Math 5 2nd Grading 37-41LP

Lesson 37: Creating Problems (with reasonable answers) Involving Addition and/ or Subtraction of Decimal Numbers Including Money Week 2 OBJECTIVES: Creating problems(with reasonable answers) involving addition and/ or subtraction of decimal numbers including money Value Focus : Speed and accuracy

Prerequisite Concept and Skills: • Writing the correct equation in solving a given problem involving either addition or subtraction of decimals including money • Solving word problems involving either addition or subtraction of decimals including Money • Creating problem involving addition and/ or subtraction of decimal numbers including money Materials: Play/ Real money, Chart, Real objects (found in the surroundings) References: Lesson Guide in Elem. Math 5 p.268-270, Math for Life p.222-223 Instructional Procedures: A. Preliminary Activities 1. Drill Have pupils answer some mental computation. 25 + 20 = 83 – 24 = 75 – 27 = 17 – 8 = 39 + 27 = 2. Review Conduct a review on adding or subtracting decimal numbers including money using problem solving. 3. Motivation How do we solve problem very fast or easily when we are in a group? B. Developmental Activities 1. Presentation Present the following problems. 1. It was mother’s birthday. Nina Gave her a pair of slippers that cost Ᵽ55.50 and a bandana worth Ᵽ27.75. How much in all did Nina spend for the gifts? Ask: What is the cost of the slippers? The bandana? How much was spend in all? Write the equation of the given problem. 1. The distance from Vigan to Laoag is 82.29 km. The distance from Vigan to Baguio is 195.6 km. How much farther is Baguio than Laoag from Ask: What is Vigan? the distance from Vigan to Laoag? What is the distance from Vigan to Baguio? How much farther is Baguio than Laoag from Vigan? Write the correct equation of the given problem. 2. Aling Pasing charged Mrs Tuazon Ᵽ257.25 for the uniforms of her children. Mrs Tuazon paid Ᵽ300. How much is her change? Ask: How much was charge for the uniforms? How much was paid by Mrs. Tuazon? How much

change did she received? Write the correct equation of the given problem. 2. Performing the Activity Group the class into 4 or 5 groups. Let the group work together to find the answers to the given problems. Lat the different group display their outputs and ask them to discuss their answers. Expected answers: Problem 1 Solution : • Understand: The problem asks for the costs of the slippers and the bandana. • The given facts are: Ᵽ55.50, Ᵽ27.75 • Plan: The operation to be used • Equation: Ᵽ55.50 + Ᵽ27.75 = N • Answer: Nina pays Ᵽ83.25 in all. Problem2 Solution: • Understand: The problem asks for the distance of the places. • The given facts are: 195.6 km, 82.29 km • Plan: What operation is to be used • Equation: 195.6 km – 82.29 km = N • Answer: Baguio is 113.31 km far than Laoag from Vigan. Problem 3 Solution: • Understand: The problem ask for the amount of change receive after paying the charge. • The given facts are: Ᵽ300, Ᵽ257.25 • Plan: How to solve for the change to be receive/ The operation to be used • Equation: Ᵽ300 - Ᵽ257.25 = N • Answer: Mrs. Tuazon receives Ᵽ42.75 change. 3. Processing the Activity After all the groups have presented, ask: How dod you find the activity? How did you find the answer to the first problem? What are the steps in solving wor problem? What about the second problem? 4. Reinforcing the Concept and Skill A. Lead the pupils to understand more about solving word problems involving addition and/or subtraction of decimal numbers including money under Math for Life 5 p.223 Sample: 1. For his father’s birthday, Glen bought a gift worth Ᵽ185.90. He paid it using a five hundred-peso bill. From the change, he bought a bouquet of flowers that cost Ᵽ80.75 for his mother. How much money was left to him? 2. Jay paid Ᵽ45.95 for a sketchpad andⱣ124.55 for a set of pencils. How much money did he start with, if his change was Ᵽ29.50? 3. A triangle has sides measuring 3.25 cm, 5.275 cm, and 6.1 cm. What is its perimeter?

B. For more practice, have pupils work on the following word problem, then, call some pupils to show their answers on the board. Sample: 1. Anton is buying supplies for his school project. The items he is buying and their prices are listed below. What is the total cost of the items? Illustration board = Ᵽ22.45 Pentel pen = Ᵽ98.70 Art paper = Ᵽ15.65 Glue = Ᵽ35.95 2. In a sale, a cellphone was sold at Ᵽ2,681.25. If its regular price was Ᵽ3,575, how much less was the sale price? 3. Alvin bought a bunch of flowers for Ᵽ140.50. If he gave Ᵽ100 bill and a Ᵽ50 bill, how much was his change? 5.Summarizing the Lesson Lead the pupils to give the following generalization by asking: What steps did you learn to solve a mathematical problem? The steps to follow in solving mathematical problem: 1. Analyze the word problem by identifying: a. What is asked? b. What are the given facts? 2. Decide the process 3. Write the mathematical sentence/ equation 4. Solve the problem C. Assessment A. Solve each problem by following the correct steps. 1. Ellen has Ᵽ7.35 while her brother has Ᵽ4.95. How much money do they have? How much more does Ellen have than her brother? 2. Out of her Ᵽ1 350.00 savings, Lea bought a presence worth Ᵽ476.95 for her mother. She bought a photo album that cost Ᵽ200.75. How much of her savings were left? B. Create one word problem involving addition and/ or subtraction of decimal numbers including money. D.Home Activity Remediation Find the answers to the problems below. 1. A meat vendor has 56.8 kilos of pork. She sold 49.5 kilos. How many kilos were left? 2. Ameter measures about 39.37 inches. How much longer is a meter than a yard? Enrichment Solve the following problem. 1. At enrolment time, Mrs. Tuazon paid Ᵽ825.50 for Jolo’s fees, Ᵽ637.80 for Lovely’s fees, and Ᵽ425.75 for Steph’s fees. What was total amount she spent for the fees? 2. Victor cut a 2.5 m of wire from a 9 m wire to repair the fence. Then he cut another 4.25 m to make a clothesline. How long was the wire left? 3. Lita needs 1.25 m of green ribbon and 1.6 m of yellow ribbon for her art project. How many meters of ribbon does she need?

Prepared: MARITES L. UBALDO Teacher III

Lesson 38: Visualizing Multiplication of Decimal Numbers Using Pictorial Models Week 13 Objectives: Visualizes multiplication of decimal numbers using pictorial models Value focus: Keep one’s work and work area neat and clean Prerequisite Concepts and Skills • Visualizing multiplication of decimals using models • Drawing and coloring neatly the decimal models • Appreciating the value of clean work Materials: Flash cards, colored chalk, drawings References: Lesson Guide in Elem. Math 5 p.274, TG in Math Elem. Level p.174 Instructional Procedure: A. Preliminary Activities 1. Drill Group the class into 4 or 5 groups. Conduct a drill using flash cards with a fraction written on it. The first member of the group will go to the board and make an illustration of the fraction. The one with correct drawing gets the point. Continue until everyone has participated. 2. Review Have a review in solving a word problem mentally. Sample: 1.) Aling Rosa bought 0.8 kg of hotdog. She placed 0.25 kg of it in the refrigirator and cooked the rest. How much hotdog did she cook? 2.) A Math book is 0.6 dm thick. A Science book is 0.2 times as thick. How thick is the Science book? B. Developmental Activities

1. Presentation Using a transparent plastic. *Mr. Tuazon’s farm is 0.3 km long and 0.1 km wide. How big is his land? 1 / 10 x 3 / 10 = 3 / 100

0.3 or 3 / 10

0.1 or 1 / 10

a. Into how many parts the whole is divided? b. How is 0.3 shown in the grid? What about 0.1? c. How many squares are double shaded? In fraction form write 1/10 of 3/10 = 1/10 x 3/10 = 3/100. Another way of writing fractions is in decimal form, 0.1 of 0.3 = 0.1 x 0.3 = 0.03 d. How many decimal places are there in both factors? How about in the product?

2. Performing the Activity Have the pupils to work in group. 1. Coloring (using paper grid).

` 0.8

0.8

1 0.60 1.6 How many grids did we use to show 0.8? Why? 2.

Use of Number Line 2 x 0.8 = N 0.8 0.8 1 8

2 3 9 10

4 0.8

5

6

7

8

9 10 0.8

0

1 2

3

4 5

6

7

0

.1

.2 .3 .4 .5

. 6 .7 .8 .9

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.9 2.0 How many number line did we use to show 0.8? Why? The number line above shows that when we joined the two eight tenths, we completed one line of 1.6. Therefore, 2 x 0.8 = 1.6. 3. Processing the Activities After the group presented and checked their work, call on the leader of each group to relate what they had done in using the grid and/ or number line. Ask: How did you find the activity? Which is easier to use? The grid or number line? Who finished first? 4. Reinforcing the Concept and Skill A. Use the number line to show the product of the following. 1. 0 1 2 3 x 0.4 2. 0

1

2

3 4 x 0.6 B. Using paper grid, show the product of the numbers by shading it more darkly. 1. 0.5 x 0.4 = 2. 0.7 x 0.8 = C. Give the factors of the illustration showing the products of the following:

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

0

1 ____ x ____ = ____

2

_____ x ______ = ______ 5. Summarizing the Lesson Ask: How do we visualize multiplication of decimals? Multiplying decimals can be visualized by representing each factor with the horizontal and vertical lines placed over the other. The double shaded part represents the answer to the equation. 6. Applying to New and Other Situations Using an illustration, give the answers of the following situations: 1. Every morning Yvan goes jogging. He can jog a distance of 0.9 kilometer. How many kilometers can be jog in 6 days. (number line) 2. A rectangular table is 0.8 m and 0.5 m. Find its area. (Paper grid) C.Assessment A. Write the correct multiplication equation for each of the following numbers represented by the shaded region.

=

_______ __________

=

______ _______

X

X

________

________

B.Illustrate the following number sentences: 1.) 2.) 3.) 4.) 5.)

2 x 0.5 = N 0.6 x 0.7 = N 4 x 0.3 = N 0.9 x 0.2 = N 0.8 x 0.4 = N

D. Home

Activity Remediation Prepare paper grid divided into 100 equal parts ready to show your own multiplication equation of decimals. the following multiplication equations by using number lines: x 0.6 = x 0.8 = x 0.4 = x 0.9 = x 0.6 =

and be Show 1.) 0.3 2.) 0.5 3.) 0.7 4.) 0.2 5.) 0.5 E. Shade 1.) 2.) 0.3 x 0.4

Prepared: MARITES L. UBALDO Teacher III

Enrichment the figures to represent each number sentence. 0.8 x 0.3 4.) 0.9 x 0.6 3.) 0.7 x 0.7 5.) 0.4 x 0.9

Lesson 39: Multiplying Decimal up to 2 Decimal Places by 1 to 2 –digit Whole Numbers Week 13 Objectives: Multiply Decimals up to 2 Decimal Places by 1 to 2-digit Whole Numbers Value Focus: Work well with others Prerequisite Concepts and Skills • Multiplying decimals up to 2 decimal places by 1 to 2 digit whole numbers • Act promptly on given work Materials: Cards with whole and decimal numbers, charts, cubes with numbers, activity sheets References: Lesson Guide in Elem. Math 5, TIMSS Activities for lesson dev. in Math Instructional Procedure: A. Preliminary Activities 1. Drill Conduct a drill on basic multiplication facts. Use flash cards. 2. Review a. Use a dice. Tossing the dice with faces: 0.1, 0.2, 0.3, 0.3, 0.4,0.5, 0.6. b. Distribute 2 cubes to each group. c. One pupil rolls the cube and another records the face up digits. d. The group who gives the most number of correct answers wins the game. 3. Motivation Which are whole numbers? Which are decimal numbers? 2 0.7 0.5 7 4 0.8 0.9 What’s the difference between a whole number and a decimal number? Can we multiply the two numbers? B. Developmental Activities 1. Presentation Get a card with a whole number and another one with a decimal number. Let’s multiply. Example: 0.44 x 2 = ___ Strategy 1: Using Number Cards Multiply like whole numbers 0.44 X 2 Multiply each digit of the multiplicand with the multiplier. 0.88 2x4=8 Start from the hundredths to the tenths. 2x4=8 2x0=0

The answer is 0.88

How many decimal number in the multiplicand? (Two). Then put the same number of decimal places in the answer. Strategy 2: Problem opener *A faucet can fill a large pail in 0.25 minutes. How many minutes will it take to fill 3 pails? a. What is the problem asking us to find? b. How can we solve for the answer? Multiply 0.25 by 3 c. What kind of number is 0.25 and 3? d. How many decimal places are there in 0.25? What about 3? e. How many decimal places should there be in the product? Therefore: 0.25 x 3 = 0.75 2. Performing the activity Use of activity sheets Distribute the activity sheets with the following problems. A.) 0.78 2.) 0.04 3.) 0.62 4.) 0.49 5.) 0.68 X 46 x 9 x 21 x 32 x 6 a. Divide the class into groups with 5 members each. b. They will work on the activi5ty sheets. c. Remind the pupils to estimate first the products. Tell them that estimating the product before performing the actual multiplication will help them place the decimal point correctly in the final product. Remind them also to count the decimal places in the product starting from the right. Emphasize that in multiplying decimals, there is no need to line up the decimal points. d. After doing the activity, the members of the group will exchange their solutions for checking. 3. Processing the Activities • How did you find the activity? • Which method is easier? • How did you multiply decimals up to 2 decimal places by 1 to 2-digit whole numbers? 4. Reinforcing the Concept and Skills A. Tell how many decimal places each product will have without actually computing. 1. 0.64 x 5 2. 0.35 x 12 3. 0.97 x 3 4. 0.16 x 10 5. 0.46 x 6 B. Find each product. 1.) 0.33 x 26 2.) 0.95 x 18 3.) 0.84 x 15 4.) The product of 0.48 x 12 is _____. 5.) If a pin cost ᵽ0.75, how much is the cost of 7 pins? 5.Summarizing the Lesson How do we multiply decimals up to 2 decimal places by 1 to 2-digit whole numbers? To multiply decimals, multiply them as in whole numbers. The number of decimal places in the product corresponds to the total number of decimal places in the factors. 6.Applying to New and Other Situations 1. Complete the table by giving each product. X 0.26 0.58 4 13

2.Andrei bought post cards for ᵽ0.20 each. How much did he pay for 65 post cards? 3.A working student earns ᵽ0.95 a minute. How much does he earn in 4 hours? C. Assessment A. Tell whether the decimal point is written on the proper place. Put a check mark (√) in the box to indicate correct answers. 1. 0.35 2. 0.63 3. 0.12 4. 0.42 0.54 X 12 x 7 x 82 x 29 D. Home Activity Remediation Copy and give the product. 1. 0.76 2. 0.12 X 14 x 26

3. 0.57 x 6

4. 0.93 x 8

5. x 6

5. 0.38 x 47

Enrichment Write the product with the decimal point in the correct place. Be ready to read your answer. 1. 0.38 x 32 2. .67 x 18 3. 0.46 x 9 4. 0.72 x 15 5. 0.84 x8

Prepared: MARITES L. UBALDO Teacher III

Lesson 40: Multiplying Decimals With Factors Up to 2 Decimal Places Week 13 Objectives: Multiply decimals with factors up to 2 decimal places Value Focus: Sharing Prerequisite Concepts and Skills • Multiplies decimals with factors up to 2 decimal places • Tell the rules in multiplying decimals • Appreciate the value of helping one another Materials: pictures, flash cards, number cards References: Lesson Guide in Elem. Math 5 p.282 Instructional Procedure: A. Preliminary Activities 1. Drill Conduct a drill on basic multiplication facts. Use flash cards.(Relay) a. Let 3 pupils stand on the aisle of the room. b. Flash a card containing basic multiplication facts, then the pupils answer. c. The pupil who gets the correct answer first moves to one step forward. (One step for every right answer) d. The pupil who reaches the place of the teacher first wins the game. 2. Review Give the class mental computations on problem solving. a. Ann bought 7 pins. If each pin cost ᵽ0.85, how much did she pay for it? b. A sachet of sugar weighs 0.95 kg. What is the weight of 10 sachets of sugar?

3. Motivation Show a picture of a family. What can you say about the family in the picture? Why do you think the family looks happy? How do you help your younger brother or sister? B. Developmental Activities 1. Presentation Acting out the problem.  A piece of chocolate bar is 0.16 dm long. James shared it with his sister. If James got 0.2 of the chocolate bar, how long was for her sister? a. How do you find James and his sister in the story? b. In school, how will you show your care for others? c. What are we going to find in the problem? d. What are given? e. What operation will we use? f. How will you state the number sentence? Study the following solutions: Multiply the decimals as if they are whole numbers: 16 x 2 = 32 Count the number of decimal places in both factors. The number of decimal places in the factors is equal to the number of decimal places in the product. 0.16 x 0.25 = 0.032 2. Performing the Activity Tell how many decimal places each product will have without actually computing. 1. 0.6 x 0.05 = ____ 2. 0.11 x 0.7 = ____ 3. 0.58 x 0.9 = ____ 4. 0.8 x 0.12 = ____ 5. 0.95 x 0.6 = ____ 3. Processing the Activity Have the pupils focus on their work. Let them check if all their answers are correct. Recall them the decimal place in the product. Ask: How did you find the activity? How did you place the decimal point in the product? 4. Reinforcing the Concept and Skill Do the following exercises: 1. 0.23 2. 0.09 3. 0.63 X 0.4 x 0.3 x 0.5

4. 0.51 x 0.7

5. 0.9 x 0.25

5. Summarizing the Lesson Ask: How do we multiply decimals with factors up to 2 decimal places? To multiply decimals with factors up to 2 decimal places, multiply like whole numbers and count as many decimal places in the product as there are in the multiplicand and multiplier together. 6. Applying to New and Other Situations 1. Multiply and place the decimal point correctly in the product. a. 0.41 x 0.2 2. 0.24 x 0.3 3. 0.11 x 0.6 5. 0.12 x 0.4

4. 0.32 x 0.3

2. Solve.  A book is to be covered with a plastic cover 3 cm more than the dimensions of the book 0.65 dm and 0.8 dm. How much plastic cover is needed to cover it? C. Assessment A. Place the decimal point in the product. 1.) 0.6 x 0.32 = 0192 2.) 0.09 x 0.45 = 00405

3.) 0.2 x 0.45 = 0090 4.) If 0.9 x 0.45 = 0405, what is 0.90 x 0.45 = N? 5.) 0.49 times 0.7 is 0.343, what is 4.9 times 0.7? B. Multiply and place the decimal point in the product. 1.) 0.34 x 0.4 = ____ 2.) 0.6 x 0.47 = _____ 3.) 0.74 x 0.6 = _____ 4.) What is the area of a rectangle with a length of 0.75 dm and a width of 0.5 dm? 5.) What is the area of a picture frame having a length of 0.95 dm and a width of 0.6 dm? D. Home Activity Remediation A. Write in column and multiply. 1.) 0.28 x 0.3 = ___ 2.) 0.6 x 0.36 = ____ 3.) 0.7 x 0.95 = ____ 4.) 0.4 x 0.04 = ____ 5.) 0.24 x 0.6 = ____ B. Think of your own decimal numbers in hundredths and in tenths, multiply them. Construct atleast 2 problems? Enrichmet: Multiply then express answers in decimals. 1. 0.14 x 0.3 2. 0.22 x 0.4 3. 0.35 x 0.2 4. 0.41 x 0.5 5. 0.62 x 0.6

Prepared: MARITES L. UBALDO Teacher III

Lesson 41: Estimating the Products of Decimal Numbers with Reasonable Results Week 14 Objectives: estimate the products of decimal numbers with reasonable results Value Focus: Keeping the body Prerequisite Concepts and Skills physically fit • Concept of place values • Rounding numbers • Multiplying decimals Materials: cutouts, activity sheets, flash cards References; MISOSA Gr.6 Estimating quotients of decimal Instructional Procedure; A. Preliminary Activities 1. Drill Have a drill on identifying the place value of the underlined digit using flash cards.

Samples of flash cards with decimal numbers. 0.5

0.05

0.15

0.25

0.35

a. Divide the class into groups of two. Divide the class into groups of two. b. Flash the cards one at a time. Each pupil answers what’s on the card. c. Check the pupils answers. The pupil with the most number of correct answers wins. 2. Review Have a review on rounding whole numbers. Numbers Round to Tens 1. 456 _________________ 2. 575 _________________ 3. 682 _________________ 4. 735 ` _________________ 5. 848 _________________

Round to hundredths _____________________ _____________________ _____________________ _____________________ _____________________

3. Motivation Have the pupils walk 5 steps forward and backward for 2 or 3 times. Ask: How did you find the activity? Ask the pupils about the forms of exercises that are good for the body. Elicit from that exercising regularly is good for the body. This makes their body physically and mentally fit in doing mathematical problems and exercises. B. Developmental Activity 1. Presentation Present the situation below to the class. Cynthia and Cathy are competing with each other to walk a distance in one minute. Cynthia recorded a distance of 16.67 meters while Cathy had a distance of 14.45 meters. Who walked a longer distance in one minute? Ask: Who were competing to walk in one minute? How long did Cynthia walk? How about Cathy? What is asked in the problem? How will you find the answer to the problem? 2. Performing the Activities A. Have pupils work in pairs. Give them time to solve for the answer to the problem by illustration.

16

16.67

17

16.67 is nearer to 17 than to 16. Cynthia walked a distance of about 17 meters 14.0

14.45

15.0

14.45 is Cynthia walked a distance of about 14. Cathy walked a distance of about 14 meters. So, Cynthia walked a longer distance than Cathy. Solution: By following the rules in rounding whole numbers, Round off 16.67 to the nearest whole numbers 1 6.6 7

The digit to the right is greater than 5, so round up. Round off place 16.67 rounded to the nearest whole number is 17. B. Have the pupils play by pair. The pair who gets the most number of correct answers wins. Flash the cards one at a time. Let the pupils estimate the product to the nearest tenths. 0.12 x 0.3

0.11 x 0.2

0.8 x 0.25

0.11 x 0.7

0.23 x 0.9

3. Processing the Activities After all groups have played, ask, “How did you find the activity? How did you estimate number to the nearest indicated place value. 4. Reinforcing the Concepts and Skills Ask pupils to work on items 1 to 5. Checked their answers. For mastery, have them answer the items sa likod ng bahay. 5. Summarizing the lesson Lead the pupils to give the following generalization by asking: How to round / or estimate decimal numbers to the nearest nearest indicated place value. To round/ estimate the product of decimals: a.) Find the place where rounding is to be done. b.) Look at the digit to the right of the rounding place. c.) Look at the digit to right of the rounding. If the digit is less than 5, round down. If the digit is equal to or greater than 5, round up. 6. Applying to New and Other Situations Ask pupils to do the activity under below: 1.) 0.15 x 0.11 2.) 0.36 x 0.12 3) 0.26 x 0.42 5.) 0.67 x 0.38

4.) 0.64 x 0.39

C.Assessment Fill in the table by writing the. Answers to your notebook. 1) 0.57 x 0.9 2.) 0.46 x 0.89 x 0.2 3.) 0 .48 x 0.72 x 0.72

4.) 0.29

D.Home Activity Remediation Round the following decimal numbers to the nearest tenths and hundredths. Nearest Nearest Estimated Tenth Hundredths Product 1.) 0.12 x 0.93 _________ __________ __________ 2.) 0.145 x 0.56 _________ __________ __________ 3.) 0.26 x 0.165 _________ __________ __________ 4.) 0.38 x 0.32 _________ __________ __________ 5.) 0.364 x 0.14 _________ __________ __________ Enrichment Write the estimated product. 1.) 0.45 x 0.74 2.) 0.92 x 0.12 3.) 0.56 x 0.8 4.) 0.84 x 0.24 5.) 0.45 x 0.73

Prepared: MARITES L. UBALDO Teacher III