structured curriculum lesson plan day: 098 subject: mathematics grade level:

8/14/2019 Structured Curriculum Lesson Plan Day: 098 Subject: Mathematics Grade Level:

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STRUCTURED CURRICULUM LESSON PLAN

Day: 098 Subject: Mathematics Grade Level: 4

Correlations (SG,CAS,CFS): 6A5, 6B2

ITBS/TAP:

Demonstrate understanding of measurementconcepts and skills

ISAT:

Demonstrate understanding of measurementconcept and skills

Unit Focus/Foci

Fractions

Instructional Focus/Foci

Fractions of whole numbers

Materials

Six-Group Activity: Fractions and Mixed NumbersMath journals

Counters

Educational Strategies/Instructional Procedures

Warm-up Activity:

How many squares are there? (14)

Solution:

1 3 square: 12 2 squares: 4Single square: 9


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Lesson:

Divide students into pairs. Distribute 30 counters to each pair. Tell students that in this lesson they

will find the fraction of a number. Ask: How many cents there are in2

1of a dime? (5)

Have a student show this at the chalkboard by drawing ten circles and dividing them into 2 equalgroups. Tell students at their desks to show this using the counters. Inform students that another

way to find2

1of a dime would be to divide 10 by 2.

Example:05

10

102

Have them follow these procedures to solve the following problems.

1)4

1of 12 = ________ (3)

2)3

1of 15 = ________ (5)

3)6

1of 24 = ________ (4)

4) Sara had 30 stickers. She gave5

1of these away. How many did she give away? (6) How

many did she keep? (24)5)

10

1of an hour? (6 minutes)

6) Have students use the counters to show4

3of 8. (6)

Ask students if there is another way to find the answer. Have students divide 8 into 4 equal parts.

284 Next, take the 2 parts and multiply by 3. 2 3 = 6. So

4

3of 8 is 6. Write

3

2of 12.


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Tell students they are going to use the division and multiplication method to solve. Ask which

number is the numerator in the fraction3

2. (2) Ask which number is the denominator in the

fraction3

2. (3) Ask which number is going to be divided. (The whole number 12) Pose the

following question: By which number will the 12 be divided? (3 - the denominator in3

2) What is

12 3? (4) Which numbers will now be multiplied? (2 and 4) What is3

2of 12? (8) Have

students check the answer using the counters.

Write10

3of 20. Have students solve using the division or multiplication method and then check

using counters. Write5

3of 100. Ask which of the two methods would be quicker to solve this

problem. (The division and multiplication method)

Ten Statements

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

1. In the fraction5

3, the numerator is 3. (yes)

2. The first step in the division and multiplication method is to divide the whole number by the

denominator. (yes)

3. To find4

1of 12, 12 can be divided by 4. (yes)

4. The sum is the result of adding two or more numbers. (no)

5.2

1of 10 = 5. (yes)

6. To show3

1of 15 using the counters, the 15 counters would be divided into 3 groups. (yes)

7. A triangle is a polygon with 3 sides. (no)8. The division and multiplication method is quicker than the counter method for finding a

fraction of a large number. (yes)

9. The denominator in103 is 10. (yes)

10. Mode is the number that occurs most often in a set of numbers. (no)


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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 Fractions and

Mixed Numbers as a teacher directed activity.

Math Workshop

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

Integration with Core Subject(s)

LA: Understand explicit, factual information

Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: Six-Group Activity Lesson.

Technology:

Assessment

Student response during lesson Ten Statement Review

Homework

Give students 10 problems similar to those in lesson or from your text.

Teacher Notes


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Six-Group Activity

Fractions: Fractions and Mixed Numbers

Materials:

10 index cards (3 x 5)

1 black marker1 pencil

1 envelope ( 9 x 6 )

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

index cards and the pencil to write the answers of the back of the index cards.

2

2

6

2

8

2

10

2

16

8

24

8

20

10

18

6

24

6

24

3

Answers:

1 3 4 5 2

3 2 3 4 8

Have students write the whole number for each of the fractions. Show the students one card.Allow time for them to write the answer. Turn the card over and say: The answer is.

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


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Fractions and Mixed Numbers

This number line shows that4

14

= ,8

24

= , and12

34

= .

0 1 2 3 4

_______________________________________________________

0

4

1

4

2

4

3

4

4

4

5

4

6

4

7

4

8

4

9

410

411

412

413

414

4

15

416

4

On the number line, the fractions0

4,

1

4,

2

4, and

3

4are less than 1.

All of the other fractions on the number line are equal to or greater than 1. You can use division torewrite a fraction as a whole number.

Example:12

4=12 4 3

Read12

4as twelve divided by four or twelve fourths.

Example:35

7=35 7 5

Read35

7as thirty-five divided by seven or thirty-five sevenths.

Use these problems to work with students before doing the activity:32

4,

6

3,

3

3,

12

2, and

4

2.

Tell students that they are going to do an activity on fractions and mixed numbers. Lay a card onthe table and instruct the students to write the whole number for each fraction. After each answer is

written, reveal the answer on the back of the index card and say: The answer is Store thisactivity in the envelope.


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

ITBS/TAP:

Perform arithmetic operations using fractions

ISAT:

Unit Focus/Foci

Fractions


Equivalent fractions-part 1

Materials

Six-Group Activity: Reducing or Simplifying FractionsMath journalsCuisenaire rods or fraction tower cubes (optional)


Warm-up Activity:

1.21 of 14 = ______

43 of 12 = ______

2.3

1of 15 = ______

3

2of 9 = ______

3.6

1of 12 = ______

5

3of 15 = ______

4.4

1of 20 = ______

6

5of 30 = ______

5.5

1of 25 = ______

10

7of 50 = ______

Cuisenaire rods or fraction tower cubes can be used to show equivalents. Tell students thatfractions of the same amount can have different names.


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Lesson:

Draw the following two figures on the board.

Ask students how many equal parts there are in figure A. (2) Ask how many parts are shaded. (1)

Ask what fractional part of A is shaded. (2

1) Ask the same questions for figure B. (4, 2,

4

2) Ask

if the same amount is shaded in both figures. (yes)

Repeat this process with the following figures.

Display the following problem.

Kathy and Sue bought a cherry pie. They cut the pie into 6 equal pieces. Kathy ate 2 of the pieces.

Sue said, You ate6

2of the pie. Kathy said, No. I only ate

3

1of the pie. Who was right and

why? (They both were right because6

2is the same as

3

1). Illustrate for students as below.

Draw the following:

C D E F

and

G H

A B


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Tell students to look at both sets of circles. Ask: What fraction of the circles in G are shaded.

(4

2) Ask what fracion of circles in H are shaded. (

2

1) Tell students to note the dotted line

dividing the set of circles into halves. Write6

3and

2

1under figures G and H. Ask if the amounts

shaded in figures G and H are the same. (yes) Thus,6

3 and2

1 name the same amount.

Draw additional sets and ask questions about them.

Introduce the term equivalent fractions . Tell students that equivalent fractions are equal. To getequivalent fractions, draw figures as directed earlier. Another method would be to multiply thenumerator and denominator of a fraction by the same number (not 0). This method would be

quicker than the other method.

Example:

We can see by the figures that2

1 =4

2 . Add X2 above and below the equal sign in the example.

Show the multiplication process to class.

Draw:

Have students compute the equivalent fraction. (12

9) Review the multiplication with them.

2

1 =4

2

X2

2

1

= 4

2

X2

X3

4

3=

?

?

X3


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Have students compute the next problem in their journals:

X4

2

1=

?

?(

8

4)

X4

Ten Statements


1. To find equivalent fractions, multiply the numerator and denominator of a fraction by the samenumber. (yes)

2. A number that is divided by a divisor is called the dividend. (no)

3. Fractions of the same amount can have different names. (yes)4. There are 36 inches in a yard. (no)

5. 3/6 and 1/2 are different names for the same amount. (yes)6. A square is a quadrilateral with four equal sides and four equal angles. (no)

7. 1/2 and 4/8 are equivalent fractions. (yes)8. When finding an equivalent fraction, do not multiply the numerator and denominator by 0.

(yes)

9. Equivalent fractions are equal. (yes)10. Drawing figures can show that fractions are equivalent. (yes)

Free-Choice Lesson


Six-Group Activity

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

Simplifying Fractions as a teacher-directed activity.

Math Workshop



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LA: Understand explicit, factual informationSC: Analyze and interpret data

Connection(s)

Enrichment:

Fine Arts:

Home:


Technology:

Assessment

Student response during lesson, Ten Statement Review.

Homework

Have students draw figures showing3

2is equivalent to

6

4, and

4

3is equivalent to

16

9.

Teacher Notes


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Six-Group Activity

Fractions: Reducing or Simplifying Fractions

Materials:



1 envelope (9 x 6 )

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

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

612

728

39

945

2530

21

24

20

50

15

30

8

24

2

4

Answers:

1

2

1

4

1

3

1

5

5

6

7

8 2

5 1

2 1

3 1

2


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When you lay a card on the table, instruct the students to reduce or simplify the fraction using thestudy board if necessary. After the students complete a card, reveal the answer by turning it over

and saying: The answer is

Make a copy of this study board and use it when reteaching this lesson.

Reducing or Simplifying Fractions

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

the original fraction. When you have reduced or simplified a fraction as much as possible, thefraction is then in lowest terms.

Example 1. Reduce or simplify15

20.

Step 1. Find a number that divides evenly into the numerator and the denominator of the fraction.

5 divides evenly into both 15 and 20. 15 520 5

34

=

Step 2. Check to see if another number divides evenly into both numerator and denominator of thenewly-reduced fraction. Since no other number divides evenly into both 3 and 4, the fraction isreduced or simplified as far as is possible.

Example 2. Reduce48

64.

Step 1. Find a number that divides evenly into the numerator and the denominator of the fraction.

8 divides evenly into both 48 and 64.48 8

64 8

6

8

=

Step 2. Check to see if another number divides evenly into both numerator and denominator of the

newly-reduced fraction. 2 divides evenly into both 6 and 8.6 2

8 2

3

4

=

Step 3. Check to see if another number divides evenly into both the numerator and the denominator

of the newly-reduced fraction. In this case, the fraction is simplified or reduced as far as ispossible.


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Use these problems as practice problems:18

36,

5

10,

30

90, and

14

21.

Tell the students that they are going to do an activity like the one they just finished. Lay a card onthe table and have the students simplify or reduce the fraction. After they finish, reveal the answer

by turning the card over and saying: The answer is Store this activity in the envelope.


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ITBS/TAP:


ISAT:

Unit Focus/Foci

Fractions


Equivalent fractions Part 2

Materials

Six-Group Activity: Equivalent FractionsMath journalsFraction tower cubes or cuisenaire rods (optional)

4 (3x5) index cards per student


Warm-up Activity:

Distribute 4 index cards (3 5) to each student. Demonstrate and have students fold three of thecards into 4 equal pieces. Then, tell students to tear the cards along the folds, and number the cards0 through 9. There will be two extra pieces which will not be needed. On the 4th index card, have

students draw a fraction bar across the middle.

Review with students that the fraction bar separates

the numerator from the denominator. Review numerator and denominator.

Tell students to listen for a fraction and to use the number cards to make that fraction on top of the4th index card, with the fraction bar.

Review numerator and denominator.


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Lesson:

Review the definition ofequivalent fractions. Draw two identical rectangles on the chalkboard.Divide one rectangle into 2 equal parts, shading one part. Divide the 2nd rectangle into 8 equal

parts. Have a student shade in parts equal to the shaded area of the first rectangle. (4 parts)

Write3

2=

?

?on the chalkboard. Have students multiply the numerator and denominator by 5.

Ask what the equivalent fraction for3

2is. (

15

10) Do the same for

?

?

7

4= (

21

12)

Write6

?

3

1= . Ask what they would multiply 3 by to get 6. (2) Replace the ? in the circle with 2.

Ask students what they should multiply the 1 in

3

1by. (2) Draw a circle above the equal sign and

write X2 in it. Repeat this process with several more problems.

Write4

1. Ask students to name three equivalent fractions for

4

1. Ask them to explain how they

got their answers.

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 not heard in todays lesson.

1. The fraction bar separates the numerator from the denominator. (yes)

2. The denominator is the bottom part of the fraction. (yes)3. The decimal point separates the dollars from cents. (no)

4. Equivalent fractions are equal. (yes)5. To find equivalent fractions, the numerator and denominator of a fraction can be multiplied by

the same number. (yes)

6. Two yards are equal to six feet. (no)

7.2

1and

4

2are equivalent fractions. (yes)

8. Fractions of the same amount can have different names. (yes)

9. The numbers one add, are called addends. (no)10. The numerator is the top part of a fraction. (yes)

X5

X5

X?

X3

X3


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Free-Choice Lesson


Six-Group Activity

Have a group of six students, two from each ability level, completean activity on Equivalent

Fractions as a teacher-directed activity.

Math Workshop




Connection(s)

Enrichment:

Fine Arts:

Home:


Technology:

Assessment

Student responses during lesson Ten Statement Review

Homework

Given 2/5, have students find an equivalent fraction and explain how they arrived at the answer.

Teacher Notes


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Six-Group Activity

Fractions: Equivalent Fractions

Materials:


1 envelope (9 x 6 )10 Activity Cards

1 pencilScissorsGlue

Cut the activity cards out and glue one card to each index card for support. Use the pencil to write

the answer on the back of the card. Complete all cards in the same manner.

Answers:

1 2

4 8=

1 3

4 12=

3 6

4 8=

3 9

4 12=

1 4

2 8=

1 2

3 6=

3 6

5 10=

3 6

6 12=

1 2

2 4=

2 4

4 8=

Write a pair of equivalent fractions for each picture.

Make a copy of this study board to use when reteaching this activity.

Equivalent Fractions

Operations with fractions often involve finding equivalent fractions first. Fractions that areequivalent name the same value.


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Example:

Write three fractions that are equivalent to1

2.

1

2

2

4

3

6

4

8

The fractions1 2 3

, ,2 4 6

, and4

8are equivalentfractions.

You can also use multiplication to find equivalent fractions. To use multiplication, choose anumber and multiply the numerator and the denominator by that number.

Example:

Write three fractions that are equivalent to2

5.

2 2 4

5 2 10

=

2 3 6

5 3 15

=

2 10 20

5 10 50

=

The fractions4 6

,10 15

, and20

50are all equivalent to

2

5.

Use these models and problems to reteach this activity.

(1 4

2 8= ) (

1 2

4 8= )


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3

5(possible answers are

6 9 12 15 18, , , ,

10 15 20 25 30)

1

10(possible answers are

2 3 4 5 6, , , ,

20 30 40 50 60)

Tell the students that they are going to do an activity on finding equivalent fractions. Lay anactivity card on the table and ask the students to write a pair of equivalent fractions for each

picture. After displaying each card, reveal the answer by saying: The answer is


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ACTIVITY CARDS


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ACTIVITY CARDS


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ACTIVITY CARDS


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ACTIVITY CARDS


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ACTIVITY CARDS


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ACTIVITY CARDS


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ACTIVITY CARDS


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ACTIVITY CARDS


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ACTIVITY CARDS


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ACTIVITY CARDS


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Correlations (SG ,CAS,CFS): 6A4, 6A5, 6B2

ITBS/TAP:


ISAT:

Unit Focus/Foci

Fractions


Fractions in simplest form-part 1

Materials

Six-Group Activity: Raising to higher termsMath journalsSheet with 7 (2cm X 12cm) strips

ScissorsCrayons or colored pencils

1 envelope for each student


Warm-up Activity:

Have students complete the following:

1.124

1= 2.

63

1= 3.

105

2= 4.

168

1= 5.

284

1=

6.164

3= 7.

105

5= 8.

93

2= 9.

248

3= 10.

217

2=


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Lesson:

Distribute sheets with 7 (2m x 12cm) rectangles. Have students color one red, one blue, one green,one orange, one yellow, one purple and one light brown. Have students neatly cut each of the

rectangles. Tell students to write the number 1 on the orange strip. Have students take the green

strip, fold it in the middle and cut along the fold. Ask students what each part is called. (half)Have students lay the green pieces next to the orange one and note that

2

2= 1. Direct students to

write2

1on each green piece. Tell students to take the red strip and cut it in half like they did the

green one. Next, have them cut the 2 red strips in half. Ask how many red strips they have now.

(4) Ask what each piece is called. (4

1) Have students write

4

1on each of the pieces and lay them

next to the green pieces and note that 1 =2

2=

4

4. Tell students to take the blue piece and cut it in

half. Have students cut the 2 blue pieces in half. Then, have them cut the 4 pieces in half. Askstudents how many blue pieces they now have. (8) Ask what each piece is called. (

8

1) Have

students write8

1on each piece and lay them next to the red strips and note that

3

3

8

8

4

4

2

21 ==== . Show students how to divide the yellow strip into 3 equal pieces have

students cut the strips into thirds and ask what each piece is called. (1/3) Have students write 1/3on each piece, and lay them next to the blue pieces to show 1 = 2/2 = 4/4 = 8/8 = 3/3. Havestudents take the purple piece and cut it into thirds. Have students cut each into thirds in half. Ask

how many pieces they have. (6) Ask what each piece is called. ( 6

1

) Have students label the

pieces and lay them next to others and note6

6is equal to others.

Have students take the brown piece and cut it into thirds. Have students cut the thirds in half andthen cut the sixths in half. Ask how many pieces they have. (12) Ask what each piece is called.

(12

1) Have students label the pieces and lay them next to other pieces and note

12

12is equal to the

others.


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

Write2

1on the board. Using their fraction pieces, have students show

2

1and an equivalent

fraction. (12

6,

8

4,

6

3,

4

2) Have students find other equivalent fractions using their fraction strips.

Have students show12

9. Have them make an equivalent fraction using the fewest number of pieces

of one color. The pieces must be of one color. (4

3) Have students show

8

2and again find an

equivalent fraction using the fewest number of pieces. (4

1) Tell students that

4

3is

12

9in simplest

form and4

1is

8

2in simplest form.

Tell students that another way to name a fraction in simplest form is to divide the numerator anddenominator of a fraction by the same number. Tell students that there can be no remainder.

Examples:

2

1

10

5

3

1

9

3==

At this point, use fractions that can only be divided by 1 number. Do not use fractions such as12

8.

The numerator and deonminator can be divided by 2 and 4. These will be discussed in the nextlesson.

Write8

6. Ask students what number they could divide into the numerator and denominator. (2)

Write the simplest form. (4

3) Repeat this procedure with other fractions.

Have students store their fraction pieces in the envelopes. Collect them if desired.

3

3

5

5


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Ten Statements


1. The answer in subtraction is called the difference. (no)2.

12

9in simplest form is

4

3. (yes)

3. Equivalent fractions are equal. (yes)4. If one cut, thirds in half, one will get sixths. (yes)

5. There are 4 quarts in a gallon. (no)6. The line that separates the numerator from the denominator is called the fraction bar. (yes)

7.8

8

3

3= . (yes)

8. There are 180 minutes in 3 hours. (no)9. To simplify a fraction, divide the numerator and denominator by the same number. (yes)

10. To simplify12

9 , divide the numerator and denominator by 3. (yes)

Free-Choice Lesson


Six-Group Activity

Have a group of six students, two from each ability level, complete an activity on Raising to higherterms as a teacher-directed activity.

Math Workshop





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Connection(s)

Enrichment:

Fine Arts:

Home:


Technology:

Assessment

Student responses during lesson, Ten Statement Review

Homework

Have students complete these problems.

1. ______10

8= 2. ______

6

4= 3. ______

20

15=

4. ______12

6= 5. ______

18

12= 6. ______

25

20=

Teacher Notes

2

2

2

2

3

3

3

3

6

6

5

5


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Six-Group Activity

Fractions: Raising to Higher Terms

Materials:



1 envelope (9 x 6 )

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

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

15

810

23

46

36

2

7

2

10

2

12

5

6

4

5

Answers:

Answers may vary. When you look at the answers written, say okto each student if the answer iscorrect. If the answer is not correct, give the correct answer.

Lay a card on the table and give the instructions to raise the fraction to a higher term. Give thestudents time to write the answer before revealing the answer and saying: The answer is

Make a copy of this study board and use it when reteaching this lesson.

Raising Fractions to Higher Terms

Equivalent fractions can be made by raising them to higher terms. You raise fractions to higherterms by multiplying the numerator and the denominator by the same number.


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Note: You cannot use the number 1 to raise a fraction because the fraction remains the same.

Example 1. Raise1

2to a higher term.

Multiply the numerator and denominator by 3.

1 3

2 3

3

6

= ;1

2and

3

6are equivalent.

Example 2. Raise6

8to a higher term.

Multiply the numerator and denominator by 4.

6 4

8 4

24

32

= ;

6

8 and24

32 are equivalent.

Use these sample problems to show the students how to raise a fraction to a higher term. (2

9,

10

30,

8

10, and

3

7)

After you demonstrate how to solve the problems, tell the students that they are going to do an

activity that calls for them to raise fractions to higher terms. Lay a card on the table and give thestudents a chance to write the answer. After they have written the answer, turn the index card over,

reveal the answer and say: The answer is Store all materials from this activity in theenvelope.


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ITBS/TAP:


ISAT:

Unit Focus/Foci

Fractions


Fractions in simplest form-part 2

Materials

Six-Group Activity: Simplifying fractionsMath journals


Warm-up Activity:

Distribute envelopes with fraction pieces from the previous lesson.

Using their fraction pieces from the previous lesson, have students show the fraction12

8. Next,

have them show two equivalent fractions. One of those fractions must be made using the fewest

number of pieces. All pieces for each fraction must be one color.

Lesson:

Review fractions of whole numbers. Write the problems below on the chalkboard. Have students

copy and complete them in their math journals.

1.74 of 21 = ______ 2.

52 of 35 = ______


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Choose a couple of students to explain their solutions.

1) 21 7 = 3, 4 3 = 12, therefore7

4 of 21 = 12

2) 35 5 = 7, 7 2 = 14, therefore,5

2 of 35 = 14.)

Review equivalent fractions. Ask for definitions. Write the problems below on the chalkboard.

Have students copy and complete them in their journals.

3)1 8

4 ?= 4)

4 12

9 ?= 5)

36

?

6

5= 6)

40

?

5

2=

Have students explain their solutions.

Review the lesson from last class session, fractions in simplest form. Write the problems below on

the board. Have students copy and complete them in their math journals.

7)?

?

21

14= 8)

?

?

12

4=

Have students give their solutions. Write9

6on the chalkboard. Ask students to tell what number

both the numerator and denominator can be divided by. (3) Remind them that there cannot be a

remainder for either division portion. Ask students for the simplest form of9

6. (

3

2)

Write16

12 on the chalkboard. Ask students what number can be divided into both the numerator

and denominator without any remainder. Ask students if they realize that 2 answers are possible: 2and 4.

7

7

4


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Show =16

12and ask students for the solution. (

8

6) Write

8

6next to the equal sign.

12 6

16 8

=

Have students look at8

6. Ask if the 6 and 8 can be divided evenly by any number other than 1.

(yes) Ask what that number is. (2) Show: == 86

16

12? Have students complete this portion of

the problem. (4

3) Ask if the 3 and 4 can be divided evenly by any number other than 1. (no)

Therefore, this number is in simplest form. Write =16

12on the chalkboard. Ask students for the

solution. (4

3) Ask students how the solutions were different. (One had 2 steps and the other 1).

Ask which solution was quicker. (The second one with one step) Ask why it was quicker. (Thedivision was done with a larger number 4.) Tell students they should always try to divide using the

largest number possible. This will help them find their solution quicker. Write 18

12

. Repeat the

same process. Remind students that they can divide the numerator by 2, 3 and 6. Remind students

that a fraction is in simplest form when the numerator and denominator can only be evenly dividedby 1. Some students will grasp finding the greatest common factor concept before others. Stress tostudents that using more than one step to find the simplest form is alright. Write the problems

below on the chalkboard. Have students copy problems in their math journals and find the simplestform for each.

1) =12

82) =

20

183) =

24

204) =

30

24

Have students explain their solutions. If they used more than one step, ask how they could havesolved the problems quicker. (By using larger divisors) Remind students again that it is alright touse more than one step, but they should look for the largest common divisor possible.

Tell students that when they find the simplest form of a fraction that it is equivalent to the original

fraction. Therefore to find equivalent fractions, one can multiply or divide the numerator anddenominator by the same number other than 1 or zero.

2

2

2

2

4

4


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Ten Statements


1. Equivalent fractions are equal. (yes)2. To find

5

4of 10, one divides 10 by 5 and multiplies 2 4. (yes)

3. A fraction is in simplest form when the numerator and denominator can be divided evenly byonly 1. (yes)

4. Taking more than 1 step to find the simplest form of a fraction is alright. (yes)5. There are 60 seconds in a minute. (no)6. To find equivalent fractions, one can multiply or divide the numerator and denominator by the

same number. (yes)

7.4

5is an improper fraction. (no)

8. To find the simplest form of18

6 one divides the numerator and denominator by 6. (yes)

9. When the mean of a group of numbers is found, the average is found. (no)

10. If one divides the numerator and denominator of the fraction12

10by 2, one gets get

6

5. (yes)

Free-Choice Lesson


Six-Group Activity

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

Fractions as a teacher-directed activity.

Math Workshop





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Connection(s)

Enrichment:

Fine Arts:

Home:


Technology:

Assessment

Students response during Ten Statement Review

Homework

Assign students to study notes and previous homework assignments for the test. Have students

explain how to find the simplest form of20

16.

Teacher Notes


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Six-Group Activity

Fractions: Simplifying Fractions

Materials:


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 smaller numbers. Look at the followingexamples 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 anothernumber. 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 whether another numbergoes evenly into both the numerator and denominator of the fraction. In this case, the fraction issimplified 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 for simplifying 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. Begin byplacing 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 answer is


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Correlations (SG,CAS,CFS): 6A4, 5; 6B2

ITBS/TAP:



ISAT:


Unit Focus/Foci

Fractions


Formal Assessment

Materials

Prepared test


Distribute tests to students.


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Test

1) Shade in10

7of this figure.

2) Shade in4

3of this figure.

3) Shade in figure B to make it equivalent to figure A.

Write 2 equivalent fractions for each of the following:

4)2

1, _______, _______ 5)

5

2, _______, _______

6)4

3, _______, _______ 7) 1, _______, _______

Complete the equivalent fractions below.

8)93

2= 9)

164

4=

10)5

6 36= 11)

2412

7=

A. B


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Solve:

12)5

3of 35 = ______ 13)

9

1of 18 = _______

14)85 of 24 = _______ 15)

72 of 28 = _______

Write these fractions in simplest form:

16)21

14= _______ 17)

16

12= _______

18)10

8= _______ 19)

30

25= _______

Using the word box, name the parts of this fraction. Write the name on the line next to the letter.

9

6

20) A= _________________________________

21) B = _________________________________

22) C= __________________________________

Solve:

23) Tina had 20 Beanie Babies. She put4

1of them in her backpack. How many did she place in

her backpack?

24) Cory and Sam had 24 cars. If each of them took half, how many cars did they each get?

25) Kathy wants to pick4

3of the flowers in her garden. If there are 36 flowers in her garden how

many flowers should she pick?

Word Box

Dividend Fraction barNumerator Simplest form

Fraction Number

Solution Denominator

A

BC


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Ten Statements

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

lesson.

No Ten Statements today.

Free Choice Lesson

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

Six-Group Activity

No Six-Group Activity today.

Math Workshop

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



SC: Analyze and interpret data

SS: Select appropriate information for intended purpose

Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation:

Technology:


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Assessment

Formal

Homework

Teacher Notes

Answer key to test:

1) Students may shade any of the boxes.

2) Students may shade any 6 of the boxes.

3) Students may shade in any 6 of the boxes.

Possible answers (4 through 7)

4)8

4,

4

25)

15

6,

10

4

6)112

9,

8

67)

3

3,

2

2

8) 6 9) 16

10) 30 11) 14

12) 21 13) 2

14) 15 15) 8

16)3

217)

4

3

18)5

419)

6

5

20) Numerator 21) Fraction bar 22) Denominator

23) 5 24) 12 25) 27

structured curriculum lesson plan day: 098 subject: mathematics grade level:

Documents