structured curriculum lesson plan day: 033 subject: mathematics grade level:

8/14/2019 Structured Curriculum Lesson Plan Day: 033 Subject: Mathematics Grade Level:

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STRUCTURED CURRICULUM LESSON PLAN

Day: 033 Subject: Mathematics Grade Level: 4

Correlations (SG,CAS,CFS): 6C2

ITBS/TAP:Solve single step problems using multiplication

or division with whole numbers

ISAT:

Unit Focus/Foci

Multiplication and Division

Instructional Focus/Foci

Using the numbers 0, 1, 2, and 10 to multiplyLearning the multiplication facts

Materials

Six-Group Activity: Division (Solve with multiplication)Pencil

PaperMath journals

Educational Strategies/Instructional Procedures

Warm-up Activity:

Write the following number sequence on the chalkboard. 1) 575, 875; 1175; 1475, and 1775

2) 34, 51, 68, 85, and 102. Have students give the next three numbers in each sequence. (In thefirst sequence, add 300. In the second sequence, add 17.)

Lesson:

Say: If Christmas is exactly six weeks away from todays date, how do we know how many daysthat is exactly?


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We can do this by looking at a calendar and counting the days. Or we can add 7 + 7 + 7 + 7 +

7 + 7, which is 6 times 7. (7 + 7 + 7 + 7 + 7 + 7 = 42)

However, a quicker way to do this would be to multiply 6 x 7. 6 x 7 = ? (42)

Have the students solve the following problems.

1. How many days are there in 4 weeks? 4 x 7 = (28)2. How many days are there in 8 weeks? 8 x 7 = (56)3. How many days are there in 9 weeks? 9 x 7 = (63)4. How many days are there in 5 weeks? 5 x 7 = (35)5. How many days are there in 7 weeks? 7 x 7 = (49)Vocabulary

1. Multiplicand: a number that is multiplied by another number

2. Multiplier: the number that the multiplicand is multiplied by3. Product: the result of multiplying two numbers together

5 Multiplicand 3 x 5 = 15 Productx 3 Multiplier Multiplicand15 Product Multiplier

4. Area: the number of square units inside a figure

4 cm2 cm The area of the rectangle is 8 square centimeters. Area = 2 x 4 square

centimeters. Area = 4 x 2square centimeters.

To find the area: multiply the length by the width.

5. Commutative principle: the order in which two numbers are multiplied makes no

difference to the answer. Example: (3 x 5 = 15) (5 x 3 = 15)

Students will solve the add problems from their text. The teacher should collect these papers andcheck to make sure the students understand what they are doing.


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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 todayslesson.

1) Multiplying a number by two is the same as doubling the number. (yes)2) When you multiply one number by another, the answer is the product. (yes)3) Area is the number of square units inside a figure. (yes)4) To multiply by 10, put a zero to the right of the number. (yes)5) Money Matters focuses on counting, adding, and subtracting money by using examples of

raising money, shopping and combining bills of varying worths. (no)6) Multiplying a number by one does not change the number. 1 x 8 = 8 (yes)7) The goal of all work with multiplication is speedy recall. (yes)8) You can use the United States money system to understand fractions. (no)9) Making inferences provides practice in approximating sums and differences. (no)10)

Multiplying a number by zero gives a zero answer. (yes)

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 the teacher-directed activitysheet: Division (solving with multiplication).

Math Workshop

Have the students work in 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 problems

Analyze and interpret data


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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: Division (Solve with multiplication).

Technology:

Assessment

Assess each students class participation, and communication of strategies used to multiply by 0,1, 2, and 10. Assess each students ability to correctly answer 75% of computation problems.

Homework

Write these problems on the chalkboard. Have students copy the problems to take home forhomework.

1. 1 9= 2. 6 9=3. 9 9= 4. 4 4=5. 6 4= 6. 8 4=7. 7 9= 8. 9 2=9. 5 5= 10.2 5=11.3 7= 12.5 7=Explain in writing how to use addition and division to solve these problems.

13.4 9=14.5 6=


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Teacher Notes

Answers for Homework:

1. 9 2. 543. 81 4. 165.

24 6.

327. 63 8. 18

9. 25 10.1011.21 12.3513.(Answers may vary). Students can add four sets of 9s together (9+9+9+9=36) or nine sets of

four (4+4+4+4+4+4+4+4+4=36); To get the answer using division: 4 36

36

0

9

or 9 36

36

0

4

.

14.(Answers may vary). The solution to 5 6 using addition can be 5+5+5+5+5+5+=30 or6+6+6+6+6=30; To get the answer using division, 5 30

30

0

6

or 6 30

30

0

5

.


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Six-Group Activity

Division (Solving with multiplication)

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. 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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Correlations (SG,CAS,CFS): 6C2; 8D2; 9A1,5; 9D1,2

ITBS/TAP:Solve single-step problems using

multiplication or division with wholenumbers

ISAT:

Unit Focus/Foci



Continuing practice with multiplication facts 0, 1, 2, and 10

Materials

Six-Group Activity: Division (Different ways to write problems)Game mats

PaperPencilMath journals

Game markers (different colors)Multiplication cards

Constructing paper or heavy stock paper


Warm-up Activity:

Write the following on the chalkboard. Have students solve each problem.

1. 5 x 7 x 10 x 4 x 1 x 2 x 02. 3 x 4 x 2 x 7 x 1 x 0


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Ask students for the answer to each problem. Say: The answer to both problems is 0 because

any number multiplied by 0 equals 0.

Ask students to volunteer answers to the following multiplication problems:

2 x 1 = (2) 0 x 1 = (0) 2 x 9 = (18) 5 x 1 = (5) 10 x 9 = (90)2 x 5 = (10) 1 x 5 = (5) 2 x 5 = (10) 0 x 9 = (0) 5 x 10 = (50)10 x 1 = (10) 10 x 2 = (20) 0 x 5 = (0) 1 x 10 = (10) 5 x 9 = (45)

Remind students that any number times 0 is always 0.

Lesson:

Write this problem on the chalkboard: Find a pair of numbers whose product is twice their sum.(There is more than one answer: 3 6=18 and 3+6=9; 4 4=16 and 4+4=8).

Do a mental math activity with the students. Say each problem and have students give theanswer orally.

1. 2 1=(2) 2. 0 1=(0) 3. 2 9=(18)4. 5 1=(5) 5. 10 9=(90) 6. 2 5=(10)7. 1 5=(5) 8. 9 2=(18) 9. 10 5=(50)10.0 9=(0) 11.5 2=(10) 12.9 5=(45)13.0 2=(0) 14.5 10=(50) 15.10 1=(10)16.10 2=(20) 17.9 10=(90) 18.5 9=(45)Remind students that speedy recall is the basis of learning the multiplication facts.

Have the students divide into groups of four. Give each group four game markers (four different

colors), a game board, and a set of multiplication cards.

To prepare for this activity, copy enough game boards to cover the amount of groups in yourroom. There are 22 game cards per set. Copy enough sets to match the amount of groups youhave. Use whatever you have in four different colors per group so that every student has a

different color marker in each group. Do this for every group.

Read the rules of the game to all the students.


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Say:

1. This is a multiplication game to help you learn your facts.2. Each group has a game board and a marker. Each player places a marker at START.3.

Place the multiplication cards, questions side-up, in the question box on the gameboard.

4. Decide who will go first.5. Players take turns. When its your turn, do these things. First, read the top card without

picking the card up. Read all the answer choices. Second, announce your answer by saying,

for example, I choose D. Third, turn the card over and place it in the finished cards so the

correct answer shows.

6. If you answer correctly, move your token ahead the number of spaces shown on the back ofthe card. If you answer the question wrong, you do not move your marker. Instead, you

place the card face up in the middle of the capital letters, bold deck.

7. Players alternate this way until one reaches FINISH.Walk around the room to monitor each group to see how the game is going or if they needquestions answered about the game.


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GAME BOARD

START FINISH

Place card pack here.

QUESTIONS

answer side down.

Read and answer, then put

USED CARDS

cards here, answer side up.

If you stop here,mov

eupto

This space

Extra turn

Extra turn

Lose a turn

Lose a turn


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GAME CARDS

Todd has 25 pictures to put into a photoalbum. He will put 5 pictures on each page.

Which of these tells how to find out howmany pages he will fill?

A. Subtract 5 from 25B. Divide 25 by 5C. Multiply 25 by 5D. Add 25 to 5

Which Roman numeral represents thenumber 18?

A. XIXB.

XVIIIC. VIII

D. XIV

Which of these does not have a 5 in the ten-thousands place?

A. 559,056B.

775,552C. 650,055

D. 555,055

Marla picked 42 wooden blocks from herbrothers toy box. She picked 11 blue blocksand 16 red blocks. The remaining blocks

were green. How many blocks were green?

A. 17B. 19C. 12D. 15

Which digital clock shows the same time as

the analog clock?

A. 8:15B.

3:40C. 3:08

When rounded to the nearest hundred, I

become 500. When rounded to the nearestten I become 520. Which of the numbersbelow could I be?

A. 498B. 516C. 527D. 489

Which of these is the same as 7,040?

A. 7 thousands and 4 hundredsB. 700+40C. 7 thousands and 4 tensD. 70+40

If this pattern continues what number comesnext?

5, 3, 6, 4, 7, 5, 8, _____

A. 6B. 9C. 10D. 3


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The answer is If the answer is correctmove ahead

B 5

The answer is If the answer iscorrect move ahead

B 5


B 4


D 4


B 3


B 2


A 4


C 4


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GAME CARDS

Which polygon has at least one right angle?

A. B

B. D

For which number sentence could you put a 0into the box or boxes and make a number

sentence that is not true?

A. 11=11B. +11=11C. 11- =11D. 11+ = +11

What must you do to find the next number in

this pattern?

66, 63, 60, 57, _____?

A. Subtract 4 from 58B. Add 3 to 58C. Subtract 2 from 58D. Subtract 3 from 58

Zelda has 60cent in dimes, $1.25 in quarters,

and 55 in nickels. How many coins does shehave?

A. 19B. 20C. 21D. 22

I have no flat faces, no corners, and no edges.What space figure am I?

A. ConeB. CylinderC. SphereD. Cube

Ida is thinking of a number less than 3,512and greater than 3,508. Which of these

numbers could Ida be thinking about?

A. 3,507B. 3,515C. 3,510D. 3,519

Angela bought 2 packs of baseball cards.Each pack contained 8 cards. Which of these

number sentences would help Angela find outhow many baseball cards she has in all?

A. 8+2=B. 82=C. 8 2=D. 8-2=

Find the multiplication problem that has aproduct of 24?

A. 7 3=B. 12 3=C. 6 4D. 5 8


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A 4


A 4


D 3


D 3


C 6


C 2


C 4


C 4


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GAME CARDS

Who was born first? _______

A. Marissa: June 14, 1983B. Claire: February 25, 1983C.

Benji: January 4, 1984

Which sum is different from the other two?

265 340 240+26 +21 +51

A. B. C.

What is the largest 4-digit number Brandi canmake with her cards 6 8 3 7?

A. 3786B.

8763C. 6378

What is the perimeter of the rectangle?

5

3 3 3

3

A. 8B. 9

C. 15D. 16

How long is the movie?

Movie Begins Movie Ends

A. 2 hr. B. 1 hr. 50 min

C. 1 hr. 20 min

Which of these is another name for fifty two

thousand, four hundred six?

A. 520,406B.

52,460C. 52,406

D. 5,246

The four pairs of numbers are part of apattern, what is the next pattern? ______

(1,1) (2,4) (3,9) (4,16) (_ _)

A. (6,36)B. (7,49)C. (5,25)

What name is not a name for the figurebelow?

A. RectangleB. SquareC. Parallelogram


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B 2


B 3


B 4


D 4


A 5


C 2


C 3


B 5


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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 todayslesson.

1) There are 121 multiplication facts listed on the multiplication chart. (yes)2) The purpose of multiplication is speedy recall. (yes)3) When you solve a multiplication problem, the answer is the product. (no)4) Multiplication is another way to skip-count. (yes)5) (3 x 5 = 15) and (5 x 3 = 15) are examples of commutative forms of multiplication. (yes)6) dividend that are zero have no meaning. (no)7) Approximation helps students to develop a broad ability to use mathematical common sense.

(no)8) The mental math practice done during the Warm-up Activity provided practice with the

multiplication facts concentrating on 0, 1, 2, 5, 9, and 10 facts. (yes)

9)

When a student has learned the 121 facts in the multiplication chart, there will be only 24facts left to learn. (yes)

10)Multiplication and division are related. Missing term problems in multiplication get youprepared to divide. (no)

Free-Choice Lesson


Six-Group Activity

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

sheet: Division (Different ways to write problems).

Math Workshop





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


Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: See attached Six-Group Activity sheet: Division (Different ways to writeproblems).

Technology:

Assessment

Class participation, completion of fact chart, and game participation can all be implemented asinformal assessments of students progress.

Homework

Teacher Notes

Have students work cooperatively on multiplication facts. Make up a rhyme or rap to helpstudents learn the facts.


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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

72

9, 9 72

56

8, 56 8

27

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


1)36 6 6 =

A A A dividend divisor quotient

6quotient

2)

divisor

dividend

A6 36

3)

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): 6A3

ITBS/TAP:Add, subtract, multiply, and divide single and

multi-digit whole numbers

ISAT:

Unit Focus/Foci



Multiplying by 5 and 9

Materials

Six-Group Activity: Division (Dividing quotients greater than 10)

Math journals


Warm-up Activity:

Write the following problems on the chalkboard. Have students find the product for each

problem. (Students may use calculators.)

1. 5 x 7 x 10 x 4 x 1 x 2 x 0

2. 3 x 2 x 4 x 1 x 3 x 0 (0, because anything multiplied by 0 is 0.)3. 7 x 7 x 6 x 3 x 2 x 0 x 1

Mental Math: Have students recite the entire fact for each.

1. 0 x 4 = (0) 2. 9 x 2 = (18) 3. 0 x 2 = (0)4. 5 x 2 = (10) 5. 1 x 9 = (9) 6. 5 x 1 = (5)

7. 2 x 9 = (18) 8. 2 x 5 = (10) 9. 3 x 4 = (12)


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Lesson:

Recite the multiples of 5 with the class. 5 x 0 = 0, 5 x 1 = 5, 5 x 2 = 10,

5 x 3 = 15, 5 x 4 = 20, 5 x 5 = 25, 5 x 6 = 30, 5 x 7 = 35, 5 x 8 = 40, 5 x 9 = 45, and 5 x 10 = 50

After reviewing the multiples of 5 with the class, show the relationship between even multiplesof 5 and of 10.

For an odd multiple of 5 (3 x 5), the product can be found by adding 5 to the next lower evenmultiple. (2 x 5 = 10 + 5 = 15; therefore, 3 x 5 = 15)

5 x 5 = 4 x 5 = 20 + 5 = 25; therefore, 5 x 5 = 25. Have students apply the rule to 7 x 5, and 9 x5.

Tell students that all multiples of 5 end in 0 or 5. (5, 10, 15, 20, 25, 30, 35, 40, 45, 50) Oddmultiples end in 5 (5, 15, 25 35, 45, 55) and even multiples end in 0 (10, 20, 30, 40, 50).

Activity: Have students solve the following problems.

1. 4 x 9 = 2. 7 x 9 = 3. 9 x 94. 9 x 8 = 5. 9 x 1 = 6. 3 x 9 =

5. 2 x 9 = 8. 6 x 9 = 9. 5 x 9 =6. 9 x 6 = 11. 9 x 8 = 12. 9 x 4 =

Have students add the digits in each product. (The sum is 9.)

Say: You can recognize a multiple of 9 because the sum of the digits in the product is always 9.(This only works for multiples, of 9, up to 10 x 9. For greater multiples the sum of the digits may

not be 9, but it will always be a multiple of 9. Example: 11 x 9 = 99, 12 x 9 = 108.)

Ten Statements


1) All multiples of 5 end in 0 or 5. (yes)2) Odd multiples of 5 end in 5. (yes)3) To approximate an answer, the answer can be between two numbers. (no)4) There is no single best approximation method. (no)


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5) Even multiples of 5 end in 0. (yes)6) You can recognize a multiple of 9 because the sum of the digits in the product is 9. (yes)7) 7 x 5 = 6 x 5 = 30 + 5; therefore, 7 x 5 = 35. (yes)8) 9 x 9 = 81, 8 + 1 = 9; therefore, this is a multiple of 9. (yes)9) Rounding has to do with numbers that are easier to work with. (no)10)

In finding multiples of 9, the sum of the digits will either be 9 or a multiple of 9. (yes)

Free Choice Lesson


Six-Group Activity

Have a group of six students, two from each ability level, complete the teacher-directed activitysheet: Division (Dividing quotients greater than 10).

Math Workshop



LA: Understanding explicit, factual information

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


SS: Read and interpret maps, charts, tables, graphs, and cartoonsSequence information, especially using timelines

Select appropriate information for intended purpose


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7. 9 7= 8. 9 10= 9. 5 10=10.9 2=

Teacher Notes

Answer for Enrichment exercise:

Every row and column increases by one.Diagonals like this consist of the same number; each increases by one.Diagonals like this alternate between strings of consecutive odd numbers and consecutive

even numbers.

Answers to Homework:

1. 402.

543. 30

4. 275. 206. 187. 638. 909. 5010.18


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Six-Group Activity

Division (Dividing quotients greater than 10)

Materials:


1 envelope (9 x 6 )


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

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): 6B3;6C2; 8D4



ISAT:

Unit Focus/Foci



Multiplying by 3, 4, 6, and 8

Materials

Six-Group Activity: Multiplication (Multi-digit addition)


Warm-up Activity:

Write the following on the chalkboard.

Walgreens sells blank cartridges in multi-packs at a discount. You can buy cartridges in tenpacks or six packs. James purchased 72 blank cartridges by buying exactly ten discount packs.How many ten packs and six packs did he buy? (3 ten packs and 7 six packs)

Mental Math

Speedy Recall

1. 8 x 9 2. 5 x 4 3. 9 x 4 4. 1 x 8 5. 6 x 9 6. 3 x 6

7. 3 x 7 8. 8 x 5 9. 7 x 10 10. 5 x 3 11. 2 x 7 12. 9 x 6

13. 10 x 4 14. 4 x 8 15. 7 x 8 16. 6 x 6 17. 5 x 5 18. 10 x 10


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Lesson

Say: Multiples of 3 can be found by counting by 3s from a product you know.

Example: 3 x 7 = n. If you know that 2 x 7 is 14. Then 3 x 7 = 14 + 7 which equals 21.

Say: Multiples of 6 can be found by doubling multiples of 3 because 6 is twice 3.Example: 6 x 7 = n. If you know that 3 x 7 = 21Then 6 x 7 is twice 3 x 7

So 6 x 7 = 21 + 21 = 42

Say: Multiples of 4 can be found by doubling multiples of 2.

Example: 4 x 7 = n If you know that 2 x 7 = 14Then 4 x 7 is twice 2 x 7

So 4 x 7 = 14 + 14 = 28

Say: Multiples of 8 can be found by doubling multiples of 4

Example: 8 x 9 = n If you know that 4 x 9 = 36Then 8 x 9 is twice 4 x 9

So 8 x 9 = 36 + 36 = 72

Activity:

Have students multiply to solve for n.

1. 4 x 3=n 2. n x 6=30 3. 8 x 8=n

4. 7 x 3=n 5. n x 4=32 6. n x 6=42

7. 3 x n=9 8. 9 x 8=n 9. 8 x 0=n

10. n x 3=27 11. 5 x n=40 12. n x 7=28

13. 10 x n=80 14. 8 x n=48 15. 6 x n=36


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Ten Statements


1) Multiples of 3 can be found by counting by 3s from a product you know. (yes)2) 3 x 8 = 2 x 8 = 16 + 8 = 24 (yes)3) Multiples of 6 can be found by doubling multiples of 3. (yes)4) 6 x 8 = 3 x 8 = 18 + 18 = 36 (yes)5) The order in which two numbers are multiplied makes no difference to the answer. (no)6) The balance in a bank account is how much money you have in the bank. (no)7) Fractions of ten are used to describe parts of a whole. (no)8) Multiples of 4 can be found by doubling multiples of 2. (yes)9) 4 x 9 = 2 x 9 = 18 + 18 = 36 (yes)10)Multiples of 8 can be found by doubling multiples of 4. (yes)Free Choice Lesson


Six Group Activity

Have a group of six students, two from each ability level, complete the teacher-directed activitysheet: Multiplication (Multi-digit multiplication).

Math Workshop

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





SS: Read and interpret maps, charts, tables, graphs, and cartoonsSequence information, especially us ing timelines



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Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: See attached Six-Group Activity sheet: Multiplication (Multi-digit addition).

Technology:

Assessment

Homework

Teacher Notes


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Six-Group Activity

Multiplication (Multi-digit addition)

Materials:

3 x 5 index cards1 black marker1 pencil

1 (9 x 6 ) envelope

Prepare the following index cards using these problems:

35

26+

92

29+

75

25+

63

29+

39

12+

84

28+

6

16

+

45

26+

127

66+

99

+26

Answers:

35

1

1

+26

92

1

1

+29

75

0

1

+25

63

2

1

+29

39

1

1

+12

84

2

1

+28

16

6

2

1

+

45

26

1

1

+

1 27

66

3

1

+

99

26

5

1

+

Copy this study board to use it when reteaching the activity.

Multi-digit addition

Say: When adding numbers with more than one digit, in some cases, you are going to renamebecause only numbers that add up to a one digit number fit in the ones place. When a set ofnumbers add up to more than 10, you must rename to the next place.

Example: 295

267

+

Step 1: Start at the right of the problem. Add the ones, 7+5 = 12.

Ask the group if 7+5 equals more than 9.If the answer is yes, rename. 12 = 1 ten and 2 ones.

97

4

5 671

+

Start at the right in the ones place. Add 7+7 = 14. Ask the group if 7+7 equals

more than 9. If the answer is yes, rename to the tens place. 14 equals 1 ten and

4 ones.


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Tell the students that they are going to do two problems the same way, writing in words the steps

to solving the problem. Lay one card on the table, give the students four to five minutes to writethe answer to the first problem. When the time is up, show the students the written answer you

have. This paper may not be exact (teacher judgment) as to the right answer. Say: The answeris Store the index card and written answer key in the 9 x 6 envelope. Repeat this

process with the second card.


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ISAT:

Unit Focus/Foci



Engage in additional practice with multiplication speedy recall

Materials

Six-Group Activity: Multiplication (Facts)Math journals


Warm-up Activity:

Write the following problems on the chalkboard. Ask students to solve them.

1. A parent and two children have thirty $1.00 bills. They share the money equally. There isno money left over. How do they divide it? (The group is a grandmother, her son, and hisdaughter. There are only three people because the man is a parent and the grandmothers

child. Each gets $10.)2. Tom gets five basketball cards in a pack. How many cards will he get in 5 packs?


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Lesson:

Tell the students the next activity is going to assess their speed and accuracy in recalling

multiplication facts; therefore; they should work as quickly as possible. Tell them they will betimed, to work all of the problems that they know first, and go back and do the ones that they are

having difficulty with.

Allow students 15 minutes to complete the 75 problems.

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) There are 121 multiplication facts on the fact chart. (yes)2)

Accurate recall and speed are the important when using multiplication facts. (yes)3) A factor is a number that is multiplied by another number. (yes)

4) The product is the name of the answer to a multiplication problem. (yes)5) The function machine for multiplication is very similar to the function machines for addition

and subtraction. (yes)

6) When a multiplication function is performed, the answer is called a product. (no)7) One of the functions done during todays assessment was to multiply and solve for n. (yes)8) Music may be used to help students learn multiplication facts. (yes)9) Cooperative activities can be very useful to students who are learning multiplication facts.

(no)

10)Learning the facts are the keys to speedy accurate problem solving. (yes)Free Choice Lesson


Six-Group Activity

Have a group of six students, two from each ability level, complete the teacher-directed activitysheet: Multiplication (Facts).


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Math Workshop




SC: Apply scientific method to solve problemsAnalyze and interpret data



Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: See attached Six-Group Activity sheet: Multiplication (Facts).

Technology:

Assessment

Homework

Teacher Notes

Have students record real-life situations where multiplication can be used.


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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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Test

Multiply1. 2 x 1 = _____ 2. 3 x 3 = _____ 3. _____ = 6 x 4 4. 8 x 8 = _____

5. _____ = 2 x 8 6. 3 x 6 = _____ 7. _____ = 5 x 5 8. 0 x 7 = _____

9. 9 x 10 = _____ 10. _____ = 5 x 6 11. _____ = 6 x 10 12. 8 x 10 = _____

13. 4 x 7 = _____ 14. _____ = 5 x 10 15. 3 x 0 = _____ 16. 9 x 8 = _____

17. 8 x 1 = _____ 18. 5 x 2 = _____ 19. 7 x 6 = _____ 20. _____ = 7 x 9

21. 10 22. 7 23. 8 24. 7x 8 x 5 x 3 x 9

25. 6 26. 8 27. 9 28. 3x 7 x 9 x 3 x 5

29. 5 30. 6 31. 2 32. 10

x 4 x 8 x 8 x 4

33. 6 x 9 = n 34. 7 x 7 = n 35. 5 x 8 = n 36. 9 x 2 = nn = _____ n = _____ n = _____ n = _____

37. 9 x 5 = n 38. 5 x 6 = n 39. 4 x 7 = n 40. 7 x 6 = n

n = _____ n = _____ n = _____ n = _____


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41. 4 x 3 = n 42. 5 x 9 = n 43. 8 x 7 = n 44. 3 x 9 = n

n = _____ n = _____ n = _____ n = _____

How many days are there in 4 weeks?

46. How many fingers on 9 hands?

47. A pack of gum has 6 sticks. How many sticks are there in 7 packs?

48. There are 10 pencils in a package. How many pencils are there in 8 packages?

49. There are 7 new houses on the block. Each house has 3 doors. How many doors are there in all?

50. John has 9 bags of candy. Each bag has 8 pieces. How many pieces does he have in all?


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Ten Statements


No Ten Statements Today.

Free Choice Lesson


Six-Group Activity

No Six-Group Activity today.

Math Workshop






SS: Read and interpret maps, charts, tables, graphs, and cartoonsSequence information, especially using timelines


Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: No Six-Group Activity today.


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Technology:

Assessment

Formal assessment (test)

Homework

Teacher Notes

Answer Key

1. 2 2. 9 3. 24 4. 64 5. 166. 18 7. 25 8. 0 9. 90 10.3011.60 12.80 13.28 14.50 15.016.72 17.8 18.10 19.42 20.6321.80 22.35 23.24 24.63 25.4226.

72 27.

27 28.

15 29.

20 30.

4831.16 32.40 33.54 34.49 35.40

36.18 37.45 38.30 39.28 40.4241.12 42.45 43.56 44.27 45.2846.45 47.42 48.80 49.21 50.72


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Correlations (SG,CAS,CFS): 6C2; 8A2; 8B1

ITBS/TAP:Solve single-step problems using addition or

subtraction with whole numbers

ISAT:

Unit Focus/Foci



Using multiplication to solve word problems

Materials

Six-Group Activity: Division (Reading division problems)

Math journalsSmall cubes from manipulative kit

PencilOverhead Projector


Warm-up Activity:

Write the following on the chalkboard:

Find two ways to describe the following pattern, and then find the next two numbers in the

pattern 80, 72, 64, _____, _____.

(The pattern is in descending multiples of 8, or as the tens digit decreases by 1, the ones digit

increases by 2.)


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Have students write the answer to the following product as they are given orally:

a. 6 x 5 = (30) f. 7 x 5 = (35) k. 8 x 8 = (64)

b. 2 x 6 = (12) g. 6 x 10 = (60) l. 4 x 10 = (40)c. 8 x 6 = (48) h. 8 x 7 = (56) m. 9 x 6 = (54)

d. 6 x 9 = (54) i. 7 x 7 = (49) n. 7 x 8 = (56)e. 5 x 6 = (30) j. 5 x 5 = (25)

Lesson:

Say: Today we will be using charts to help solve our word problems.

Elena made a chart so she wont have to multiply each time she sells washers. Her chart looks

like this:

As I read these word problems I want you to listen carefully and write down any numbers

and operations that you think will help you solve the problem.

1. Nails cost 2 c/ each. Elena decides to make a nail chart. What will it look like? Do youthink she should make the chart? (It will look exactly like the chart for washers; no).

2. Small springs cost 7 c/ each. Make a chart for springs like Elenas chart for washers.(Chart should look like washers chart but with multiples of 7 for Amount in cents.Write the remaining problems on the chalkboard.)

3. Langs bolts cost 7 c/ each. Either make a chart for lag bolts or write what you could useinstead. (You could use the chart for the small springs).

4. Sets of hooks and eyes cost 9 c/ each. Make a hook-and-eye chart. (Chart should looklike washers chart but with multiples of 9 for amount in cents.)

5. Make a chart for sandpaper that cost 10 / a sheet. (Chart should look like washers chartbut with multiples of 10 for amount in cents.)

(Times 2)(x 2) = $.02 per washer


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Draw this chart on the chalkboard.

$ Washer Chart $

Number ofWashers

1 2 3 4 5 6 7 8 9 10

Amount inCents

2c/ 4 / 6c/ 8c/ 10c/ 12c/ 14 / 16c/ 18c/ 20c/

After helping the students work through the first two problems allow students to work in groupsto solve the 3 remaining problems. When the students have had sufficient time to solve theproblems, ask for volunteers from the groups to put a problem on the chalkboard to explain the

groups strategy.

Note: Students should be encouraged to use manipulatives to help solve the problems in thegroup activity/cooperative learning groups.

The teacher, having explained to the class and worked through the samples will now havestudents complete problems similar problems in their textbook. These papers should be collected

and corrected. Remediate where needed.

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) Todays lesson was to help students become efficient in solving multiplication wordproblems. (yes)2) Understanding and reading data from charts was essential to solving the word problems inthis lesson. (yes)

3) This lesson provided opportunity to apply the multiplication facts that we had learned. (yes)4) The Warm-up Activity showed patterns where the numbers were descending in multiples of

eight. (yes)

5) Jiros chart was made to promote the sale of his stickers on half-price day. (yes)6) Saturday was half-price day at Jiros Sticker Shop. (yes)7) Parallel lines are lines that go in the same direction. (no)8) Choosing an appropriate graph is important when interpreting graphic data. (no)9) This symbol means dividedby. Another way to write it is . Example: 7 25 . (no)10)Addition can be used to solve a subtraction problem. (no)

X 2


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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 the teacher-directed activitysheet: Division (Reading division problems).

Math Workshop






Sequence information, especially using timelines


Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: See attached Six-Group Activity sheet: Division (Reading division problems).

Technology:


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Assessment

Informally assess students participation in lesson and completion of the class assignment, with

75% of work completed correctly.

Homework

Have students make a sales tax chart for sales tax on whole dollar amounts from a grocery stores,

not clothing. (Amounts should be $1.00 to $10.00.)

Teacher Notes

When class work is finished, the teacher can review the formula for area and work through some

examples with students.


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Six-Group Activity

Division (Reading division problems)

Materials:


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

factor factor product

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; 8B4; 8C2



ISAT:

Unit Focus/Foci



Practicing multiplication and division word problems requiring missing-factor equations

Materials

Six-Group Activity: Division (Word problems)Small containers

CountersOverhead ProjectorMath journals


Warm-up Activity:

Write the following problems on the chalkboard. Have students solve.

1. John makes $6 an hour. If he makes $30 a day, how many hours does he work? (5)2. Tamla has $20. A pair of socks costs $4. How many pairs of socks can she buy with $20?

(5)

3. There are 36 cookies in the bag. If there are a dozen children present, how many cookies willeach child receive? (3)


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4. Sherri must take her medicine every 4 hours. How many times will Sherri take her medicine

in a 24-hour day? (6)

Say: Before we start with todays lesson, we are going to practice a mental math activity. Theoverhead should be set up prior to beginning the class. Present these equations. Point out the

relationship between the problem pairs as presented.

7 10=(70) 5 4=(20) 7 6=(42) 9 9=(81)

7 n=70(n=10) n 4=20(n=5) n 6=42(n=7) n 9=81(n=9)


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Problem Solving Worksheet

Use 5 small containers and 50 counters, such as buttons, cubes, beans. Share. Complete the

chart.

Number ofcounters

Number ofcontainers

How many ineach?

Remainder Fact

1. 7 2

2 8 3

3 9 4

4 9 5

5 14 4

6 9 2

7 12 5

8 14 3

9 17 3

10 19 4

11. The cast of the school play has 210 pages of lines to learn. The play is in 7 weeks. Howmany pages of lines should they learn each week?

12. The school cafeteria served 936 pieces of pizza on Monday. If each student received 3pieces, how many students did they serve?


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Lesson:

Present the following problem. Have students use mental math to solve it.

Keith earns $4 each hour at his job. Today he earned $20. How many hours did he work today?

(5)

After completing the mental math, direct the students to write the mathematics algorithms to

solve the problem. Read the problem and ask if any of the students know how to solve theproblem. Allow volunteers to solve the problem on the chalkboard.

Example 1: Keith earned $4.00 each hourKeith earned $20.00 today

4 20

20

5

Keith worked 5 hours. (5 hours x $4.00 = $20.00)20 4 =

S|T|

V|W|

n

20 4 = 5

n = 5

Explain that the known facts were: 1) Keith earns $4.00 per hour; 2) Keith earned $20.00today; and 3) n = the unknown.

8 24

24

3

8 x n = 24

8 x 3 = 24n = 3

The known facts are: 8 children and 24 cookies The cookies are to be shared equally. Find twoways to show how the cookies can be divided.

Divide the class into cooperative learning groups and allow the groups to solve the problems onthe problem-solving worksheet. Circulate among groups to make sure all students are

participating. Answer any questions.

Have students write the relationship between division and multiplication in their math journals orportfolio assessment file.


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Ten Statements


1) Multiplication and division are related. (yes)2) Practicing multiplication through regular and missing-factor problems helps to prepare

students for algebra. (yes)3) Multiplication and division are the inverse of each other. (yes)4) There are two ways to show that a problem is a division problem. (yes)5) Division is used to change ounces to pints. (no)6) Using charts can be helpful in solving multiplication and division problems. (yes)7) The two symbols seen here are both symbols which indicate that the operation needed to

solve the problem is division. (yes)8) The divisor, dividend, and quotient are all a part of a division problem. (no)9) When application of skills are reviewed, the purpose is to assess a students ability to choose

the correct operation to solve a specific word problem. (no)

10)In problem 40 8=n, the n represents the quotient. (yes)Free-Choice Lesson


Six-Group Activity


sheet: Division (Word problems).

Math Workshop

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






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Connection(s)

Enrichment: Write the following problem on the chalkboard and challenge students to find asmany patterns as they can. How many different patterns can you find in a square of 25 numbers

like the one shown.

4 5 6 7 8

5 6 7 8 96 7 8 9 10

7 8 9 10 118 9 10 11 12

Fine Arts:

Home:

Remediation:

Technology:

Assessment

1. Can students answer 75% of facts correctly? 2. Can students explain the relationship betweenmultiplication and division? 3. Can students communicate the strategies used to solve word

problems?

Homework

Have students write and solve three problems that require division.

*Note see below.


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Teacher Notes

Answer for Enrichment:

The sum of each row or column is a multiple of five.

The sums of the diagonals are equal.The sum of opposite corners are equal.The highest number equals the lowest number plus eight.

The sum of all 25 numbers equals twenty-five times the center number.The sum of the four corners equals the sum of the four middle outside numbers.The sum of all the outside numbers equals four times the sum of the numbers in the inside

square (9 numbers)The sum of the outside numbers is 12 times the center number.

Answer to Problem Solving Worksheet:

1. 3r1 2. 2r2 3. 2r1 4. 1r45. 3r2 6. 4r1 7. 2r2 8. 4r29. 5r2 10.4r3 11.30 12.312


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Six-Group Activity

Division (Word problems)

Materials:


1 envelope (9 x 6 )


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

Tell the students that when you lay an index card on the table they are going to solve the problemusing their problem solving skills.

1)

The students plan to rent boats at the lake. How many boats will the 20 students need if eachboat holds 4 students?

2) James cut a glass 12 feet long into 4 equal pieces. How long was each piece?3) Ms. Giles made 7 telephone calls. She spent 35 minutes on the telephone. What was the

average length of each call?

4) Ray received a free festival ticket for every 6 tickets he sold. How many free tickets did hereceive if he sold 36 festival tickets?

5) Jordan scored 72 points in the last 8 basketball games he played. What was the averagenumber of points he scored in each game?

Answers: (5 boats), (3 feet), (5 minutes), (6 free tickets), (9 points)

Copy this study board to use with the reteaching of this lesson.

Word problems

Review the following key words, which indicate that a word problem requires division.


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Division key words:

divided (evenly) average

split every

each out of

cut ratioequal pieces shared

Review the study board with the students and use this sample word problem:

Mrs. Alfred has 20 candles to use for table decorations. She wants to decorate 5 tables. Howmany candles can she put on each table? Ask: What are the key words that let you know this is adivision problem? Can you use multiplication to solve this problem? (yes) If so, what would

the problem be? (5 4 = 20)

Tell the students that they are going to do five word problems the same way they did the

example. Tell them they have a minute to solve each problem. While revealing the answer say,The answer is Store the index cards and study board in the 9 x 6 envelope.


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multiplication or division

ISAT:

Unit Focus/Foci

Multiplication & Division


Dividing problems

Materials

Six-Group Activity: Division (Dividing quotients greater than 10)

Math journalPencils

Play moneyCruncher


Warm-up Activity:

Write the following problem on the chalkboard. Have students solve.

The sports program at the Nash Camp has 24 campers. Find all the ways that 24 campers can

form equal-sized teams for the different events on Fun Day. (There are 8 ways: 1 team of 24, 2teams of 12, 3 teams of 8, 4 teams of 6, 6 teams of 4, 8 teams of 3, 12 teams of 2, and 24 teamsof 1.)


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Review the following vocabulary words.

Inverse operation - an operation that undoes the results of another operation.

Remainders - a number less than the divisor that remains after the dividend has beendivided by the divisor as many times as possible.

Inverse operations:

1. 8 + 6 = (14) 2. 5 x 8 = (40)14 - 8 = (6) 40 5 = (8)14 - 6 = (8) 40 8 = (5)

n + 6 = 14 n x 8 = 40(n=8) (n = 5)

Remainder: 6 R-1

4 25

241

When 25 is divided by 4, the quotient is 6; however the inverse will show that 6 x 4 is 24.Since one can not be divided by 4, the remainders is added when checking by performing

the inverse operation.

Lesson:

Present each of the problems to students. Discuss each.

Say: Eight children want to divide 80 cents equally. How much will each child get? 8 8010

Eight children want to divide 83 cents equally. How much will each child get? 8 83 . After each

child gets 10 cents, there are still 3 cents left over. We cannot always divide a whole number of

things equally, there is something left over, or remaining. We write this: 10 R3

8 83

When we read this answer, we say 10 remainder 3.

Nine children want to divide 60 cents equally. How much will each child receive? How much

will be left now?6 R6

9 60

9 x 6 = 54 60 - 54 = 6


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Each child gets 6 cents, and there are 6 cents remaining.

Assign the following 20 problems to be completed by students as independent practice.

Problems:

1) 6 36 2) 8 50 3) 9 45 4) 5 38

5) 7 50 6) 3 23 7) 10 51 8) 4 18

9) 5 55 10) 7 56 11) 4 21 12) 5 44

13) 3 17 14) 6 43 15) 3 25 16) 10 76

17) 9 37 18) 7 57 19) 8 41 20) 9 30

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) The inverse of division is multiplication. (yes)2) The inverse of addition is subtraction. (no)3) a. (6 x 6 = 36) b. ( 6 406 ) c. (40 - 36 = 4) are example of multiplication/inverse operation of

division b., and the remainder c.. (yes)4) The dividend is a term which describes a part of a division problem. (yes)5) 25 pennies cannot be evenly distributed between six people. (yes)6) 376 , is an example of a division problem with a remainder. (yes)7) Addition, subtraction, multiplication and division are the four basic operations for practicing

whole-number arithmetic. (no)8) When practicing inverse operations and missing term problems, the process readies students

for algebra. (yes)

9) Parallel lines are lines that go in the same direction. (no)10)Manipulatives used to solve division problems server as concrete reinforcers. (yes)Free-Choice Lesson


Six-Group Activity


sheet: Division (dividing quotients greater than 10).


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Math Workshop




SC: Apply scientific method to solve problemsAnalyze and interpret data


Sequence information, especially using timelinesSelect appropriate information of intended purpose

Connection(s)

Enrichment: Have students solve the following problem:

Sue and Paul made a puzzle. The numbers from 1-16 are arranged in the puzzle so that the sumof each row and each column is the same. Also, the two diagonals have the same sum, althoughthis is a different number than sum of the rows and columns. Paul and Sue have arranged some

of the numbers for you. Complete the puzzle.

5 16

6

14

13 9

Fine Arts:

Home: Have students create five problems with remainders use manipulative to show whatfunctions were used.

Remediation: See attached Six-Group Activity sheet: (Dividing quotients greater than 10)

Technology:


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Assessment

Informally assess students, class participation. Assess students ability to attain 80% correct on

computation problems.

Homework

Dictate these problems to the students for homework.

1. 8 72 2. 9 543. 8 32 4. 9 365. 8 64 6. 8 167. 8 72 8. 8 409. 8 56 10.9 27

Teacher Notes

Remind students to sharpen their skills in multiplication facts. Make note of any students who

are experiencing difficulties and provide extra help.

Answer to Enrichment exercise:

50

17 5 1 16 34

6 15 11 2 34

3 10 14 7 34

13 4 8 9 34

34 34 34 34 50

Answers for Homework:

1. 9 2. 6 3. 4 4. 4 5. 86. 2 7. 9 8. 5 9. 7 10.3


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ISAT:

Unit Focus/Foci



Division with remainders review

Materials

Six-Group Activity: Division (Using multiplication to check answers)Base ten blocks

CountersWorksheet: Division


Warm-up Activity:

Write the following on the chalkboard.

Stacey brings three quarters to the candy store. She likes penny candy. She likes blow pops

priced at ten for $1.00, Fruit chews at four for $.36, hats at three for $.21, hearts at two for $.30;and kisses at $.29 each. Does Stacey have enough money to buy one of each of her favoritecandies? If so, does she have money left over? If not, how much more money does she need?

(One of each costs $.70, so she has $.05 remaining.)


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Have students solve the following problems.

1

5

9 21 56 38 25

13 19 29 8 0

17 23 19 42 16

.

.

.

.

.

4 29 2. 8 34 3. 4 36 4. 6 50

6 20 6. 7 29 7. 8 43 8. 5 39

2 10. 6 11. 6 12. 3

9 14. 5 15. 0 16. 5

5 18. 4 19. 7 20. 3

Play the Thumbs Up, Thumbs Down game with the mental math activity for remainders.

Lesson:

Have the students recall the multiplication facts and that multiplication is the inverse of division

when solving problems in this lesson.

Have the students solve problems on the division worksheet independently. Students may usebase ten blocks or counters to solve problems.

Collect the worksheets. Review them to assess students strengths and deficiencies. Allow

students to work in cooperative learning groups to solve problems #1 through #4. Circulatearound the groups to check the answers, allow a few students to go to the chalkboard to solveand explain a few of the problems.

Write these problems on the chalkboard.

June has 26 postcards. She wants to send three postcards to each of eight friends. How manypostcards will she have left? (2)

Jim has 50 pennies. He wants to divide them evenly among six friends. How many pennies will

he have left? (2)

Joe wants to give an equal number of stickers to each of his four friends. If he has 31 stickers,

how many will each friend get? How many will he have left? (7r3)

Kim has 26 photos she took at the class play. Four photos will fit on each page of her photo

album. How many pages will the 26 photos completely fill up? (6)

Present the following problem. Have students answer the related questions.


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Ten Statements


1) Algorithyms are steps needed to solve some problems. (yes)2) Multiplication facts are important to division, because multiplication is the inverse operation

of division. (yes)3) A remainder is less than the divisor that remains often the dividend has been divided by the

divisor as many times as possible. (yes)

4) Coordinate grids are important when one teaches the convention for graphing ordered pairsof numbers. (no)

5) In this lesson, division with remainders was the primary focus. (yes)6) A dividend is a number that is divided by a divisor. (yes)7) The metric system is a system for measuring. (no)8)

Missing-factor problems are introduced to show the inverse relationship betweenmultiplication and division. (yes)

9) The remainder is the number left over after dividing. (yes)10)Factors are two or more numbers that are multiplied. (no)Free-Choice Lesson


Six-Group Activity


sheet: Division (Using multiplication to check answers).

Math Workshop





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Connection(s)

Enrichment: Have students solve the following problem. What was the original problem?What numbers fit into each space? Try one number at a time.

Fine Arts:

Home:

Remediation:

Technology:

Assessment

Formal Assessment: Check that students achieve 80% mastery.

Homework

Write these problems on the chalkboard. Have children solve them for homework.

1. 7 31 2. 6 323. 8 67 4. 4 315. 4 30

__ __ 4 __ __

__ 4 __+ 8 __ __

__ __ __ 8


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Teacher Notes

Answers for Enrichment exercise:

424

848

9328

+

22

848

or 448

9408

224

42

896

+

Answers for Homework problems:

1. 4r3 2. 5r2 3. 8r3 4. 7r3 5. 7r2Answers for Worksheet:

1. 4 2. 6 3. 34. 4 5. 6 6. 57. 5 8. 8 9. 910.6 11.4 r 4 12.8r 313.5 4 14.7r 2 15.8 no16.6 canoes 17.8 1 foot of plastic left over18.5 rows, 2 horses left over


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Division Worksheet

Find the missing factors and the quotients.

1. mmmmmmmm

mmmm

_____ 3 = 1212 3 = _____

2.mmmmmm mmmmmm

mmmmmm_____ 3 = 1818 3 = _____

3. mmmmmm

mmm

_____ 3 = 99 3 = _____

4. mmmmmmmm

mmmm

mmmm

_____ 4 = 1616 4 = _____

5.mmmmmmmmmmmm

mmmmmm

mmmmmm

_____ 4 =2424 4 = _____

6. mmmmmmmmmm

mmmmm

mmmmm

_____ 4 = 2020 4 = _____

7.

9 45 8.

9 72 9.

7 63 10.9 54

11.9 40 12.8 67 13.7 39 14.5 37


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Correlations (SG,CAS,CFS): 6C3; 6D1

ITBS/TAP:Solving single-step problems using

division with whole numbers

ISAT:Solve word problems requiring computations

with whole numbers

Unit Focus/Foci



Assessing division facts

Materials


Formal assessment (See attached.)


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Test

Complete these charts.

1. Betty works in a candy store. Bubble gum costs 3 each.

Number of pieces ofBubble gum 1 2 3 4 5

Amount (in cents)

2. Josh works in a store that sells stickers for 10 each.

Number of stickers 2 4 5 7 9

Amount (in cents)

Divide

3. 18 6 = _____ 4. 24 4 = _____ 5. 21 7 = _____ 6. 20 5 = _____

7. 30 6 = _____ 8. 48 8 = _____ 9. 36 9 = _____ 10. 42 7 = _____

11. 4 32 12. 5 29 13. 6 41 14. 5 24

15. 7 50 16. 8 40 17. 3 29 18. 2 12

19. 9 55 20. 6 58 21. 4 30 22. 5 43

23. Cathy has 27 stickers. She gives 6 stickers to each of her 4 friends. How many stickers willshe have left?

24. Billy has 40 pieces of candy. He wants to divide them into equal piles of 7. How many will

he have left?

25. Bernadette has 38 dolls. She wants to line them up on 5 shelves. How many completeshelves will she have?


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Ten Statements


No Ten Statements today.

Free- Choice Lesson


Six- Group Activity

No Six-Group Activity today.

Math Workshop






SS: Read and interpret map, charts, tables, graphs, and cartoonsSequence information, especially using timelines


Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: No Six-Group Activity today.


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Technology:

Assessment

Formal

Homework

Teacher Notes

Answer key for test:

Each answer in problems 1 and 2 are worth 3 points. Problems 3-25 are worth 3 points each.

1. 3, 6, 9, 12, 15 2. 20, 40, 50, 70, 90 3. 34. 6 5. 3 6. 47.

5 8.

6 9.

410.6 11.8 12.5R4

13.6R5 14.4R4 15.7R116.5 17.9R2 18.619.6R1 20.9R4 21.7R222.8R3 23.3 24.525.7

structured curriculum lesson plan day: 033 subject: mathematics grade level:

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