High Equations MASSI

BACK TO Mathematics Activities for Scripted Systematic Instruction

Activity: Working at a Hardware Store

Grade Band: High School

Concept: Equations

Common Core State Standard	Core Content Connectors	MASSI OBJECTIVES
This lesson is linked to standards of mathematical practice and not specific CCSS.	HS H.NO.3a2 Rewrite mathematical statements (e.g., an expression) in multiple forms.	Making Sets Using a variable to represent an unknown number Writing expressions with unknown numbers Simplifying expressions

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

Combined materials provided: bolts (at least 100 total), washers (at least 100 total), small brackets (at least 100 total), zip top bags

Teacher materials: Pictures of hardware stores, dry erase marker

Student materials (need one set for each student): bolts, washers, small brackets, zip top bags, pencil

Worksheets: There are student worksheets to review each component of the lesson.

Assessments: Progress Monitoring for taking data during the lesson; Skills Test

TEACHING OVERVIEW: The first section of the MASSI provides remedial practice on making sets and using a letter to represent an unknown number. The lesson then moves to learning the symbol use and how to write an expression to represent unknown numbers. The lesson moves on to introduce the CCC target component where students learn to write the expression multiple ways by simplifying it. The CCC targets used for the MASSIs will be aligned with the Assessment Tasks but use different examples.

BUILD ESSENTIAL UNDERSTANDING: CONCEPT AND SYMBOLS: Creating Sets

(Skip this section for students who understand these relationships and can identify these concepts).
INTRODUCE ACTIVITY: "Today we are going to learn skills you will need when you have a job. One type of job that you might have is working at a hardware store. Here are some pictures of a hardware store. Have any of you ever been to a hardware store?" Give students the opportunity to answer yes/no. "What are some hardware stores you've been to?" Give students a moment to respond with local hardware store names, you may provide choices for students that need support. "Hardware stores sell a lot of different types of items. Some items they sell are bolts, washers, and brackets. Here are some bolts, washers, and brackets." Show students the bolts, washers, and brackets.

INTRODUCE THE PROBLEM: "Today we are going to practice learning how to find formulas to help us gather items like bolts, washers, and brackets for a customer at a hardware store."

MODEL THE PROCESS: Show students the bin of bolts. "Bolts get sold in bags of 5. In order to get these bolts ready to sell, we need to each make five sets of five. Watch me make two sets of five." Count aloud as you take each bolt and place it in one pile (1, 2, 3, 4, 5), then count aloud again as you place each bolt in a second pile (1, 2, 3, 4, 5). "Then we put each set into a zip top bag, like this." Put each set of bolts into its own bag.

STUDENT PRACTICE: Give each student 21-24 bolts, so student has more bolts than needed to ensure that s/he stops at the proper stopping point. Use LEAST INTRUSIVE PROMPTS script as needed to help students with each step.

**Note: Change numbers daily to prevent rote memorization.
**Note: If students are unable to physically move the bolts, the teacher may move them while the student counts aloud. If the student is nonverbal, counting may be done using an assistive technology device or with a response board (containing the numbers 1-10 or higher when appropriate). The student should "count" by pointing to the bolt, then pointing to the corresponding number. For example, the student points to the first bolt and points to the number one, then points to the second bolt and points to the number two, etc. Student may also tap as teacher counts or move hands/AT scanner from number to number as teacher counts. Look for an action that the student can perform independently and encourage this action as the tiles are counted. Some examples are: a tap, a head nod, blink, leg movement, finger movement.

CHECK AND SCORE

Step	Teacher Says/Does	Student Response
1	"I need some help. Make five sets of five bolts."	Student moves five bolts into the first set while counting 1, 2, 3, 4, 5.
2	Wait after student finishes the first set for them to independently initiate making the second set of five or say "What's next?"	Student moves five bolts into the second set while counting 1, 2, 3, 4, 5.
3	Wait after student finishes the second set for them to independently initiate making the third set of five or say "What's next?"	Student moves five bolts into the third set while counting 1, 2, 3, 4, 5.
4	Wait after student finishes the third set for them to independently initiate making the fourth set of five or say "What's next?"	Student moves five bolts into the fourth set while counting 1, 2, 3, 4, 5.
5	Wait after student finishes the fourth set for them to independently initiate making the fifth set of five or say "What's next?"	Student moves five bolts into the fifth set while counting 1, 2, 3, 4, 5.

"Good work making sets. Now let's put each set into a zip top bag." Have students put each set into its own zip top bag. "I'll take any leftovers you have."

INTRODUCE THE PROBLEM: Show students the bin of washers. "Washers get sold in bags of 8. In order to get these washers ready to sell, we need to each make four sets of eight."

MODEL THE PROCESS: "Watch me make two sets of eight." Count aloud as you take each washer and place it in one pile (1, 2, 3, 4, 5, 6, 7, 8), then count aloud again as you place each washer in a second pile (1, 2, 3, 4, 5, 6, 7, 8). "Then we put each set into a zip top bag, like this." Put each set of washers into its own bag.

STUDENT PRACTICE. Give each student 33-36 washers, so student has more washers than needed to ensure that s/he stops at the proper stopping point. Use LEAST INTRUSIVE PROMPTS script to help student with each step as needed.

CHECK AND SCORE

Step	Teacher Says/Does	Student Response
6	I need some help. Make four sets of eight washers.	Student moves eight washers into the first set while counting 1, 2, 3, 4, 5, 6, 7, 8.
7	Wait after student finishes the first set for them to independently initiate making the second set of eight or say "What's next?"	Student moves eight washers into the second set while counting 1, 2, 3, 4, 5, 6, 7, 8.
8	Wait after student finishes the second set for them to independently initiate making the third set of eight or say "What's next?"	Student moves eight washers into the third set while counting 1, 2, 3, 4, 5, 6, 7, 8.
9	Wait after student finishes the third set for them to independently initiate making the fourth set of eight say "What's next?"	Student moves eight washers into the fourth set while counting 1, 2, 3, 4, 5, 6, 7, 8.

"Good work making sets. Now let's put each set into a zip top bag." Have students put each set into its own zip top bag. I'll take any leftovers you have.

INTRODUCE THE PROBLEM: Show students the bin of brackets. "Brackets get sold in bags of 3. In order to get these brackets ready to sell, we need to each make six sets of three.
" MODEL THE PROCESS: "Watch me make two sets of three." Count aloud as you take each bracket and place it in one pile (1, 2, 3), then count aloud again as you place each bracket in a second pile (1, 2, 3). "Then we put each set into a zip top bag, like this." Put each set of brackets into its own bag.

STUDENT PRACTICE. Give each student 20-25 brackets, so student has more brackets than needed to ensure that s/he stops at the proper stopping point. Use LEAST INTRUSIVE PROMPTS script to help student with each step as needed.

CHECK AND SCORE

Step	Teacher Says/Does	Student Response
10	"I need some help. Make six sets of three brackets."	Student moves three brackets into the first set while counting 1, 2, 3.
11	Wait after student finishes the first set for them to independently initiate making the second set of three or say "What's next?"	Student moves three brackets into the second set while counting 1, 2, 3.
12	Wait after student finishes the second set for them to independently initiate making the third set of three or say "What's next?"	Student moves three brackets into the third set while counting 1, 2, 3.
13	Wait after student finishes the third set for them to independently initiate making the fourth set of three or say "What's next?"	Student moves three brackets into the fourth set while counting 1, 2, 3.
14	Wait after student finishes the fourth set for them to independently initiate making the fifth set of three or say "What's next?"	Student moves three brackets into the fifth set while counting 1, 2, 3.
15	Wait after student finishes the fifth set for them to independently initiate making the sixth set of three or say "What's next?"	Student moves three brackets into the sixth set while counting 1, 2, 3.

"Good work making sets. Now let's put each set into a zip top bag." Have students put each set into its own zip top bag. "I'll take any leftovers you have."

BUILD ESSENTIAL UNDERSTANDING: CONCEPT AND SYMBOLS: Using a Variable to Represent an Unknown Number

(Skip this section for students who understand these relationships and can identify these concepts).

INTRODUCE THE PROBLEM: "Part of the job at the hardware store requires keeping track of inventory, or how many items are in stock. We may know how many bags are in stock, but what if we don't know how many bolts, washers, or brackets are in each bag? We can use a variable, or a letter, to represent the unknown number of bolts, washers, and brackets. Variables can be any letter. Sometimes people use an "x" as a variable, and sometimes people take the first letter of the item to help them remember what the variable represents. For example, they may use the letter "b" to represent "brackets" since the word "brackets" starts with the letter "b". Since we have two words that start with "b"- "bolts" and "brackets", we will practice with the variable "x" for bolts and "b" for brackets."

MODEL THE PROCESS: Show the students four new bags of bolts (possibly different sizes to make it clear they are different). "I don't know how many bolts are in each bag, but I know that each bag has the same number of bolts." Count the number of bags. "1, 2, 3, 4. I have four bags of bolts. If I wanted to write this down, first I write the number of bags, 4" (write the number 4 on the board). "Then I can write a variable to represent the unknown number, because I don't know how many bolts are in each bag. I'm going to use the letter "x" for bolts, so I would write 4x." Write the letter "x" next to the number four. "Can you find the variable?" Wait for students to identify "x" as the variable.

STUDENT PRACTICE: "Good, let's practice with a few for you." Give each student worksheet 1. Use LEAST INTRUSIVE PROMPTS script to help student with each step as needed. **Note: Change numbers daily to prevent rote memorization.

**Note: Have the students write the number and letter on the worksheet, but do not score writing ability. If students are unable to write the number/letter, they can use number stamps, Velcro numbers, an assistive device, or direct the teacher to write it for them.

CHECK AND SCORE

Step	Teacher Says/Does	Student Response
16	Give each student 5 bags of bolts. "If we didn't know how many bolts were in each bag, how would we write the total number of bolts? Use the letter "x" to represent an unknown number."	Student counts the number of bags (either out loud or to themselves) and writes "5x".
17	Give each student 7 bags of washers. "If we didn't know how many washers were in each bag, how would we write the total number of washers? Use the letter "w" to represent an unknown number."	Student counts the number of bags (either out loud or to themselves) and writes "7w".
18	Give each student 4 bags of brackets. "If we didn't know how many brackets were in each bag, how would we write the total number of brackets? Use the letter "b" to represent an unknown number."	Student counts the number of bags (either out loud or to themselves) and writes "4b".

This may be a good stopping point. Let students practice working at a setup hardware store in your classroom. Demonstrate how to be the employee taking orders, then have students take turn taking orders. There is a worksheet with this level. You can use this for additional guided practice or to send home as homework.

Equations Skills Test	Teacher Says/Does	Student Response	Error Correction
	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.
NOW Stop the lesson here and repeat tomorrow if student is not yet getting at least 11 independent correct responses. Score responses 1-18 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 expressions as soon as possible, move into the second part of the lesson as soon as possible. Then to hit the target CCC for this grade level, move to the last part of the lesson (simplifying an expression). You can skip this Conceptual Foundation section to move on if students have mastered it.

HS BUILD A GRADE ALIGNED COMPONENT (Part 1): Creating an Expression to Represent a Story Problem

INTRODUCE THE PROBLEM: Now, you will show students how to create an expression representing an order at a hardware store. An expression has no "=" sign unlike an equation which does have an "=" sign. "When you work in a hardware store, there will be times you need to take an order for more than one customer at once. There's a way we can write down an expression to represent orders from multiple customers for multiple items. An expression is like an equation but has no equals sign."

MODEL THE PROCESS: Use Teacher Demonstration Card. "Here is an example: "At the hardware store, Betty needs 2 bags of bolts and 5 bags of washers. Juan needs 4 bags of bolts and 1 bag of washers." Watch me as I write this on the board. We don't know how many bolts and washers are in each bag, so we will use the letter "x" to represent the number of bolts in each bag and the letter "w" to represent the number of washers in each bag. First, Betty ordered 2 bags of bolts, so I write "2x". Now I write a plus. Betty also wanted 5 bags of washers, so I write "5w". Now I write a plus. Juan wanted 4 bags of bolts, so I write "4x". Write plus. He also wanted 1 bag of washers, so I write "1w"." The expression should be 2x + 5w + 4x + 1w.

STUDENT PRACTICE: Each student also needs worksheet 2. "Look at your worksheet. Let's read the problem together. Nala needs 8 bags of bolts and 3 bags of washers. Wally needs 1 bag of bolts and 6 bags of washers. Use the letter "x" to represent the number of bolts in a bag and the letter "w" to represent the number of washers in a bag." Use LEAST INTRUSIVE PROMPTS script to help student with each step as needed.

**Note: Have the students write the numbers/digits on the worksheet, but do not score 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.
**The full correct answer is 8x + 3w + 1x + 6w (this is broken down into task analyzed steps)

CHECK AND SCORE

Step	Teacher Says/Does	Student Response
19	"Write the expression that represents this problem."	Student writes/stamps/uses Velcro numbers/points to/eye gazes to write 8x.
20	Wait for students to independently write plus or say "What do you write next?"	Student writes/stamps/uses Velcro numbers/points to/eye gazes the plus sign.
21	Wait for students to independently write 3w or say "What do you write next?"	Student writes/stamps/uses Velcro numbers/points to/eye gazes to write 3w.
22	Wait for students to independently write plus or say "What do you write next?"	Student writes/stamps/uses Velcro numbers/points to/eye gazes the plus sign.
23	Wait for students to independently write 1b or say "What do you write next?"	Student writes/stamps/uses Velcro numbers/points to/eye gazes to write 1x.
24	Wait for students to independently write plus or say "What do you write next?"	Student writes/stamps/uses Velcro numbers/points to/eye gazes the plus sign.
25	Wait for students to independently write 6w or say "What do you write next?"	Student writes/stamps/uses Velcro numbers/points to/eye gazes to write 6w.

"Great work writing the expression 8x + 3w + 1x + 6w! Let's practice one more before we practice working at the store."

STUDENT PRACTICE: Look at your worksheet. Let's read the problem together. Pierre needs 1 bag of washers and 3 bags of brackets. Adara needs 4 bags of washers and 5 bags of brackets. Use the letter "w" to represent the number of washers in a bag and the letter "b" to represent the number of brackets in a bag. Use LEAST INTRUSIVE PROMPTS script to help student with each step as needed.

**The full correct answer is 1w + 3b+ 4w + 5b (this is broken down into task analyzed steps)

CHECK AND SCORE

Step	Teacher Says/Does	Student Response
26	"Write the expression that represents this problem."	Student writes/stamps/uses Velcro numbers/points to/eye gazes to write 1w.
27	Wait for students to independently write plus or say "What do you write next?"	Student writes/stamps/uses Velcro numbers/points to/eye gazes the plus sign.
28	Wait for students to independently write 3b or say "What do you write next?"	Student writes/stamps/uses Velcro numbers/points to/eye gazes to write 3b.
29	Wait for students to independently write plus or say "What do you write next?"	Student writes/stamps/uses Velcro numbers/points to/eye gazes the plus sign.
30	Wait for students to independently write 4w or say "What do you write next?"	Student writes/stamps/uses Velcro numbers/points to/eye gazes to write 4w.
31	Wait for students to independently write plus or say "What do you write next?"	Student writes/stamps/uses Velcro numbers/points to/eye gazes the plus sign.
32	Wait for students to independently write 5b or say "What do you write next?"	Student writes/stamps/uses Velcro numbers/points to/eye gazes to write 5b.

"Great work writing the expression 1w + 3b + 4w + 5b!"

This may be a good stopping point. Let students practice working at a setup hardware store in your classroom. Demonstrate how to be the employee taking orders. Create sample order scenarios with multiple orders for multiple items. Then have students take turn taking orders by creating expressions as they go. There is a worksheet with this level. You can use this for additional guided practice or to send home as homework.

Equations Skill Test	Teacher Says/Does	Student Response	Error Correction
	Give each student the Equations Skills Test 2. 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.
NOW Stop the lesson here and repeat tomorrow if student is not yet getting at least 8 independent correct responses on this section. Score responses 19-32 on the Equation Progress Monitoring Sheet if you did not do so while teaching.		NEXT Remember the goal is for students to hit the target CCC for this grade level, move to the last part of the lesson (simplifying an expression). You can skip this Symbol Use section to move on if students have mastered the skills.

HS BUILD A GRADE ALIGNED COMPONENT (Part 2): Simplifying Expressions (Writing equations in multiple forms)

INTRODUCE ACTIVITY AND PROBLEM: "We've already learned how to write an expression, but we must also simplify the expression to make it easier for us to get the items the customer wants. Before, we wrote an expression for a problem about Betty and Juan's order. Now we are going to learn to simplify the expression. Today, we will use the letter "b" for bolts and "w" for washers. I showed you how to write the expression for the following problem: "Betty needs 2 bags of bolts and 5 bags of washers. Juan needs 4 bags of bolts and 1 bag of washers." I wrote: 2b + 5w + 4b + 1w." Write 2b + 5w + 4b + 1w on the board for students to look at.

MODEL THE PROBLEM: "If Betty wants 2 bags of bolts and Juan wants 4 bags of bolts, we can combine them together. 2 bags plus 4 bags is 6 bags, so I write "6b"." Cross off 2b and 4b in the expression above and write a new expression below that starts with 6b. "Remember, we can only add together the types that are the same, which means they have the same letter. Let's finish simplifying this expression. If Betty wants 5 bags of washers and Juan wants 1 bag of washers, how many bags of washers do we need all together? We need 6 bags of washers all together, so I write "+ 6w" here." Cross off the 5w and 1w in the expression above and write 6w in the expression below. See below for an example of how the expression/visual should look when you write it on the board.

STUDENT PRACTICE: "Now it's your turn. Simplify the expressions on your worksheet." Give students worksheet 3. Look at your worksheet. It has the same problem from before. Let's read the problem together. Nala needs 8 bags of bolts and 3 bags of washers. Wally needs 1 bag of bolts and 6 bags of washers. We wrote that expression as: 8b + 3w + 1b + 6w. Use LEAST INTRUSIVE PROMPTS script to help student with each step as needed.

**Note: Have the students write the area into the formula on the worksheet, 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.

**Note: In the following problem, students are required to add. If students are unable to add 3+6 independently, it is ok to provide them with a calculator or other visual; however they must do the work independently. Be consistent with the type of accommodation provided here.

CHECK AND SCORE

STEP	Teacher Says/Does	Student Response
33	Now, you need to simplify this expression. Start by looking at 8b, which number represents the same item (bolts)?	Student points to, says, or otherwise identifies 1b.
34	Good, now add together 8b plus 1b and write your answer below.	Student adds 8b + 1b to equal 9b and writes 9b in the expression below.
35	We can cross out those numbers in the first expression.	Student crosses off the numbers 8b and 1b from the top expression.
36	Now look at 3w, which number represents the same item (washers)?	Student points to, says, or otherwise identifies 6w.
37	Now write the plus sign below.	Student writes/Velro's/selects/stamps the plus sign.
38	Good, now add together 3w plus 6w and write your answer below.	Student adds 3w + 6w to equal 9w and writes 9w in the expression below.
39	You can cross those numbers off the first expression.	Student crosses off the numbers 3w and 6w from the top expression.

Great work today! You simplified 8b + 3w + 1b + 6w to 9b + 9w. I'm very proud of you.

STUDENT PRACTICE: Let's do another by yourself. Look at your worksheet. Let's to do other problem from before. Let's read the problem together. Pierre needs 1 bag of washers and 3 bags of brackets. Adara needs 4 bags of washers and 5 bags of brackets. We wrote that expression as: 1w + 3b + 4w + 5b. Use LEAST INTRUSIVE PROMPTS script to help student with each step as needed.

CHECK AND SCORE

Steps	Teacher Says/Does	Student Response
40	Now, you need to simplify this expression. Do not provide additional verbal instructions outside of prompting strategies.	Student adds 1w + 4w to equal 5w and writes 5w in the expression below.
41	Wait for students to independently cross off the numbers or say "What's next?"	Student crosses off the numbers 1w and 5w from the top expression.
42	Wait for students to independently write the plus sign next to 5b or say "What's next?"	Student writes/Velcro's/selects/stamps the plus sign.
43	Wait for students to independently add 3b plus 5b or say "What's next?"	Student adds 3b + 5b to equal 8b and writes 8b in the expression below.
44	Wait for students to independently cross off the numbers or say "What's next?"	Student crosses off the numbers 3b and 5b from the top expression.

Good job! You simplified 1w + 3b + 4w + 5b to 5w + 8b. You are doing nice work today.

This may be a good stopping point. Let students practice working at a setup hardware store in your classroom. Demonstrate how to be the employee taking orders, and then have students take turn taking orders writing down and simplify expressions as they go. There is a worksheet with this level. You can use this for additional guided practice or to send home as homework.

Equations Skill Test	Teacher Says/Does	Student Response	Error Correction
	Give each student the Equations Skills Test 3. 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.

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: Setup a mock hardware store in the classroom or other space in the school. Have students practice getting orders from customers with multiple orders for groups of items. Make sure students write down the orders and simplify the expressions appropriately.

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 and talk with the general education teacher for more ideas.

Component	Activity	What Student Does	Generalization/ Fluency
Simplify linear equations with more than two types of variables	Students are presented with multiple customers with orders for bolts, washers, and brackets.	Students simplify orders for bolts, washers, and brackets.	Different amounts and items daily.
Rewrite statements in more than one form	Present students with orders for three types of items and ask them to rewrite the expressions in more than one way.	Students rewrite the expressions in more than one way.	Different numbers daily.
Substitute values for variables and simplify (e.g., 2a + 3a; where a=4 bolts)	Have students calculate the total items by substituting a value for the variable.	Students simplify the expressions by replacing the letters/variables with varying amounts.	Different numbers/amounts daily.

Printable Materials

Progress Monitoring and Skills Test

Teacher Demonstration Card 1

Worksheet 1

Worksheet 2

Worksheet 3

High School Equations MASSI Smartboard notebook