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NCSC Math Activities with Scripted Systematic Instruction (MASSI):

Middle School Equations

Keri Bethune

Julie Thompson

Alicia Saunders

Diane Browder

Amy Lehew

January 2013

Revised September 2017

Reposted March 11, 2013

Reposted March 11, 2013

MASSI: Math Activities with Scripted Systematic Instruction Activity: Going BowlingGrade Band: Grades 6-8Concept: Equations

Florida Standard Access Points MASSI OBJECTIVESMAFS.6.EE.2.7Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.

6th MAFS.6.EE.2.AP.7b

Solve real-world, single-step linear equations involving positive rational numbers.

Write an equation given story problem and solve equation.

MAFS.7.EE.2.4Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

7th MAFS.7.EE.2.AP.4b

Solve equations with one variable based on real-world problems.

Write an equation given story problem and solve equation.

MAFS.8.EE.3.7Solve linear equations in one variable. 8th

MAFS.8.EE.3.AP.7a Simplify linear equations and solve for one variable.

Given multiplication equation solve for variable.

Be sure to provide specific practice to students on the skills that correspond to their grade level.

Teaching Materials: story problems (cut apart and laminated), equation template (one for teacher and each student, laminated), number line (one for teacher and each student, laminated), bowling photos, isolating and solving for variable template (one for teacher and each student, laminated). Note: Teachers may rewrite story problems using names of the students in the class.

Other Materials: calculators for each student; snack and other items students could practice buying and selling at a bowling alley concession stand; realistic looking pretend money or real money

Worksheets: worksheet for each section of lesson

Assessments: progress monitoring and skills tests for each section of lessonMASSI: Middle School Equations, Reposted March 11, 2013 3

TEACHING OVERVIEW: The first section of the MASSI provides remedial practice on identifying numbers in story problems. For students with no number recognition skills, rewrite story with numerals and add objects or pictures above numbers to help them identify. 6th and 7th graders will learn to create an addition equation, using a variable for an unknown number, from a story problem and solve for the variable. This is a good review for your 8th graders. 8th graders will be doing the same thing but with multiplication story problems. This is useful for your 6th and 7th graders to gain fluency with equations and practice calculator skills, or you can provide 6 th and 7th graders with more addition problems with one variable while 8 th graders work on multiplication.

SCRIPT FOR LESSONBUILD ESSENTIAL UNDERSTANDINGS – CONCEPT AND SYMBOLS: Identifying the Number from a Sentence (Skip this section for students who understand these relationships and can identify these concepts)

INTRODUCE ACTIVITY: Today we are going to learn how to keep track of our money when we go bowling. Here are some pictures of a bowling alley. Have any of you been bowling before? Give students opportunity to answer yes/no. We have to pay to go bowling. It costs money for shoes, games, and snacks. Today we are going to practice learning how to keep track of what we might spend at a bowling alley by using variables in our equations.

INTRODUCE THE PROBLEM: Display story problem. Here is a story about going bowling. “Lucia had $15 for bowling. Lucia spent $8 on shoes and games. She spent the rest on snacks. How much did Lucia spend on snacks?”

MODEL THE PROCESS: The first thing I need to do to answer the story problem is to write an equation, but before I can write an equation I need to find the numbers in my story problem. Do you see any numbers? Give students opportunity to answer yes/no. Point to a number. Wait 4 seconds for students to respond. Here is a number. Circle 15. It is number 15. Do you see another number? Give students opportunity to answer yes/no. Point to a number. Wait 4 seconds for students to respond. Good. That is number 8. Circle 8.

STUDENT PRACTICE: Now it is your turn to practice. Display story problem. Use CONSTANT TIME DELAY script as need to help students with each step. *Note: in this exercise, change numbers daily to prevent rote memorization.

CHECK AND SCOREMASSI: Middle School Equations, Reposted March 11, 2013 4

STEP Teacher Says/Does Student Response1. Let’s try another problem. “Shawn has 5 dollars in his hand. He

has more in his pocket. He has 12 dollars in total. How many are in his pocket?” Circle the numbers.

Student circles/eye gazes to numbers in story problem.

6th 7th BUILD A GRADE ALIGNED COMPONENT: Creating an Equation 8th BUILD ESSENTIAL UNDERSTANDING: Symbol Concept INTRODUCE PROBLEM: Display “Shawn” story problem. We are going to solve these problems. In both of the problems there is a number we don’t know yet. We will solve the problem using a variable. A variable is a letter that can be used in place of a number you don’t know yet.

MODEL THE PROCESS: Model using Equation Template. Let’s review our story problem about Shawn. I am going to read the three sentences. One doesn’t have a number. We’ll use a letter when we don’t know the number. Let’s put them in our equation as we go. “Shawn has 5 dollars in his hand.” How many dollars are in his hand? Provide wait time for students to respond. Yes, 5. Write five on line. He has more in his pocket? Provide wait time for students to respond. We don’t know do we? There isn’t a number. Let’s use a “p” for pocket. Write + p. I am writing “+ p” because we know that Shawn had 5 dollars in his hand AND some dollars in his pocket. I want to add the 5 and the p. Point to last line in problem. He has 12 dollars in total. How many in total? Provide wait time for students to respond. Yes, 12. So my equation is 5 + p = 12.

STUDENT PRACTICE: Display “Slade” story problem. Provide student with the Equation Template. Use SYSTEM OF LEAST PROMPTS script as needed to help students with each step.

CHECK AND SCORE

Step Teacher Says/Does Student Response2. Let’s read the problem together. “Slade bought 2 candy bars.

Later he bought more candy. He ate 4 pieces total.” Write the equation that represents this problem. Use the letter c to represent the unknown amount of candy. Write the first number.** Have the students write the numbers/digits on the template, but do not

Student writes/stamps/uses Velcro numbers/points to/eye gazes to write 2.

**The full correct answer is 2 + c = 4(This is broken down into task analyzed

MASSI: Middle School Equations, Reposted March 11, 2013 5

Step Teacher Says/Does Student Responsescore writing ability. If students are unable to write the number, they can use number/letter stamps or direct the teacher to write it for them.

steps)

3. Wait for students to independently write plus or say “What do you write next?”

Student writes/stamps/uses Velcro numbers/points to/eye gazes to the plus sign.

4. Wait for students to independently write c or say “What do you write next?”

Student writes/stamps/uses Velcro numbers/points to/eye gazes to write c.

5. Wait for students to independently write equal or say “What do you write next?”

Student writes/stamps/uses Velcro numbers/points to/eye gazes to the equal sign.

6. Wait for students to independently write 4 or say “What do you write next?”

Student writes/stamps/uses Velcro numbers/points to/eye gazes to write 4.

Great work writing the equation 2 + c = 4! Let’s practice one more before we read about going bowling. Display “Jacob” story problem. Provide student with Equation Template. Use SYSTEM OF LEAST PROMPTS script as needed to help students with each step.

CHECK AND SCORE

Step Teacher Says/Does Student Response7. Let’s read the problem together. “Jacob paid 4 dollars for shoes.

Then he paid for the game. He used all of the $10 that he brought.” Write the equation that represents this problem. Use the letter g to represent the unknown cost of the game. Write the first number.

Student writes/stamps/uses Velcro numbers/points to/eye gazes to write 4.**The full correct answer is 4 + g = 10 (this is broken down into task analyzed steps)

8. Wait for students to independently write plus or say “What do you write next?”

Student writes/stamps/uses Velcro numbers/points to/eye gazes to the plus sign.

9. Wait for students to independently write g or say “What do you write next?”

Student writes/stamps/uses Velcro numbers/points to/eye gazes to write g.

10. Wait for students to independently write equal or say “What do you write next?”

Student writes/stamps/uses Velcro numbers/points to/eye gazes to the equal sign.


Step Teacher Says/Does Student Response11. Wait for students to independently write 10 or say “What do you write

next?”Student writes/stamps/uses Velcro numbers/points to/eye gazes to write 10.

Great work writing the equation 4 + g = 10!

This may be a good stopping point. Let students practice working to buy a snack at the bowling alley. They can make a selection and purchase with response options provided if needed. You can use the worksheet for this level as additional guided practice or to send home as homework.

Teacher Says/Does Student Response Error Correction

INDEPENDENT PRACTICE: Equations Skills Test

Give each student the Equations Skills Test 1. Read directions for each problem and have student select response. Record whether response is correct or incorrect.

Only provide praise for completing assessment (if student needs encouragement). Do not provide specific praise for correct answers while student is testing.

Once the student has completed the test, review missed problems with the student.

NOWStop the lesson here and repeat tomorrow if student is not yet getting at least 6 independent correct responses. Score responses 1-11 on the Equation Progress Monitoring Sheet if you did not do so while teaching.

NEXT Remember the goal is for students to be able to write equations given story problem and solve the addition equation 6th 7th to find the variable, and given multiplication solve to find variable8th. As soon as possible, move into the remainder of the lesson to hit the target Access Points for this grade band. Be sure to provide some practice for students at their specific grade level concept even if they have not achieved mastery of previous concepts.


6th 7th BUILD A GRADE ALIGNED COMPONENT: Solving Equation for Variable 8th BUILD ESSENTIAL UNDERSTANDING: Continue Building Symbol Concept

INTRODUCE THE PROBLEM: Now we have learned to write equations when we have a story problem. Let’s learn how to solve the equations. Yesterday we wrote an equation for the story problem about Shawn. Let’s read the story problem again: “Shawn has 5 dollars in his hand. He has more in his pocket. He has 12 dollars in total. How many are in his pocket?” Remember, the equation was 5 + p = 12. Let’s learn how to solve for p.

MODEL THE PROCESS: Display Equation Template with number line. We can use a number line to solve this problem. I will put my finger on 5 and count how many jumps it takes to get to 12. Place your finger on five and count. One. Two. Three. Four. Five. Six. Seven. I will write p equals seven. He has $7 in his pocket.

STUDENT PRACTICE: Now it’s your turn to solve an equation for a variable. Display story problem, write equation on paper with c=___, and give students number line. *Note: you can adapt this by making it larger for students to eye gaze towards, or make tactile by using puffy paint on each point on the number line, etc. Use MODEL-LEAD-TEST script to teach counting on number line if needed.

CHECK AND SCORE

Step Teacher Says/Does Student Response12. Look at the story problem. “Slade bought 2 candy bars. Later he

bought more candy. He ate 4 pieces total.” The equation is 2 + c = 4. Use the number line to solve the problem. What number do you start at?

Student points to, says, or otherwise indicates 2. Note: If needed circle numbers, or have student circle numbers, so they remember where to start and stop.

13. Good. Now what number will you count to? Student points to, says, or otherwise indicates 4.

14. Start at 2 and count until you get to 4. Student places finger on (or begins eye gaze) 2 and counts jumps…One. Two (stopping at number 4).

15. What does c equal? Write it. Student points to, says, or otherwise identifies 2 and writes 2.


Great work today! You solved the equation for c. C equaled 2 candy bars. Let’s do another. Display “Jacob” story problem. Use MODEL-LEAD-TEST script to teach counting on number line if needed.

Step Teacher Says/Does Student Response16. Let’s do the other problem from before. Let’s read the problem

together. Jacob paid 4 dollars for shoes. Then he paid for the game. He used all of the $10 that he brought.” We wrote that equation as: 4 + g = 10. Now, you need to solve for g. Do not provide additional verbal instructions outside of prompting strategies.

Student points to, says, or otherwise indicates 4.

17. Wait for students to begin counting up or say “What’s next?” Student places finger on (or begins eye gaze) 4 and counts jumps…One. Two. Three. Four. Five. Six (stopping at number 10).

18. Wait for students to write 6 or say “What’s next?” Student points to, says, or otherwise identifies 6 and writes 6.

Good job! You solved 4 + g = 10, and g = $6. You are doing nice work today.

This may be a good stopping point. Let students practice working to buy a snack at the bowling alley. They can make a selection and purchase with response options provided if needed. Model writing down the equation before giving the order. There is a worksheet with this level, which can be used as additional guided practice or to send home as homework.



INDEPENDENT PRACTICE:Equations Skill Test

Give student the Equations Skills Test 2. Read directions for each problem and have student select response. Record whether response is correct or incorrect.



NOWStop the lesson here and repeat tomorrow if student is not yet getting at least 4 independent correct responses. Score responses 12 - 18 on the Equation Progress Monitoring Sheet if you did not do so while teaching.

NEXT Remember the goal is for students to be able to write equations given story problem and solve the addition equation 6th 7th to find the variable, and given multiplication solve to find variable8th. As soon as possible, move into the remainder of the lesson to hit the target Access Points for this grade band. Be sure to provide some practice for students at their specific grade level concept even if they have not achieved mastery of previous concepts.

8th BUILD A GRADE ALIGNED COMPONENT: Solving Multiplication Equation for VariableINTRODUCE THE PROBLEM: Sometimes we might need to solve for a variable in a multiplication equation. Listen to this word problem. “Marion paid for 4 bowling games. It cost 20 dollars total. How much did each game cost?” The key word “each” tells us this is a multiplication problem. We want to know the price of each game, so we will use the variable “g” for games.

MODEL THE PROCESS: Display the equation and template for multiplication. See next page for the “process for isolating a variable.” For more on isolating variables, see the Curriculum Resource Guide for Equations. Note: Students may not know that if the number (known as coefficient) and letter are next to each other that it means to multiply, even if there is no multiplication sign. They also may not MASSI: Middle School Equations, Reposted March 11, 2013 10

know to divide when numbers are written over and under a line. Please explain this to your students if they do not have these pre-requisite skills. The equation for this problem is “4 times g equals 20”. Point to g. The first step is to isolate the variable. That means that g needs to be alone on this side of the equation (point to left side of equation). Remember, both sides of the equation must be equal! So, whenever we change one side of the equation, we must change the other side in the same way. In order to isolate the variable, we use the inverse operation to undo the side of the equation with the variable. Can you show me the side with the variable? Wait for student(s) to point. Inverse operation means opposite operation, so the inverse operation of multiplication is division. What is the inverse operation of multiplication? Wait for students to respond. Yes, division is the inverse operation, so we must divide both sides by 4 to get g alone. Let’s write that on the equation template. Watch what I write. Underline each side of the equation and write 4 below the line. The fours on top and bottom cancel each other out. So we can draw an X over them. Draw an X on both 4s on the left side. Rewrite the equation so that it says g = 204 . Point to this equation and say, This is what the equation looks like after we cancel out the 4s. Now we have isolated the g. We just need to divide 20 by 4 to solve for g. Display calculator. I will use my calculator to solve for g. First I will type 20, then push the division sign, then push 4, and lastly push equal {or ENTER depending on calculator type}. The answer is 5. G = five. That means each game cost five dollars.

Process for Isolating a Variable


STUDENT PRACTICE: Display story problem that begins with “3 groups of friends came to the bowling alley.” Give students blank “isolating and solving for variable" template. Use SYSTEM OF LEAST PROMPTS script as needed to help students with each step.

CHECK AND SCORE

Step: Teacher Says/Does Student Response19. Here is another multiplication word problem. Let’s read the

problem together. “3 groups of friends came to the bowling alley. Each group was the same size. There were 12 friends altogether. How many were in each group?” Below is the equation for this problem. It says 3 times g = 12. g stands for group. Write the equation on your paper. Write the first number in the yellow box.

** Have the students write the answer on the template, but do not score writing ability. If students are unable to write the number, they can use number stamps or direct the teacher to write it for them.

Student writes 3 in yellow box.

20. Now write the variable in the blue box. Student writes g in blue box.21. Write the total in the purple box. Student writes 12 in purple box.22. Remember we need to isolate the variable. Write the equation

again and divide both sides by three.Student writes equation on next line and divides each side by three.

23. Point to the left side of their equation. The threes cancel each other out on this side. Cross out the threes.

Student crosses out the threes on the left side.

24. Write the variable and the left over numbers below. Student writes the remaining variable and numbers below.

25. Good you isolated the variable. Now use your calculator to divide 12 by 3. Type 12.

Student types 12 into calculator.

26. Push divided by. Student pushes division symbol.27. Push 3. Student pushes 3.28. Push enter. Student pushes enter.29. Write your answer. Student writes answer.


Great job solving the multiplication equation. Now let’s do another. Display problem 4x=20. Give students blank “isolating and solving for variable" template. Use SYSTEM OF LEAST PROMPTS script as needed to help students with each step.

CHECK AND SCORE

Step: Teacher Says/Does Student Response30. Here is another multiplication equation. It says 4 times x = 20.

Solve for x. Do not provide additional verbal instructions outside of prompting strategies.

Student writes equation on his/her paper.

31. Wait for students to rewrite equation below or say “What’s next?” Student rewrites equation on next line.32. Wait for students to divide both sides by 4 or say “What’s next?” Student divides both sides by 4.33. Wait for students to cross out fours on left side or say “What’s next?” Student crosses out fours on left side.34. Wait for students to rewrite remaining numbers below or say “What’s

next?”Student rewrites remaining numbers below.

35. Wait for students to use calculator to solve for x or say “What’s next?” Student uses calculator to solve for x.36. Wait for students to write answer or say “What’s next?” Student writes answer below.

Good job! You solved the equation 4x = 20 and found that x=5. You are doing nice work today.

This is the end of the lesson. Let students practice working to buy a snack at the bowling alley. They can make a selection and purchase with response options provided if needed. Model writing down the equation before giving the order. There is a worksheet with this level. You can use this for additional guided practice or to send home as homework.


INDEPENDENT PRACTICE:Equations Skills Test

Give student the Equations Skills Test 2. Read directions for each problem and have student select response. Record whether response is correct or incorrect.



Troubleshooting and Data-Based Decision Making for Equations Test:


If student is unable to complete any items on the equations test independently and correctly, go back and teach one problem step-by-step.

MASSI CULMINATING ACTIVITY: Go bowling! Have students use the equations to figure out how much money they need.

BUILD TOWARDS FULL GRADE LEVEL COMPETENCE

Here are ideas to build competence towards the full grade level competence using this same activity. See the unit plan for more ideas and talk with the general education teacher for more ideas.

Component Activity What Student Does Generalization/ Fluency

Write subtraction, multiplication, and division equations with one variable from story problem.

Students are presented with variety of story problems related to bowling.

Students writes equation based on story problem.

Different amounts and story problems daily.

Solve subtraction, multiplication, and division equations with one variable.

Present students with variety of story problems. Teach them the rule: “What you do to one side, you must do the same to the other,” as well as inverse operations.

Students solve the equations to find the value of the variable. Aim to have students do it independently without using the Task Analysis or equation template.

Different numbers, types of equations, and story problems daily.


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