ACADEMIC
PREPARATION
WEEK THREE DAY
ONE
Lesson Title: Fractions: Mixed Numbers, Proper and Improper, Reducing, Changing Improper Fractions to whole or mixed numbers
Subject
Matter/Life Skill Area: Academic
Strand, Math Skills
Learning
Level/Prerequisite Skills: 9th
grade reading/math level
Lesson
Length: Two
hours
Instruction
Type (small group, individual, lecture etc.): Whole group instruction with individual practice
Overview
and Rationale:
Fraction skills are needed for the GED exam, as well
as workplace applications. Students will get an introduction to fractions,
including terminology used in math that uses fractions. This introductory lesson
in fractions will include; common denominators, reducing fractions, mixed and
improper fractions, changing improper fractions to whole or mixed numbers.
Learning
Objectives / Skills:
At the completion of this lesson, students will be
able to reduce fractions, understand common denominators, and solve problems
that use improper or mixed fractions.
Skills: Arithmetic, problem solving, monitors and
corrects performance
Materials
/ Equipment Needed:
Construction
paper squares for tactile lesson, four squares for each student and markers
Contemporaries
GED math book (Book Five) or a comparable text if Contemporaries is not
available (Steck-Vaughn, etc.)
Pencils
and paper
Chalkboard
and chalk
How
to Prepare:
The instruction should have an understanding of the
fractions topic, should review the lesson completely, and make sure that
materials are on hand for this activity. If the recommended text is not
available, insure that a comparable resource is available for student practice.
Introduction
/ Warm Up / Review:
Ask students to recall what they know about fractions
and write responses on board. Review responses and ask students for examples of
elicited responses. Add any vocabulary words that are missing from the list. Ask
students to supply an example of new words as well.
Have students copy vocabulary words and accompanying
examples into notebook for references during the week of Fractions instruction.
Presentation of
Lesson:
Give
four construction paper squares to each student. Students will use squares for
hands-on demonstration of fractions concepts.
1.
Have students fold 1st square in half and tear apart. Mark each part
with 1/2
2.
Have students fold 2nd square in half, tear apart, and then
do again for each part. Mark each part with 1/4.
3.
Have students fold 3rd square in to 8 parts, tear each
section and mark with 1/8.
4.
Students repeat the process with the last square, making 16 sections and
marking with 1/16.
Have
students line up parts like this:
|
1/2
1/2 |
|
1/4
1/4
1/4
1/4 |
|
1/8
1/8 … |
|
1/16
… |
Ask students to compare the squares and elicit
comments about differences. Write comments on board. Help students to recognize:
Fractions are parts of a whole
Numerator and denominator
The smaller the pieces, the larger the denominator
number
Practice /
Activity:
Lesson and
Practice: Mixed Numbers
Draw three circles on the board and divide each
circle into four pieces. Lightly color in the first two circles and 1/4 of the
third circle.
Ask students how much all of the circles represents
together. Answer: 2 1/4
Let students know that they will be working with
whole numbers and fractions. When a whole number has a fraction with it, we call
it a mixed number.
Have students complete Exercise 2 on pg. 81
Lesson and
Practice: Proper and Improper Fractions
Write these three fractions on the board: 2/3,
99/100, 1/5
Ask students to comment on a feature that all three
have. They should say that all three have a smaller numerator than denominator.
These are called "Proper Fractions."
Have students call out other examples of proper
fractions and write them on the board.
Discuss if any are not proper fractions.
Write these three fractions on the board: 2/2, 7/2,
24/21
Ask students to comment on a feature that all three
have. They should say that all three have a larger numerator than denominator.
These are called "Improper Fractions."
Show students that any number over itself equals one.
Use a visual picture on the board if necessary.
Have students do Exercise 3 and 4, pg. 82-83 in text.
Lesson and
Practice: Reducing Fractions
Let students know what skills will be covered in
today's lesson (see title).
Have students recall which is numerator and which is
denominator.
Explain that fractions can equal the same whole but
be broken down into smaller pieces. Have them refer back to construction paper
squares for a visual representation.
Let students know that these are called
"equivalents"
Show students that they can simplify (or reduce/ find
equivalents) by dividing both the numerator and the denominator by the same
number to simplify but the chosen number must divide evenly into both the
numerator and the denominator.
Let students know that you may have to repeat the
process until a number cannot be found to divide by for both.
Write the following on the board (or use Exercise 5,
pg. 84-85 in text):
6/10 4/6
14/20 4/32
18/36 18/24
25/35 45/50 15/40
45/60 30/45
10/25
Give students time to practice simplifying/reducing.
Exercises 6 and 7, pg. 85 can be used for additional
practice.
Be sure to tell students that fractions must be
reduced to their lowest terms on the GED test. The answer will be incorrect if
not reduced.
Lesson and
Practice: Changing Improper Fractions to Whole or Mixed Numbers
Ask students to recall rule for the GED test about
reducing fractions. They should say that they must reduce to the lowest terms.
Tell students that that means that they must also
change an improper fraction to a whole or mixed number.
Ask students if they recall from their experience how
you change an improper fraction. Give an example of dividing the denominator
into the numerator. The remainder is the numerator over the original
denominator. Use the following examples:
Set One: 4/4 15/5
6/2
Set Two: 20/6 19/3
27/8
Ask students to change the fractions on scratch
paper. Have students give answers and write answers on board.
Ask students what is the difference between set one
and set two. ( whole numbers/ mixed numbers)
Have students complete Exercise 9, pg. 88-89
Application/Transfer:
While students are working in their math book, write
the following on the board:
4 2/3 80/81
5/4
Students should be able to name each fraction. Ask
students what their names are and write under each fraction. Ask students if any
should be reduced or changed.
Have a student change 5/4 to a mixed number.
For students who need additional practice, Steck-Vaughn
has a Fractions pamphlet with many fractions for various practice worksheets.
Reflection by
Teacher:
Were students able to distinguish the various types
of fractions and where they able to name them? Did they remember that all
fractions must be reduced to the lowest terms on the GED test? Will students be
able to use this skill without referring to the text for the procedures?
Planning for
Next Lesson:
Review the lesson and any problem areas students may
have had. Be sure to refer students to the appropriate instructional software
they can use during the Technology strand.
ACADEMIC
PREPARATION
WEEK THREE DAY
TWO
Lesson
Title: Fractions:
Adding, Subtracting, Multiplying, Dividing Fractions
Subject
Matter/Life Skill Area: Academic
Strand, Math Skills
Learning
Level/Prerequisite Skills: 9th
grade reading/math level
Lesson
Length: Two
hours
Instruction
Type: Whole
group instruction with individual practice
Overview
and Rationale:
Fraction skills are needed for the GED exam, as well
as workplace applications. Students will continue working with fraction skills
that are necessary for competency on the GED exam. This lesson will include
information on how to add, subtract, multiply, and divide fractions.
Learning
Objectives/ Skills:
At the completion of this lesson, students will be
able to add, subtract, multiply and divide fractions. Students will also be able
to understand how to find a common denominator and adding and subtracting unlike
fractions.
Skills: Arithmetic/Mathematics, problem solving,
reasoning
Materials/
Equipment Needed:
Contemporaries GED math book (Book Five)
Pencils and paper
Chalkboard and chalk
Introduction /
Warm up /Review:
Ask students to recall the names of some of the
fractions learned in the last lesson. They should recall: mixed numbers, proper
and improper fractions, reducing, changing improper fractions to whole or mixed
numbers. Review any procedures that students may have forgotten.
Ask students to recall any information that they have
previously learned about adding, subtracting, multiplying, or dividing
fractions. Write any responses on board. Ask students what they would like to
know when working with fractions.
Presentation of
Lesson:
Divide the board into four sections.
In the first section, write, " 2/4 + 1/4= "
on the board. Ask students to comment about a common feature both fractions
have. They should say that the denominators are the same. Show students that you
can add these easily just by adding the numerators. Put the answer after the
equal sign and write in capital letters "LIKE." Do the same with a
subtraction example by changing the plus to minus.
In the second section, write, " 2/4 + 1/2 =
" on the board. Again, ask students to remark about the fractions. They
should say that the denominators are different. Tell students that if you only
add the numerators and the denominator remains the same, what denominator do you
use? Let students know that these fractions are "UNLIKE" and that they
will learn how to "find a common denominator" so that they can be
added or subtracted.
In the third section, write " 2/4 x 1/3 = "
on the board. Write, "DOESN'T
MATTER" on the board. Ask students how they would solve this problem. Show
students that multiplying fractions is an easy skill, that you multiply
numerator to numerator and denominator to denominator. Let students know that
they will learn a short cut called, "cancelling."
In the last section, write 1/3 divided by 1/6 =
Also write, "INVERT" under the second fraction. Ask students
what invert refers to. They should say that you need to switch numerator and
denominator. Tell students that in addition to that, they must also switch the
sign to multiplication. Give an example. Let students know that inverting is a
fraction skill only used when dividing fractions.
Practice
/ Activity:
Lesson and
Practice: Like Fractions; Adding and Subtracting.
Ask students to recall the term "Like
Fractions" and what it means.
Write the following examples on the board and give
students the opportunity to tell you how to complete the examples:
1/5 + 3/5
6/8 + 1/8 7/9 -
1/9 5/ 7 - 1/7
Then put the following example on the board:
7/8 + 3/8 =
Students should answer 10/8. Ask them what kind of
fraction it is and what they must do to finish the problem to correctly answer
on the GED test.
Students should answer that it is an improper
fraction and must be changed to a mixed number, and reduced if necessary.
Have students complete Exercise 10 and 11, pgs.90-91
For exercise 12, show students how to regroup or
borrow from a whole number. Do exercise 12, pg. 93
Lesson and
Practice: Unlike Fractions; Adding and Subtracting
Ask students to recall the term "Unlike
Fractions" and what it means.
Write the following examples on the board and give
students the opportunity to tell you how to complete the examples:
1/5 + 3/4
6/8 + 1/2 7/9 -
1/4 5/ 7 - 1/3
Tell students that they will still add/subtract
unlike fractions in the same way as like fractions, but they must first find a
"common denominator." Let
them know that since the pieces are not the same, they cannot be
added/subtracted yet, but when they convert the pieces they can they add or
subtract, whichever operation is called for.
Show students how to find a common denominator by
first testing the larger denominator as the common denominator. Numbers should
be evenly divisible and students will need to go through the multiplication
table of the largest denominator.
Practice several problems on the board. Additionally,
have students practice several problems individually on paper.
Have
students complete Exercise 13, 14, 15, and 16, pgs.94-98
Guide
students through any difficult areas. Use the board to highlight any problems
that cause difficulty.
Lesson and
Practice: Multiplying Fractions
Let students know that multiplying fractions less
complicated than adding or subtracting fractions.
Key students in to the word "product" means
to multiply.
Let students know that they multiply straight across
for numerators, and straight across for denominators.
Do a few multiplication problems on the board for
demonstration. Follow up with students working some problems individually.
Let students know that there is a short cut for
multiplying and ask if anyone is familiar with the term "cancelling."
Write, or demonstrate on board, any feedback from students
Show students that you can cancel if you can find a
number that divides evenly into a numerator of one fraction and a denominator of
another fraction. Make it clear that they cannot be the same fraction.
Practice several cancelling fractions on the board.
Have
students complete Exercise 17, 18, 19, and 20, pgs. 100-104
Guide
students through any difficult areas. Use the board to highlight any problems
that cause difficulty.
Lesson and
Practice: Dividing Fractions
Remind students of the word "Invert" and
ask what the word implies. Let students know that when dividing fractions, the
fraction that they are dividing by must be inverted, and that it is called a
"reciprocal."
Let them know that any amount being divided must come
first and that the fraction you are dividing by comes second. Only the fraction
you are dividing with (the second fraction) is inverted.
Once the fraction has been inverted, change the
division sign to a multiplication sign and proceed as if it is a multiplication
problem.
Remind students that with all fractions problems,
improper fractions must be changed to a mixed number and all fractions must be
reduced.
Have
students complete Exercise 21, 22, and 23, pgs. 106-109
Guide students through any difficult areas. Use the
board to highlight any problems that cause difficulty.
Application /
Transfer:
Divide the board into four areas and write
"Like," "Unlike," "Doesn't matter," and
"Invert" on the board.
Tell students that each square represents a procedure
when adding, subtracting, multiplying and dividing, and that more than one skill
will be represented in two of the squares.
Ask students if they can recall the different
procedures for adding, subtracting, multiplying and dividing and what category
they would put the procedure.
Adding and subtracting go in two categories, like and
unlike. Multiplication goes to the 'doesn't matter' category, and division to
the invert category. Review if necessary.
Reflection
by Teacher:
Were students able to perform the various types of
fractions applications and where they able to name them? Did they remember that
all fractions must be reduced to the lowest terms on the GED test? Will students
be able to use this skill without referring to the text?
Planning for
Next Lesson:
If any students requested additional instruction, make note of what areas were difficult and address the topic in class the next day as part of the review process. Address any other problem areas students might be having and cover those topics as well.
ACADEMIC PREPARATION
WEEK THREE DAY THREE
Lesson Title:
Organizing for the GED Essay
Subject Matter / Life Skill Area: Academic/Writing
Learning Level / Prerequisite Skills: 9th
Grade reading and Math
Lesson
Length: Two
hours
Instruction
Type: Teamwork,
individual reflection
Overview
/Rationale:
The purpose of this lesson is to give students a
chance to experiment with several different methods of organizing ideas for
essay writing and to consider which method(s) they prefer. It also prepares
students for writing their own essay in week 4.
Learning
Objectives / Skills:
At the completion of this lesson, the student will be
able to demonstrate three ways to organize ideas prior to essay writing and to
consider which method(s) might work best for him/her.
Skills:
Organization techniques, teamwork, critical thinking
Material/Equipment
Needed:
Large
sheets of paper
Colored
markers
Overhead
Projector or chalkboard
Handout: A
How to Prepare:
Because of the limited class time, organization is
crucial for this activity to be successful. The teacher will need to decide how
many workstations (in multiples of 3) she will need for the size of her class.
For maximum participation, groups of 3 or 4 are best. So, for a small class of
up to 12 people, only 3 stations will be needed. Classes of 13 –24, will need 6, (2 for each organizing
technique). Each station will need large sheets of paper and colored markers.
The teacher also needs to consider the best topics to
use for students to practice organizing idea. Because of the limited time, the
teacher may want to choose topics students have already discussed or which are
fairly generic.
Introduction
/Warm Up / Review:
Writing an essay is an important skill to master in
preparation for the GED test. During the next few weeks, there will be many
opportunities to practice the necessary skills for writing a good essay. Today
we are going to look at what an essay is and how to organize ideas around a
topic.
Elicit from students the parts of a paragraph: topic
sentence, supporting sentences, and concluding sentence.
Explain that an essay is a group of paragraphs organized around a topic
and includes: an introductory paragraph, which includes a thesis statement,
several body paragraphs which support one’s thesis, and a concluding
paragraph. The key to writing a good essay is to organize one’s ideas around a
topic.
There are many ways to do this; we’re going to try
out 3 different ways: clustering, webbing and outlining.
Presentation
of Lesson:
Demonstrate on the chalkboard or overhead what each
method looks like (see Hand out) and where key information goes in each one. As
a whole group, fill in a few lines on each.
Practice
/ Activity:
Assign students to teams of 3 – 4 members. Each team will rotate through the workstations at ten-minute intervals. Assign a topic and tell students they have ten minutes to brainstorm main ideas and supporting details/statements for that topic using the organizing technique at their station. They should record their ideas on the large white paper at each station. Give a 3-minute warning. Then have students move to the next station for a new topic and a different organizing technique. When students have visited each station, ask a representative from each group to present their diagrams to the whole class.
Have each group discuss their
organization of topic A first so that the class can see how the three different
methods worked with each topic
Application /
Transfer:
Have students reflect on this process in their journal writing—which method did they prefer, -why---which method do they feel would be most helpful to them in essay writing---are there other ways to organize information and ideas which would be better?
Reflection by
Teacher:
Was the class organized effectively so that the activity moved smoothly?
Were all of the students
actively engaged in their teams? Did students have enough time for reflection?
Planning
for Next Lesson:
Preview the coming weeks lessons that are focused on
essay writing. Revisit essay-writing skills with each lesson, building upon past
skills so that students have a full range of information and skills.
Review
fractions in remaining time.
Hand-out A
Webbing
Outlining
ACADEMIC
PREPARATION
WEEK THREE DAY
FOUR
Lesson
Title: Probabilities:
What are the Chances When Job Seeking? , Order of Operations: Who's on First?
Subject
Matter/Life Skill Area: Academic
Strand, Math Skills
Learning
Level/Prerequisite Skills: 9th
grade reading/math level
Lesson
Length: Two
hours
Instruction
Type: Whole
group instruction with individual practice
Overview and
Rationale:
Students will need to practice probability math
skills and will use job seeking as the bases for solving probability problems.
Also, students need to be familiar with the order of operations when solving
math equations on the GED exam.
Learning
Objectives / Skills:
At the completion of this lesson,
Students will be able to understand and utilize probability skills when
solving math problems, as well as discussing job opportunities. Students will
also become familiar with the order of operations in mathematical equations.
Skills: Arithmetic/Mathematics, problem solving,
reasoning
Materials /
Equipment Needed:
Handout: What
Are the Chances When Jobseeking?
Bag of M & M's candy
Contemporaries GED math book (Book Five)
Pencils and paper
Chalkboard and chalk
Introduction
/ Warm up / Review:
Bring
out the bag of candy and ask students what are the chances that if you take out
ten M & M's, some will be red. Ask them to give you a number of red ones and
write it as a fraction on the board. Example: eight red = 8/10. Continue with
other colors until students have understood that probability means
"chance."
Ask
students to give you other examples of probability: such as weather, having a
cold in the winter, finding jobs.
Ask them to give you examples: such as one day of
rain/out of seven days in a week, one cold during one season of winter, finding
two jobs/out of filing twenty job applications. Write their examples as
fractions on the board and read them back as a probability sentence.
Ask students what a probability problem resembles. They should say "fractions."
Write 2/10's on the board and ask students what needs
to be done on the GED exam to make this a correct answer. They should say
"reduce to the lowest terms" and then have them reduce the fraction.
Presentation of
Lesson:
Give students ten M&M's. Ask how many there are
all together. Tell students that ten is the total outcome (write on board) and
it goes on the bottom of a fraction. Ask students to recall what the bottom
number is called. They should say denominator. Ask a student to tell you how
many blue M&M's they have. Write that number on top of the ten and label it
"favorable outcome."
Practice
/ Activity:
Have students practice writing fractions for the
various colors that they have. The amount of fractions will vary depending on
the color, but the total outcome will be ten for each student.
Get feedback from students and write the various
probabilities on the board. Have students circulate and notice the various
groupings of each student, that not all students have the same probabilities.
Students can eat their M&M's if they wish.
Application
/ Transfer:
Have students complete Exercise 1, 2, and 3, pages
117-120
Guide students through any difficult areas. Use the
board to highlight any problems that cause difficulty.
Give students handout, "What are the Chances
When Job Seeking"
The handout has various problems that focus on job
seeking skills and incorporates probability skills. Give students time to work
on the worksheet. Troubleshoot when necessary. Encourage students to solve the
problems but looking back to the text for further explanation, or by asking
another student for help.
Explain to students that you don't always get the
first job that you apply for and often takes applying for many jobs to get one
job. Relay any personal experiences in looking for a job. Emphasize the
importance of continuing job hunting even when you get no response.
Reflection
by Teacher:
Were students able to connect probability problems
with real life situations? Were students successful in learning the concepts of
probability problems?
Order of
Operations: Who's on First?
Introduction
/ Warm up / Review:
Ask students whether they put on their socks first or
their shoes. Ask students to describe starting a car and backing out of a
driveway. Write responses on board, beginning with "Open the car door, get
inside, put the key in the ignition, etc. Ask students if there is a certain
order for doing activities that have multiple steps. Write responses on board.
Ask students to tell you how they would go about
applying for a job that they were interested in. Write the responses on the
board. It should look something like: Make contact with the organization, get an
application, fill it out, etc. Let students know that math has a certain order
and that to solve certain problems, you must follow the order.
Presentation of
Lesson:
Write "Order of Operations" on the board
and number underneath, 1., 2., 3.
Ask students if they know/recall the order of
operation. If correct, write on board:
Do operations within parentheses.
Do multiplication or division.
Do addition or subtraction.
Do several equations on the board using multiple
operations. Ask students to guide you through solving the equations. Leave the
order on the board for several examples, and then "inadvertently"
erase the order prompt.
Practice
/ Activity:
Do several more guided problems on the board, having
students verbally work the problems and to guide you through solving the
problems.
Have students complete Exercise 13, pg. 47 Guide
students through any difficult areas. Use the board to highlight any problems
that cause difficulty.
Application/Transfer:
Ask students to recall any problems that were
questionable. Work through any problems on the board as a group.
Reflection
by Teacher:
Were students able to able memorize the order of
operations? Can they relate it to life experiences such as applying for jobs?
Planning
for Next Lesson:
If any students requested additional instruction,
make note of what areas were difficult and address the topic in class the next
day as part of the review process. Address any other problem areas students
might be having and cover those topics as well.
ACADEMIC
PREPARATION
WEEK THREE DAY
FIVE
Lesson
Title: Fractions
Review
Subject
Matter/Life Skill Area: Academic
Strand, Math Skills
Learning
Level/Prerequisite Skills: 9th
grade reading/math level
Lesson
Length: Two
hours
Instruction
Type: Whole
group review with small group and individual practice
Overview and
Rationale:
Students should have the opportunity to review all
math applications learned during the week. Contemporary's GED book: Test Five
has a fractions review exercise on pg. 114-115 that touches upon all topics
learned this week.
Learning
Objectives / Skills:
At the completion of this lesson, students will be
able to understand and utilize various fraction applications, including adding,
subtracting, multiplying and dividing. Students will also review familiar
fractions terminology such as mixed fractions, improper fractions, like/unlike
fractions, probability, and order of operations.
Skills: Arithmetic/Mathematics, problem solving,
reasoning
Materials/
Equipment Needed:
Contemporaries GED math book (Book Five)
Pencils and paper
Chalkboard and chalk
Poster paper (one paper for each pair/ two problems
each page) with various fractions, probability, and order of operations problems
made ahead of class. Problems may be taken from previous lessons.
Introduction
/ Warm up / Review:
Ask students to recall math skills learned during
instruction for the week. Write responses on board. If students elicit
vocabulary, ask for examples. If students elicit examples, ask for
identification. Fill in any missing skills that were learned during the week,
that were not listed during feedback.
Presentation of
Lesson:
Have students work with a partner. Hand out poster
paper with problems for each pair to work. Let students know that they need to
be able to explain how they worked the problems, that they should work together
as a team to solve the problems and report back to the class.
Practice /
Activity:
Give
pairs about 20 minutes to solve the problems and be ready to report back.
Give each pair enough time to present their problems
to the group. Have a question and answer period after each presentation.
Application /
Transfer:
After pairs have finished their presentations, cover
any questions that the group may have. Have students complete the Fractions
Review on pages 114-115
Students should feel comfortable with skills learned
during the week and how they apply in the world of work. Students should have an
awareness also that finding a job may require filling many job applications, but
the "probability" of finding a job will be higher with more effort.
Reflection
by Teacher:
Were students able to present information to the
class in a skillful/comfortable fashion? Were students able to complete the
review lesson with proficiency?
Planning
for Next Lesson:
Remind students to access the fractions lessons on
the appropriate software program in the technology strand.
If time allows, have students write in their journals.