structured curriculum lesson plan day: 117-118 subject: mathematics grade level:

8/14/2019 Structured Curriculum Lesson Plan Day: 117-118 Subject: Mathematics Grade Level:

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STRUCTURED CURRICULUM LESSON PLAN

Day: 117-118 Subject: Mathematics Grade Level: 4

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

ITBS/TAP:

Perform computations involving fractions

ISAT:

Perform computations involving fractions

Unit Focus/Foci

Fractions

Instructional Focus/Foci

Multiplying fractions, whole numbers and mixed numbers

Materials

Six-Group Activity: Multiplying short cutMath journals

Educational Strategies/Instructional Procedures

Warm-up Activity:

Write these problems and instructions on the chalkboard.

Rewrite the following whole numbers and mixed numbers as improper fractions.

1.

48

=

2.

31

5

3.

42

3

4.

92

=

5.

63

4

Rewrite the following improper fractions as whole numbers and mixed numbers.

6.

204

7.

185

8.

227

9.

306

10.

3310


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Review the answers with students.

1.32

82.

16

53.

14

34.

18

25.

27

4

6. 5 7.3

35

8.1

37

9. 5 10.3

310

Lesson:

Instruct students to take note in their math journals.

Multiplying fractions

Write1

2

3

6 on the chalkboard.

Step 1: Multiply the numerators. Ask students what the product is. (3)

1

2

3

6

3 =

Step 2: Multiply the denominators. Ask students what the product is. (12)

1

2

3

6

3

12 =

Step 3: Simplify the answer. Divide the numerator and denominator evenly by a number other

than 1.

12

36

312

14

= =

Repeat this process for2

5

1

4 and

3

4

4

6 .

1

10

1

2,


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Multiply fractions and whole numbers

Write 41

2 on the chalkboard.

Step 1: Have students rewrite the problem, changing the whole number to an improper fraction.Review the procedure for this.

41

2

4

1

1

2 =

Step 2: Multiply the numerators.

41

2

4

1

1

2

4 = =

Step 3: Multiply the denominators

4 12

41

12

42 = =

Step 4: Simplify the answer.

41

2

4

1

1

2

4

22 = = =

Repeat this process for4

52 and

2

36 . 1

3

54

Multiplying fractions and Mixed Numbers

Write1 1

210 2

on the board.

Step 1: Instruct students to rewrite the problem changing the mixed number to an improperfraction. Review the procedure for this

21

10

1

2

21

10

1

2 =

Step 2: Multiply the numerators.

2 25

12

125

12

12 = =

Step 3: Multiply the denominators.

22

5

1

2

12

5

1

2

12

10 = =


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Step 4: Simplify the answer.

12 2 1 12 6 11 1 or 1

10 10 5 10 5 5= = = =

Repeat this process for 12

9

2

3and 4

1

6

1

5. (

22

27

5

6,)

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. When multiplying fractions, multiply the denominators. (yes)2. Before multiplying a fraction and a mixed number, change the mixed number to an improper

fraction. (yes)

3. A square is a rectangle with four congruent sides. (no)4. When multiplying fractions, multiply the numerators. (yes)

5. The last step in multiplying fractions is to simplify the answer. (yes)6. The answer in multiplication is called the product. (yes)7. To simplify an answer, divide the numerator and denominator evenly by a number other than

1. (yes)8. Before multiplying a whole number and a fraction, change the whole number to an improper

fraction. (yes)9. An outcome is a possible result in a probability experiment. (no)

10. An obtuse angle is one with a measure greater than 90o but less than 180o . (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 students, two from each ability level, complete an activity on Multiplying short

cut 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


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Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: Six-Group Activity Lesson.

Technology:

Assessment

Student response during lessonTen Statement Review

Homework

Assign students to make up the following: problems for multiplying fractions times fractions;problems for multiplying a fraction times a whole number and (2) problems for multiplying amixed number times a fraction. Tell them to solve each problem.

Teacher Notes


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Six-Group Activity

Fractions: Multiplying Shortcut

Materials:

15 index cards (5 x 7)

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 cards and use the pencil to write the answers on the back of the cards. Do not write the finalanswer; just write the shortcut steps.

2

6

3

4

7

8

4

5

1

5

5

6

12

24

12

13

4

6

3

8

9

10

5

6

2

7

7

8

3

9

3

4

5

10

2

4

3

8

2

6

3

6

1

3

2

12

3

6

2

6

1

4

4

11

11

12

5

15

5

6

Answers1

2

2

6

//

//3

4

1

2

7

82

/

/45

1

1

51/

/56

1

12

242

12

13

1

1

2

4

6

//

//3

8

1

2

3

2

9

10

//

//

//

5

6

1

2

1

1

2

7

//

//7

8

1

4

3

93 / /34

1

5

105 /24

1

1

4

3

8

//

//2

6

1

2

13

6

/

/1

31

1

4

12

12

/

//3

63

12

6

/

/1

42

1

1

4

11

11

12

1

3

5

153

5

6

1

When you lay an index card on the table, explain that the students are going to look at theproblem to see if they can use a shortcut to multiply the fractions. If so, they are going tocomplete the shortcut without giving the solution.

Say: Canceling is a shortcut in multiplication of fractions. It is just like reducing or simplifying.

It means dividing the numerator of one fraction and the denominator of another fraction by anumber that divides evenly into both before actually multiplying. You dont have to cancel to get

the right answer, but it does make it easier to multiply the problem.


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Example:7

22

11

14

Step 1: Cancel 7 and 14 by 7.17

22

/

11

142

7 7 1 = and 14 7 = 2 .Cross out the 7 and 14.

Step 2. Cancel 11 and 22 by 11.1

2

7

22

/

11

14

1

2

11 11 1 11 = and 22 = 2 .Cross out the 11 and 22.

Step 3. Multiply across the new numbers.

1 1 1 2 == and 2 = 4.

The answer is 14

.

Copy this studyboard and use it to reteach this lesson.

Shortcut to Multiplying Fractions

Step 1: Look at the problem as if you were looking at the letter X. If the numerator of the first

fraction and the denominator of the second fraction can divide into one or the other evenly, crossthem out.

Example:1

3

3

5

5

9

/ /

(9 divided by 3 = 3)

Cross both 3 and 9 out and put a 3 under the 9 because 3 divides 9 three times. Cross out the 3and put a 1 above it because 3 divides itself one time.

Step 2: Look at the denominator of the first fraction and the numerator of the second fraction.Ask yourself, can they divide one or the other evenly? If the answer is yes, cross out both

numbers and divide.


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Example:1 /

/

//

3

5

5

91

1

3

Draw a line through both numbers and divide. 5 divides 5 one time. Now

you are ready to multiply.1

1

1

3

3

5

5

9

//

//

=1

3. The answer is

1

3.

Explain to the students that taking a shortcut in multiplication of fractions saves them the step of

reducing at the end. Example:3

5

5

9=

15

45

15

45must be reduced or simplified to

1

3.

Review the steps with the group and write a sample problem for them to solve together. Tell the

students you want them to risk writing the answers to an activity called Shortcuts. Explain thatthe rules are the same as those on the study board. Lay one card on a flat surface and give the

students one to two minutes to risk writing the steps to the shortcut, not the answer. When thetime is up, turn the card over revealing the answer, and say: The answer is Give thestudents two or three seconds to check their answers.


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Correlations (SG,CAS,CFS): 6A5

ITBS/TAP:

Perform arithmetic operations involvingfractions

ISAT:


Unit Focus/Foci

Fractions


Focus decimal equivalent

Materials

Six-Group Activity: Place ValueHomework worksheet

Math journals


Warm-up Activity:

Write these problems and instructions on the chalkboard.

Tell students to complete the following equivalent fractions in their math journals.

1.4

10

40= 2.

8

10 100= 3.

2

10 100=

4.450

100

45= 5.

30

100 10= 6.

70

100

7=

Review the answers in Teacher Notes with students.


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Lesson:

Instruct students to take note in their math journals. Write all examples on the chalkboard.Fractions and decimals can name the same number in different ways. Tell students they can

write six tenths as a fraction or a decimal. Remind students that zero is written before the

decimal point to show that the amount is less than 1 whole.fraction =

6

100 6. decimal

Therefore, six over ten is equivalent to zero point six.

Read the following numbers to students and have students write them as a fraction and a

decimal: four tenths and thirty-four hundredths.4

10,0.4 and

34

100,0.34.

Call on several students to go to the chalkboard. Read a number to each one of them. They must

write the number in fraction or decimal form. Call on several more students to write the other

form of each of those numbers.

Tell students that they can write fractions greater than 1 as mixed number or as a decimal.Remind students that a mixed number is greater than 1.

mixed number = 16

1016. decimal

Read the numbers below to students at the chalkboard and have them write them as mixed

numbers or as decimals. Call on other students to go to the board and write these same numbersin the other form.

a) nine and seven tenthsb) ten and eighty-four hundreds

c) and two and seven hundredths

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 todayslesson.

1. To estimate is to find a number that is close to the exact answer. (no)

2. One can write two and seventeen hundredths as a mixed number or as a decimal. (yes)3. Fractions and decimals can name the same number in different ways. (yes)4. Six over ten is equivalent to zero point six. (yes)

5. Mixed numbers are greater than 1 whole. (yes)


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6. An arc is a part of a circle or curve between two points. (no)7. One can write eight tenths as a fraction or a decimal. (yes)

8. Zero point fifty-six is equivalent to fifty-six over one hundred. (yes)9. A degree is a unit used to measure angles. (no)

10. Write a zero before the decimal point to show the amount is less than 1 whole. (yes)

Free-Choice Lesson


Six-Group Activity

Have a group of students, two from each ability level, complete an activity on Place Value as ateacher-directed activity.

Math Workshop



LA: Understand explicit, factual information

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 cartoonsSequence information, especially using timelines

Select appropriate information for intended purpose

Connection(s)

Enrichment:

Fine Arts:

Home:


Technology:


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Assessment

Students response during lesson and Ten Statement review.

Homework

Write the following fractions and mixed numbers as decimals.

1.

3

10= _____

2.

375

100= ____

3.

9

100= ____

4.

19

10= _____

5.

23

100= ____

Write the following decimals as fractions and mixed numbers.

6.7 57. = _____

7.0.2=_____

8.8.7=_____

9.0.05=_____

10.0.89=_____

Teacher Notes

Key for the Warm-up Activity

1.

100

2.

80

3.

20

4.10

5.3

6.10


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Six-Group Activity

Decimals: Place Value

Materials:

1 picture of a number line

10 index cards (3 x 5)1 pencil

1 envelope (9 x 6 )


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

0.25 0.12 0.31 0.13 0.19

0.29 0.36 0.38 0.40 0.17

Answers:

D A F B C

E G K H J

Match each number with a point on the number line.

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


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Place Value

In our base-ten system, each place is 10 times greater than the value of the place to its right.

Conversely each place is also1

10of the value of the place to its left. You can extend a place-

value chart to include place values less than 1.

Thousands Hundreds Tens Ones Tenths Hundredths Thousandths

4 5 7 2 . 6 9 4

A decimal point separates the ones and tenths places.

You can write this number in different ways:

Standard Form: 4,572.694

Expanded Form: 4,000 + 500 + 70 + 2 + 0.6 + 0.09 + 0.004

Word Form: Four thousand, five hundred seventy-two and six hundred ninety-four thousandths

Short Word Form: 4 thousand, 5 hundred, 72 and 694 thousandths

Decimals that name the same amount are equivalent decimals.

0.5 = 5 tenths

.050 = 50 hundredths

.005 = 500 thousandths

Display the number line and tell the students that when you show them a card, you want them toidentify that point on the number line. After allowing students time to write the answer, turn thecard over and say: The answer is Store this activity in the envelope.


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0

.1

A

B

J

C

D

E

F

G

H

0.2

0.3

0.40

K

NUMBERLINE


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Correlations (SG,CAS,CFS): 6A3, 6A4, 6A5; 6B1

ITBS/TAP:

Perform operations involving fractions

ISAT:

Perform operations involving fractions

Unit Focus/Foci

Fractions


Comparing fractions and decimals

Materials

Six-Group Activity: Comparing and ordering decimals and fractionsMath journals


Warm-up Activity:

Write the problems and instructions on the chalkboard.

Write the fraction or mixed number and the decimal equivalent for each of the following:

1. six and seven hundredths2. eighteen hundredths

3. four tenths4. ninety-four and one hundredth

5. twelve and three tenths

Review the answers with students.

(Answers are in the Teacher Notes.)

Lesson:

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


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Comparing fractions and decimals.

Write9

1000.6 on the chalkboard. Ask students how they can compare these two amounts.

(Change the fraction to a decimal or the decimal to a fraction.) Remind students that both ways

are acceptable. Ask what the comparison symbol is called. (Chevron)

Example A: Change the fraction to a decimal. Have students look at9

100and ask what the

decimal equivalent is (0.09). Write=0.09 next to9

100.

Review steps for comparing decimals.

Compare the whole numbers first

Compare the places to the right of the decimal point one at a time

Write a comparison symbol (, or =) between the numbers.

9

100=0.009


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An equivalent fraction can be written for6

10having a denominator of 100.

Write =60

100next to the

6

10in the problem.

Compare the fractions. ( 9 60

100 100< ) Therefore 9

100< 0.6.

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 todayslesson.

No Ten Statements today.

Free-Choice Lesson


Six-Group Activity

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

ordering fractions as a teacher-directed activity.

Math Workshop



LA: Understand explicit, factual informationUnderstand the meaning of words in context

SC: Apply scientific method to solve problems

Analyze 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:

Remediation:

Technology:

Assessment

Students response during lesson and Ten Statements review.

Homework

1) Compare by changing the decimal to a fraction.

30.6

5d

3____

5d

2) Compare by changing the fraction to a decimal.

30.7

20d

___ 0.7d

Teacher Notes


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Six-Group Activity

Fractions: Comparing and Ordering Decimals and Fractions

Materials:

10 index cards (3 x 7)

1 envelope (9 x 6 )1 black marker

1 pencil


the index cards. Use the pencil to write the answer on the back of each card.

17

100

=83

100

=30

15

100

=52

1

100

=73

2

1,000

=

0.64= 0.90= 3.45= 0.29= 4.003=

Answers:

0.17 0.83 15.30 1.52 2.073

64

100

9

10

453

100

29

100

34

1,000

Write each fraction or mixed number as a decimal. Write each decimal as a fraction or as amixed number.

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


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Comparing and Ordering Decimals and Fractions

You can write fractions and mixed numbers as decimals.

40.4

10

= 4 tenths5

21 21.05

100

= 21 and 5 hundredths

It is often helpful to know decimal equivalents for common fractions.

50.5

10=

1

2Simplest form

250.25

100=

1

4

60.6

10=

3

5

To compare a fraction and a decimal, first write both in the same form.

Step 1. Compare1

2and 0.7.

1 5

2 10= 0.5

0.5 < 0.7

10.7

2<

Compare3

100and 0.03.

30.03

100=

Compare7

410

and 3.2.

4 > 3 so7

4 3.210

>

Use these problems to reteach this activity.

191,000

14291,000

7.050 0.218

Answers:

0.019 9.142 75

100

218

1,000


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Tell the students that they are going to do an activity that calls for them to write fractions as

decimals and decimals as fractions. Lay a card on the table and allow students time to solve theproblem before revealing the answer by turning the card over and saying: The answer is


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Correlations (SG,CAS,CFS): 6A3, 6A4, 6A5, 6B1

ITBS/TAP:


ISAT:


Unit Focus/Foci

Fractions


Mixed practice

Materials

Math journals


Warm-up Activity:

Using the digits 1, 2, 4 and 8, create two fractions whose sum must equal 1.

48

12

1+ =

Lesson:

Write the problems below on the chalkboard or duplicate for the class. Allow students time to

complete them. Call on various students to explain how they solved them. This would also be agood time to help students having any difficulties.

Multiply. Write product in simplest form.

1.1

3

5

7

5

21 =

2.2

7

7

8

1

4 =

3.

61

51

1

5 =


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4. ( )3

510 6 = 5.

1 1 13 1

3 3 9

=

6.2

53

1

21

2

5 =

Rewrite the following numbers as decimals and fractions in simplest form.

4. nine-tenths

10

9and9.0

5. two and twenty-five hundredths. 2.25 and 21

4

Compare. Use , or =.

Solve by changing the fractions to decimals.

7. ( )35

0.27

100

d 8. ( )3

0.75

5

d

Solve by changing the decimals to fractions.

9.

( )2

0.510

d

10.

( )1

0.24

d

Solve. Show your work.

11. Rene practices the piano for1

2

an hour each day. Bill practices the piano for 0.6 hour each

day. Who practices the longer period of time? (Bill)

12. Katie needs 0.6 cup nuts and10

7cup raisins for her cookies. Which is the least amount?

(0.6 cup of nuts)


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Ten Statements

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

lesson.

1. Before multiplying a whole number and a fraction, change the whole number to an improper

fraction. (yes)2. When comparing a decimal and a fraction, change the fraction to a decimal or the decimal to

a fraction. (yes)3. Area is the number of square units needed to cover a region or figure. (no)4. A composite number has more than two factors. (no)

5. An answer is in simplest form if the numerator and denominator can only be evenly dividedby 1. (yes)

6. When multiplying fractions, multiply the numerators and then multiply the denominators.(yes)

7. One can name the same number as a fraction and a decimal. (yes)8. Range is the difference between the greatest and least numbers in a group of numbers. (no)9. Five tenths can be written as five over ten or zero point five. (yes)

10. A chevron is a comparison symbol. (yes)

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




SC: Apply scientific method to solve problems

Analyze and interpret data




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Connection(s)

Enrichment:

Fine Arts:

Home:


Technology:

Assessment

Student response during lessonTen Statement review

Homework

Remind students to study notes and assignments for test.Compare 5 multiplication problems. Then show the complete solutions.

Teacher Notes


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Day: 125 Subject: Mathematics Grade Level: 4

Correlations (SG,CAS,CFS): 6A3, 6A4, 6A5, 6B1

ITBS/TAP:


ISAT:


Unit Focus/Foci

Fractions


Formal Assessment

Materials


Prepare the following test for students.


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Test

Write the following numbers as decimals.

1. sixty-seven hundredths _________________

2. 37

10_______________

Write the following numbers as fractions.

3. two and thirteen hundredths _______________

4. 0.9 _______________

Compare. Use , or =.

Solve by changing the fractions to decimals.

5. 0.55 7

106. 3

100.4

Solve by changing the decimals to fractions.

7. 0.88

108.

3

200.65

Multiply. Write the product in simplest form.

9. =2

1

4

310. =

9

37


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11. =9

5

5

312. = 4

8

3

13.10

3 =

3

214. =

5

3

3

13

15. =10

1

2

12 16. =

7

2

10

7

17. =4

115

Solve. Show your work.

18. Sam has2

3

pound of apples and Sue had5

6

pound of apples. Who had the most apples?

19. Kevin has3

4of a pie. Tony had 0.9 of the pie. Who had the most pie?

20. Kim had 1.4 bag of chips. Debbie had 1 12

bag of chips. Who had the least amount of chips?


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Ten Statements

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

lesson.

No Ten Statement 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




SC: Apply scientific method to solve problemsAnalyze and interpret data



Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation:

Technology:


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Assessment

Homework

Teacher Notes

Answer Key

1. 0.67 2. 3.7

3. 213

1004.

9

10

5. < 6.

structured curriculum lesson plan day: 117-118 subject: mathematics grade level:

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