Structured Curriculum Lesson Plan Day: 078 Subject: Mathematics Grade Level:

8/14/2019 Structured Curriculum Lesson Plan Day: 078 Subject: Mathematics Grade Level:

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STRUCTURED CURRICULUM LESSON PLAN

Day: 078 Subject: Mathematics Grade Level: 4

Correlations (SG,CAS,CFS): 6A3

ITBS/TAP:Perform arithmetic operations involving

integers, fractions, decimals, and percents

ISAT:

Unit Focus/Foci

Decimals

Instructional Focus/Foci

Reading, writing, and identifying decimals expressed through thousandthsMaterials

Six-Group Activity : Decimals (place value)Decimal modsOverhead projectorOverhead transparenciesStudents’ homework papersPlace value chart

Educational Strategies/Instructional Procedures

Warm-up Activity:

Teacher will tell students to pretend they each have $5.00 and want to purchase specific items.Teacher will read an item and its price. Students will raise their left hands if they have enoughmoney, and their right hands if they do not. (Students will ignore sales tax for this exercise.)

Two magazines for $1.95 each (left hands)Five notebooks for $1.10 each (right hands)Two T-shirts for $2.50 each (left hands)Four candy bars for $1.10 each (left hands)Four erasable pens for $1.25 each (right hands)





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6) Twenty dollars minus eighty-five cents is nineteen dollars and fifteen cents. (yes)7) The first three decimal places are tenths, hundredths, and thousandths. (yes)8) A decimeter is one tenth of a meter. (no)9) A decameter is ten meters. (yes)10) When reading a number, say “and” whenever you see a decimal point. (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 teacher directed activitysheet Decimals (place value)

Math Workshop

Have the students work in the Math 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 cartoonsSequence information, especially using timelinesSelect appropriate information for intended purpose

Connection(s)

Enrichment:

Fine Arts:

Home: Find the total cost of groceries for the family for a week; then estimate the total cost forthe year (parent and student).

Remediation: See attached Six Group Activity Sheet Decimals: Place value



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Technology:

Assessment

Student performance on homework assignment.

Homework

Each student will write two original word problems relating to place value of decimals.

Teacher Notes



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Six Group Activity

Decimals: Place value

Materials:

15 (3 x 5) index cards1 black marker1 pencil1 (9 ½ x 6 ½) envelope

Prepare these index cards using the black marker and the pencil to write the answers on the back.

1. 264.20 2. 54,912 3. 8,342.09 4. 37.045 5. 39.2646. 391.40 7. 795.261 8. 471.003 9. 921.203 10. 926.1511. 3.09 12. 1314.26 13. 596.263 14. 45.391 15. 376.02

1. For the first five numbers, what place is the 4 in?2. For the second, five numbers ask: What place is the 1 in?3. For the third set, write the place value for the three?

Answers:1. ones2. thousands3. tens4. hundredths5. thousandths6. ones7. thousandths8. ones9. ones10. tenths11. ones12. hundreds13. thousandths14. tenths15. hundreds

Copy and use as a study board with the lesson





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Correlations (SG,CAS,CFS): 6B1


decimals

ISAT:

Unit Focus/Foci

Decimals


Place valueMaterials

Six-Group Activity : Decimals (number line)Decimal mods / overhead projector / overhead transparencies


Warm-up Activity:

Write the following five sets of numbers on the chalkboard.$2.80 $2.85$0.025 $0.25$2.50 $2.05$10.440 $10.52$315,000 $315.10

The students are to copy and compare using the symbols <, >, and = (“less than,” “greater than,”and “equal to”). *Note: These symbols have been introduced previously. These symbols shouldbe visible on classroom teaching displays, and should be recorded in the student notebooks. If there are students who have difficulty with the use of the symbols, six-group activity may beused to reteach necessary skills.



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Have volunteers to share answers with the class. Class will discuss answers, while studentscorrect their papers.

Lesson:

The teacher will distribute decimal mods to class. The teacher will have sorted materials intosets containing: one flat, ten rods, ten cubes, and ten tiles. (These materials may be usedindividually or in pairs.) Allow five to seven minutes for students to explore and becomefamiliar with materials. As a volunteer to tell what he/she has noticed about the materials. Youshould have responses like this, “ten of these will make or is equal to one of those,” etc.

The teacher will display one of each figure from the overhead or chalkboard, tell its name andvalue.

Example: This is a cube. It equals one-hundredth or (0.01). This is a tile. A tile is equal to onethousandth or (0.001). The students will draw pictures of each figure, write its name and value

in decimal notation.Write a whole number such as 6,452, 279 on the chalkboard or over head transparency.

While pointing to each digit, ask what place it is in. Ask students what they are actually doing asthey move to the left (multiplying by ten); as they move to the right (dividing by ten).

Annex a four place decimal to this whole number (Ex. 23,532,598,135). Starting at the nine, ask students to predict the name of the place that the eight is in. Remind them to use the decimalmods and refer to their notes to help find the answer. Students should be able to state that this

place is one-tenth of one, and can be written 0.1 or1

10. Continue discussion as to the place

value of the 1, the 3, and the 5. Stress that they are continuing the pattern that they saw in thewhole number of dividing by ten each time they move one place to the right. Ask students whythere is no “oneth” place. (Answer: there isn’t a “oneth” place because the first decimal place isone-tenth of one; therefore its place is the tenth place).

Returning to the number (23,532,698,135), ask for the value of each digit. Example: The two,in the millions place has a value of two millions (2,000,000). The three in the thousandths placehas a value of three thousandths (or 3,000). The three thousandths place has a value of threethousandths (or 0.003). The teacher should display both ways of writing the value of the digits.*Note: Students should write this in their notes.



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Ten Statements

Review the ten statements and have the students write yes if they heard it in today’s lesson andno if they did not. If the answer is no , say: The statement is true, but it was not heard in today’slesson.

1) The top number in a fraction is called the numerator. (no)2) A tile in the decimal mods is worth 0.001. (yes)3) Ten rods in the decimal mods kit equals one flat. (yes)4) Some of the multiples of two are four, six, and eight. (no)

5) In the decimal mods kit, the value of a rod is1

10of the value of a flat. (yes)

6) There is no “oneth” place in our number system. (yes)7) The factors of eight are one, two, four, and eight. (no)8) One tenth is the first decimal place to the right of the decimal point. (yes)9) A five in the tenths place is worth ten times more than a five in the hundredths place. (yes)

10) A decimal can be converted into percent. (yes)

Free Choice Lesso n


Six Group Activity

Have a group of six students, two from each ability level, complete teacher directed activitysheet Decimals (number line)

Math Workshop

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




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

Sequence information, especially using timelinesSelect appropriate information for intended purpose



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Connection(s)

Enrichment:

Fine Arts:

Home: Select 5 items from a mail-order catalog and calculate the total sales tax and anyshipping charges (parent and student).

Remediation: See attached Six Group Activity Sheet Decimals: Number line

Technology:

Assessment

Teacher observation of class participation

Homework

Students will find newspaper or magazine articles containing decimals, cut these out and tape orpaste them to notebook paper. If they cannot find articles, they may write five decimals of theirown. They will make up five questions about each decimal, which are similar to questionsdiscussed today, or which reflect questions they are interested in, or concepts they are stillconfused by.

Teacher Notes



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Six Group Activity

Decimals: Number line (graphing decimals)

Materials:

7 (5 x 7) index cards10 (3 x 5) index cardsContact paper7 black crayons or washable markers (fine line)1 paper towel to be cut up into 6 pieces1 pencil1 (9 ½ x 6 ½) envelope

Prepare these 5x7 index cards. Copy the number line and tape it to the 5 x 7 index card. Cut thecontact paper the same size as the 5 x 7 card and cover the card with the contact paper.

0 .5 1 1.5 2 2.5 3 3.5 4 4.5 5

Prepare these 3x5 index cards using the black marker.2; 1.3; 2.5; 4.8; 3.7; 0.75; 4.2; 5; 1.5; 2.2

The teacher will show the answers on their graph card. Xerox this study board to aide inreteaching of this activity.

Graphing decimals

The number line below shows each whole number divided into ten equal parts, or tenths.

0 1 2 3 4 5 6 7 8 9 10 11

From one number to the next number there are ten tenths.

Example:0 1



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Bernadette’s eight and six tenths are recorded on the number line.

Carl did four and five tenths hours and it is recorded on the number line.

Say this to the students:

We are going to do an activity that requires you to plot numbers on the number line. I am goingto show you a card and I want you to use the crayon or marker to plot your answer. The teacherwill place an index card on a flat surface. Give the students 3 to 4 seconds to mask their answer.The teacher should use the extra card to mark the correct answer to show the students. Beforeyou show the correct answer say, “The answer is……” do the remaining cards the same way.Store the index cards and study board in the 9 ½ x 6 ½ envelope.

Tell the students that they are going to do an activity that calls for them to plot numbers on thenumber line. Lay a card on the table and allow students to solve the problem. While revealingthe answer and say, ”The answer is……” Store the activity and study board in the 9 ½ x 6 ½

envelope.



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Correlations (SG,CAS,CFS): 6B1


decimals

ISAT:

Unit Focus/Foci

Decimals


Comparing and orderingMaterials

Six-Group Activity : Decimals (comparing and ordering)Overhead projectorOverhead transparencies


Lesson:

Teacher will dictate a number such as 420.086. Students will write this number on their papers.Teacher gives directions such as “Circle the digit in the hundreds place. Underline the digit inthe hundredths place. Put a box around the digit which is worth ten times as much as the eight,”etc. Volunteers will come to the overhead projector to show how they followed each directionand explain why.

Direct students to take notes. Teacher will stress the importance of writing decimals verticallywhen comparing or ordering them, and that they can annex zeroes to the right of any decimalwithout changing the value of that decimals. Annexing zeroes gives each decimal an equalnumber of digits and makes it easier to see which one is greater or less than the other. Forexample, if you are asked to compare 4.6 and 9.27, you may write these decimals the followingway.



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9.274.6

A student looking at the problem the way it was originally written may think the first fraction issmaller because three is smaller than twenty-seven. However, when problems are written

vertically and zeroes are annexed to the right, it is easy to see that 40 hundredths is greater than29 hundredths.

Students will complete five problems from part 1 and 5 problems from part 2 on p. 64. Studentsmay choose to work alone or with a partner.

Student volunteers will provide answers for problems they completed, and explain their methodsfor comparing and ordering. Teacher will accept alternate methods if they are logical and if theywill work all the time.

Teacher will display 15.79 and 15.8 and ask whether the first one is greater than, equal to, or less

than the second one, and why.Ten Statements


1) When comparing two decimals that are written horizontally, it may be helpful to rewritethem vertically. (yes)

2) You can annex as many zeroes as you want to the right of a decimal without changing thevalue of that decimal. (yes)

3) Eight equals eight point zero equals eight point zero. (yes)4) Four tenths is greater than thirty-nine hundredths. (yes)5) To multiply two fractions, first multiply the numerators, then multiply the denominators.

(no)6) After multiplying two decimals, make sure your product has the same number of decimal

points that you had in your factors. (no)7) If you have a remainder after doing a division problem, you can sometimes express that

remainder as a decimal. (no)8) Six is equal to six point zero. (yes)9) Seven point ten is greater than seven point zero one. (yes)10) Two point eight six is equal to two point eight six zero. (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 Decimals (comparing and ordering)

Math Workshop



LA: Understanding explicit, factual information

Understanding the meaning of words in contextSC: Apply scientific me thod to solve problemsAnalyze and interpret data


Connection(s)

Enrichment: Have students find the frequencies of their five favorite radio stations (example -107.5) and graph them in order of decreasing MHz/kHz.

Fine Arts:

Home: Compare the cost of different brands of one item in the supermarket to find the best buy(parent-child).

Remediation: See attached Six Group Activity Sheet Decimals: Comparing and ordering

Technology:



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Assessment

Completed assignment, class participation

Homework

Students may select one worksheet (Reteaching, Practice, or Enrichment) to complete, afterteacher displays and explains directions for each. Or, teacher may assign the proper worksheetto each student, depending on his or her informal observations of level of mastery.

Teacher Notes



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Six-Group Activity

Decimal (Comparing and ordering decimals)

Materials:

10 index cards (5 x 7)1 black marker1 pencil1 envelope (9 ½” x 6 ½”)

Prepare the index cards using the black marker to write problems on the front of the cards anduse the pencil to write the answers on the back.

1. 450.17; 450.1; 450.09 6. 34.2; 39.02; 39.12. 58.83; 58.71; 55.84 7. 40.3; 41.2; 42.23. 39.09; 36.6; 32.91 8. 5.75; 15.75; 57.5

4. 27.08; 29.14; 29.32 9. 429.02; 429.39; 429.65. 1.15; 1.26; 0.94 10. 201.5; 201.6; 201.9

Answers:

1. 450.09; 450.1; 450.172. 55.84; 58.71; 58.833. 32.91; 36.6; 39.094. 27.08; 29.14; 29.325. 0.94; 1.15; 1.266. 34.2; 39.02; 39.17. 40.3; 41.2; 42.28. 5.75; 15.75; 57.59. 429.02; 429.39; 429.610. 201.5; 201.6; 201.9

Copy this study board and use it to reteach the concepts of comparing and ordering decimals.

Decimals (Comparing and ordering decimals)

Say: When comparing decimals, look from left to right. Example: 3.068, 3.7, 3.084



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Look at the place value chart.

Ones . tenths hundredths Thousandths3 . 0 6 83 . 7

3 . 0 8 4

First compare the whole numbers.

The ones value for each number is the same.

Next look at the tenths place.

0.7 > 0.0 so 3.7 is the greatest number.

Look at the hundredths place.

0.08 > 0.06 so 3.068 is the least number.

Tip: The further the numbers go back behind the decimal, the smaller it gets. .084 is in the same place value space as .068 so compare the number, .084 is larger than .068.

Show the students 201.5 and 201.66. Have them look at the whole numbers first. 201 and 201are the same. Now look at the first number behind the decimal points; they are 5 and 6. Thenumber 6 is larger than 5, so the number 201.66 is larger than 201.5.

Tell the students that you are going to show them some cards with sets of decimal numbers on

them and you want them to put the numbers in order from least to greatest. Allow students touse the place value chart if they need it.

Lay a card on a flat surface and give the students up to one minute to write the numbers in order.When you turn the card over to reveal the answer say: The answer is…… Continue with theremaining index cards until finished. Call the next group and do the same activity. Store theindex cards and study board in the 9 ½” x 6 ½” envelope.



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Correlations (SG,CAS,CFS): 6C1


decimals

ISAT:

Unit Focus/Foci

Decimals


Adding and subtracting decimals and describing and demonstrating understanding of the inverserelationship between adding and subtracting

Materials

Six-Group Activity : Decimals (tenths)Overhead projectorOverhead transparencies


Warm-up Activity:

Ask the students to show thumbs up if they have enough money to purchase the item and thumbsdown if they do not have enough money to purchase the items.

Students have $100.00.

Do you have enough money to purchase? ↑ thumbs up, ↓ thumbs down

1. four bath robes that cost $29.00 each ___ ↓2. A video game that cost $59.00 and 3 cartridges for $4.99 each ___ ↑

3. Six cassettes that cost $9.99 each and 4 games that cost $8.50 each ___↑



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Teacher may choose to do a couple of additional warm-up. Examples if needed.

Lesson:

Write sample problems on transparency and explain, step-by-step, how to write decimal

problems vertically, and line decimal points up in order to add or subtract. The sample problemsall deal with money, so this is a review of a previous lesson. If a group of students seems to stillbe having problems with adding or subtracting money, the teacher can use the play money setduring the six-group activity.

Examples: In order to add, the problem $0.70 + $8.98 should be written as follows.

$0.70×$8.98

In order to subtract, the problem must be written as $15 - $12.87$15.00

−$12.87

Circulate giving help as needed. Students may work alone or with a partner. If partners getstumped, they may also ask other student/partners for help. After sufficient time is allowed,answers will be discussed as a whole class. Student volunteers may come to the chalkboard oroverhead transparency to teach problems in which they feel confident. The teacher may teachany problems which stumped the entire class, or which no one in class attempted.

Teacher will demonstrate that addition and subtraction are inverse operations, meaning that one

can “undo” the other. For example, if you add 9.98 to 0.80, you get 10.78. If you subtract 0.80from 10.78, you get 9.98. If you subtract 9.98 from 10.78, you get 0.80.

Students will summarize main points from the lesson in their math journals.

Ten Statements


1) When problems involving addition or subtraction of decimals are written horizontally, it isuseful to rewrite them vertically. (yes)

2) You must line up the decimal points when writing a problem vertically before you add orsubtract. (yes)



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3) The largest decimal number is not necessarily the one with the most number of digits. (yes)4) The larger number must go on top when writing a problem vertically that involves

subtraction of decimals. (yes)5) When subtracting decimals, you may annex as many zeroes as necessary to the right of the

decimal number. (yes)

6)

Seven point four and seven point four zero have the same value. (yes)7) Perimeter means the distance around a figure. (no)8) Area is expressed in square units. (no)9) There are four quarts in a gallon. (no)10) If you pay for an item that costs $8.08 with a ten dollar bill, your change will be $1.92. (yes)

Free Choice Lesson


Six Group Activity

Have a group of six students, two from each ability level, complete teacher directed activitysheet Decimals (tenths)

Math Workshop






Connection(s)

Enrichment: Students can make their own cross number puzzle involving addition orsubtraction of decimals.





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Six Group Activity

Decimals: Tenths

Materials:


Prepare these index cards using the black marker and use the pencil to write the answers on theback.

410

29

108

108

510

143

106

101

107

1036

110

63

10

Answers: .4 2.9 .8 8.5 14.3 .6 .1 .7 36.1 6.3

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

Decimals - tenths

Decimals are names for fractional numbers. Fractions can be written with a denominator of 10,100, 1000, etc. A decimal can be used to name the number.

710

= .75

10= .5 2

310

= 2.3

The dot in the decimal is called the decimal point. It is written to the right of the ones place.The first place to the right of the decimal point is the tenths place.

310

or .3 is shaded.

12

10or 1.2 is shaded.





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Correlations (SG,CAS,CFS): 6B3, 4; 6C4; 6D1, 2


integers, fractions, decimals, and percents

ISAT:

Unit Focus/Foci

Decimals


Problem-solvingMaterials

Six-Group Activity : Decimals (lining decimals up)Overhead projector


Warm-up Activity:

Present this problem on the chalkboard.

Find a decimal number that is equally greater than 1.7 and less than 7.1 (4.4). Show how youarrived at the answer.

Lesson:

Model problem-solving techniques, such as:

1. Skim entire problem for the main idea.2. Read problem carefully to find out what question you are being asked to answer.3. What key words give hints about processes you will use? 4.



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4. What numbers are given, and what do they represent?5. Is there any missing information?6. Is there too much information?7. What answer seems reasonable (an estimate)?

Teacher will also warn about certain pitfalls, such as reading too fast and not seeing the words.Students will then choose four more problems to solve, and write their strategies for solving.Write-ups should include any “traps” they see which might fool someone, and their own methodsfor avoiding these pitfalls.

Volunteers will then discuss each problem. Allow two or three students to “teach” each problemto show various methods that could be used in arriving at the correct answer. Stress that even if some students did not arrive at the correct answer, their thinking steps and problem-solvingmethods are still valuable.

Ask students who do not answer correctly what they would change next time they are confronted

with a similar problem. Teacher will model good strategies for any problems that were notattempted, or for which no students had a correct answer. Students will take notes in their mathnotebooks.

Ten Statements


1) The bottom number in a fraction is called a denominator. (no)2) Presidential elections are held every four years. (yes)3) The next Presidential election will be in the year 2000. (yes)4) Fractions can be used to show part of a whole. (no)5) When you know the size and number of equal parts, you can multiply the size by the number

of equal parts to find the total. (yes)6) Fractions can be used to show part of a set. (no)7) When you know the total and how many equal parts, you can divide the total by the number

of equal parts to find the size of each part. (yes)8) When you know how much an item costs and how much change someone received, you can

add to find out what amount he/she gave in payment. (yes)



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9) When you know how much money is in someone’s savings account, and what that person’ssavings goal is, you can subtract to find out how much more he/she has to save. (yes)

10) When you know a business owner’s sales and expenses for a week, you can add the sales,and subtract the expenses to find his or her profit. (yes)

Free Choice Lesson


Six Group Activity

Have a group of six students, two from each ability level, complete teacher directed activitysheet Decimals (lining up decimals)

Math Workshop

Have the students work in the Math Workshop after completing their Free Choice Lesson .Integration with Core Subject(s)




Connection(s)

Enrichment: Students can write a story problem in which the final answer is already given, andtheir partners will have to work backwards to fill in missing numbers and their labels.

Fine Arts:

Home: Parents can help students study for test.

Remediation: See attached Six Group Activity Sheet:



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Technology:

Assessment

Completed assignments, class participation

Homework

1. 2.60+3.2 2. 5.26+26.3 3. 9.61+3.1 4. 10.36+9.21 5. 11.03+12.1+2.3

6. Explain in writing step by step how to solve one of the five problems.

Teacher Notes



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Six Group Activity

Decimals: Lining decimals up

Materials:

20 index cards (3 x 5)1 black marker1 pencil1 envelope (9 ½ x 6 ½)

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.

1) 59.2 + 322.1 + .2 2) 6.1 + .002 + .1 3) 7.21 + 3.2 + 54) 2.34 + 1.346 + .2 5) 9 + 23.2 + 3.1 6) 6.24 + 21.1 + .217) 9.23 + .23 + 10.211 8) 54.12 + 321.2 + .03

9) 7.1 + 9.3 + .02 10) 5.21 + .36 + 69Answers:

1)59.2

322.1+ .2

2)6.1

.002+ .1

3)7.213.2

+ 54)

2.341.346

+ .2

2)9

23.2

+ 3.1

6)6.24

21.1

+ .21

7)9.23

.23

+10.211

8)54.12

321.2

+ .03

9)7.19.3

+ .0210)

5.21.36

+69.

Next, prepare another set of cards using the answers (addition problems) above. Write theseusing black marker. On the back of the cards, write the answers to these addition problems.

1. 381.5 2. 6.2023. 15.41 4. 3.8865. 35.3 6. 27.557. 19.671 8. 375.359. 16.42 10. 74.57



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Have the students who are above or at grade level write and answer the problems.

Addition of decimals

Say: When adding decimals line the points up first and then write the numbers in the correct

order. Example: If a problemhas two sets of numbers (26.3 + .021), rewrite the problem vertically.

Step 1: Write the decimals.Step 2: Write the numbers in the correct order.

26.3+ .021

Step 3: Then you are ready to add.26.3

+ .02126.321

Step 4: In the answer, bring the decimal straight down. (26.321)

Explain how to solve addition of decimals problems using the study board as a guide. After youexplain how to do the problems, tell the students that they are going to do an activity calledlining up decimals . Explain that to line the decimals up and write the numbers in the correctorder. Say: Don’t write the answer because we want to work on ordering the numbers.

Say: I am going to lay a card down and I want you to write the problem vertically. Lay one

index card on a flat surface and give the students five or six seconds to write the answer. Whenthe time is up, turn the index card over and say: The answer is…… Go to the next card andrepeat the process.

Tell the students that they are going to do an activity called adding decimals.

Lay a card on a flat surface Turn the card over to reveal the answer and say: The answer is…Go to the next card and repeat the process. Call the next group and do the same activity. Storethe index cards and study board in the 9 ½” x 6 ½” envelope.



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Correlations (SG,CAS,CFS): 6A3,6; 6B1,3,4; 6C1,4; 6D1,2

ITBS/TAP:Computation adding and subtracting decimals

ISAT:

Unit Focus/Foci

Decimals


Formal Assessment-place value, comparing, addition and subtraction

Materials

Number cubes 0-5 and 5-10Overhead projectorOverhead transparencies


Warm-up Activity:

See attached (Mathematics Assessment)



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Mathematics Assessment

Add, subtract, multiply and divide:

1) 5.2 2) 7.81 3) 7.69 4) 5.43-2.15 -3.20 +3.20 +4.83

5) 1.72 + 3.14 =

6) 5.29 - 3.24 =

7) 14.82 - 11.1 =

8) 4.5 + 6.5 =

9) John rode his bike 500 meters in 1 minute and 49.7 seconds. Tory rode 500 meters in twominutes and 3.1 seconds. By how much did John beat Tory?__________________________

10) 7.2 x 10 = 11) 63.4 ÷ 10 =

12) 26.1 x 100 = 13) 42.5 ÷ 10 =

14) 8.9 x 1000 = 15) 44.8 ÷ 100 =



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Compare: Draw <, >, or = to make each statement true.

16) 0.3 ___ 0.4 17) 0.5 ___ 0.50

18) 0.947 ___ 8.32 19) 4.703 ____ 4.73

20) 7.99 ____ 8.0

21) Round 0.587 to the nearest hundredths.

22) Round 0.72 to the nearest tenth.

23) Round 0.1459 to the nearest thousandths.

24) Round 2.79 to the nearest tenth.

25) Round 5.368 to the nearest hundredths.

There is no Warm-up, remediation, or homework today. As a free choice activity, students maychoose one or more games to play when their tests are completed.



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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 No Six-Group Activity today.

Math Workshop

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





Connection(s)

Enrichment:

Fine Arts:

Home:



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Remediation:

Technology:

Assessment

Homework

Teacher Notes

Answers to Assessment:

1. 3.052. 4.613. 10.894. 10.26

5.

4.866. 2.057. 3.728. 119. 46.610. 7211. 6.3412. 261013. 4.2514. 890015. 0.44816. <17. <18. <19. >20. <21. 0.5922. 823. 14624. 2.8025. 5.4



510



Correlations (SG,CAS,CFS): 6C2; 7B1; 8D5


decimals. Choose and apply problemsolving strategies,

ISAT:Solve word problems requiring computation

with decimals.

Unit Focus/Foci

Decimals


Estimating products of decimals

Materials

Six-Group Activity : Decimals (rounding)


Warm-up Activity:

a). Round these decimals to the nearest whole number.

67.15 45.674

0.6214 15.749

b). Find the sum or difference

16.3 + 40.7 92.5 - 71.3

5.006 + 442.17 + 587.408



511

Lesson:

Vocabulary - ReviewApproximate, product, factors, area in context. Have student fill in blanks.

The word _____________ is a signal to estimate an answer. You can round the ___________-ina multiplication problem and multiply them to find the ______________. You can multiply thelength of a rectangular figure by its width to find its ______________. (approximate, factors,product, area).

Area is the amount of space covered by a flat surface.

Example: You want to cover your bedroom floor with carpet. The length of your room is 12.3.Its width is 9.8. Find the approximate area of your floor.

Step 1: First round each decimal to the nearest whole number. 12.3 = 12 (12.3 is about equal to

12) 9.8 = 10Step 2: Multiply the new numbers. 12 x 10 = 120. Area is always expressed in square units, sothe final estimate is 180 square feet for the room area.

Example 2: The carpet costs $18.98 per square foot. About how much should your expect topay to carpet your room? ( This time use a compatible number instead of rounding to the nearestwhole number. $18.98 ≈ 20. 120 square feet times $20.00 equals about $2,400. You canexpect to pay about $2,400 to carpet your room.

Ask students whether it is good to estimate more or less than the exact amount in this situation(answer: It’s better to over-estimate because it is better to save a little too much money than tocome up short).

Give the students a few more similar problems to work with you and a few to try independently.Close by discussing answers to the problems done independently. Discuss in depth to make surethey understand concepts and vocabulary.



512

Ten Statements


1) The area of a rectangular - shaped figure can be found by multiplying the length of the figuretimes it width. (yes)

2) Area is expressed in square units. (yes)3) Area is the amount of space covered by a flat surface. (yes)4) In a multiplication problem, the numbers to be multiplied are called factors. (yes)5) The answer to a subtraction problem is called the difference. (no)6) The answer to a multiplication problem is called the product. (yes)7) You can round the factors of a multiplication problem to help you estimate the answer. (yes)8) Rounding a decimal to the nearest whole number or using compatible numbers are two ways

to help you estimate. (yes)

9)

The perimeter is the distance around a figure (no).10) The surface area of a box is the sum of the area of all of the surfaces of the box. (no)

Free Choice Lesson


Six Group Activity

Have a group of six students, two from each ability level, complete teacher directed activitysheet Decimals (rounding)

Math Workshop

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






513


Connection(s)

Enrichment: Student can measure a one inch by one inch square and cut it out. Using this as apattern, they can cut 100 more. They choose three rectangular objects and predict their area.Students can cover these objects with the square inches and count them to find the exact area.They can also count the length and width, then multiply them to verify that this is another way tofind area. This activity also reinforces the reason for reason for measuring area in square units.

Fine Arts:Home: Parents can assist students in measuring the area of a table to buy a table cloth of theright size, etc.

Remediation: See attached Six Group Activity Sheet Decimals: RoundingTechnology:

Assessment

Participation, completed assignment

Homework

Have students write five problems of their own involving estimating products with decimals.

Teacher Notes



514

Six-Group Activity

Decimals (Rounding)

Materials:

10 index cards (3” x 5”)1 black marker1 pencil1 envelope (9 ½” x 6 ½”)

Prepare the following index cards using the black marker to write the problems on the front of the cards and use the pencil to write the answers on the back.

Nearest Whole Number Tenths Hundredths

9.82, 28.7, 49.5 .76, .145, .98 .877, .215, .449, 36.50

Answers: 10; 29; 50; .8; 1; .88; .22; .45; 37.

Copy this study board use this to reteach the lesson.

Rounding decimals

Say: Decimals are rounded the same way whole numbers are rounded. 8.625

8.625 rounded to the nearest one is 9. Since the numeral to the right of the ones (6) is 5 or greater, the ones number is rounded up.

8.625 rounded to the nearest tenth is 8.6. Since the numeral to the right of the tenths (2) is lessthan 5, the tenths number is rounded down.

8.625 rounded to the nearest hundredth is 8.63. Since the numeral to the right of the hundredths(5) is 5 or greater, the hundredths number is rounded up.

Review the steps for rounding decimals and use the study board for help. Show the numbers31.17, .98, and 4.999. Ask the students some questions about these numbers.

Say: Round 31.17 to the nearest whole number . (31)What number are you looking at for rounding this number? (1)

Is this number greater than or less than 5? (less than)



515

Ask the same questions about the other numbers.

Tell the students that they are going to do an activity the same as the one they just did.Lay a card on the table and give the students time to write the answer. As you reveal the answer,say, The answer is…… Store the index cards and study board in the 9 ½” by 6 ½” envelope.



516



Correlations (SG,CAS,CFS): 6C2; 6D2


decimals.Choose and apply problem-solving strategies

for problems involving decimals.

ISAT:

Unit Focus/Foci

Decimals


Multiplying decimals by powers of ten.

Materials

Six-Group Activity : Decimals (hundredths)Calculators


Warm-up Activity:

Have students mentally solve problems similar to mental math 1) (25 × 10) and2) (12 × 10). Remind them if necessary, to start by writing the 25 (or 12). Next count thezeroes in the power of ten and put the same number of zeroes to the right of the first number youwrote. So 27 × 10 = 270, 27 × 100 = 2700, 27 × 1000 = 27000 etc.

Lesson :

In your lesson on multiplying whole numbers by powers of ten, (10,100, 1000, 10,000, 100,000etc.), you learned to write as many zeroes to the right of one factor as you see in the factor that isthe power of ten.



517

When you multiply a decimal by a power of ten, move the decimal point to the right as manytimes as you see zeroes in the power of ten.

Use your calculator.

Multiply4.86 × 10 record your results4.86 × 100 record your results4.86 × 1000 record your results4.86 × 10,000 record your results

Write your own rule for multiplying a decimal by a power of ten

Predict what 4,86 × 100,000,000 would be: 486,000,000

Verify your prediction by using your calculator.

Sometimes you have enough digits within your factor to move the decimal point. Example:92.376 × 100 = 92.376. What must you do when you do not have enough digits in your number?(If no one volunteers, ask them to refer to the record of results from step two above). Answer:Move the decimal point as far as you can then write as many zeroes to the right of the number asnecessary to complete the move. Example: 92.376 × 10,000 = 9,237,600

Provide guided and independent practice from selected problems in your math book. Close bydiscussing answers to problems assigned in Step 6. Stress the difference between having enoughdigits to move the decimal point the required number of places and not having enough digits.(More as far as you can then add as many zeroes as necessary to the right to complete the

move). Show how this differs from writing zeroes in whole numbers.

Example: 3,914 × 1000 = 3,914,00039.14 × 1000 = 39,140



518

Ten Statements


1) To multiply a whole number by a power of ten, write s many zeroes to the right of that wholenumber as there are zeroes in the power of ten.

2) To multiply a decimal by a power of ten, move the decimal point to the right as many placesas there are zeroes in the power of ten.

3) To divide a decimal by a power of ten, move the decimal point to the left as many places asthere are zeros in the power of ten. (no - The statement is true, but it was not discussedtoday).

4) To round a decimal, look at the digit to the right of the digit to be rounded. (no)5) To multiply a decimal by a power of ten, when you don’t have enough digits to move the

decimal point, move as far as you can, then write as many zeroes as necessary ( to the right)

to complete the move.6) To compare decimals, write them vertically and line up the decimal points. (No)7) Power of ten are numbers like 10, 100, 1000, etc.8) 4.17 × 10 = 41.79) 4.17 × 100 = 41710) 4.17 × 1000 - 4,170

Free Choice Lesson


Six Group Activity

Have a group of six students, two from each ability level, complete teacher directed activitysheet Decimals (hundredths)

Math Workshop

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





519



Connection(s)

Enrichment: Tell students that scientist use powers of 10 to express huge numbers for example,the distance Neptune is from the sun is 4.5 × 109 miles. This kind of number expression is calledscientific notation.

1). 10 9 (read “10 to the ninth power) means to multiply 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 ×10) and that the product contains 9 zeroes. 1,000,000,000 ( read “one billion” elicit avolunteer to read if possible)

2). Multiply 4.5 × one billion to find the distance from Neptune 4.500,000,000 - 4,500,000,000

have a volunteer read the answer (four billion, five hundred million miles).3). Have student write a paragraph explaining why they think scientists use scientific notation.

Fine Arts:

Home:

Remediation: See attached Six Group Activity Sheet Decimals (hundredths)

Technology:

Assessment

Class participation, completed assignment.

Homework

Tell students to explain to parents/guardians how to multiply decimals by powers of ten, thenassign parents ten problems to solve. Parents sign a form that their children explained theconcept adequately. (your can prepare the form ahead of time).

Teacher Notes



520

Six-Group Activity

Decimals (Hundredths)

Materials:



37100

419100

749

10098

1001

61100

7100

86100

9 4100

55100

9 2100

Answers: .37; 4.19; 7.49; .98; 1.61; .07; .86; 9.04; .55; 9.02


Decimals-Hundredths

Say: The first place to the right of the decimal point is the tenths place. The second place is the

hundredths place. Each figure is divided into 100 equal parts. Each part is

1100 or .01 of the

area.

26100

or .26 is shaded.



521

154

100or 1.54 is shaded.

Say: A decimal with one digit to the right of the decimal point is read as “tenths.” A decimalwith two digits to the right of the decimal point is read as “hundredths.”

.65 = sixty-five hundredths

.03 = three hundredths5.32= five and thirty-two hundredths

Review the study board with the students and use this problem to ask questions.

1067

100





523



Correlations (SG,CAS,CFS): 6A1,2,3; 6B3,4; 6C1,2,3


fractions, decimals and percents

ISAT:

Unit Focus/Foci

Decimals


Multiplying a decimal by a whole numberMaterials

Six-Group Activity : Decimals (multiplying tenths)Decimal Mods


Warm-up Activity:

Put the following problem on the chalkboard. Tell students to round the factors to the nearestwhole number and then multiply. *Rounded numbers at side in parenthesis.

1. 8.3 = (8) 2. 7.4 = (7) 3. 5.866 = (6)x 2.4 = (2) x 4.4 = (4) x 2.8 = (3)

4. 4.82 x 22.1 5. 6.3 x 5.5(5) (22) (6) (6)



524

Guide the students through the first problem without the decimal. Then remind the students todo the following: 1. Multiply as you would if you had two whole numbers. 2. Put the decimalpoint in the answer as many places from the right as it is in the decimal factor. (Example: 2 x21.4)

Example: 21.4x 242.8

Place the decimal point in the answer one place from the right.

Have students write in math journal in their own words the rule for placing the decimal in theproduct.

Lesson:

After having reviewed the rules for placement of decimals in the product, (see Warm Up) putthese problems on the chalkboard. Students are to solve and place the decimal point in eachproduct. (Be sure to explain that if there are not enough places, that they should add a zero orzeroes to the right of the product to make the needed places to place the decimal. (Example:0.943 x 10,000.)

Example: 0.943 x 10,000 = 0.9430

Guided Practice:1. 0.0004 2. 0.031 3. 4.65

x 7 x 6 x 8

*Note: Five or greater is rounded up, (4) or lesser number are rounded down.

4. 0.0571 5. 4.85 6. 14.032x 3 x 6 x 8

To provide additional practice see any text with multiplying a decimal by a whole number maybe used. “Roll a Harder Decimal” may also be used for reinforcement. (Consult Game Mat forrules.)



525

Ten Statements


1) One strategy used to place decimals in products is to multiply as you would whole numbersand count the places in the factor to place the decimal. (yes)

2) If there are not enough places to place the decimal in the product, add zeroes to the right of the product to make digits to place the decimals. (yes)

3) The rule for rounding is five or more is rounded up less, less than five is rounded down.(yes)

4) When you round numbers you are rounding them to the nearest whole number. (yes)5) Equivalents are numbers that have the same value. (no)6) To find an equivalent decimal for a fraction, divide numerator by the denominator. (no)7) Example number two shows how zeroes are added to provide needed digits in the product to

place the decimal point. (yes)8) Mathematical reasoning is one of the objects of the Roll a Harder Decimal Game. (yes)9) “Roll a Harder Decimal” is designed to be played by two persons. (no)10) The quotient in a division problem is the answer. (no)

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 activitylesson: Decimals (multiplying tenths)

Math Workshop

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





526



Connection(s)

Enrichment: Use any text available with the kinds of problems in this lesson.

Fine Arts:

Home: Have students find the cost of a burger and fries from fast food establishments, andcalculate the cost to buy a meal for themselves and five friends.

Remediation: See attached Six-Group Activity Lesson: Decimals (multiplying tenths)

Technology:

Assessment

70% on items in this lesson and class participation.

Homework

Round the problems then answer them.

6.5 8.2 567 9.2 5.9+2.4 × 3.9 - 28 +3.7 × 4.8

Teacher Notes

Answer key for Warm-up Activity:

1. 2 x 8 = 16 2. 4 x 7 = 28 3. 3 x 6 = 18 4. 5 x 22 = 110 5. 6 x 6 = 36

Answer key for Guided Practice:

1. 0.0028 2. 0.186 3. 37.20 4. 0.17135. 29.1 6. 112.256



527

Six-Group Activity

Decimals (Multiplying tenths)

Materials:



209× .3

69 8.× 3

.6

87×

.5

9 6.×

.8

2 9.×

Answers:

.3

62.7

2 092

×

3

209.4

6 9 82 .×

.6

52.2

4 87×

.5

4.80

3 9 6.×

.8

2.32

7 2 9.×


Multiplying tenths

Say: The number of decimal places in the product equals the sum of the number of decimal places in the factors.

Step 1: Multiply4.3

.3×

129

Step 2: Place the decimal point in the product so that the number of places in the product is thesum of the number of places in the factors.

4.3 decimal place

.3 decimal place

2 decimal places

←

× ←←1 29.

Use the study board as a guide to solving and asking questions about this problem.5.2

.5×



528

How many numbers are to the right of the decimal points? (2)What is the first step in solving this problem? (5 × 2)What is the answer? (10)What is the next step? (5 × 5 and add the 1 you carried)What is the answer? (25 + 1 = 26)

What is the answer to the multiplication portion of the problem? (260)Where does the decimal point go in the product? (2.60)

Tell the students that they are going to do an activity similar to the problem they just worked.Tell them you want the problem multiplied and the decimal point written in the answer. Lay acard on the table and give the students time to write the answer. As you reveal the answer say:The answer is…… Store the activity and the study board in the 9 ½” x 6 ½” envelope.



529



Correlations (SG,CAS,CFS): 6A3; 6C1,2



ISAT:

Unit Focus/Foci

Decimals


Zeroes in the productMaterials

Six-Group Activity : Decimals (multiplying hundredths)Decimal Mods


Warm-up Activity:

Tell the students that to separate the whole numbers from the fraction, a point is placed betweenthem. This is known as a decimal point, and a number that has a decimal point is called adecimal number. (Put example on the chalkboard or overhead.)

Example: 538.6 means 5 hundred, 3 tens, 8 ones and 6 tenths, and is read “five hundred thirty-eight point six”.

Thousands Hundreds Tens Ones Tenths5 3 8 6

Explain that sometimes a number has no whole numbers, just tenths. Example: 0.2 means no

ones and 2 tenths, and is read zero point two.



530

Now have the students take out a sheet of paper, and draw boxes for a decimal number like thefollowing.

Examples : 1.

·The teacher will place the following boxes on the chalkboard.

1 4 6 9

2. The students are told to choose two of the numbers from those given to make a decimalnumber with ones and tenths.

3. It is possible to make 12 different decimal numbers. How many can you find? Put them inorder from largest to smallest.

(Answer: The twelve possible numbers are 9.6, 9.4, 9.1, 6.9, 6.4, 6.1, 4.9, 4.6, 4.1, 1.9, 1.6, 1.4.)Lesson:

On the overhead or on the chalkboard, put the following examples up and explain that when thenumber 8.14 is multiplied by 10 and by 100 that the position of the decimal point differs in thetwo answers.

8.14 8.14 Now ask the students to write the rule for multiplying by ax 10 x 100 power of ten (10). Show example. Answer: Move the decimal

000 000 point to the right as many places as there are zeroes in the power8140 0000 of ten (10). Example: 12.757 x 100 = 12.75.7 = 1,275.7.

81.40 81400814.00

*If you do not have enough places to move the decimal point write zeroes to the right of thenumber. 0.842 x 10.000 = 0.8420 = 8,420

Guided Practice: Complete these exercises by placing the decimal point in the product.

1. 3.61 x 10 = 36.1 (A) 2. 0.033 x 1000 = 0.33 (A)3. 16.8 x 1,000 = 16.800 (A) 4. 419.60 x 100 = 41960. = 41,960 (A)



531

Now have the students complete the following activity on their own.

1. 0.03 x 1000 = 30 (A)2. 68.7 x 10 = 687 (A)3. 0.056 x 100 = 5.6 (A)

4. Jackie is buying collector baseball cards at $0.19 each. If he buys 1000 cards how much willthey cost? $190 (A)5. 101 = 10

102 = 10 x 10 = 100103 = 10 x 10 x 10 = 1,000104 = 10 x 10 x 10 x 10 = 10,000105 = 10 x 10 x 10 x 10 x 10 = 100,00

The above configuration is an example of power of 10 . (A)

Ten Statements


1) To separate the whole numbers from the fraction a decimal point is placed between them.(yes)

2) A number that has a decimal point is called a decimal number. (yes)3) When solving decimal problems it is possible to have tenths and no whole numbers. (yes)4) The largest fraction possible from these numbers 1 4 6 9 , 9.6. (yes)5) The smallest fraction possible using the numbers in the boxes in statement number four is

1.4. (yes)6) A liter is the basic unit of capacity in the metric system. (no)7) The rule for multiplying by power of ten is to move the decimal point as many places to the

right as there are zeros in the power of ten. (yes)8) The centiliter is a unit of measure in the metric system equal to 0.01 liter. (no)9) When solving problems with decimals, if there are not enough places to move the decimal

point you should write zeros to the left of the number. (yes)10) Quotient is the answer in a division problem. (no)

Free Choice Lesson


Six Group Activity

Have a group of six students, two from each ability level, complete teacher-directed activitysheet: Decimals (zeros in the product)



532

Math Workshop






Connection(s)

Enrichment: Have students write five true/false statements about the topic. Example: It ispossible to write decimals that have no whole numbers, just tenths. 0.2, zero ones and 2 tenths.(true)

Fine Arts:

Home:

Remediation: See attached Six-Group Activity sheet

Technology:

Assessment

Class participation, 75% on activities from the lesson.

Homework

Write three problems with zero in the product.

Teacher Notes



533

Six Group Activity

Decimals: Multiplying hundredths

Materials:


Prepare these index cards using the black marker and use the pencil to write the answers on theback.

47.89

3.6× 93.64

1.87× 47.93

8.5×

Answers:

4 7. 89

3.6

28734+ 14367

172.404

2 2 2

×

9 3. 64

1.87

65548

749120+ 936400175.1068

2 5 3

2

1

×

4 7. 938.5

2 3965

+407.405

6 7 2

1

1

×

38344

Copy this study board to help reteach the lesson.Multiplying hundredths

Remember: The number of decimal places in the product equals the sum of the number of decimal places in the factors.

Step 1: Multiply

3. 651251

3651+182557302916401

1 1

×



534

Do a sample problem and use the study board to show the students the steps to solving amultiplication of decimal problem.

Tell the students that they are going to do some problems like the sample one they just did. Laya card on the table. Give the students time to write the answer. As you reveal the answer say:

”The answer is……” Store the activity and study board in the 9 ½ by 6 ½ envelope.



535






ISAT:

Unit Focus/Foci

Decimals


Multiplying decimals by a decimalMaterials

Six-Group Activity : Decimals (lining decimals up)Decimal Mods


Warm-up Activity:

Write the following problems with directions as written. Have students complete per directions.

1. 39.94 (round to nearest whole number)2. 4.85 x 2 (round to nearest whole number and find the product)3. 16.3 + 40.7 (find the sum)4. 92.5 - 71.3 (find the difference)5. 4.62 x 4 (find the product)6. 23.6 x 3 (find the product)

Answer Key: 1. 40 2. 10 3. 57.0 4. 21.2 5. 18.48 6. 70.8

Allow about ten minutes to complete, then give answers if students were unable to solve. Giveexplanations as needed.



536

Lesson:

Before getting into the lesson, remind the students that when area is measured it is measured insquare units.

To find the area, you multiply the length by the width.Example: 2.5 yards x 4.5 yards = 11.25 yards . Explain that when you multiply a decimal by adecimal, multiply as you would with whole numbers, then count the numbers behind the decimalto determine where the decimal point should go in the product.

Example: 1.6 (1 place after the decimal point)x 2.6 (1 place after the decimal point)

9632

4.16 (2 places after the decimal point)

Remind students that sometimes it is necessary to place zeros along with digits in the factors inthe product in order to place the decimal point correctly. This is done when multiplying bywhole numbers and decimals as well as multiplying two decimals.

Example: .1 (1 place after the decimal)x .2 (1 place after the decimal)0.02 (need to add a zero in order to correctly place the decimal)

Have the students solve these problems to get practice with multiplying two decimals.

A. 825 (multiply as you would a whole number)x 15

Ans.: 12375

B. Count the decimal places after the decimal point.Ans. (2) 8.25 (places after the decimal point)Ans. (1) x 1.5 (places after the decimal point)Ans. (3) 12375 (total places after the decimal point)

C. Place the decimal point in the answer.8.25

x 1.512375 (Ans. 12.375)



537

Instruct the students to write each product, placing the decimal point carefully.

1. 5.8 x 7.5 2. 9.8 x 5.25 3. 4.1 x 8.525 4. 1.2 x .25. 103.2 x 9.5 6. 49.3 x 5.2 7. 2.25 x 6.8 8. 8.7 x 0.0025

Answer key:1. 43.50 2. 51.450 3. 34.9525 4. 0.245. 980.40 6. 256.36 7. 15.300 8. 0.02175

If the text is not available, any text with the kind of problems in this lesson may be used.

Ten Statements

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

lesson.

1) Area is measured in square units. (yes)2) To find the area of a rectangle, you multiply the length by the width. (yes)3) To determine where a decimal should be placed when multiplying a decimal by a decimal

multiply as with whole numbers, then add up the number of places after the decimal points inthe factors to determine where the decimal point should go in the product. (yes)

4) It is necessary to place zeros in the factors of the product to correctly place the decimal whensolving some problems. (yes)

5) (5.8 x 7.5 = 43.50) is an example of multiplying a decimal by a decimal. (yes)6) The numbers in an addition problem are called addends. (no)7) (39.94) ≈ 40 is an example of rounding to the nearest whole number. (yes)8) You do not have to line up the decimal point in order to multiply. (no)9) Count the decimal places after the decimal point. (yes)10) Withdraw: to take money out of the bank. (no)

Free Choice Lesson




538

Six Group Activity

Have a group of six students, two from each ability level, complete teacher-directed activitysheet Decimals (lining decimals up)

Math Workshop





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

Sequence information, especially using timelinesSelect appropriate information for intended purpose

Connection(s)

Enrichment: Any problems like the ones shown in the lesson.

Fine Arts:

Home: Have students measure a window and a door in his/her home. Tell how many squarecentimeters are in each. Tell what he or she did to determine how many centimeters wereneeded.


Technology:

Assessment

75% successful completion of lesson and class participation.



539

Homework

Complete.

1. 2.5 × 3.2

2.

4.6×

.33. 5.26 × .034. 95.2 × .55. 62.2 × 5.1

Teacher Notes



540

Six Group Activity

Decimals: Lining decimals up

Materials:

20 index cards (3 x 5)1 black marker1 pencil1 envelope (9 ½ x 6 ½)

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) 59.2 + 322.1 + .2 2) 6.1 + .002 + .1 3) 7.21 + 3.2 + 55) 2.34 + 1.346 + .2 5) 9 + 23.2 + 3.1 6) 6.24 + 21.1 + .218) 9.23 + .23 + 10.211 8) 54.12 + 321.2 + .03

9) 7.1 + 9.3 + .02 10) 5.21 + .36 + 69Answers:

3)

59.2322.1

+ .2

3815.

2)

6.1.002

+ .1

6 202.

3)

7.213.2

+ 5

1541.

4)

2.341.346

+ .2

3886.

4)

9

23.2+ 3.1

35 3.

6)

6.24

21.1+ .21

27 55.

7)

9.23

.23+10.211

19.671

8)

54.12

321.2+ .03

375 35.

9)

7.19.3

+ .02

16 42.

10)

5.21.36

+69.

7457.

Next, prepare another set of cards using the answers (addition problems) above. Write theseusing black marker. On the back of the cards, write the answers to these addition problems.

11. 381.5 12. 6.20213. 15.41 14. 3.88615. 35.3 16. 27.5517. 19.671 18. 375.3519. 16.42 20. 74.57



541

Have the students who are above or at grade level write and answer the problems.

Copy this study board and use it with the lesson. Store the index cards and the study board in the9 ½” x 6 ½” envelope.

Addition of decimalsSay: When adding decimals line the points up first and then write the numbers in the correct order. Example: If a problemhas two sets of numbers (26.3 + .021), rewrite the problem vertically.

Step 1: Write the decimals.Step 2: Write the numbers in the correct order.

26.3+ .021

Step 3: Then you are ready to add.26.3+ .021

26.321

In the answer, bring the decimal straight down.

Explain how to word addition of decimals problems using the study board as a guide. After youexplain how to do the problems, tell the students that they are going to do an activity calledlining up decimals. Explain that to line the decimals up and write the numbers in the correct

order. Say: Don’t write the answer because we want to work on ordering the numbers.

Say: I am going to lay a card down and I want you to write the problem vertically. Lay oneindex card on a flat surface and give the students five or six seconds to write the answer. Whenthe time is up, turn the index card over and say: The answer is…… Go to the next card andrepeat the process.

Tell the students that they are going to do an activity called adding decimals.

Lay a card on a flat surface Turn the card over to reveal the answer and say: The answer is……



542






ISAT:

Unit Focus/Foci

Decimals


Using Decimals: weight & volumeMaterials

Six-Group Activity : Number line (graphing decimals)Decimal ModsMetric measure containers


Warm-up Activity:

Put the following drawings on an overhead. Ask students to look at the drawings and shade inthe decimal amounts below each at their seats.

.4 + 0.6 .4 + 0.6 = ___ (10)

Ans. (shade 4 sections) Ans. (shade six sections) Ans. (color the whole drawing)





544

Ten Statements


1) Volume is a term used to describe the number of cubic units it takes to fill an object. (yes)2) One milliliter is one thousandth of a liter. 0.001 L) (yes)3) The drawings in the Warm Up show fractions as well as decimal amounts. (no)4) Weight is a term used to tell how heavy something is. (yes)5) One kilogram is equal to a thousand grams. (yes)6) A man’s shoe weighs about 500 grams. (yes)7) Mathematical reasoning is one of the objects of roll a harder decimal game. (no)8) Kilogram is a unit of metric weight. (yes)9) 30 grams is equal to 0.040 kilograms. (yes)10) Equivalents are numbers that have the same value. (no)

Free Choice Lesson


Six Group Activity

Have a group of six students, two from each ability level, complete teacher-directed activitysheet: Number Line (graphing decimals)

Math Workshop








545

Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: See attached Six-Group Activity Lesson: Number line (graphing decimals)

Technology:

Assessment

Class participation at the 70% level, successful completion of classroom material

Homework

Write out the differences between weight and volume and give an example of each. Tell whatunits are used for each.

Teacher Notes



546

Six Group Activity

Decimals: Number line (graphing decimals)

Materials:

7 (5 x 7) index cards10 (3 x 5) index cardsContact paper7 black crayons or washable markers (fine line)1 paper towel to be cut up into 6 pieces1 pencil1 (9 ½ x 6 ½) envelope

Prepare these 5x7 index cards. Copy the number line and tape it to the 5 x 7 index card. Cut thecontact paper the same size as the 5 x 7 card and cover the card with the contact paper.

0 .5 1 1.5 2 2.5 3 3.5 4 4.5 5

Prepare these 3x5 index cards using the black marker.2, 1.3, 2.5, 4.8, 3.7, 0.75, 4.2, 5, 1.5, 2.2

The teacher will show the answers on their graph card. Copy this study board to aide inreteaching of this activity.

Graphing decimals

The number line below shows each whole number divided into ten equal parts, or tenths.

0 1 2 3 4 5 6 7 8 9 10 11

From one number to the next number there are ten tenths.

Example:0 1

Bernadette’s eight and six tenths are recorded on the number line.



547

Carl did four and five tenths hours and it is recorded on the number line.

Say this to the students:

We are going to do an activity that requires you to plot numbers on the number line. I am going

to show you a card and I want you to use the crayon or marker to plot your answer. The teacherwill place an index card on a flat surface. Give the students 3 to 4 seconds to mask their answer.The teacher should use the extra card to mark the correct answer to show the students. Beforeyou show the correct answer say, “The answer is……” do the remaining cards the same way.Store the index cards and study board in the 9 ½ x 6 ½ envelope.

Tell the students that they are going to do an activity that calls for them to plot numbers on thenumber line. Lay a card on the table and allow students to solve the problem. While revealingthe answer and say, ”The answer is……” Store the activity and study board in the 9 ½ x 6 ½envelope.





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Formal Assessment

Students should come prepared with paper and pencils.

Find the value of the missing number.

1. 12 km = _____ m (Ans. 12000 m)2. 8 m = _____ dm (Ans. 80 dm)3. 6 cm = _____ m (Ans. 0.06 m)

Add or Subtract

4. 6.29 - 3.24 = _____ (Ans. 3.05)5. 1.62 + 3.14 = _____ (Ans. 4.76)6. 6.12 - 2.37 = _____ (Ans. 3.75)7. 1.6 8. 6.06 9. 6.74

+ 1.52 - 2.21 - 2.423.12 (A) 3.85 (A) 4.32 (A)

Solve.

10. Jan walked 200 meters1 minute and 40.1 seconds. Joy walked 200 meters in 2 minutes and1.1 second. By how much did Jan beat Joy? (21)

Draw <, >, or = to make each statement true.

11. 0.5 ___ 0.2 (Ans. >) 12. 0.76 ___ 0.8 (Ans. <)13. 0.6 ___ 0.8 (Ans. <) 14. 0.6 ___ 0.49 (Ans. >)

Write each amount as a decimal.

15. 7 nickels = _____ (Ans. $0.35)16. 9 dimes and 0 cents = _____ (Ans. $0.90)

Write in standard form.

17. 6 ones, 3 tenths, and 8 hundredths _____ (Ans. 6.38)18. 9 ones, 4 tenths, and 6 hundredths _____ (Ans. 9.46)



550

Multiply.

19. 10 x 9.5 = _____ (Ans. 95) 20. 0.41 x 10 = _____ (Ans. 4 .1)21. 6.3 x 100 = _____ (Ans. 630) 22. 5.8 x 7.5 = _____ (Ans. 43.5)

23. Complete the register with the given figures.

Number Date Description of Transaction Payment Deposit Balance201 2/2 Phone -$97.45 $0 $714

6164499

202 2/8 Gitanone clothes -$145.06 +$202.00 471673

9393

203 2/11 Electric -$49.05 $624.8204 2/15 Repair -$107.00 $210.00 834 88 $727.88

Mortgage -$407.00 $320.88Misc. -$90.00 $230.88

24. Estimate to find the exact answer.

0.7 x 0.6 = _____ (Ans. 0.42) 2.7 x 3.9 = _____ (Ans. 10.53)

25. What is the rule for multiplying by powers of 10?

Students may utilize the Game mats or Free Choice Lesson and go into the math workshop oncethe assessment is completed.

Teacher may also choose to prepare an activity sheet.



551

Ten Statements


No Ten Statements today

Free Choice Lesson


Six Group Activity

No Six-Group Activity today.

Math Workshop






Connection(s)

Enrichment:

Fine Arts:

Home:




Documents

Structured Curriculum Lesson Plan Day: 078 Subject: Mathematics Grade Level: