structured curriculum lesson plan day: 109 subject: mathematics grade level:

8/14/2019 Structured Curriculum Lesson Plan Day: 109 Subject: Mathematics Grade Level:

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STRUCTURED CURRICULUM LESSON PLAN

Day: 109 Subject: Mathematics Grade Level: 4

Correlations (SG,CAS,CFS): 6A4, 6A5, 6C5

ITBS/TAP:

Perform arithmetic operations involvingfractions

Demonstrate understanding of measurementconcepts

ISAT:

Perform computations involving fractions

Unit Focus/Foci

Fractions

Instructional Focus/Foci

Adding fractions with like denominators

Materials

Six-Group Activity: Subtracting like fraction and mixed numbersMath journals

Overhead projectorPensTransparency

Homework worksheet

Educational Strategies/Instructional Procedures

Warm-up Activity:

Write these problems on the chalkboard.

Tell students to rename these improper fractions as whole numbers or mixed numbers.

1. ____

3

6= 2. ____

10

13= 3. ____

8

15= 4. ____

7

14=

5. ____12

13= 6. ____

5

10= 7. ____

2

3= 8. ___

9

14=

Review the answers with students.


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Lesson:

Instruct students to take notes in their math journals. Write all examples on thechalkboard.

Review parts of a fraction: numerator, denominator and fraction bar. On a

transparency, draw the following:

+ =

4

1

4

2

Ask students for the sum.

43 Draw the following box next to the equal sign and write

the sum beneath it.

4

3

Ask students to look at the denominators. Did the denominator change for the sum?(No) What happened with the numerator? (They were added.)

Have students draw the following figures in their math journals. Instruct students to thenshade in the figures to show the sum and then write the sum.1.

1.

3

1+

3

1=

+ =


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2.

+ =

83 +

84 =

Draw the following figures on a transparency.

Have students draw the figures below in their math journals. Ask students to shade in thefigures to show the fractions, add the fractions, and then shade in the final figure to show

the sum.

+ =

8

3+

8

2=

Write =+12

1

12

7on the chalkboard or transparency. Take students through the following

steps for finding the sum of these two fractions with like denominators.

Step 1: Add the numerators.

=+12

1

12

7 8

Step 2: Use the like or common denominators.

=+12

1

12

7

12

8

Step 3: Write the sum in simplest form.

=

=3

2

412

48

3

2

12

8

+ =

6

1+

6

4=

6

5


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Remember that a fraction is in simplest form when the denominator can only be evenlydivided by 1.

Tell students that the problems can be solved horizontally or vertically.

Write the problems below on the chalkboard. Call on 3 students to solve while the otherswork as many as possible in their journals.

1. 2. 3.

15

10

15

3

+

20

4

20

7

+

10

1

10

5

+

Write

4

1

4

1+ . Ask students for the sum.

4

2Ask if the sum is in simplest form. (No)

Ask how they know. (If the numerator and denominator can be divided by a numberother than 1, the number is not in simplest form.) Ask by what number the numerator

and denominator can be divided. (2) Write24

22

. Ask for the solution.

2

1Ask if

2

1

is in simplest form. (Yes) Ask how they know. (The numerator and denominator canonly be divided by 1.)

Write6

2

6

1+ . Have students copy and solve in their math journals. Remind students that

the sum must be in simplest form. Have a student come to the chalkboard to solve theproblem and explain the solution.

Write4

2

4

3

4

3++ on the chalkboard. Have students copy and compute in their journals.

Remind students that the answer must be in simplest form.

= 2

4

8Ask how they

arrived at 2 from4

8. (Divided 8 by 4)

Tell students that writing fractions in simplest form includes changing the answer to a

proper fraction.


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Write6

5

6

2+ vertically on the chalkboard. Have students copy, compute and simplify.

=

6

11

6

7Have a student explain the solution.

Write11

7

11

9

11

10++ vertically on the chalkboard. Have students copy, compute and

simplify.

=

11

52

11

26. Have a student explain the solution.

Ten Statements

Review the ten statements and have students writeyes if they heard it in todays lessonand no if they did not. If the answer is no, say: The statement is true, but it was not

heard in todays lesson.

1. When adding fractions with the same denominator, add only the numerators. (yes)2. A fraction is improper if the numerator is larger than the denominator. (yes)

3.6

2is not in simplest form because the numerator and denominator can be divided by

2. (yes)4. There are 52 weeks in a year. (no)5. When adding fractions with the same denominators the denominator remains the

same for the sum. (yes)6. One can add fractions when they are lined up horizontally or vertically. (yes)

7. In the problem 7

4

7

1

+ , add the numerators 1 and 4. (yes)8. A chevron is a comparison symbol. (no)9. A fraction is in simplest form if the numerator and denominator can only be evenly

divided by 1. (yes)10. A line segment is a straight figure with two endpoints. (no)

Free-Choice Lesson

Have students choose a lesson from the Free-Choice Activity sheet (one box per day).

Six-Group Activity

Have a group of six students, two from each ability level, complete an activity on

Subtracting like fractions and mixed numbers as a teacher directed activity.


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Math Workshop

Have students work in theMath Workshop after completing their Free-Choice Lesson.

Integration with Core Subject(s)

LA: Understand explicit, factual information

SS: Sequence information, especially using timelines

Select appropriate information for intended purpose

Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: Six-Group Activity Lesson.

Technology:

Assessment

Student response during lessonTen Statement Review

Homework

Have students solve the following problems.See attached sheet for Homework Sheet

Teacher Notes


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Homework

Add. Write each sum in simplest form.

1. ____7

1

7

3

=+ 2. ____175

17

3

=+

3. ____12

7

12

5=+ 4. ____

10

8

10

3

10

9=++

5. ____16

10

16

11=+ 6. ____

20

15

20

15

20

15=++

7. ____15

7

15

5

15

7=++ 8. ____

24

7

24

8

24

9=++


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Six Group Activity

Fractions (renaming): Subtracting Like Fractions and Mixed Numbers

Materials:

10 index cards (5 x 7)Glue

Scissors1 pencil

1 envelope (9 x 6 )

Prepare the following index cards by cutting out the activity cards and gluing them to the

index cards. Use the pencil to write the answers on the back of the cards:

31

4

yd7

8

22

3

1

2

year Donnie, 11

4

7 inches 31

5hrs 4

1

10miles Daryl, 1

1

4mi 2

1

5mi

Lay a card on the table and have the students read the card and answer the question.

After the answer is written, reveal the answer by turning the card over and say: Theanswer is

Make a copy of this study board and use it to reteach this activity.

Subtracting Like Fractions and Mixed Numbers

When subtracting fractions with like denominators, subtract the lesser numerator from the

greater numerator and keep the denominator the same.

Example: Subtract6

10

3

10.


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Step 1. Subtract the numerators.6

10 =

3

10

3

Step 2. Write the common denominator.3

10

Step 3. Simplify or reduce if necessary.

Example: Subtract 3 21

6

2

6 .

Subtract mixed numbers the same way. Regroup to borrow if necessary.

Step 1. Subtract the whole numbers 3-2=1

Step 2. Subtract the fractions 26 =16 16

The answer is 11

6.

Tell the students that they are going to do an activity just like the one they just finished.Lay one card on the table and give the students time to solve the problem. When the

students finish the problem, reveal the answer by turning the card over and saying: Theanswer is


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Activity Cards

Sam bought 374yards of carpet to put in the

hallway. He only used2

44

yards. How

much carpet does Sam have left over?

Carrie saves2

16 of her weekly earnings.

How much of her earnings does she spend?


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Activity Cards

The teacher filled2

33

albums with color

proofs. She filled 1 album with black-and-white proofs. How much more space do the

color-proofs take up?

Ines spends about8

12of the year traveling

on business. Marilyn spends about2

12of the

year away on business. About how much

less time does Marilyn spend traveling on

business than Ines?


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Activity Cards

Bonnie can run about2

44 miles each day.

Donnie can run3

54 miles each day. Who

can run the greater distance, and by howmuch more?

Two workers were fitted for uniforms.

Jims inseam measured1

372 inches and

Raymonds measured1

302 inches. How

much longer will Jims pants be thanRaymonds?


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Activity Cards

Joan and Burn are working on a curriculumproject. They have spent the last several

Saturdays writing lessons. Joan worked3

105

hours on Saturday. Burn worked for 275

hours. How many more hours did Joan

work?

Sam and Marlene are meeting at a local

caf. Sam must travel 123

10miles to get

there. Marlene must travel 82

10miles. How

much further must Sam travel?


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Activity Cards

Jonny and Daryl are working toward fitness

goals. Jonny can walk about 234

miles each

day. Daryl can walk 344

miles each day.

Who can walk the greater distance, and by

how much more?

Hanna also wants to meet Sam at the local

caf. If Marlene traveled2

810

miles and

Hanna traveled4

1010

mile. How many miles

further than Marlene must Hanna travel to

meet Sam?


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ITBS/TAP:

Perform arithmetic operations involvingfractions.

ISAT:

Perform computations involving fractions.

Unit Focus/Foci

Fractions


Subtracting fractions with like denominators

Materials

Six-Group Activity: Subtracting fractions with like denominatorsStudent math journals

Envelopes with student fraction piecesTransparency fractions pieces


Warm-up Activity:

Write these problems and instructions on the chalkboard.

Add. Write each sum in simplest form.

1. ____5

4

5

2=+ 2. ____

12

3

12

1=+ 3. ____

2

1

2

3=+


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Step 3: Write the difference in simplest form.

3

2

12

8=

=

3

2

412

48

Write the problems below on the board. Have students copy, compute, and write thedifferences in simplest form.

1. ==5

1

5

42. =

4

1

4

33. =

16

4

16

14

Have students complete the problems on the board and have them explain their solutions.

Ten Statements

Review the ten statements and have the students writeyes if they heard it in todayslesson and no if they did not. If the answer is no, say: The statement is true, but it wasnot heard in todays lesson.

1. When subtracting fractions with the same denominatiors you use the like or commondenominator. (yes)

2. The formula for finding area is length times width. (no)3. A fraction is in simplest form if the numerator and denominator evenly divided by

one. (yes)4. When subtracting fractions with like or common denominators you subtract only the

numerator. (yes)

5. In the problem4

1

4

3 the difference will have 4 as the denominator. (yes)

6. An acute angle is less than 90 degrees. (no)

7. The last step in finding the difference between 2 fractions is to write the answer issimplest form. (yes)

8. In the problem4

1

6

5 you subtract the numerator 1 from the numerator 5. (yes)

9. The oppostie of addition is subtraction. (no)

10.3

2is in simplest form because the numerator 2 and the denominator 3 can only be

evebly divided by 1. (yes)


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Free Choice Lesson


Six-Group Activity


Subtracting fractions with like denominators as a teacher directed activity.

Math Workshop



LA: Understanding explicit, factual information

SS: Sequence information, especially using time linesSelect appropriate information for intended purpose

Connection(s)

Enrichment:

Fine Arts:

Home:


Technology:

Assessment

Student response during lessonTen Statement Review

Homework

Explain how to solve10

5

10

9 .

Teacher Notes


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Six Group Activity

Fractions (renaming): Subtracting Fractions with Like Denominators

Materials:

10 3 x 5 index cards1 black marker

1 (9 x 6 ) envelope

Prepare the following index cards and sample rules:

1

2-

2

4(1

4)

8

10-

3

10(

5

10)

11

12-

3

12(

8

12)

4

6-

3

6(1

6)

12

15-

2

15(10

15)

6

9-

3

9(3

9)

6

8-

5

8(1

8)

10

12-

5

12(

5

12)

3

12-

2

12(

1

12)

13

22-

3

22(10

22)

Copy the study board and use it to reteach the lesson.

Place an index card on the table with a subtraction of fractions with like denominators.

Explain that you subtract the numerators and leave the denominator the same. Example:

5

10-

3

10(

2

10) . If you taught simplifying then the answer is

1

5if not

2

10. Write other

sample problems and have students answer questions on how to solve the problem.

Give the students a sample problem and explain the rules for doing the problem with

them.

Note: If you did not teach reducing, have the students solve the problem with no

reducing.

Sample Rules

When subtracting fractions with like denominators, subtract the numerator and do nothing to thedenominators because they are the same. Move the like denominator under the numerator.

Example:3

5-

2

5(1

5)

Explain to the students that we are going to do an activity dealing with subtraction of

fractions with like denominators. The students are going to risk writing the answers.

Place an index card on the table. Give the students 1 to 2 minutes to write the answer. asyou turn the index card over say, The answer is Check for correct answers. Storeyour cards and study boars in the envelope


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Correlations (SG,CAS,CFS): 6A4, 6A5, 6C

ITBS/TAP:


ISAT:


Unit Focus/Foci

Fractions


Adding and subtracting mixed numbers with like denominators

Materials

Six-Group Activity: Adding like denominatorsMath journals


Warm-up Activity:


Add or subtract. Write the answers in simplest form.

1.

7

3

7

2

+

2.

4

2

4

1

+

3.

8

6

8

6

+

4.

10

310

9

5.

9

09

7

6.

16

416

14

Review the answers with students. Answers are in the Teacher Notes.


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Lesson:

Instruct students to take notes in their math journals.Write the problem below on the chalkboard or a transparency.

Bob walked for821 hour on Saturday and

811 hour on Sunday. What is the total time that

Bob spend walking? Ask what operation should be used to solve the problem.

(Addition). Write the addition problem on the chalkboard.

21

8

11

8+

Show this problem using the transparency fraction pieces. Line the whole strips up next

to each other. Next, line up the8

2and

8

1. Ask students how much you have.

8

32

Write this problem on the chalkboard or a transparency:

6

33

6

12

+

Orally, review the steps below to solve the problem.

Step 1: Add the fraction parts.

6

4

6

33

6

12

+


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Write

2

8

54

+

and

5

7

46

on the chalkboard. Ask what students should do when adding a

whole

number to a mixed number or subtracting a whole number from a mixed number. (Addzero to or subtract zero from the fractions and then add or subtract the whole numbers.)

Write the following problems on the chalkboard. Have students work them out in theirjournals while other students work them out on the chalkboard.

1. 2. 3. 4.

3

12

3

24

+

9

71

9

73

8

41

8

65

6

25

6

12

+

Ten Statements

Review the ten statements and have students writeyes if they heard it in todays lesson

and no if they did not. If the answer is no, say: The statement is true, but it was notheard in todays lesson.

1. 100 centimeters =1 meter. (no)2. In the last step of adding or subtracting mixed numbers, write the answer in simplest

form. (yes)

3. In the problem7

35

7

16 + , add

7

3

7

1+ first. (yes)

4. A rectangle has 4 sides. (no)

5. In the first step of adding or subtracting mixed numbers, add the fraction part. (yes)6. When adding mixed numbers and part of a mixed number is missing, add zero to the

fraction. (yes)7. When subtracting mixed numbers do not write the zero if the difference or the

fraction part is zero. (yes)

8. In the second step of adding and subtracting mixed numbers, add the whole numbers.(yes)

9. In the problem8

12

8

74 , subtract 24 in the second step. (yes)

10. A line is longer than a line segment. (no)


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Free-Choice Lesson


Six-Group Activity

Have a group of six students, two from each ability level, complete an activity on Adding

like denominators as a teacher directed activity.

Math Workshop




SS: Select appropriate information for intended purpose

Connection(s)

Enrichment:

Fine Arts:

Home:


Technology:

Assessment

Student response during lesson

Ten Statement Review


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Homework

Add the following. Write answers in simplest form.

1.

3

2

1

2

+2.

5

32

5

16

+3.

4

31

4

14

+

4.

5

7

37

+5.

10

32

10

35

+

Teacher Notes

Answers to warm-up activity:

1.)5

72.)

3

43.)

11

24.)

3

55.)

7

96.)

5

8


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Six-Group Activity

Fractions: Adding Fractions with Like Denominators

Materials:

10 index cards (3x 5)

1 black marker1 pencil

1 envelope (9 x 6 )

Prepare the following index cards:

1

3+

1

3(2

3)

4

6+

1

6(5

6)

3

5+

1

5(4

5)

4

8+

2

8(6

8)

3

10+

2

10(

5

10)

8

12 +

2

12 (

10

12)

3

7 +

2

7 (

5

7)

10

20 +

1

20 (

11

20)

3

9 +

2

9 (

5

9)

3

12 +

2

12 (

5

12)

Solve the addition problems of fractions with like denominators. Lay a card on the table

and have the students write the answer. After each answer is written, reveal the answeron the back of the index card.

Copy this and use it to reteach the lesson. Give the sample problem to see if studentsunderstand the rules for adding fractions with like denominators.

Adding Fractions with Like Denominators

Place a card on the table and explain the steps for solving an addition of fractions

problem. Show students3

5+

1

5. Say: Add the numerators (3 + 1 = 4). The

denominator remains the same. The answer is4

5. Say: I am going to show you a set of

cards with addition problems of fractions with like denominators on them. I want you to

solve the problems.

When adding fractions with like denominators, add the numerators. Dont do anything to

the denominator because it is the same. Write it under the numerator. Example:

26

+ 26

= 46

.

Explain to the students that they are going to do an activity on solving addition problems

of fractions with like denominators. Tell them when you lay the index card on the table,they are going to risk writing the answer. Give the students one to two minutes to solvethe problem. As you turn the card over, say: The answer is Do the rest of the cards

the same way. If you have not taught reducing fractions, just have the students completethe problems with no simplifying. Store the index cards and study board in the envelope.


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Have students show this addition using their fraction pieces originally developed in

lesson ___. (one pink and one blue green) Ask if the2

1piece could be replaced by

another piece. (Yes) Ask how many6

1pieces would be needed to replace the

2

1piece

(3). Have students replace the2

1 piece with the (3) one-sixth pieces. Ask what6

1

6

3 +

equals.

6

4Ask if the answer is in simplest terms. (No) Ask for the answer in simplest

terms. Have a student explain how to simplify6

4(Divide the numerator and

denominator by 2.) Repeat this process with

8

1

4

1

+

.

Point to the first problem

6

1

2

1

+

again. Have students look at the denominators. Ask if

they are the same. (No) Tell students that they are now going to add these fractionswithout their fraction pieces. To do so, the fractions must have a common (or like)denominator. Ask if the smaller denominator can be divided into the larger one (6)

without a remainder. (Yes, 326 = ) Tell students that because 6 can be evenly divided

by 2, that 6 will be the common denominator. Write

66

1

621

=+

=on the chalkboard or

transparency. Have students look at62

1= and ask students what denominator 2 can be

multiplied by to get 6. (3). Write X3 below the equal sign. Tell students that they must

multiply the numerator 1 by 3 also. Write X3 above the equal sign and ask students for

the product of 31x . (3) Write the 3 above the six.

Next, have students look at61 . Since this fraction always has the common denominator

it is not necessary to do any multiplication. However, you may wish to demonstrate forstudents why it is unnecessary.

X1

X1


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Repeat this process with .

1 16 6

1 1

6 6

4 26 3

=

+ =

3

3

=


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Write

3

2

5

1

+

on the chalkboard or a transparency.

Ask if the denominators are the same. (No) Ask if the smaller denominator can bedivided evenly into the larger denominator. (No) Tell students that another way to find a

common denominator is to multiply the two denominators. Ask students for the product

of 5 and 3. (15) Write15

= next to each of the fractions. Ask students how to complete

the equivalent fractions. Then have students add and simplify if necessary.

15

13

15

10

3

2

15

3

5

1

=+

=

Write

2

1

7

3

+

on the chalkboard. Repeat the process above.

Write the following problems on the chalkboard or transparency and have students cometo the board or overhead to complete them. The rest of the class can solve them in their

journals. Remind students that they must simplify their answers.

1)

10

3

5

1

+

2)

5

3

6

1

+

3)

5

1

2

1

+

4. Sara bought8

5pounds of tomatoes and

4

1pound of onions. What was the total

weight of the vegetables?


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Ten Statements



1. If one multiplies the denominator by a number, one must also multiply the numerator

by this same number. (yes)2. Parallel lines are lines that do not intersect. (no)

3. To add two fractions, common or like denominators are needed. (yes)

4. In the problem6

1

3

1+ , the denominator 6 can be evenly divided by the denominator 3.

(yes)

5. Composite numbers are numbers having more than 2 factors. (no)6. Another way to find a common denominator is to multiply the two denominators.

(yes)

7. In the problem31

41 + , multiply the 3 and 4 to get a common denominator. (yes)

8. The LCD of 3 and 9 is 9. (yes)

9. After finding a common denominator, equivalent fractions can be made. (yes)10. A quadrilateral is a polygon with 4 sides. (no)

Free-Choice Lesson


Six-Group Activity


Subtracting fractions with like denominators as a teacher directed activity.

Math Workshop




Understand the meaning of words in context

SC: Apply scientific method to solve problemsAnalyze and interpret data

SS: Read and interpret maps, charts, tables, graphs and cartoons

Sequence information, especially using timelinesSelect appropriate information for intended purpose


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Connection(s)

Enrichment:

Fine Arts:

Home:


Technology:

Assessment

Homework

Teacher Notes


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Six Group Activity

Fractions (renaming): Subtracting Fractions with Like Denominators

Materials:

10 3 x 5 index cards1 black marker

1 (9 x 6 ) envelope

Prepare the following index cards and sample rules:

1

2-

2

4(1

4)

8

10-

3

10(

5

10)

11

12-

3

12(

8

12)

4

6-

3

6(1

6)

12

15-

2

15(10

15)

6

9-

3

9(3

9)

6

8-

5

8(1

8)

10

12-

5

12(

5

12)

3

12-

2

12(

1

12)

13

22-

3

22(10

22)

Copy the study board and use it to reteach the lesson.

Place an index card on the table with a subtraction of fractions with like denominators.

Explain that you subtract the numerators and leave the denominator the same. Example:

5

10-

3

10(

2

10) . If you taught simplifying then the answer is

1

5if not

2

10. Write other

sample problems and have students answer questions on how to solve the problem.

Give the students a sample problem and explain the rules for doing the problem with

them.

Note: If you did not teach reducing, have the students solve the problem with no

reducing.

Sample Rules

When subtracting fractions with like denominators, subtract the numerator and do nothing to thedenominators because they are the same. Move the like denominator under the numerator.

Example:3

5-

2

5(1

5)

Explain to the students that we are going to do an activity dealing with subtraction of

fractions with like denominators. The students are going to risk writing the answers.

Place an index card on the table. Give the students 1 to 2 minutes to write the answer. asyou turn the index card over say, The answer is Check for correct answers. Storeyour cards and study boars in the envelope


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Day: 113-114 Subject: Mathematics Grade Level: 4


ITBS/TAP:


ISAT:


Unit Focus/Foci

Fractions


Subtracting fractions with unlike denominators

Materials

Six-Group Activity: Subtracting mixed numbers with unlike denominatorsMath journals

Envelopes with studentTransparency fraction pieces

Homework worksheet


Warm-up Activity:


Find a common or like denominator for each of these pairs of fractions.

1.4

3and

8

12.

2

1and

5

3


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Solve. Simplify the sums.

3. 4. 5.

4

35

4

+

4

1

21

3

1

+

Answers: Answers may vary for 1 and 2.

1) 4, 8, 16 2) 10 3)7

44)

4

31 5)

12

11

Lesson:

Instruct students to take notes in their math journals. Write all examples on the

chalkboard.

Write

8

1

2

1

on the chalkboard or a transparency.

Have students show this using their fraction pieces. (One pink and one blue) Ask if the

2

1piece can be replaced using

8

1pieces. (Yes) Ask how many

8

1pieces would be

needed to replace the2

1piece. (4) Have students replace the

2

1piece with (4) one-

eighth pieces. Ask what4 1

8 8 equals.

8

3Ask if the answer is in simplest form.

(Yes.)

Repeat this process with

4

1

12

11

.

3

72

14+


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Point to the first problem again.

8

1

2

1


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181

Have students look at the denominators. Ask if they are the same. (No) Tell studentsthat they are now going to subtract these fractions without their fraction pieces. Ask how

they can do this. (Find a common or like denominator) Ask how they can find acommon denominator. (Divide the smaller denominator evenly into the larger

denominator or multiply the two denominators.) Solve both ways with the class

reviewing steps used in previous lessons or adding fractions with unlike denominators.

8

3

8

8

1

8

4

2

1

and

8

3

16

6

16

2

8

1

16

8

2

1

Tell students to note that both ways yield the same solution. Ask which way had less

steps. (The division method) Ask why. (It was unnecessary to simplify the answer.)

Ten Statements

Review the ten statements and have students writeyes if they heard it in todays lessonand no if they did not. If the answer is no, say: The statement is true, but it was notheard in todays lesson.

1. One can find a common denominator by multiplying the denominators of the

fractions being subtracted. (Yes)2. The fractions of 8 are 1, 2, 4 and 8. (no)

3. There are 4 quarts in a gallon. (no)

4. In the problem8

1

2

1 , eight can be the common denominator because one can

divide the denominator (2) into the denominator (8) evenly. (yes)5. To solve a fraction with different denominators, frist find the LCD. (yes)

6. In order to subtract fractions, one needs to have common or like denominators. (yes)

7. In the problem3

1

7

6 , one needs to multiply the denominators to find a common

denominator. (yes)8. After finding a common denominator, one make equivalent fractions. (yes)9. A pentagon has five sides. (no)

10. If one multiplies the denominator by 4, one must multiply the numerator by 4. (yes)

2x

2x

8x

4x 8x

2 2


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Free-Choice Lesson


Six-Group Activity


Subtracting mixed numbers with unlike denominators as a teacher directed activity.

Math Workshop




Connection(s)

Enrichment:

Fine Arts:

Home:


Technology:

Assessment



Homework

(See attached)

Teacher Notes


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Homework

1.

14

5

7

6

2.

4

3

7

6

3.

24

8

12

5

4.

12

1

6

5

5.

15

2

5

2


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43/57


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186

Example:

1.

9

15

7

15

215

3

5

+

=

2.

7

11

4

11

3

11

3.

4

1

6

3 3

4

711

12

+

4.

8

+

41

7

121

7

5.

5

7

9

24

9

33

93

1

3

=

6.

7

1

3

4

31

3

Review adding and subtracting fractions with unlike denominators. Write problems onthe chalkboard and have students solve them while the remainder of the class solves them

in their journals. Have students explain their solutions.

Examples:

7.

4

16

1

8

6

16

3

8

+

=

8.

2

9

1

6

7

18

+

9.

3

20

1

5

3

10

13

10

13

10

+

=


45/57


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188



Connection(s)

Enrichment:

Fine Arts:

Home:


Technology:

Assessment



Homework

Tell students to study for the test.

Teacher Notes


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189

Six-Group Activity

Fractions: Simplifying Fractions

Materials:

20 index cards (3 x 5)

1 envelope (9 x 6 )1 black marker

1 pencil

Prepare the following index cards using the black marker to write the problems on the

front of the cards. Write the answers on the back of the cards in pencil.

2

2(1)

2

4(1

2)

6

12(1

2)

9

12(

3

4)

15

18(5

6)

66

(1) 510

(12

) 812

( 23

) 1010

(1) 515

(13

)

4

10(2

5)

3

3(1)

9

18(1

2)

6

8(3

4)

12

24(1

2)

5

20(1

4)

7

14(1

2)

3

15(1

5)

4

12(1

3)

8

8(1)

Place the study board on the table with an example of a fraction that needs to be

simplified. Say: Simplifying a fraction means writing it an easier way with smallernumbers. Look at the following examples to see how fractions are reduced.

Example 1: Simplify15

20.

Find a number that divides evenly into the numerator and the denominator of the fraction.

Ex: 5 divides evenly into both 15 and 20.15 5

20 5

=3

4.

Check to see whether or not the numerator and denominator can be divided evenly byanother number. Since 3 and 4 cannot both be divided evenly by another number, the

fraction is reduced as far as possible.

Say: Look at the second example:48

64.


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190

Find a number that evenly divides the numerator and the denominator. 8 goes evenly into

both 48 and 64.48

64 =

8

8

6

8

Check to see if another number goes evenly into both the numerator and denominator of

the fraction. Two evenly divides goes evenly into both 6 and 8. Check to see whetheranother number goes evenly into both the numerator and denominator of the fraction. Inthis case, the fraction is simplified as far as possible.

When you reduce a fraction, the value does not change. A reduced fraction is equal to

the original fraction.

Write the name of the activity and materials needed on the front of the 9 x 6

envelope and store the index cards and study board in it. Explain the rules forsimplifying or reducing fractions. Copy this study board.

Simplifying Fractions

Rule #1: If the numerator and denominator are the same, the fraction equals 1. Example:6

6= 1,

5

5= 1.

Rule #2: If the numerator can divide evenly into the denominator, this is a way to simplify.

5

10; 5 goes into 10 two times and 5 goes into itself one time. The answer is

1

2.

3

6;

3 goes into 6 two times. 3 goes into itself one time. The answer is1

2

.

The numerator can divide the denominator evenly. Ex.:2

10=

1

5.

Rule #3: If the second rule wont work, find a number (except 1) that can divide the

numerator and denominator evenly. Example:6

8; 2 can divide into 6 and 8 evenly.

6

8

2

2=

3

4.

Find the number that can divide both the numerator and denominator evenly. (3)

Ex.:6

9 3

3 =2

3

When the numerator and denominator are the same, the fraction always equals one. Ex.:6

6= 1;

5

5= 1.


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Tell the students that they are going to risk writing the answers to these problems. Beginby placing an index card on a flat surface. Give the students one to two minutes to write

the answer. When giving the answer, turn the index card over and say: The answeris


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Six-Group Activity

Fractions: Simplifying Fractions

Materials:

20 index cards (3 x 5)1 envelope (9 x 6 )

1 black marker1 pencil

Prepare the following index cards using the black marker to write the problems on thefront of the cards. Write the answers on the back of the cards in pencil.

2

2

(1)2

4

(1

2

)6

12

(1

2

)9

12

(3

4

)15

18

(5

6

)

6

6(1)

5

10(1

2)

8

12(2

3)

10

10(1)

5

15(1

3)

4

10(2

5)

3

3(1)

9

18(1

2)

6

8(3

4)

12

24(1

2)

5

20(1

4)

7

14(1

2)

3

15(1

5)

4

12(1

3)

8

8(1)

Place the study board on the table with an example of a fraction that needs to besimplified. Say: Simplifying a fraction means writing it an easier way with smaller

numbers. Look at the following examples to see how fractions are reduced.

Example 1: Simplify15

20.

Find a number that divides evenly into the numerator and the denominator of the fraction.

Ex: 5 divides evenly into both 15 and 20.15 5

20 5

=3

4.

Check to see whether or not the numerator and denominator can be divided evenly by

another number. Since 3 and 4 cannot both be divided evenly by another number, the

fraction is reduced as far as possible.

Say: Look at the second example:48

64.


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Find a number that evenly divides the numerator and the denominator. 8 goes evenly into

both 48 and 64.48

64 =

8

8

6

8

Check to see if another number goes evenly into both the numerator and denominator of

the fraction. Two evenly divides goes evenly into both 6 and 8. Check to see whetheranother number goes evenly into both the numerator and denominator of the fraction. Inthis case, the fraction is simplified as far as possible.

When you reduce a fraction, the value does not change. A reduced fraction is equal to

the original fraction.

Write the name of the activity and materials needed on the front of the 9 x 6

envelope and store the index cards and study board in it. Explain the rules forsimplifying or reducing fractions. Copy this study board.

Simplifying Fractions

Rule #1: If the numerator and denominator are the same, the fraction equals 1. Example:6

6= 1,

5

5= 1.

Rule #2: If the numerator can divide evenly into the denominator, this is a way to simplify.

5

10; 5 goes into 10 two times and 5 goes into itself one time. The answer is

1

2.

3

6;

3 goes into 6 two times. 3 goes into itself one time. The answer is1

2

.

The numerator can divide the denominator evenly. Ex.:2

10=

1

5.

Rule #3: If the second rule wont work, find a number (except 1) that can divide the

numerator and denominator evenly. Example:6

8; 2 can divide into 6 and 8 evenly.

6

8

2

2=

3

4.

Find the number that can divide both the numerator and denominator evenly. (3)

Ex.:6

9 3

3 =2

3

When the numerator and denominator are the same, the fraction always equals one. Ex.:6

6= 1;

5

5= 1.


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Tell the students that they are going to risk writing the answers to these problems. Beginby placing an index card on a flat surface. Give the students one to two minutes to write

the answer. When giving the answer, turn the index card over and say: The answeris


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ITBS/TAP:


ISAT:


Unit Focus/Foci

Fractions


Formal Assessment-Adding and subtracting fractions and mixed numbers

Materials

Educational Strategies/Instructional Procedure

Distribute test.


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Test

Find a common denominator for each of the following pairs of fractions.

1.

1 1and2 4

___________

2.

3 7and5 8

___________

3.

5 1and6 4

___________

Add or subtract. Write the sum or difference in simplest form.

4.

4 3+

8 8= ________

5.

5 8+

12 12= _______

6.

4 1-

9 9= ________

7.

9 0-

12 12= _______

8.

+

2

9

1

3

9.

+

1

2

5

8

10.

-

1

5

1

4

11.

-

1

6

4

5

Rewrite these fractions as proper fractions.

12.

7

5

13.

15

3

14.

27

4

15.

11

2

Add or subtract. Write the sum or difference in simplest form.

16.

6

+

1

12

5

12

3

17.

15

3

2+

18.

218

3

9

19.

2

+

5

8

7

8

5

20.

919

10

115

- 10


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Solve.

21. Keesha bought3

4yards of fabric. She needs

2

3yards to make a skirt. How much

fabric will she have left?

22. Sam needs 238

gallons of blue paint and 118

gallons of white paint. How much paint

does he need altogether?

23. Tamika has4

5quarts of cherry Kool-Aid and

1

3quarts of lemonade. How much

more Kool-Aid than lemonade does she have?

24. Terry baked 3 dozen cookies. She needs to bake 11

2 dozen more. How many

cookies will she have baked?

25. Explain how to find a common denominator for1

3and

5

6.


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Ten Statements



No Ten Statements today.

Free-Choice Lesson


Six-Group Activity

No Six-Group Activity today.

Math Workshop




Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation:

Technology:

Assessment

Formal Assessment

Homework

Teacher Notes


57/57

Answer Key for Test:

Possible answers for 1 to 3.

1. 2, 8 or any multiple of 4. 2. 40 or any multiple of 40. 3. 12, 24 or any multiple of 12.

4.

7

8

5.

11

12

6.

1

3

7.

3

4

8.

5

9

9.

11

8

10.

1

20

11.

19

20

12.

1

2

5

13.

5

14.

36

4

15.

51

2

16.

91

2

17.

71

3

18.

92

3

19.1

82

20.

44

5

21.1

12

22.

31

2

23.

7

15

24.

41

2dozen

25. Multiply the denominators or you can divide the larger denominator by the smallerdenominator.

structured curriculum lesson plan day: 109 subject: mathematics grade level:

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