DAY 1 “Hook” Direct Instruction/Go over examples(this may take the entire period) Students create equations(may have to be done on Day 2) Hand out Formative assessment #1 for homework. Get a feel for how the students are progressing and adjust as necessary.

Introduction to Lesson - “Hook” Teacher: First I want us to start to with this activity. I will try to guess your birthday by having you do some operations. Try not to use a calculator. 1)Write the number that represents the month in which you were born. Example: 1 = January, 2 = February,... So on. 2) Multiply the previous number by 2. 3) Add 6 to that last number. 4) Now multiply that new number by 50. (Ask if anyone knows a shortcut ie: multply by 5 and then add a zero at the end) 5) Take the day of the month and add it to the previous number. Example: February 29 would be 29, April 1 is going to be 1. 6) Share that number with your someone first and check your work. 7) Now share that number with me and I will guess your birthday. Who thinks this is a trick? Who thinks its magic? (Explain that the trick is how to quickly undo all the operations they used so that you can extract their birthday. Explain that because you are able to do this fast, then it seems like its some kind of magic trick.)

Box 1 Add/Subtract Integers Box 2 Add/Subtract Variables Box 3 Multiply Terms by Integers Box 4 Divide Terms by Integers The next five slides(slides 3 to 7) contains the instructions that needs to be cut so that they can be separated into four different boxes that will be in front of the class. The teacher will use the strips to demonstrate a few examples starting on slide #8. The strips of instructions should be prepared ahead of time. The set up of the class might look like the diagram below.

ADD/SUBTRACT INTEGERS(BOX 1) CUT OUT EACH SLIP AND LAMINATE FOR FUTURE USE (ADD/SUBTRACT INTEGERS) ADD 1 on both sides ADD 2 on both sides ADD 3 on both sides ADD 4 on both sides ADD 5 on both sides ADD 6 on both sides ADD 7 on both sides ADD 8 on both sides ADD 9 on both sides ADD 10 on both sides SUBTRACT 1 on both sides SUBTRACT 2 on both sides SUBTRACT 3 on both sides SUBTRACT 4 on both sides SUBTRACT 5 on both sides SUBTRACT 6 on both sides SUBTRACT 7 on both sides SUBTRACT 8 on both sides SUBTRACT 9 on both sides SUBTRACT 10 on both sides

ADD/SUBTRACT INTEGERS(BOX 1) CUT OUT EACH SLIP AND LAMINATE FOR FUTURE USE ADD 11 on both sides ADD 12 on both sides ADD 13 on both sides ADD 14 on both sides ADD 15 on both sides ADD 16 on both sides ADD 17 on both sides ADD 18 on both sides ADD 19 on both sides ADD 20 on both sides SUBTRACT 11 on both sides SUBTRACT 12 on both sides SUBTRACT 13 on both sides SUBTRACT 14 on both sides SUBTRACT 15 on both sides SUBTRACT 16 on both sides SUBTRACT 17 on both sides SUBTRACT 18 on both sides SUBTRACT 19 on both sides SUBTRACT 20 on both sides

ADD/SUBTRACT VARIABLES(BOX 2) CUT OUT EACH SLIP AND LAMINATE FOR FUTURE USE (ADD/SUBTRACT VARIABLES) ADD 1x on both sides ADD 2x on both sides ADD 3x on both sides ADD 4x on both sides ADD 5x on both sides ADD 6x on both sides ADD 7x on both sides ADD 8x on both sides ADD 9x on both sides ADD 10x on both sides SUBTRACT 1x on both sides SUBTRACT 2x on both sides SUBTRACT 3x on both sides SUBTRACT 4x on both sides SUBTRACT 5x on both sides SUBTRACT 6x on both sides SUBTRACT 7x on both sides SUBTRACT 8x on both sides SUBTRACT 9x on both sides SUBTRACT 10x on both sides

MULTIPLY all terms by 2 MULTIPLY all terms by -2 MULTIPLY all terms by 3 MULTIPLY all terms by -3 MULTIPLY all terms by 4 MULTIPLY all terms by -4 MULTIPLY all terms by 5 MULTIPLY all terms by -5 MULTIPLY all terms by 6 MULTIPLY all terms by -6 MULTIPLY TERMS BY INTERGERS(BOX 3) CUT OUT EACH SLIP AND LAMINATE FOR FUTURE USE (MULTIPLY INTEGERS)

DIVIDE all terms by 2 DIVIDE all terms by -2 DIVIDE all terms by 3 DIVIDE all terms by -3 DIVIDE all terms by 4 DIVIDE all terms by -4 DIVIDE all terms by 5 DIVIDE all terms by -5 DIVIDE all terms by 6 DIVIDE all terms by -6 DIVIDE TERMS BY INTERGERS(BOX 3) CUT OUT EACH SLIP AND LAMINATE FOR FUTURE USE (DIVIDE INTEGERS)

Teacher: I want to demonstrate how to create/assemble your equations. I will only choose operations from Box 1 and Box 2 for this example. First I will think of my favorite number, during this demonstration I am telling you the number I am thinking of but when you are creating your equation make sure that you don’t reveal your favorite number. In order to hide my favorite number, I will use “v” for my favorite number. Step 1: Set your variable equal to your favorite number.V = 7 Step 2: Choose an operation from Box 1 (ADD 10 on both sides)V + 10 = 7+10 Step 3: Combine like terms(I just want to show you the new equation)V + 10 = 17 Step 4: Choose an operation from Box 12(SUBTRACT 8x on both sides)V – 8V + 10 = 17 – 8V Step 5: Combine like terms(Notice that I changed “x” into “v” so that the variables are the same) Why do I want the variables to match? -7V + 10 = 17 – 8V My assembled equation is -7V + 10 = 17 – 8V I can show another example unless unless you wish to try it on your own now. Box 1 Add/Subtract Integers Box 2 Add/Subtract Variables Example #1 (Approximately 15 minutes)

Teacher: How do you solve the equation I just created? Step 1: Set your variable equal to your favorite number.V = 7 Step 2: Choose an operation from Box 1 (ADD 10 on both sides)V + 10 = 7+10 Step 3: Combine like terms(I just want to show you the new equation)V + 10 = 17 Step 4: Choose an operation from Box 12(SUBTRACT 8x on both sides)V – 8V + 10 = 17 – 8V Step 5: Combine like terms(Notice that I changed “x” into “v” so that the variables are the same) Why do I want the variables to match? -7V + 10 = 17 – 8V Solve: -7V + 10 = 17 – 8V-7V + 10 = 17 – 8V Step 1: Step 2: Step 3: Step 4: Teacher: Recall the steps/operations that we applied to create the equation. Teacher: Did anyone else try a different sequence of steps? Who tried a different order of steps? Student: Yes/No... Teacher: Please tell the class your sequence and I can write it on the board.

Example #2 (Approximately 10 minutes) Step 1: Set your variable equal to your favorite number.k = -2 Step 2: Choose an operation from Box 1 (ADD 5 on both sides)k + 5 = Step 3: Combine like terms(I just want to show you the new equation)k + 5 = 3 Step 4: Choose an operation from Box 2(ADD 2x on both sides)k k = 3 + 2k Step 5: Combine like terms(I changed “x” into “k” so that the variables match) Why do I want the variables to match? 3k + 5 = 3 + 2k Step 6: Choose another operation from Box 3(Multiply all terms by 4)4(3k + 5 = 3 + 2k) Step 7: New Equation12k + 20 = k Step 8: Associative Property(Re-arrange the terms)12k + 20 = 8k + 12 Teacher: I will demonstrate how to create/assemble another equation. Now I will choose operations from Box 1, Box 2 and Box 3 for this example. Remember not to reveal your favorite number or you can choose a different one. Replace your number with a variable, I’m going to change variable and use “k”. Box 1 Add/Subtract Integers Box 2 Add/Subtract Variables Box 3 Multiply Terms by Integers

Teacher: How do you solve the equation I just created? Teacher: Recall the steps/operations that we applied to create the equation. Teacher: Did anyone else try a different sequence of steps? Who tried a different order of steps? Student: Yes/No... Teacher: Please tell the class your sequence and I can write it on the board. Step 1: Set your variable equal to your favorite number.k = -2 Step 2: Choose an operation from Box 1 (ADD 5 on both sides)k + 5 = Step 3: Combine like terms(I just want to show you the new equation)k + 5 = 3 Step 4: Choose an operation from Box 2(ADD 2x on both sides)k k = 3 + 2k Step 5: Combine like terms(I changed “x” into “k” so that the variables match) Why do I want the variables to match? 3k + 5 = 3 + 2k Step 6: Choose another operation from Box 3(Multiply all terms by 4)4(3k + 5 = 3 + 2k) Step 7: New Equation12k + 20 = k Step 8: Associative Property(Re-arrange the terms)12k + 20 = 8k + 12 Solve: 12k + 20 = 8k k + 20 = 8k + 12 Step 1 Step 2: Step 3: Step 4: Step 5: Step 6:

EXAMPLE #3 (Approximately 10 minutes) Step 1: Set your variable equal to your favorite number.k = -2 Step 2: Choose an operation from Box 1 (ADD 5 on both sides)k + 5 = Step 3: Combine like terms(I just want to show you the new equation)k + 5 = 3 Step 4: Choose an operation from Box 2(ADD 2x on both sides)k k = 3 + 2k Step 5: Combine like terms(I changed “x” into “k” so that the variables match) Why do I want the variables to match? 3k + 5 = 3 + 2k Step 6: Choose another operation from Box 4(Divide all terms by 3) then reduce fractions if possible. Step 7: New equation Teacher: I will demonstrate how to create/assemble another equation. Now I will choose operations from Box 1, Box 2 and Box 4 for this example. Remember not to reveal your favorite number or you can choose a different one. Replace your number with a variable, I’m going to change variable and use “k”. Box 1 Add/Subtract Integers Box 2 Add/Subtract Variables Box 4 Divide Terms by Integers

Teacher: How do you solve the equation I just created? Teacher: Recall the steps/operations that we applied to create the equation. Teacher: Did anyone else try a different sequence of steps? Who tried a different order of steps? Student: Yes/No... Teacher: Please tell the class your sequence and I can write it on the board. Solve: Step 1 Step 2: Step 3: Step 4: Step 5: Step 6:

INTRUCTIONAL PLAN (Approximately 15 minutes) Step 1: Set your variable equal to your favorite number.n = -5 Step 2: Choose an operation from Box 1 (ADD 5 on both sides)n + 5 = Step 3: Combine like terms(I just want to show you the new equation)k + 5 = 3 Step 4: Choose an operation from Box 2(ADD 2x on both sides)k k = 3 + 2k Step 5: Combine like terms(I changed “x” into “n” so that the variables match) Why do I want the variables to match? 3k + 5 = 3 + 2k Step 6: Choose another operation from Box 4(Divide all terms by 3) then reduce fractions if possible. Step 7: New equation Teacher: I will demonstrate how to create/assemble another equation. Now I will choose operations from Box 1, Box 2, Box 3 and Box 4 for this example. Remember not to reveal your favorite number or you can choose a different one. Replace your number with a variable, I’m going to change variable and use “k”. Box 1 Add/Subtract Integers Box 2 Add/Subtract Variables Box 4 Divide Terms by Integers Box 3 Multiply terms by Integers

Teacher: How do you solve the equation I just created? Teacher: Recall the steps/operations that we applied to create the equation. Teacher: Did anyone else try a different sequence of steps? Who tried a different order of steps? Student: Yes/No... Teacher: Please tell the class your sequence and I can write it on the board. Solve: Step 1 Step 2: Step 3: Step 4: Step 5: Step 6:

STUDENTS TURN Direct instruction may use up most of the period if not entire period. After the direct instruction and examples, students can now pick instructions from the boxes(see next slide for instructions) and start creating their own equations. They can take the slips home with them to complete their equation if the teacher wishes(this may spill over to Day 2 or even start on Day 2) Don’t forget slides #18 and #19 are handed out for homework(Formative assessment #1)

Students assemble their own equation Think of your favorite number and select your own variable that represents your favorite number. You may choose “x” or “y” as your default. You may also use any letter but try not to use the letter “O” or “I” because they can be mistaken for numbers. Select an “operation slip” from each box and attempt to create your equations. There should be two boxes but I will add two more boxes once we’ve completed a few exercises. I will walk around to help but until I am able to get to you, look back at my example and try to do as much on your own. If you are confused or lost, do not be afraid to ask others around you for their help. Make sure you do not reveal your favorite number.

Formative Assessment(In Class or Homework) – page 1 Step 1: Set your variable equal to 9 Step 2: ADD 5 on both sides of the equation Step 3: Combine like terms(Write down the new equation) Step 4: Subtract 3x on both sides of the equation(Remember to match your variables) Why do you want the variables to match? Step 5: Combine like terms(Write down the new equation) 1) Create a linear equation using the instructions below. Step 1: Set your variable equal to -5 Step 2: Subtract 6 on both sides of the equation Step 3: Combine like terms when necessary. (Write down the new equation) Step 4: Multiply all the terms by 2 Step 5: Combine like terms when necessary.(Write down the new equation) 2) Create a linear equation using the instructions below.

Formative Assessment(In Class or homework) – page 2 3) Create a linear equation using the instructions below. Step 1: Set your variable equal to -5 Step 2: Subtract 6 on both sides of the equation Step 3: Combine like terms(Write down the new equation) Step 4: Add 7x on both sides of the equation(Remember to match your variables) Why do you want the variables to match? Step 5: Combine like terms(Write down the new equation) Step 6: Multiply all the terms by 3 Step 7: Write down your new equation. 4) Solve the equation below. List your steps on the left side of the table. Solve: 21 – 6x = 2x – 6x = 2x - 11

DAY 2 Go over any questions students may have on formative assessment #1(10 minutes). Students have their own equations that they can display(give students the opportunity to create their equation if they were unable to during DAY 1). Gallery walk of students(25 – 30 mins). Teacher observes and gives feedback. Students solve equations that are not their own(students should be doing this during the gallery walk) Hand out Formative assessment #2 for homework(Students can start early if they are finished with the gallery walk).

GALLERY WALK Students should be displaying their equations along the wall so that other students can attempt to solve them. The teacher should be observing and checking the equations over to make sure that feedback is given(level of feedback is up to teacher discretion). As they walk around students will be solving other equations and the teacher should encourage students to continue to solve multiple equations and checking the solution with the equation owner. Teacher should also encourage students to discuss the problems with each other and compare their strategies. This allows for peer feedback to happen. It will be up to the teacher to determine when the gallery walk will conclude but make sure there will be time for the class to reflect back on the activity. Aside from small groups discussing the problems during the gallery walk, the class should also have an opportunity to have a discussion as a whole. In addition to peer feedback the students will also get teacher feedback.

DAY 3 Continued class discussion. Go over homework(formative assessment #2) questions. Summative assessment.