per group will be assigned to draw for a given round based on seat position.  ( I explain how I use seat positions in this post)  The drawer will get a cluster of terms that are related (eg., mean, median, mode).  He or she will draw pictures representing the words until the team guesses all of the words in the cluster.  When the team has guessed all of the words, the drawer stands and says “Got it”.   At that point, all other teams stop drawing.  The winning team gets a point.   Ideally, the game continues long enough for the drawer task to rotate through each member of the group.   In reality, I know there will be days when I just don’t have time for that, so the game will stop when time is up.   The winning team is the one with the most points.  (They will each get a piece of candy.)

I will have a set of cards for each table group and give the drawer the cards that are the cluster for their group.   I could do this by posting the words on the Promethean Board, but then I would have to ensure that everyone except the drawer was facing away from the board.   That seems like it would take more transition time than I want, so I decided to go with the cards.


This can be played with two different variations.

Variation 1:  

Students stand next to their desks and act out the word card displayed using the document camera or Promethean Board.   Students get “think” time after seeing the word and then are told to act it.   This feels more like an activity than a game to me, so I will probably use this when I am shorter on time.

Variation 2:  

Students work with their table group.   A designated group member is the actor (the actor will be determined by seat position within the group – e.g., Deltas do the first round, Sigmas the second, and so on).  Each table group will be given a set of cards.   The actors stand in front of their table group and begin to act out the term.   When the team has guessed the term, the actor raises the term card in the air to indicate his  or her team has correctly found the term.    The first team to identify the term gets a point.   The team with the most points at the end of the allotted time is the winner.



Accommodating Imperfection – Proportional Relationships Cards with Multiple Variations For Play

Successful design is not the achievement of perfection but the minimization and accommodation of imperfection. – Henry Petroski

I know that I will not ever design the perfect lesson any more than I will ever create the perfect design as an engineer.  I’m not sure that perfect exists in this world.   While Dr Petroski (a civil engineering and history professor at Duke University) focused his work on failure analysis in an engineering context, the underlying principle he espouses applies to my work as an educator as well.    On any given day, I know that some students will walk away  not having fully mastered the concepts addressed in class.   So, I plan ways to revisit concepts in small chunks of time until everyone does “get it.”  When I plan ways to revisit concepts, I try to create activities that I can use a lot of different ways because I want to be able to use them more than once rather than having to create an endless array of materials.

Proportional Relationships – What I Want Them To Know

I want students to know that proportional relationships are linear and go through the origin.

Proportional Relationships – What I Want Them To Be Able To Do

I want to ensure that students see proportional relationships in tables, graphs, equations, and word problems.   In each representation, I want them to see the constant rate of change and that there is no “start-up” value (the y-intercept is 0).     I want to incorporate Trail’s work (Twice-Exceptional Gifted Children) to support conceptual learners, so I envision a whole-part-whole instructional sequence:    what is a proportional relationship; how do you see it in a table, how do you see it in a graph, how do you see it in an equation, how do you see it in a word problem;   how is the constant rate of change shown in each representation, how is the “no-start up” shown in each representation (compare and contrast these in the different representations).

Proportional Relationship Cards

I created a set of 48 cards.   There are twelve cards for each of the four representations.   The cards can be used separately or together.   That is, I can use just the cards relating to a single representation if I want to focus on that representation.   Alternatively, I can use cards from all four representations if I want students to make connections across representations.   You can download the cards and game instructions by clicking on the link below the photos.

Proportional Relationship Card Sort and Game

Activity 1 – Quiz-Quiz-Trade

Quiz-Quiz-Trade is a Kagan Cooperative Learning Structure.   In this structure, students partner and quiz each other.   Then, they find a new partner and repeat the process.   Marzano’s research (Classroom Instruction That Works) shows that using cooperative learning structures produces gains of 27%    It also shows that incorporating movement increases levels of engagement (The Highly Engaged Classroom).


Activity Two – Give One, Get One

Like Quiz-Quiz-Trade, students work with a partner and quiz each other.   I will use this activity when I want students to make connections across representations.   It incorporates movement and a cooperative learning structure.   It is outlined in Marzano’s The Highly Engaged Classroom.   I have students form two lines facing each other with about three feet in between the lines (the structure does not specify this, but I find it works well this way).   Each student is given a card.   I will give one line a single representation and the other line a different representation.   The cards for partners will be different representations of the same problem.   Each partner will have to find the rate of change and the y-intercept using their card.   When a partner has found them, he or she steps forward.   When both partners are in the middle, they quiz each other on what the rate of change is/how it is shown on their card and on the y-intercept/how it is shown in their card.  When they are done, they step back into the line.   When all the pairs are done,  have one line pass their card to the next person and the other line shift (line one passes the card down one, line two shifts up one).

This is an activity that I do for 5 minutes at the end or start of class.   I end it based on time.   I don’t try to have every student do every problem.

Activity Three – Rummy

Students play in groups of 2 to 4 players.   They use the entire set of 48 cards to match the table, graph, equation, and word problem.


This is an activity I will use so that students compare and contrast the different representations.   Marzano’s research (Classroom Instruction That Works) shows that finding similarities and differences can produce gains of 45%.   His research (The Highly Engaged Classroom) also shows that using a game increases levels of engagement.

I may have students play the game in heterogenous groups as a general review activity.

I may use this as a differentiated instruction activity.  I will have students play the game in groups according to their level of mastery.   Students who have not attained mastery play the game.   Students who have attained mastery play a different game reflective of their own skill gaps.

I will have students play the game for 5-10 minutes at the end of class.   If the game is not over, the player with the most sets wins the game (and a piece of candy)

Activity Four – Card Sort with Three Variations

Students work individually, in pairs, or in table groups to sort the cards.   In the first variation, they work with a single representation and sort them into proportional/not proportional categories.   In the second variation, they work with a mixture of representations to sort them into proportional/not proportional categories.   In the third variation, they work with a mixed set of representations and find the matching cards (same situation represented in a table, graph, equation, word problem).

I may have students work in table groups as a general review activity.

I may have students work with intentional pairing.   In this scenario, I pair a student who is struggling with the concept with a student who has mastered the concept.    As they sort the cards, the discussion is scaffolded for the student who has not yet attained mastery.

I may have students work individually and use this as a formative assessment.





Timber! DI Decimal Division Jenga

When I first started teaching middle school, I guess you could say I was a generalist.  I tended to see my students as a single body.  I thought about what they knew or didn’t know as a group.   I would look at mastery levels on tests and then decide that I needed to do some reteaching on specific concepts based on the performance of the whole group.

Over the last few years, I have shifted my focus to the specific.   Now, I track each student’s performance on each of the standards or skills that I address in my course.  I use an excel spreadsheet with the various standards/skills as the column headings and the kids (grouped by period) as the row headings.   At the start of the year, I give a pre-assessment for the course so that I know where everyone is starting.   After each quiz or test, I update levels of mastery in the spreadsheet based on each student’s demonstrated mastery.   I use this data on a daily basis to ensure that each student is working on things at his or her level.    My goal is to have every single student with full mastery by the end of the year.   I don’t always completely meet this goal, but I come a lot closer to it than I did before I started doing this.

As I said in yesterday’s post, I use the last five to ten minutes of class every day for review and reteaching.   I try to make the review focused and fun.   Since it is a review/reteach, I have already taught the concept conceptually.   Sometimes, the review continues to be conceptual.   Sometimes, it  is just working with a skill.


One of the activities I use is Decimal Division Jenga.  I like the use of a game to practice.   Everyone knows a game is more fun than a worksheet and Marzano’s research supports this in The Highly Engaged Classroom.


I have decimal division problems on Jenga blocks.   Students pull blocks from the Jenga tower and have to do the decimal division problem.   They check their work with a calculator.   If they got the problem correct, they keep the block.   If they made a mistake, they put the block back on top of the tower.   If a player topples the tower, he or she must put all of his or her blocks back and rebuild the tower (the other players keep their blocks).   Their are several free blocks in the tower.   No player is allowed to have more than 3 free blocks.   If he or she does, the free block must be replaced and another block drawn.   The player with the most blocks when I call time is the winner and receives a piece of candy.

Decimal Division Jenga

I have three versions of this game.   The first version has problems in which a decimal is divided by a whole number.   The second version of the game has problems in which a decimal is divided by a decimal.   The third version of the game has problems in which a decimal is divided by a decimal resulting in a solution with zeros in the quotient.   I assign students to the appropriate version of the game based on their pre-assessment results initially.   I circulate between the games and monitor their work.   I work with students individually on their specific errors.   As students demonstrate sufficient levels of mastery over time, I shift them to a more difficult version of the game.   Eventually, everyone is playing only the most difficult level of the game.  You can download the file with the problems for all three levels by clicking on the link below the photo.

I let students know which version of the game they are playing using an index card system. I have an index card for each student with his or her name on it.   I write the name of the game they are playing in colored ink.   The color of the ink matches a piece of paper under the Jenga tower.   They match the color on their card to the color of the paper and go to the correct game pretty seamlessly.