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Introduction to Percent Concepts
Objectives:
§
To define benchmark percents of a given
number
§
To explain the strategy used to define
percents
§
To compare and defend strategies used
to find percent
§
To compare and choose the lesser of two
values involving %
§
To apply the skill(s) to real life
situations
Download as Microsoft
Word Documents:
Instructional
Plan Template
Mathematics
Governor’s Institute 2005
Names
of group members: Barbara Lilley, Anne Caggiano, Tammy
Grimes, Judy Durrell,
Linda Carmichael
Topic/Theme: Introduction to Percent Concepts
Level: Grades 6 to 8
Time
Element: 2 - 3 days
NCTM
Standards Addressed:
Number and Operation Standard
·
Work
flexibly with fractions, decimals, and percents to solve problems;
·
Develop
meaning for percents greater than 100 and less than 1;
Measurement Standard
·
Use
common benchmarks to select appropriate methods for estimating measurements;
·
PA
Math Standards Addressed:
2.2.8.
Computation and Estimation
·
B. Add, subtract, multiply and divide different
kinds and forms of rational numbers including integers, decimals, fractions, percents
and proper and improper fractions.
·
D. Estimate the value of irrational numbers.
2.4.8.
Mathematical
Reasoning and Connections
·
B. Combine numeric relationships to arrive at a
conclusion.
2.5.8.
Mathematical
Problem Solving and Communication
·
C. Justify strategies and defend approaches used
and conclusions reached.
Math
Assessment Anchors Addressed:
6A. Numbers and Operations
·
6A.1.3.1 Select, use or develop regions and/or sets
(e.g., circle graph, hundred blocks) to model percents to 100%
6D. Algebraic
Concepts
·
6D.1.1.1 Create, extend or find a missing element in a
pattern displayed in a table, chart or graph (pattern must show at least 3
representations)
8A Numbers and Operations
·
8.A.3.2.1
Estimate answers to problems involving simple percents (1%, 10%, 15%, 20%, 25%,
50% or 75%)
·
8.A.2.2.1 Select or use ratios, proportions and
percents to solve problems (e.g., tax, discounts, etc.- straight computation or
word problems).
1.2.
Reading Critically in All Content
Areas
·
1.2.8. A Read and understand
essential content of informational tests and documents in all academic areas.
1.6. Speaking and Listening
·
1.6.8 A. Listen to others
·
1.6.8 C. Speak using skills appropriate to formal
speech situations
·
1.6.8 D. Contribute to discussions
·
1.6.8 E. Participate in small and large group
discussions and presentations
Objectives:
1.
To define benchmark percents of a given number
2.
To explain the strategy used to define percents
3.
To compare and defend strategies used to find percent
4.
To compare and choose the lesser of two values involving %
5. To apply the skill(s) to real
life situations
Instructional
Strategies and Plan (include strategies used to help different types of
learners, i.e. auditory, visual, etc):
1.
Assess prior knowledge and make connections using a short,
introductory activity. Teacher begins by asking leading questions as to where
percents are used in real life. Distribute to each small group a napkin and a
bag of M&Ms to model the activity questions. Distribute an M&M activity
sheet to each small group and allow time for each group to complete the
activity. Groups are to discuss, come to
a conclusion and record responses on activity sheet. The class will then
compare the responses looking for any patterns. The teacher then asks leading
questions to elicit a discussion and comparison of strategies. (Good for
tactile and visual learners)
2.
Present the lesson using the “ladder” organizer activity. Place
the transparency of the activity sheet on the overhead to demonstrate the
process. Point out the benchmarks listed on the “ladder”. Begin with an easy number (e.g. 80) Write
this number above the first “ladder”. Ask for 50% of 80. Discuss what 50% means
and record ‘40’ opposite the 50% label (benchmark). Continue with 25% using the
strategy that 25% would be half of 50%. Ask what 25% of 80 would be based on
this strategy and record ‘20’ opposite the 25% label. Proceed to 75% using the
strategy of adding 25% and 50%. Determine the value and record ‘60’ opposite
the 75% label. Continue the process until the remainder of
the labels have a recorded percentage.
Distribute a percent activity sheet to each student. Provide a number for the students and have them record it above the first “ladder”. Since this would also be 100%, record it next to the 100% label accordingly. Repeat the process used on the overhead as a whole class. Encourage students to describe the strategies used and compare with other students’ strategies. Provide another number and have students write this above, and next to the 100%, on the second “ladder”. This time, the students will complete the process with the partner. Provide a third number and have the students complete it individually. Check student work by recording the correct answers on the overhead transparency. (Good for visual and auditory learners) Assign the remaining “ladders” for homework. Again, the teacher should provide the numbers. Students are to complete the ladders and describe the strategies used to determine the pre-selected percentages.
Materials/Resources:
1.
M&Ms (1 bag per group)
2.
M&M activity sheet (1 per group)
3.
Percent activity sheet (1 per student)
4.
Relay activity cards (1 set per team)
5.
Overhead projector
6. Transparency of Percent activity
sheet
7. Napkins
Interdisciplinary
Connections:
·
·
Technology: Students requiring Enrichment will create Spread
Sheets on Excel to map the various states sales tax.
·
Other: Social Studies (state tax), Consumer Math,
Economics
Assessment
Strategies:
·
Formative
Evaluation (checking student understanding during the lesson):
·
During class students will work in small
groups to complete 2 “Ladder” activities in order to demonstrate
comprehension. Then students will
complete 2 more for homework to demonstrate individual comprehension.
·
During “Playground Percents”
students will work in groups to demonstrate ability to identify percents for
specified numbers
·
Summative
Evaluation (How will it be determined that the objectives were achieved?):
·
“Switch Quizzes”; Students will work in pairs. Each student will develop a quiz for the
Ladder worksheet. Each student will pick
a number. After they have completed all
the percents for that number they will then give the number to their partner
and the partner must develop the required percents for that number. Upon completion they will switch and check
the tests for accuracy.
Correctives/Remediation:
·
Have
cards available with the correct for students to choose from for each
Ladder.
·
Have
students work with a partner.
·
Limit
the number of percent choices used on the Ladder.
Extensions/Enrichment:
·
Play
“Playground Percents” (See attached worksheet)
·
Complete
“Tipping & Taxing” worksheet (See attached worksheet)
·
Play
“Polly’s Percent Camp” (See attached worksheet)
Special
Accommodations (special needs students)
·
Description
of the Special Needs student selected:
·
Tommy
– This student has been sick very often.
Because of this, his attendance at school has been erratic. He loves to experiment with things. However, at home, he is busy performing all
kinds of experiments with household items.
His schoolwork has also been poor.
It is unclear whether this is because of his attendance or a difficulty
acquiring school related information.
·
Accommodations
to use with this student:
·
Photocopy
a reliable student’s class notes and send home with materials necessary to
complete the activities, including a package of m&m's.
·
Assign
a reliable homework buddy to list and explain the assignments to be completed.
·
List
homework online.
·
Assign
student to present one of his ladders to the class.
Extension Activity – “Playground
Percents”
Objective: To practice using
mental math to find percents.
Materials: Chalk, 1 set of
cards per team (teacher-prepared
beforehand)
Procedure:
1.
Draw a chalk “percent ladder” on the blacktop for each team, (use all percents
on the activity sheet ladder except the 1% and the .5%).
2.
Divide the class into groups of about 5.
3.
Each group designates a “runner” who will be responsible for
writing the answers on the “ladder”.
4.
Position the runner at the 100% place on the ladder with a piece
of chalk.
5.
Distribute a set of cards to each group with each set containing
the same numbers.
6.
The teacher announces the target number (e.g.120).
7.
The runner writes that number opposite the 100% and returns to the
group.
8.
As the group agrees upon a number, the runner goes to the ladder
and places that number card opposite the selected percent. When the group
agrees that all of the number cards have been placed correctly, they sit down.
9.
Each team that has all of the number cards placed correctly scores
10 points. The first team to finish correctly scores an additional 10 points
and the second team to finish correctly scores an additional 5 points.
10.
Play 5 rounds, each with a different number, but the same card
set. The team with the most points after 5 rounds is declared the winner.
Suggested target numbers: 40, 60, 120, 180 and 240
Card set would include: 2,3,4,6,8,9,10,12, 15,16,
18, 20, 24, 30, 34, 36, 45, 48, 51, 60, 72, 90, 96, 102, 120, 135, 153, 180,
204.
Directions: POLLY’S PERCENT PRISON CAMP
(Best Buy Percent Relay)
To Start: Arrange student teams
in groups of five or six. Have each
team sit in one row of desks. Pass out
problems to each student. Player #1 in
each team is given two percent problems.
He/she will find both solutions and determine the least expensive
solution. That solution is then passed
back to Player #2 on their team. Player
#2 will use this amount to find the solution to his/her two percent
problems. Again, he/she will determine
the least expensive of the solutions.
All the current solutions are then filled-in and passed back to Player
#3. Play continues until Player #5 has
all five final solutions.
Player #5 (or Player #6) should then add the total cost of the five
items needed to attend Camp.
The team(s) with the correct answer is the winner:
Tuition: $304.00
Calculator: $75.00
Pocket
Protector: $10.00
Beanie
Hat: $15.00
Sweater
Vest: $30.00
Total: $434.00
Extensions/Tie-Breakers:
Question: If you are earning
$9.00 scrubbing lockers on Saturdays, how many hours will you have to work to
earn your camp money?
Ans: $434.00 
$9.00 = 48.22 hours or 48
hours and 13.2 minutes
Question: What would you have to
earn per hour to only work 25 hours?
Ans: $434.00
25 =
$17.36 per hour
Question: If you have to pay 16%
Federal Tax on your salary, how much will you have to earn to pay the total
cost of the camp?
Ans: $516.67
POLLY’S PERCENT PRISON CAMP
Scenario :
Your teacher knows how much
you all love math and especially percent problems! As a reward, you have all been signed up to
attend Polly’s Percent Camp during summer vacation. (Hold back your excitement!)
As an added bonus, your teacher
is going to let you scrub lockers on Saturdays to earn money for tuition and
supplies to attend the Camp – Yeah!!
Your
team’s goal is to shop for the best buys for tuition and supplies for you to
attend the Camp.
Player #1 – TUITION
In June: In July:
$340.00 with a 10% discount. $380.00 with a 20% discount.
-
- - - - - - - -
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- - - -
Pass to
Player #2 –
TUITION: $
__________________
Player #2 – PURPLE POLKA-DOTTED PERCENT CALCULATOR
At Staples: At
Office Max:
________________ - $204.00 ________________
- $154.00
(Tuition) (Tuition)
with a
25% discount. with a 40% discount.
-
- - - - - - - -
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- - - -
Pass to
Player #3 –
tuition: $____________________
calculator: $____________________
Player # 3 - NERD POCKET
PROTECTOR
At Wal-Mart: At
K-Mart:
_______________ - $35.00 ________________
- $55.00
(Calculator) (Calculator)
with a
75% discount. with a 40% discount.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- - - - - - - - - - - - - - - -
Pass to
Player #4 -
Tuition: $___________________
Calculator: $___________________
Pocket
protector: $___________________
Player #4 – Beanie hat
At BeanieWorld: At HatsRUs:
___________________ with a ___________________
+ $2.00
(Pocket Protector) (Pocket Protector)
50% price increase. with a 30% increase.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- - - - - - - - - - - - - - - - -
Pass to Player
#5 -
Tuition: $___________________
Calculator: $___________________
Pocket
protector: $___________________
BEANIE Hat: $___________________
Player #5 – GREEN AND
At Salvation Army: At
Goodwill:
___________________ with a ________________ +
$10.00
(Beanie Hat) (Beanie Hat)
100% increase. with a 20% increase.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- - - - - - - - - - - - - - - - -
Player #5 keeps (or pass to
Player #6) –
Tuition: $___________________
Calculator: $___________________
Pocket
protector: $___________________
BEANIE Hat: $___________________
Sweater
vest: $___________________
Player #5 (or Player #6):
FIND TOTAL
COST OF POLLY’S PERCENT CAMP:
Total
cost: $___________________
Name________________________________________________
Date__________________________________________________
Introduction to Percents –Extensions/Enrichment
Tipping and Tax Worksheet
1. Your family has gone out to dinner. Your bill was $50.
a. The service was adequate and you want to leave a 15% tip. What is the amount of the tip?
b. The service was terrible so you want to leave a 10% tip. What is the amount of the tip?
c. The service was excellent so you want to leave a 20% tip. What is the amount of the tip?
2. Your family has gone out to dinner and your bill was $50.
a. You live in PA where the tax is 6%. What is the amount of tax that you will pay?
b. You live in NY where the tax is 8%. What is the amount of tax that you will pay?
c. You live in MD where the tax is 5%. What is the amount of tax that you will pay?
d. You
live in
3. Calculate your total bill for each situation.
a. Your
family is dining in
b. You have gone to dinner in PA and the service was exceptional. Your meal bill was $80. How much will you pay?
4. At a fast-food restaurant, you do not tip but you must pay tax. If you go to Wendy’s and order from the $.99 menu, how many items can you but with $5?
Name_________________________
Date__________________________
Percent Activity
Directions: Open the bag of M&Ms and sort,
according to color, on
your desk/table. Then answer the following questions.
- Which color represents the smallest
percent of the whole bag?
1A.
Estimate this percent. _________%
- Which color represents the largest
percent of the whole bag?
2A.
Estimate this percent. _________%
- Which color(s) represents about 50% of
the whole bag?
3A.
Explain your choice. _________________________
___________________________________________.
- Which color(s) represent about 25% of
the whole bag?
4A.
Explain your choice. _____________________________
- Which color(s) represent about 10% of
the whole bag?
5A.
Explain your choice. __________________________
____________________________________________.
