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Artifact 2a - Percentages, Alternative Co- Teaching 1

Artifact 2a: Lesson Plan 2a – Percentages, Alternative Co-Teaching

Lesson Plan 2a

Donna Carbone

Practicum/Internship In Inclusion Settings

EDU 724

August 1, 2010


Introduction

My students are a sixth grade math class of 20 students. There are seven Tier III math

students, and two of the seven students have IEPs. Most students in the school live below the

poverty level, with over 90% qualifying for Free and Reduced Lunch. This lesson uses shopping

as motivation. Whether it is fast food or “luxury” items, our students love to think about things

they would like to buy. Simply finding a percent of a number does not have meaning for my

students. In order for them to make a connection, the skill needs an application that is

meaningful in their lives. The lesson links finding percentages to discounts and sale prices of

kid-friendly items. Because this is the first opportunity the students have to find a percent of a

number, the prices will be whole numbers to simplify calculations.

This lesson plan is a math lesson on using the cross-product method to find a percentage

of a number. Cross-products have not been previously taught in sixth grade. I had an opportunity

to observe a new teacher in several of her eighth grade math classes last year, as part of a

mentoring program. I was struck by the success of ALL of the students in finding the percentage

of a number using the cross-product method. Their success rate was much higher than the rate in

sixth grade, where the math textbook uses a multiplication method. A check-in with the seventh

grade teacher revealed she taught the cross-product method, too. The seventh grade students

were as successful as the eighth graders. We will introduce the method in sixth grade this year to

be consistent and, hopefully, as successful. Two other methods will be introduced in an

extension activity for Group 1. Group 1 will use the alternate methods as quick ways to check the

reasonableness of an answer. The lesson is planned for a sixty minute block.

The Do Now will be a review of decimal subtraction with regrouping, as this is the operation the

students will use when subtracting a discount from the original price. The Do Now is a whole


group activity.

The alternative co-teaching approach is used for the remainder of this lesson. The

twenty students in this class will be divided into three groups. Group 1 will have the Tier I

students. Groups 2 and 3 will divide the remaining students, making heterogeneous groups of

Tier II and Tier III students. The two students with IEPs will be put in different groups, one in

Group 2 and the other in Group 3.

The Teach To for all three groups starts with a preview of vocabulary, a must for ELL

students. Vocabulary words include: original price, discount, % off, half off, and sale price and

cost. Each group also has a graphic organizer to review for the method(s) they will use.

Group 1 will first learn the cross-product method to find the percentage of a number.

Group 1 is made up of the top math students in this class, who should quickly catch onto the

cross-product process. After Group 1 masters the cross-product process, they will be given

extension activities involving other ways to find the percentage of a number: proportional

reasoning and decimal multiplication. For our top students it is a way to introduce number

manipulation, a precursor to solving equations for a variable.

Groups 2 and 3 have more review and remedial needs. Since discounts are always

subtracted from the original price, both Groups 2 and 3 will move onto a quick revisit to the Do

Now operation, decimal subtraction with regrouping. They will then begin finding percentages

using the cross-product method.

The Alternative co-teaching approach continues with the Guided Practice and the Check

For Understanding. The Guided Practice is a worksheet on finding the amount of a discount, and

determining the resulting sale price or cost. Group 1 will be directed to the use each of the three

methods at least once. It will be their choice of which method is used on a problem. Groups 2


and 3 will only use the cross-product method. Because each teacher is working with small

groups, any student who needs help will be evident.

The Check For Understanding continues the work with small groups. To make the

exercise interesting, there will be three sets of cards for each group. One set of index cards will

have pictures of items from catalogs or sale circulars, the second set will have random prices

listed, and the third set will have sales phrases, such as: “HALF OFF!, Marked down 25%” etc.

Three picks gives the group an item, a price and a discount and from there, each group member

works individually to find the sale price. Every student will have at least one opportunity to pick

a card. After two or three items, depending on time, the class reassembles for the assessment.

This lesson provides an opportunity to vary the approach and have a different teacher

take the lead (Friend, 2008). This will be the first time cross-product is used in grade six, and

only the Title I math teacher is familiar with all of the methods. It makes sense that the Title I

teacher has the lead teacher role for this lesson To bring the rest of the team up to speed, Title I

has made a teacher reference sheet (attached) with an example of each percentage process. The

reference sheet will be reviewed at the Team Planning meeting, and can be used during the

Teach To. The reference sheet is an example of teachers sharing knowledge and skills, a

personal prerequisite present in successful co-teaching as listed in the checklists in Friend

(2008).

Changing the usual groupings and the lead teacher role builds student interest in the

lesson because it is not the norm. Teachers and students learn more about each other, which

only can help the lines of communication. More importantly, our special education students

have a chance to work with a variety of classmates and the general education teacher. “If the

general education teacher sometimes works with the group needing remediation, less stigma may


occur” (Friend, 2008, p. 74).

The Guided Practice worksheet has kid-friendly graphics, and allows for practice of skills

in a fun way. I tried to use items that they would like to buy. The Check For Understanding

activity gives everyone a chance to participate in an interactive activity. It has an element of

surprise and excitement since three students are selecting cards to make up one problem.

Students have the chance to work collaboratively, replicating the example set by their teachers.

Working closely with a small group allows the teacher to see the progress of each

student with both the Guided Practice and the Check For Understanding. Both students with

IEPs are receiving services as part of the general education class. There is a graphic organizer

for their use, vocabulary is previewed, and the content has been taught in small chunks.

The biggest challenges for this lesson are the teacher pacing, the class noise level, and the

content knowledge of the teachers. Since each teacher is not teaching the exact same content,

they must be aware of where the others are in the lesson. As a team, we agree that students need

to be attentive, and not chattering, during the Teach To. As students work together and discuss

their solutions, the noise level understandably increases during Guided Practice and the Check

For Understanding. Until every group has moved on from the Teach To, teachers must monitor

their students’ voice levels, and keep them low. The teacher reference sheet was developed to

address the issue of content knowledge. Using the sheet as a guide during the team planning

meeting, and having the opportunity to review the lesson plan, should make all of the teachers

comfortable with the content of the lesson. As with all of the other co-teaching approaches, I

would use the alternative co-teaching approach again, especially if there is a group of students

very much ahead or very much behind the rest of the class. But since we don’t want to single out

certain groups as being “different” on a regular basis, I would not use it as often as I would


parallel teaching. I do like the idea of teachers switching the lead teacher role. As a Title I or a

Special Education teacher, being the lead teacher periodically helps to establish the fact that one

is indeed a “real” teacher.

One addition I would consider for this lesson is to ask students to bring in sales fliers

from their newspapers. If there were suitable sales phrases, such as 10 % off or save 25 %, they

could be used on the cards for the Check For Understanding activity. It would also be interesting

to see the sale phrases and items in any Spanish-language newspapers they have access to. We

could make dual-language cards to further strengthen a connection.


LESSON PLAN # ____ Grade 6 Math: Percentages – Cross-Product Method - Week of: Do Now: (5 minutes) $3.00 – 0.86 16 – 1.59 $9.00 – 7.39 Aim: Students will calculate a percentage of a number, (discount) with 80% accuracy. Students will subtract discount from the original price to determine sale price with 80% accuracy. MCF Standards Addressed: 6.N.9 Select and use appropriate operations to solve problems involving addition, subtraction, multiplication, division, and positive integer exponents with whole numbers, and with positive fractions, mixed numbers, decimals, and percents Materials: Teacher Reference Sheet, Guided Practice worksheet, Independent Practice worksheet, Student Graphic Organizer, Three sets of cards for Check For Understanding. Alternative Co-Teaching Class of twenty is divided into three groups. Group 1: Tier I students: Title I Math Teacher Group 2: heterogeneous groups of Tier II and Tier III students : General Education Teacher Group 3: heterogeneous groups of Tier II and Tier III students : Special Education Teacher Prep work assignments: Cards for Check For Understanding: Title I Teacher Copies of worksheets: Classroom Teacher Moving students into groups: All Three Teachers Teach To: (15 minutes) Small Group activity for all groups: Vocabulary preview: original price, discount, % off, half off, and sale price and cost. Review Graphic Organizer. Followed by: Group 1: Teacher models examples of Cross-Product Method (found on Reference Sheet/ Graphic Organizer) Group 1: Teacher models examples of Proportional Reasoning and Multiplication Methods (found on Reference Sheet/Graphic Organizer) Groups 2 and 3: Teachers review subtraction of decimal from a whole number (from Do Now) Groups 2 and 3: Teachers model examples of Cross-Product Method (found on Reference Sheet/Graphic Organizer)


Guided Practice: (20 minutes) Students determines the cost (i.e sale price) of the items on the Guided Practice worksheet (see attachment) Group 1: Teacher works with students to complete problems. Group 1 uses three methods to find percentages. Students use graphic organizer. Groups 2 and 3: Teachers work with students to complete problems. Groups 2 and 3 only use cross-product method. Students use graphic organizer.

Guided Practice Wrap Up - Check for Understanding (5 minutes) Teachers continue small group work. Each group has three sets of cards. One set of index cards will have pictures of items from catalogs or sale circulars, the second set will have random prices listed, and the third set will have sales phrases, such as: “HALF OFF!, Marked down 25%” etc. Three picks gives the group an item, a price and a discount and from there, each group member works individually to find the final price. Every student will have an opportunity to pick at least one card. Students work individually to calculate the discount and the sale price or cost. Independent Practice (10 minutes): Assessment, (attachment) Closure: (5 minutes) Teacher-talk only. Wrap up the lesson with a review of the cross-product steps


TEACHER REFERENCE SHEET

There are many ways to teach finding percentages.

Method 1. is the cross product method used in the 7th and 8th grade textbooks and

is the method we propose using. It is a good lead in for solving algebraic equations.

Methods 2-3 are alternative ways to find a percentage, and will be used as

extension activities. We can teach these methods as ways to check if an answer is

reasonable.

Find the amount of discount if you know the price.

(15% discount on an item whose price is $12.00)

1. use part to whole ratio and cross product method:

part %

------- = ---

whole 100

n 15

= --- = --- (Then cross multiply: part X 100 = % X whole)

1200 100

= n X 100 = 15 X 1200

= n X 100 = 18000 (STOP HERE AND SAY: what number times 100 = 18000?)

= 100n = 18000 (then solve. What operation “undoes” multiplication…)

= 100n 18000 (Division, so divide both sides by 100 to isolate variable )

--- = ----

100 100

= n= 180 cents = $1.80 Cost = $12.00 – 1.80 = $10.20


Ways to check the Reasonableness of an Answer

2. Proportional Reasoning

Make a chart, start with 100% of the cost is 12.00, then work to the right

% 100% 10% (move decimal 1 5% (1/2 of 10%) 15 % (5% + 10%)

cost 12.00 1.20 place left) 0.60 0.60 + 1.20= 1.80

3. find the amount of the discount (discount = % of price)

15% of $12.00

= 0.15 X $12.00 =

SALE PRICE = $12.00 - 1.80 = $10.20

Other examples to use:

25 % of $60 = $15; $60 - $15 = $45

Half off $34! 50 % of $34 = $17. $34 - $17 = $17

10% discount, price = $55; 10% = $5.50. $55 – $5.50= $49.50

10% off $43 = $4.30; $45 – $4.30 = $40.70


Name: Date:

Guided Practice IT’S ON SALE!!!

Price: $15.00 10 % off Sale Price: ________________

Price: $25.00 20 % discount Sale Price: _______________

Price: $50 take 25 % off sale! Sale Price: ____________

Price: $3.00 Half off sale! Sale Price: _____________


Name: Date:

Independent Practice IT’S ON SALE!!!

Price: $350.00 40 % off Sale Price: ____________

Price: $70.00 Half off! Sale Price: ____________

Price: $22.00 5 % discount Sale Price: _____________

Price: $30.00 10 % off! Sale Price: _____________


STUDENT GRAPHIC ORGANIZER – FINDING PERCENTAGES

**** THE CROSS-PRODUCT METHOD ****

Example: Find a 10% discount on an item whose price is $14.00

*Set up a part –to- whole ratio as follows:

part %

------- = ----

whole 100

*Fill in the numbers from the problem:

n 10

= ----- = ----

1400 100

* Cross multiply: part X 100 = % X whole

= n X 100 = 10 X 1400

= 100n = 14000

* Divide both sides of the equation by 100

= 100n = 14000

----- -------

= 100 100

* Isolate variable and Solve

n = 140; Discount = 140 cents or $1.40

Sale price or Cost = $14.00 – 1.40 = $12.60


STUDENT GRAPHIC ORGANIZER 2 – FINDING PERCENTAGES

**** PROPORTIONAL REASONING METHOD ****

Example: Find a 15% discount on an item whose price is $12.00

* Make a chart, start with 100% of the cost is 12.00

% 100%

amount 12.00

* To go from 100 % to 10 %, move the decimal point 1 place to the left

Do the same for the cost

% 100% 10% (move decimal 1

amount 12.00 1.20 place left)

* To go from 10 % to 5 %, divide in half. Do the same for the cost

% 100% 10% (move decimal 1 5% (1/2 of 10%)

amount 12.00 1.20 place left) 0.60

* To find 15 % add 10 % plus to 5 . Do the same for their costs

% 100% 10% (move decimal 1 5% (1/2 of 10%) 15 % (5% + 10%)

amount 12.00 1.20 place left) 0.60 0.60 + 1.20= 1.80

3. MULTIPLICATION METHOD

To find the amount of the discount (discount = % of price) 15% of $12.00

*Translate: % to decimal . Translate “of” to X. Multiply

= 0.15 X $12.00 =


References

Friend, M. (2008). Co-teach! A handbook for creating and sustaining effective

classroom cartnerships in inclusive schools. Greensboro, NC: Marilyn Friend Inc.

Nevin, A., Thousand, J., & Villa, R. (2009). Co-teaching at a glance. Port Chester, NY: Dude.

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