Structured Curriculum Lesson Plan Day: 066 Subject: Mathematics Grade Level:

8/14/2019 Structured Curriculum Lesson Plan Day: 066 Subject: Mathematics Grade Level:

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STRUCTURED CURRICULUM LESSON PLAN

Day: 066 Subject: Mathematics Grade Level: 4

Correlations (SG,CAS,CFS): 6C1,6C3

ITBS/TAP:Perform arithmetic operations

ISAT:Perform computations

Unit Focus/Foci

Long Division

Instructional Focus/Foci

Dividing by a 1-digit divisor

Materials

Six-Group Activity: Division (using multiplication to check the answer)

Educational Strategies/Instructional Procedures

Warm-up Activity:

Reproduce this paper and cut it into strips of 5 problems per strip. This is a timed activity it

should only take 5 minutes per strip.

1. 24 8= 2. 27 9= 3. 30 6= 4. 28 4= 5. 15 3=

6. 48 8= 7. 36 9= 8. 72 8= 9. 35 7= 10. 64 8=

11. 5 30 12. 7 42 13. 5 55 14. 9 271 15. 7 21

Lesson:

Teacher will review vocabulary. Write the words on the chalkboard and have the students copythem in their math notebook.


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1. The dividend is a number that is divided by the divisor.

2. The divisor is the number the dividend is divided by.3. The quotient is the answer (other than the remainder) to a division problem.

4. The remainder is a number smaller than the divisor that is left after the dividend has beendivided by the divisor as many times as possible.

Write this example on the chalkboard. You can make each part a different color.

quotient5 R 1remainder

divisor4 21 dividend

201

Write 6 2=____. X X X X X XHave students copy this in their journals. Ask students how they could group the Xs, so that

they show 6 2. Student response should be to make 3 groups of two. Have a student go to the

board and circle the groups.

XX XX XX

Repeat this process with 24 6. ( xxxxxx xxxxxx xxxxxx xxxxxx )

Next write 327 5. Ask students if drawing X's and circling the groups of 3 in this problem

could be done quickly. (no)

Write 12 3=____. Tell the students they can subtract 3 from 12 until there is nothing left. 12-

3=9, 9-3=6, 6-3=3, 3-3=0

Ask how many times 3 was subtracted from the 12. (4) therefore 12 3=4.

Have students look at 327 3 again. Ask if repeated subtracting 3 from 327 could be done

quickly. (no)

Tell students that division is a faster way to subtract.

Write 32 6=___. Tell students that this is the equation form. Write 6 32 . Tell students this

is the working form and that this is how they will set up future problems.

Example: 6 32


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Step 1: Divide. How many times can 32 be divided by 6? (5) Ask students where they should

write the 5. (above the 2 in the dividend) Ask why the 5 should not go above the 3 in thedividend. (3 is not being divided by 6). Write the 5 in the quotient. 5

6 32

Step 2: Multiply. Ask students or the product of 6x5 (30). Ask students where to write theproduct of 6x5 (under the 32). Write the 30 under the 32.

5

6 32

30

Step 3: Subtract. Ask students for the difference of 32 and 30 (32-30=2). Write the difference.5

6 32

-302

Check the difference to make sure it is smaller than the divisor. If it is not, it means that the digitwritten in the quotient is too small.

Step 4: Remainder. Remember the remainder must be smaller than the divisor write the

remainder next to the quotient.5 R2

6 32

-30

2

Write 7 43 and 8 48 . Have students copy and compute in their math notebooks. Assign

students to come to the board and explain how they solved these problems. (6R1 and 6).

Tell students that multiplication is the opposite of division. Therefore they can check theirproblems by multiplying the quotient by the divisor and then adding the remainder if there isone.

6R1

Show 7 43

-42

1


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Ask: 1) What is the quotient? (6) Write 6

2) What is the divisor? (7) Write x7.

6 7

3) What is the product of 6 x 7? (42)6

7

42

4) What is the remainder? (1) Write +1.6

7

42

+1

5) What is the sum of 42 + 1? (43)

6 7

42+ 143

6) What is the dividend? (43)

7) Is the answer to question check the same as the dividend? (yes)

Have students check 8 48 . Then your answer is correct.

Write 5 105 . Ask students what they will do.

Step #1: Divide. Ask students:

1) If they can divide 1 by 5. (no)2) If they can divide 10 by 5. (yes)3) What 10 5 is. (2)

4) Where they will write the 2. (above the 2) Show this. 2

5 105

Ask students what they will do in step 2. (multiply)


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Step #2: Multiply. Ask students:

1. What they will multiply (2x5).

2. What the product of 2x5 is. (10)3. Where they will write the product. (under the 12 in the dividend). Show this.

Show this. 2

5 105

10Ask students what they will do in Step #3. (subtract)

Step #3: Subtract. Ask students.

1. What they will subtract. (10-10).2. What is the difference of 10-10. (0)

Show this: 25 105

-10

0

Tell students that because there is another digit (the 5) in the dividend that this problem will haveanother step.

Step #4: Bring down the next number in the dividend. Show the 5 being brought straight downon the problem.

2

5 105

-10

5

Tell students that they will repeat Steps 1 to 3. Step #1: Divide. Ask students.

1. What they think they should divide. (5 5)

2. What 5 5 is equal to. (1)3. Where they should write the 1. (above the 5 in the dividend.


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Show this. 21

5 105

-10_

5

Step #2: Multiply. Ask students.

1. What to multiply. (1x5)

2. For the product of 5x1 (5)

Show this: 21

5 105

-10

5-5

0

Ask students:

1. If theres another number in the dividend to bring down? (no)2. If there is a remainder. (no)

Have students to check the problem in their math notebook.

21x 5105

Have a student come to the chalkboard and show the checked answers.

Tell students that when they have to bring down a number in the dividend and repeat steps 1 to 3,that they are doing long division.


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Write 4 94 . Have students copy and compute in their math notebooks. Tell them to also check

the problem.

23R2 23

4 94 x 4

-8 92

14 + 2-12 94

2

Have a student complete the problem at the chalkboard. Write , ,-, , R on the chalkboard.

Tell students these symbols show the order of the steps used in long division. The R means

write the remainder up next to the quotient.

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) 7 is a prime number. (no)2) There are 60 minutes in an hour. (no)3) The divisor is the number the dividend is divided by. (yes)4) To check a division problem you multiply the quotient times the divisor. (yes)5) The number being divided is called the dividend. (yes)6) Division is a faster way to subtract. (yes)7) The opposite of multiplication is division. (yes)8) The quotient is the answer to a division problem. (yes)9) A rectangle is a four-sided figure with equal opposite sides. (no)10)The remainder must be smaller then the divisor.Free Choice Lesson

Have the 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 teacher directed activitysheet Dividing (greater than 10)


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Math Workshop

Have the students go into theMath Workshop after completing their Free Choice Lesson.

Integration with Core Subject(s)

LA: Understanding explicit, factual informationUnderstanding 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

Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: See attached Six Group Activity Sheet Dividing: Greater than 10

Technology:

Assessment

Informal: Student response during lesson and Ten Statements. Quiz, next class session.

Homework

Have students divide and check the following problems.

1. 5 45 2. 8 328 3. 4 271 4. 6 518 5. 3 272

2. 4 253 7. 5 79 8. 4 718

Teacher Notes


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Unit Focus/Foci

Long Division


Dividing larger numbers by 1-digit divisors and dividing numbers with zeros

Materials

Six-Group Activity: Division (reading division problems)


Warm-up Activity:

Have the students write the steps for long division in their math notebooks. Also have them

explain how to check a division problem.

Lesson:

Review the last lesson. Write the steps and vocabulary on the chalkboard.. 1.Vocabulary:

dividing, divisor, quotient, remainder, difference, long division. 2. Review steps for short

and long division ( , , ,,R-). 3) Division is the opposite of multiplication write 6 1375 .


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Write 6 200 . Have students compute and check the problem in their math notebook while a

student solves the problem at the chalkboard. 3334 R2 1

6 20006 33

-18 x 6

20 198-18 + 2

20 200

Write: 1) 2 300 2) 8 350 3) 7 480

Assign students to compute and check the problems on the chalkboard while remaining students

work them in their journals.

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 todayslesson.

1) R with an upward arrow is the symbol for writing the remainder next to the quotient. (yes)2) Division is the opposite of multiplication.(yes)3) Numbers are divisible by 3 if the sum of there digits is divisible by 3. (no)4) The number being divided is called dividend.(yes)5) The steps for division are divide, multiply, and subtract. (yes)6) The distance around a circle is called the circumference.(no)7) After the first digit is written in the quotient, there must be digits above the remaining digits

in the dividend.(yes)8) To check a division problem you will multiply the quotient by the divisor. (yes)9) The prime factorization of 9 is 3x3. (no)10)When doing long division, you will have to divide 2 or more times.(yes)Free Choice Lesson


Six Group Activity

Have a group of six students, two from each ability level, complete teacher directed activitysheet Division (reading division problems)


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Math Workshop







Connection(s)Enrichment:

Fine Arts:

Home:

Remediation: See attached Six Group Activity Sheet Division: Reading division problems

Technology:

Assessment

Homework

1. 26724 2. 67529 3. 5101104. Explain in writing how to solve this problem: 6935 .

Teacher Notes


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Six-Group Activity

Division (Reading division problems)

Materials:

10 index cards (5 x 7)1 black marker1 pencil

1 envelope (9 x 6 )

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

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

How many groups of 2 in 6? (3) How many groups of 5 in 15? (3)How many groups of 2 in 12? (6) How many groups of 5 in 10? (2)How many groups of 2 in 8? (4) How many groups of 3 in 18? (6)

How many groups of 5 in 10? (2) How many groups of 6 in 12? (2)How many groups of 5 in 20? (4) How many groups of 4 in 12? (3)

Copy this study board to use in reteaching this lesson.

Reading Division Problems

Say: When multiplying two numbers, you can change the position of the same numbers anddivide. 6 3 = 18 18 3 = 6

Multiplication and division are inverse operations. You can check to see if you have the rightanswer for a multiplication problem by dividing.

Example: 7 2 = 14 8 5 = 4014 2 = 7 40 5 = 8

5 3 = 15

product factor factor

15 3 = 5


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You can divide to find a missing factor. When you find a missing factor, you are finding a

quotient.

Multiplication sentence: missing factor 5 3 = 15

Division sentence: 15 3 = 5

quotient

Review the study board with the students and give them some this sample problem. 4 3 = 12.

Ask: How can you rearrange the numbers to show division? (12 3 = 4, 12 4 = 3) Ask thesame questions using these problems:

6 3 = 18; 3 3 = 9; 4 4 = 16; 6 4 = 24; 5 4 = 20

Tell the students that they are going to risk writing the answers to some multiplication problems.Say: I am going to show you a card with a multiplication question and I want you to write the

answer. How many groups of 3 in 5? Lay one card on the table and give five seconds to writethe answer. While revealing the answer on the back of the card, say: The answer isComplete the rest of the cards the same way. Store the index cards and study board in the 9 x

6 envelope.


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Correlations (SG,CAS,CFS): 6C1,3



Unit Focus/Foci

Long Division


More practice dividing by a 1-digit divisor

Materials

Six-Group Activity: Division (solve with multiplication)Math journals


Warm-up Activity:

Have students do the following problem.

Jessie opened her math book. The sum of the two page numbers was 93. What were the pagesnumbered? (46, 47)

Lesson:

Review division vocabulary, steps for long division, and how to check a division problem(inverse operation) orally with class. Call on students to explain the various steps in the divisionprocess.


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6) The divisor is the number the dividend is divided by. (yes)7) The steps for division are divide, multiply, and subtract. (yes)8) The inverse operation for division is multiplication. (yes)9) Perimeter is the distance around a figure. (no)10)When doing long division, you will have to divide 2 or more times. (yes)Free Choice Lesson


Six Group Activity

Have a group of six students, two from each ability level, complete teacher directed activity

sheet Division (dividing greater numbers by one)

Math Workshop

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






Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: See attached Six Group Activity Sheet Division: Dividing greater numbers by

one


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Technology:

Assessment

Student response during lesson, Ten Statement Review

Homework

Study for the test.

Teacher Notes

Answers:

1. 168 R3 2. 62 3. 58 4. 162 5. 1666 R46. 1204 7. 120 R4 8. 2422 R1 9. 45 R1 10.1361


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Six-Group Activity

Division (Solving with multiplication)

Materials:


1 envelope (9 x 6 )

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

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

2 18 7 28 8 24 6 24 455

8 56 9 72 3 21 8 40 2 12

7 63 9 45 8 32 2 10 6 42

Answers:

2 18

18

97 28

28

48 24

24

36 24

24

45 45

45

9

8 56

56

79 72

72

83 21

21

78 40

40

52 12

12

6

7 63

63

9 9 45

45

5 8 32

32

4 2 10

10

5 6 42

42

7

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

Division (Solving with Multiplication)

Say: Multiplication can be used to solve division problems. The division problem 36 6 can be

solved by using 6 times the number that equals 36. (6) 36 6 = 6, 6 6 = 36

Look at the division problem 7 56 . Say: Think of what number times the divisor 7 equals 56.

7 8 = 56 7 56

56

8


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Look at the improper fraction36

9. Think: What number times 9 equals 36. 9 4 = 36.

36

94

?=

Review the study board with the students and use the sample problems to ask questions.

8 72 9 63 7 35 6 42

Ask the question: What times the divisor equals the dividend? Ask this for all the problems. Letthe students know that this will play a part in solving problems with larger divisors and

dividends.

Tell the students that they will write the answers to some division problems. Display a card onthe table and give the students five seconds to write the answer to the problem. Do this with the

rest of the cards. As the answer is revealed, say: The answer is Store the index cards andstudy board in the 9 x 6 envelope.


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Write the following problem on the board. Have students compute the answer using the

calculators.

8 4796 Answer: 599 R4

Tell students that sometimes after converting the remainder it is still a decimal. Write

91 27 591, . Have students find the remainder. Their final screens should show 17.999999. Tell

them to round 17.999999 up to the nearest whole number which is 18. The remainder is 18.Have students check the problem on their calculators by multiplying 3 0 3 x 9 1

+ 1 8 .

Choose 10 problems from the text and have students solve them using the calculators. Teachershould include 2 or 3 of the word problems below.

Have students use their calculators to solve the following story problems.

1. The mail -order store printed 6,784 catalogs. They wrapped them in bundles of 7. Howmany bundles did the store receive? (969R1)

2. Jan has $349. She wants to put an equal amount in each of her 3 piggy banks. Whats thelargest amount she can put in each of her banks? ($116) How much will she have left?

($1.00)

3. Julie owes $3072 for her car. She has 12 more payments to make for her car. What is the

amount of each of her payments? ($256)

Ten Statements

Review the ten statements and have the 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) In the answer 19.94, the whole number is 19. (yes)2) The first step in converting a decimal remainder is to subtract the whole number. (yes)3) The answer in subtraction is called the difference. (no)4) In the problem 678 34 the divisor is 34.(yes)5) The top number in a fraction is called the numerator. (no)


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6) When dividing on a calculator, the remainder will appear in decimal form. (yes)7) If after converting the remainder it is still a decimal, round it up to the nearest whole number.

(yes)

8) To check a division problem on the calculator you must multiply the divisor times thequotient and add the remainder. (yes)

9)

2 is the only even prime number. (no)10)To convert the decimal remainder you subtract the whole number and multiply by thedivisor. (yes)

Free-Choice Lesson


Six-Group Activity


sheet Division (Word problems)

Math Workshop





SS: Read and interpret maps, charts, tables, graphs, and cartoonsSequence information, especially using timelinesSelect appropriate information for intended purpose

Connection(s)

Enrichment:

Fine Arts:

Home:


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Remediation:

Technology:

Assessment

Student response during lesson, Ten Statement review

Homework

Study for test.

Teacher Notes

If you are using the Math Explorer calculators there is a int button. To find the answer for127 8 press 1 2 7 int 8 =. On the screen will appear 15 7

123

123

Q R


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Unit Focus/Foci

Long Division


Problem Solving

Materials

Six-Group Activity: Division (different ways to write problems)


Warm-up Activity:

Teacher writes this problem on the chalkboard and explains to the students TAP A = UP

Replace the letters with digits to make the division problem work. If a letter appears more than

once replace it with the same digit each time. Each letter represents one digit. Here are twosolutions: (TAPA = UP, 120 2 = 60; 240 4 =60)

Lesson:

John wants to buy some soda pop. An eight ounce carton costs 72 cents, a four ounce cartoncosts 48 cents.a. How much does soda pop cost per ounce for the 4 ounce carton? (12)

b. How much does soda pop cost per ounce for the 8 ounce carton? (9)c. Which is the better buy? (8 ounces)


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I. Six oranges cost 96. How much does one orange cost? (16)

You divide 96 by the 6 oranges.16

6 96

-6_

36-36

0

II. Three basketball cards cost 75. How much is that per card? (25)

You divide 75 by the amount 3, your quotient (answer) is the number 25. 25 cents.

The divisor is the number you divide with, the dividend is the number being divided, and thequotient is the answer.

IV. Four cans of tuna fish cost $4.68 or 468 cents. How much is that per can? ($1.17 or 117cents)

4 68

17

4

6

4

28

28

0

$4.

$1.

You can check your division problem by multiplying. You multiply the divisor times the

quotient to give you the dividend.

Example: 2$1.17x 4

$4.68 Check

V. If three CDs cost $39, how much does one CD cost?

Divide 39 by 3 39 3 or 3 39 which equals $13. To check this we multiply 3 times 13 to get39. This is the check.


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VI. A 5 pound bag of frozen French fries cost $2.15 (215 cents) and a 7 pound bag of frozen

French fries cost $3.22 (322 cents). Which bag is the better buy? Why?a. $ .43 a pound for the 5 pound bag

5 15$2.

-20

15b. $ .46 a pound for the 7 pound bag.

7 22$3.

-28

42The five pound bag is a better buy.

VII. Nine boxes of candy cost $8.73 (873 cents). How much is that per box? (97)

Ten Statements


1) The quotient is another word for answer. (yes)2) The divisor is the number you divide with. (yes)3) The dividend is the number being divided. (yes)4) You check your division problem by multiplying. (yes)5) Dividing can be used to determine the better buy. (yes)6) 14 7 = 2 = 2 x 7 = 14. (yes)7)

You can determine the price of a single item by dividing. (yes)8) There are one hundred centimeters in one meter. (no)

9) The basic unit of measurement in the United States currency is the dollar. (no)10)Kilo means thousand. (no)Free Choice Lesson


Six Group Activity

Have a group of six students, two from each ability level, complete teacher directed activitysheet Division (2-digit by 2-digit)


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Six-Group Activity

Division (Different ways to write problems)

Materials:


1 envelope (9 x 6 )


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

36 6 5 2545

512 2 60 10

15

36 18 25 5 8 64

32

2

72 9 8 56 27 954

9

56

8

Answers:

6 3636

6, 25

25

5 5, 45 5, 5 45

12

2, 2 12

60

10, 10 60

15 3 , 3 1518

6, 18 6

25

5, 5 25

64

8, 64 8 2 232, 32

729

, 9 72 568

, 56 8 279

, 9 27 54 9 , 9 54 56 8 , 8 56


36 6 6 =

A A A dividend divisor quotient

6quotient

divisor

dividend

A

6 36

36

6

numerator

denominator

improper fraction


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Say: All of the examples show division. The problem is read thirty six divided by six equals six.

1stproblem - When writing a division problem, the number that is being divided comes first. 36,

the division sign comes next, then the equal sign (=), then the quotient (6).

2

nd

problem - The divisor is on the outside, the dividend is on the inside of the division symboland the quotient is located on the top of the problem.

3rdproblem - This is an improper fraction and to make it proper divide the numerator 36 by thedenominator 6 which equals 6.

Use the study board to review writing division problems in different ways. Sample problems:

5 25 , 50 10 , 15 3 .

Ask the questions: How do we rewrite 5 25 to show division? ( 25 525

5 , ) How do we rewrite

5 25 to show division? (25 5 ,25

5) Ask the same questions for the other division problems.

Have students write the answers to some division problems like the ones just finished. Say: Iam going to show you a card and you write another way to write that division problem. Displayan index card on the table and give the students 30 seconds to write the answer. While revealing

the answer say, The answer is Complete the rest of the cards in the same way. Store thestudy board and activity in the 9 x 6 envelope.


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Correlations (SG,CAS,CFS): 6C1,3



Unit Focus/Foci

Long Division


Formal Assessment-Dividing by 1-digit numbers

Materials

Teacher prepared test


Test: Long Division (See attached)


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Test

Look at this division problem and choose words from the word box to answer the questions.

80 R5 Word Box

6 485 product dividenddivisor factorremainder sum

difference quotient

1. 80 is the ___________.

2. 6 is the ____________.3. 5 is the ____________.

4. 485 is the __________.

Solve.

5

8

.

.

8 2400 6. 9 200 7. 5 484

7 865 9. 6 1946 10. 4 215

Divide and check this problem.

11. 6 206

12. Penny works in a gift store. She has to put 126 beanie babies on the shelves. She must put 9on each shelf. How many shelves will she need?

13. Justin has saved 3,629 stamps. If he places 8 on a page how many pages will he need?

14. Kevin has $1.50. Can he buy 8 pencils at $.25?

15. Complete the division problem for this check?

74x 4

296+ 2

298


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Remediation: See attached Six Group Activity Sheet No Six-Group Activity today.

Technology:

Assessment

Formal

Homework

Teacher Notes

Answer key for test:

1. quotient 2. divisor 3. remainder 4. Dividend5. 300 6. 22 R2 7. 96 R4 8. 123 R4

9. 324 R2 10. 53 R3 11. 34 R2 2 12. 1434

x 6204+ 2

20613. He will need 454 pages (actual answer to division problem 453 R5)

14. no15. 74 R2

4 298

28

18

16

2


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Divisibility rules are shortcuts used to determine whether or not a number is divisible by another

number.

1. A number is divisible by 2 if the digit in the ones place is an even number (0, 2, 4, 6, 8).2. A number is divisible by 5 if the last digit of the number is a 0 or 5.

3. A number is divisible by 10 if the last digit of the number is a 0.

Write 412, 369, 247, 584, 986. Tell students that no matter how large a number is they can

quickly determine the divisibility of a number by using the rules.

Write 3448.

Ask: Is this number divisible by 2? (YES).How do you know? (the digit in the ones place is even)Is this number divisible by 5? (NO)How do you know? (the last digit is not a 0 or a 5)

Is this number divisible by 10? (NO)How do you know? (the last digit is not a zero)

Repeat this process with the following numbers: 48 and 3845Draw the following chart. Have students copy and complete it in their journals.

Divisible by

Number 2? 5? 10?

1. 2,184

2. 4,170

3. 48,209

4. 806,4955. 118,050

Ten Statements


1) A number is divisible by 2 if the digit in the ones place is an even number. (yes)2) Divisibility of large numbers can be quickly determined by the use of divisibility rules. (yes)3) Addends are the numbers that are added. (no)4) A number is divisible by 10 if the last digit is a 0. (yes)5) 24 can be divided by 9 but is not divisible by 9. (yes)


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6) The bottom number of a fraction is called the denominator. (no)7) Ten to the third power is equal to 1000. (no)8) A number is divisible by 5 if the last digit is a 0 or 5. (yes)9) A divisibility rule is a shortcut used to determine whether or not a number is divisible by

another number. (yes)

10)10.A number is divisible if it can be divided without a remainder. (yes)

Free Choice Lesson


Six Group Activity

Have a group of six students, two from each ability level, complete teacher directed activitysheet Division: (quotient when it contains hundreds)

Math Workshop



LA: Understanding explicit, factual information

Understanding the meaning of words in contextSC: Apply scientific method to solve problems

Analyze 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:


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Remediation:

Technology:

Assessment

Informal: Students responses during lesson, Ten Statement review and Homework problems.

Homework

Students will write 2 numbers for each divisibility rule. These problems should be mixed up.

They will be used for the warm up next class.

Teacher NotesAnswer Key

# 2 5 10

1 Y N N2 Y Y Y

3 N N N

4 N Y N

5 Y Y Y


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Six-Group Activity

Multiplication (facts)

Materials:

10 (3x5) index cards1 black marker1 dice, numbers 1-6

1 (9 x 6 ) envelope

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

cards..

1 2 3 4 5 6 7 8 9 0

The answers may vary because of the dice.

Copy this study board to add in the reteaching lesson.

Multiplication Table

Display the following chart for students to study.Say: Multiply the number on the top by the number on the left.

3 x 2 = 6

X 0 1 2 3 4 5 6 7 8 9

0 0 0 0 0 0 0 0 0 0 0

1 0 1 2 3 4 5 6 7 8 92 0 2 4 6 8 10 12 14 16 18

3 0 3 6 9 12 15 18 21 24 27

4 0 4 8 12 16 20 24 28 32 36

5 0 5 10 15 20 25 30 35 40 45

6 0 6 12 18 24 30 36 42 48 54

7 0 7 14 21 28 35 42 48 56 63

8 0 8 16 24 32 40 48 56 64 72

9 0 9 18 27 36 45 54 63 72 81


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Tell the students that they are going to do an activity called Facts. Each student will get a turn

to throw the dice. The teacher will show a card, and the students will multiply what is on thedice by the number card.

Example: 3

Give the students five seconds to write each answer. Before saying the correct answer, say: The

answer is Then say the answer. Have the students do about 20 problems. Store the studyboard and index cards in the 9 x 6 envelope.


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Correlations (SG,CAS,CFS): 6C2,3; 6D1



Unit Focus/Foci

Long Division


Dividing by a 2-digit divisor

Materials

Six-Group Activity: Division (dividing quotients greater than 10)Math journals

Reproduced quiz (optional)Reproduced homework assignment (optional)


Warm-up Activity:

Strips Timed Activity

Round the following number to the nearest ten.

1. 47 2. 83 3. 51 4. 68 5. 36

6. 12 7. 94 8. 49 9. 23 10. 7211. 64 12. 32 13. 89 14. 40 15. 5716. 73 17. 28 18. 35 19. 77 20. 92


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Lesson:

Write 23 90 . Ask students what their first step will be. (divide) Ask them if they know exactly

how many times 90 can be divided by 23. Tell them that they may need to estimate whendividing by a 2-digit number. Tell them also that very few people know all the time tables for 2-

digit numbers.

Underline the 2 in 23 and the 9 in 90. Ask students how many times 2 goes into 9.

(approximately 4) Tell them that the 4 will be their estimate and it may or may not be right. If itdoes not work, the estimate will need to be adjusted. Ask where the 4 will be written. (abovethe zero) Make sure students understand why. If needed explain that 9 cannot be divided by 23,

but 90 can. Show the 4 in the quotient. 4

23 90

Ask what should be done in step 2. (multiply 4 x 23) Students may have difficulty multiplying

on the problem. To help them, write the following problem on the chalkboard.

23x 4

Ask students which digits they should multiply first. (3 and 4) Ask students for the place value

of the 3. (ones) Have students look back at their division problem. Tell them that whenmultiplying they should visualize the 4 in the quotient below the 23 in the divisor.

Ask students which digit in the 23 that they should multiply by 4 first. (3) Ask why. (The 3 isin the ones place and you start multiplying from the ones place.) Ask for the product of 3 x 4.

(12) Write the product 12 on the multiplication problem. 123

x 42

Have students go back to the division problem. Tell students that they will need to write the 12differently on this problem. Tell them to write the 2 below the 0.

23 90

2

4

Ask where they put the 1 they carried on the multiplication problem. (above the 2)Tell them they will do the same on the division problem.

4 123 90

2


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Go back to the multiplication problem and ask which digits will be multiplied next. (4 and 2)

Ask for the place value of the 4. (tens) Ask for the product of 4 x 2. (8)

Remind students to add the number that they carried to the 8. They now have 9. Write the 9 onthe multiplication problem.

123

x 492

Have students go back to the division problem. Tell them to go through the multiplicationprocess on the division problem. 4 x 2 = 8, add the 1 that they carried to get 9. Ask students

where they should write the 9. (below the 9 in 90)

23 90

92

4

Ask students what the next step will be. (subtraction)

23 90

92

4

Students should see that they cannot subtract 92 from 90. Ask them what they think it says about

the 4 in the quotient. They should recognize that it is incorrect. Some students may recognizethat the 4 is too large and needs to be smaller. If not, ask students if they think the 4 should bechanged to a larger or smaller number. Students should be aware that multiplying 23 by 5 would

create an even larger number, therefore, they should try a number smaller than 4. Studentsshould also note that if the product of the digit in the quotient and the divisor is too large that the

digit in the quotient is also too large.

Tell students that since this is just an example that they should add the following notation to the

problem.

23 90

92

4

too large

Then have students rewrite the problem 23 90 . Tell students that for future problems they will

simply erase the incorrect information and continue.


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Ask what number they think they should try now. (3) Write the 3 in the quotient.

Ask students what they will be multiplying (23 x 3). Have a student tell which digits will be

multiplied first (3 and 3). What is the product of 3 x 3? (9) Where will the 9 be written? (belowthe 0)

323 90

Ask: What digits will be multiplied next? (2 and 3) What is the product of 2 x 3? (6) Where

will the 6 be written? (under the 9 in 90)3

23 90

69

Ask students what they will be subtracting. (90 - 69)

23 90

69

3

Have students compute the difference. In this case it will be necessary to borrow.

23 9 0

6 9

21

310 8

Ask: Is the difference smaller than the divisor? (yes) Is there a number to be brought down?(no) Therefore, the 21 is what? (the remainder) Where is the remainder written? (next to the

quotient)3R21

23 9 0

6 9

8 10

2 1

Make sure students understand that it is not uncommon to have to rework part(s) of a divisionproblem because the estimate (for the quotient) is too large or too small.


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Write the following problem on the chalkboard.

32 98

64

34

2

Ask students what is wrong with this problem. (The remainder is larger than the divisor) Ask

students what this says about the quotient. Students should recognize that the quotient is toosmall.

32 98

64

34

2

too small

Tell students to look at the remainder and the divisor. Ask how many times the divisor of 32 can

go into the remainder of 34. (one time) Ask students how this information affects the quotient.

Students should recognize that the quotient should be increased by 1. Change the quotient to 3and rework the problem with the class.

32 98

96

2

3

Ask if the remainder is smaller than the divisor. (yes) Write the remainder next to the quotient.

3R2

32 98

- 962

Write the following problems. 1. 33 60 2. 45 90 3. 24 300

Have students compute and check the problems in their journals. While students are working intheir journals, have 3 students come to the chalkboard to compute and check these problems.

1R27 2 12R12

1. 33 60

33

27

2. 45 90

90

3. 24 300

24

60

48

12


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Ten Statements


1) If the remainder is larger than the divisor, then the quotient is too small. (yes)2) A cube is a solid figure with six identical sides. (no)3) If the product of the digit in the quotient and the divisor is too large than the digit in the

quotient is too large. (yes)4) To check a division problem, you multiply the quotient times the divisor. (yes)5) The divisor is the number the dividend is divided by. (yes)6) Area is measured in square units. (no)7) After subtracting in a division problem you check the difference to make sure it is smaller

than the divisor. (yes)8) It is not uncommon to have to rework parts of a division problem. (yes)9)

Each side of a cube is a square. (no)10)When dividing by a 2-digit number you may need to estimate. (yes)

Free Choice Lesson


Six Group Activity


sheet Division (dividing quotients greater than 10)

Math Workshop






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Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: See attached Six Group Activity Sheet: Quotient when it contains hundreds

Technology:

Assessment

Informal: Student response during lesson, Ten Statement review, and homework

Homework

Teacher will write the following problems on the chalkboard or reproduce copies for the class.

Look at the problems below. In your journals explain what is wrong with them. Then reworkthe problems correctly and check them.

1. 26 80

52

28

22. 22 80

-88

4

Teacher Notes


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Six-Group Activity

Division (Dividing quotients greater than 10)

Materials:


1 envelope (9 x 6 )



1575 6 369 2 47

Answers:

231

2

5

7

15

1575

r 361

3

6

9

63

3696

r 123

1

6

7

4

472

r


Dividing Quotients Greater than 10

Say: Step 1: 7 497 . Find the tens. 497 contains 49 tens. 49 7 = 7. Write the 7 in the

quotient in the tens place. Multiply. 7 7 = 49. Subtract. 49 - 49 = 0.

Example: 7 497

49

7

0


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Step 2: Find the ones. Bring down the 7 ones. 7 7 = 1. Write the 1 in the quotient in the ones

place. Multiply. 1 7 = 7. Subtract. 7 - 7 = 0.

Example:71

0

7

7

49

4977

Use the study board to explain the steps in this sample problem. 3 155

Ask these questions about the problem: What is the first step? (find the tens) What number is inthe tens place in the dividend? (15) How many 3s are there in 15? (5) Where do you put the5? (over the five in the tens place) What is the next step? (Multiply 5 3 = 15 and put the 15

under the first 15) What is the next step? (find the ones) What are you dividing? (5

3 = 1)Where do you write the 1? (over the 5 in the ones place) What do you do now? (multiply 3 1 =

3) Where do you put the 3? (under the 5 and subtract) What is the remainder? (2) What is thefinal answer? (51 r 2)

Tell the students that they are going to risk writing the answers for three problems the same waythey did the sample problem. Display an index card on the table and give the students time to

write the answer. When revealing the answer say: The answer is Complete the rest of theactivity the same way. Store the index cards and study board in the 9 x 6 envelope.


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Correlations (SG,CAS,CFS): 6C1,2,3; 6D1,2



Unit Focus/Foci

Long Division


More dividing by a 2 -digit divisor

Zeroes in the dividend and quotient

Materials

Six-Group Activity: (solve with multiplication)

Math journals


Warm -up Activity:

Duplicate the problem below and have students label the parts of the division problem. Students

may use their notes.R4

39 82

78

4

2

Lesson:

Teacher and students may refer to text for examples of long division with 2 -digit divisors.

Review all division steps and vocabulary when working the next problem together. Write

51 493 . Have students copy in journals. Remind students to keep all digits in straight columns

when working these problems.


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Ask: 1. What is the first step in this problem? (divide)

2. How do you find the first digit in the quotient? (divide the 5 into 49 or round 51 to 50and divide 50 into 493)

3. What is the first estimate for the quotient? (9)4. What is the next step? (Multiply 9 x 51)

5. Where will the product of9 x 51 be written? (below the 493)

Work through the multiplication orally.

51 493

459

Ask: What is the next step? (subtract 493-459) Have students find the difference. Write thedifference on the problem

51 4 93

4

98

59

34

Ask: What is the next step? (write remainder next to the quotient) How is a division problem checked? (by multiplying the quotient times the divisor and

adding any remainder.)

Have students check the problem.

9 R34Show 51 493

459

34

51x 9

459+ 34493

Write 39 420 . Have students find the solution to the first estimate by multiplying and

subtracting, and then stop. Their problems should look like this.


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39 420

39

3

5

Teacher will show all steps on the problem as they are discussed.

Ask: What step is next? (bring down the 0)

*Teacher will show this with an arrow. 1

39 420

39

30

What step is next? (divide 39 into 9)

How many times can 30 be divided by 39? (0) Where is the zero written? (In the quotient above the zero in the dividend.)

*Tell students it is very important to write this zero in the quotient. Omitting it will create anincorrect quotient. In the quotient there must be a digit above all digits in the dividend to the

right of the first estimate.

Ask: What step comes next? (multiply 0 x 39)

Where is the product written? (under the 30) What step comes next? (subtract 30 -0)

What is the difference? (30)

What step comes next? (put the remainder next to the quotient)

Have a student check the problem on the board while the other students check the problem intheir journals.

10 R30

39 420

3930

0

30


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39

x 1000

39390

+ 30420

Discuss what would have happened if the zero had not been placed in the quotient. Havestudents work the check using 39 x 1.

39x 1

39+3069

Have them compare this answer to the dividend.

Write the following problems on the board. Have students come to the board to compute andcheck the problems.

1. 20 170 2. 21 190

Answers 1. 8 R10 2. 9 R1

Ten Statements



1) Omitting a zero estimate in the quotient will create an incorrect quotient. (yes)2) When dividing a large number by a 2 -digit divisor you will estimate. (yes)3) You check a division problem by multiplying the quotient times the divisor, and adding any

remainder. (yes)

4) There are 3600 seconds in 60 minutes. (no)5) The dividend is the number being divided? (yes)6) 900 + 70 + 5 is the expanded form of 975. (no)


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7) In the quotient there must be a digit above all digits in the dividend to the right of the firstestimate. (yes)

8) 100 is divisible by 10. (no)9) It is important to keep digits in straight columns when dividing. (yes)10)The remainder is written next to the quotient. (yes)Free Choice Lesson


Six Group Activity

Have a group of six students, two from each ability level, complete the teacher directed activity

Sheet: Dividing money

Math Workshop







Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: See attached Six Group Activity sheet: Division (Solve with multiplication).


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Technology:

Assessment

Student response during lesson, Ten Statement Review

Homework

Students will create 2 long division problems with 2-digit divisors. Dividends must have 4 or 5digits. Students will show the solutions and checks on the books of their papers. Have themleave space for the problems to be worked by a student during the warm-up next class session.

Teacher Notes


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Six-Group Activity

Division (Solving with multiplication)

Materials:


1 envelope (9 x 6 )



2 18 7 28 8 24 6 24 455

8 56 9 72 3 21 8 40 2 12

7 63 9 45 8 32 2 10 6 42

Answers:

2 18

18

97 28

28

48 24

24

36 24

24

45 45

45

9

8 56

56

79 72

72

83 21

21

78 40

40

52 12

12

6

7 63

63

9 9 45

45

5 8 32

32

4 2 10

10

5 6 42

42

7


Division (Solving with Multiplication)

Say: Multiplication can be used to solve division problems. The division problem 36 6 can be

solved by using 6 times the number that equals 36. (6) 36 6 = 6, 6 6 = 36

Look at the division problem 7 56 . Say: Think of what number times the divisor 7 equals 56.

7 8 = 56 7 56

56

8


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Look at the improper fraction36

9. Think: What number times 9 equals 36. 9 4 = 36.

36

94

?=

Review the study board with the students and use the sample problems to ask questions.

8 72 9 63 7 35 6 42

Ask the question: What times the divisor equals the dividend? Ask this for all the problems. Letthe students know that this will play a part in solving problems with larger divisors and

dividends.

Tell the students that they will write the answers to some division problems. Display a card onthe table and give the students five seconds to write the answer to the problem. Do this with the

rest of the cards. As the answer is revealed, say: The answer is Store the index cards andstudy board in the 9 x 6 envelope.


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Correlations (SG,CAS,CFS): 6C1,2,3; 6D2



Unit Focus/Foci

Long Division


Dividing multiples of ten by 1 and 2-digit numbers

Materials

Six-Group Activity: Multiplication (rounding)Math journals


Warm up:

Write the following problems on the chalkboard.

1. 80 x 900 2. 70 x 70 3. 200 x 50 4. 600 x 600

5. 80 x 70 6. 60 x 3000 7. 400 x 20 8. 900 x 90

9. 500 x 400 10. 90 x 80 11. 2000 x 30 12. 700 x 6000

Answers:

1. 72,000 2. 4,900 3. 10,000 4. 360,0005. 5,600 6. 180,000 7. 8,000 8. 81,000

9. 200,000 10. 7,200 11. 60,000 12. 4,200,000


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Lesson:

While working the following problem orally with students review long division terms and steps,

how to check the problem, how to work with zeros, and inverse operation for division andmultiplication.

Example: 7 900 Answer: 128 R4

*Make sure students keep numbers in straight columns, do not forget to bring down zeros in thedividend, and do not omit the zeros in the quotient.

Have students divide and check the following problems in their journals.

1

4

.

.

62 980 2. 35 700 3. 46 980

23 800 5. 84 267 6. 71 492

Have students go to the chalkboard to complete and check the problems.

Ten Statements



1)

To check a division problem multiply the quotient times the divisor and add the remainder.(yes)

2) Omitting a zero in the quotient will create an incorrect quotient. (yes)3) The answer in addition is called the sum. (no)4) In the problem 64 7, seven is the divisor. (yes)5) The inverse operation for multiplication is division. (yes)6) 4 quarts are equal to 1 gallon. (no)7) Keeping the numbers straight during long division will help you keep from mixing up

numbers. (yes)8) 7 is a prime number. (no)9) The answer in division is called the quotient. (yes)10)After the first digit is written in the quotient you must have a digit above the remaining digits

to the right in dividend. (yes)


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Free Choice Lesson


Six Group Activity

Have a group of six students, two from each ability level, complete teacher directed activitySheet: Multiplication (rounding)

Math Workshop



LA: Understanding explicit, factual information

Understanding the meaning of words in contextSC: Apply scientific method to solve problems

Analyze and interpret dataSS: Read and interpret maps, charts, tables, graphs, and cartoons

Sequence information, especially using timelines

Select appropriate information for intended purpose

Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: See attached Six Group Activity Lesson: Multiplication (rounding)

Technology:


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Use these example problems to explain how to round numbers.

Example: 563, 421

Ask these questions:

1)

For the number 563, what is the last number to the left? (5)2) Which number are we rounding? (6)3) What is the rule for numbers that are 5 or higher? (round up if the number is 5 or higher)4) What will we round the number up to? (600)5) Look at the number 421. What number are we rounding? (4)6) What is the number next to the 4 on the right? (2)7) What is the rule for numbers that are 4 or less? (round down)8) What would the new number be? (400)Tell the students that they are going to do an activity that involves rounding multiplicationproblems. Let the students know that they dont have to multiply; they will just round both

numbers in the problem. Tell the students that when a card is placed on the table, they have oneminute to write the answer before it will be revealed. When the minute has passed, turn the card

over to reveal the answer and say: The answer is Complete the remaining cards in the sameway.

Store the index cards and study board in the (9 x 6) envelope.


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Correlations (SG,CAS,CFS): 6C1,2,3; 6D2



Unit Focus/Foci

Long Division


Mixed practice

Materials

Six-Group Activity: Division (using multiplication to check the answer)Math journals


Lesson:

Review the following information: All terms and steps for long division during this lesson, andrulers for divisibility by 2, 5, and 10.

Copy and complete this chart. Write yes or no in the boxes.

Number Divisible by

2 5 10

1. 684

2. 2000

3. 175

4. 314,675


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Six-Group Activity

Division (Using multiplication to check the answer)

Materials:


1 envelope (9 x 6 )


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

6 315 9 243 3 137

Answers:

6 315

30

15

12

3

523

r

52

312

3

315

6

9 243

18

27

63

63

0

9

27

243

3 137

12

2

17

15

2

45r

45

135

2

137

3


Using Multiplication to Check the Answer

Say: Multiplication can be used to check the answer to a division problem. Multiply the

quotient by the divisor. Add any remainder to the product. If the work is correct, the answer

will be the same as the dividend.

Example: 7 58156

83

21

21

0

quotient

7 divisor581 dividend

83


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2 195

18

15

14

1

quotient

divisor

+ remainderdividend

97

2

194

1195

Use the study board to explain how to do this sample problem. 5 435

Ask these questions: What is the first step in solving the problem? (find the tens) What are we

dividing? (43 5) What is the answer? (8 r3) Where do we write the 8? (over the 3) What is8 5? (40) Where do we write the 40? (under the 43) What is the next step? (435 - 40 = 35)What is the next step? (35 5 = 7) What is the answer? (87) How can we check the answer

using multiplication? (87 5 = 435)

Tell the students that they are going to risk writing the answers to three problems the same way

they did the sample problem. Display a problem on an index card on the table and give thestudents time to write the answer. While revealing the answer say: The answer is Complete

the rest of the cards the same way. Store the index cards and study board in the 9 x 6 envelope.


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Correlations (SG,CAS,CFS): 6C1,2,3; 6D1,2



Unit Focus/Foci

Long Division


Formal Assessment-Dividing by 1 and 2-digit numbers

Materials


Test (See attached)


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Test

Divide.

1

4

.

.

49 7 = 2. 27 9 = 3. 64 8 =

6 30 5. 5 35 6. 8 32

7. Group the xs so they show 15 3.

x x x x x x x x x x x x x x x

8. Division is a fast way to ___________.

Look at this division problem. Use the terms in the word box to answer the following.

52 R11

18 947 Word Box90 quotient product47 sum divisor36 remainder dividend

11 factor division

9. 18 is the ___________.10. 11 is the ___________.11. 947 is the __________.

12. 52 is the ___________.13. James collected 560 miniature cars. He wants to put them in boxes. Each box holds 7 cars.

How many boxes will he need?

Divide.

14

17 910

. 8 260 15. 5 955 16. 12 360

45 18. 4 1000 19. 6 5842.


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Complete the divisibility chart.

Number Divisible by

2 5 10

1. 6852. 4369

3. 7862

4. 1270

24. Divide and check

8 689


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Ten Statements


No Ten Statements Today.

Free Choice Lesson


Six Group Activity

Have a group of six students, two from each ability level, complete teacher directed activitySheet: Dividing money

Math Workshop




SC: Apply scientific method to solve problems

Analyze and interpret dataSS: Read and interpret maps, charts, tables, graphs, and cartoons


Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation:

Technology:


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Assessment

Formal

Homework

Teacher Notes

Each answer is worth three points.

Documents

Structured Curriculum Lesson Plan Day: 066 Subject: Mathematics Grade Level: