MATH 6 QUARTER 1 WEEK 6 | MUTI-STEP PROBLEM INVOLVING WHOLE NUMBERS AND DECIMALS

Summary

In this educational video, Teacher F explains how to solve multi-step math problems involving whole numbers and decimals. The lesson covers essential strategies and tools for tackling problems that require multiplication, addition, and subtraction. Teacher F demonstrates how to use a four-step process: understanding the problem, planning with the correct operations, solving for the answer, and checking the solution. Practical examples are provided, including calculating earnings with overtime, determining savings, and solving real-life scenarios. The video aims to enhance problem-solving skills and higher-order thinking. Viewers are encouraged to subscribe, like, share, and follow on social media for more lessons.

Takeaways

• 📘 The lesson focuses on solving multi-step math problems involving whole numbers and decimals.
• 👨‍🏫 Teacher F introduces the four-step problem-solving process: understand, plan, solve, and check.
• 🔢 The first activity involves identifying the four steps in solving word problems and writing hidden questions for each step.
• 💼 A real-world example is provided where Mr. Fernandez earns a certain amount for overtime, and students are taught to calculate his total earnings for a week.
• 💰 The lesson includes practical applications such as calculating earnings, savings, and taxes, making it relatable to everyday life.
• 📈 Students learn to use multiplication and addition to solve for earnings and savings, emphasizing the importance of these operations in problem-solving.
• 📉 The concept of withholding tax is introduced, showing how it affects an individual's take-home pay.
• ⏱️ Time management is factored into calculations, as seen in the example where overtime and holiday work hours are considered.
• 🍌 A shopping scenario is used to demonstrate how to calculate the total cost of items bought, such as fruits.
• 📝 The importance of checking one's work is emphasized through the 'check and look back' step to ensure accuracy.
• 🎓 The lesson concludes with an invitation for students to create their own problems, fostering creativity and deeper understanding.

Q & A

What are the four steps in solving word problems as outlined in the script?

The four steps are: 1) Understand the problem, including what is asked and the given facts. 2) Plan the operation to be used and formulate the number sentence. 3) Solve the problem and write the answer. 4) Check and look back to ensure the answer makes sense.

How much does Mr. Fernandez earn for working 45 hours in one week according to the script?

Mr. Fernandez earns 1,389 pesos and 40 centavos for working 45 hours in one week.

What is the total amount Lucy saves in a year if she earns 1,525 pesos a week and saves 15%?

Lucy saves 11,895 pesos in a year.

What is the actual monthly pay Mrs. Bionz receives after withholding tax, if her monthly salary is 15,000 pesos and the tax is 5,275 pesos and 75 centavos?

Mrs. Bionz's actual monthly pay after withholding tax is 9,724 pesos and 25 centavos.

How much does a clerk earn for working 3 hours of overtime and 5 hours on a holiday, if the regular rate is 45 pesos and 50 centavos per hour, the overtime rate is 1.5 times the regular, and holiday pay is double the regular rate?

The clerk will earn 2,479 pesos and 75 centavos for the overtime and holiday work.

What is the total weekly earnings of Sarah who works 8 and 5/10 hours a day from Monday to Friday and 6 and 7/10 hours on Saturday, with a pay rate of 55 pesos and 25 centavos per hour?

Sarah earns 2,721 pesos and 6 centavos in a week.

How much will a customer pay for 5 and 2/5 kilos of bananas at 25 pesos per kilo and 3 and 7/10 kilos of grapes at 180 pesos per kilo according to the script?

The customer will pay 8006 pesos and 25 centavos.

What is the strategy for solving multi-step problems involving whole numbers and decimals as taught by Teacher F?

The strategy involves understanding the problem, planning the operations, solving the problem, and checking the answer to ensure it makes sense.

How does the script encourage the development of higher-order thinking skills in students?

The script encourages higher-order thinking skills by having students solve multi-step problems that require deep thinking and the application of fundamental operations.

What is the purpose of the learning tests in the script?

The purpose of the learning tests is to practice and reinforce the four-step problem-solving strategy for word problems involving whole numbers and decimals.

Outlines

00:00

📘 Introduction to Multi-Step Math Problems

Teacher F introduces a math lesson focusing on multi-step problems involving whole numbers and decimals. The lesson aims to enhance students' problem-solving skills using real-life scenarios. The teacher outlines four essential steps for solving word problems: understanding the problem, planning the approach, executing the solution, and checking the answer. The lesson emphasizes the importance of using appropriate strategies and tools to solve complex math problems efficiently.

05:01

💼 Calculating Earnings with Overtime

The script presents a problem-solving scenario involving Mr. Fernandez, an office clerk who earns 28 pesos and 50 centavos per hour. His overtime pay is 1.75 times his regular rate, and he works 45 hours in a week. The solution involves calculating his regular earnings for 40 hours and his overtime pay for the additional 5 hours. The teacher demonstrates how to use multiplication and addition to find Mr. Fernandez's total weekly earnings, which amounts to 1,389 pesos and 40 centavos after following the four-step problem-solving process.

10:04

🏦 Monthly Salary and Withholding Tax

Mrs. Bionz, with a monthly salary of 15,000 pesos, has a withholding tax of 5,275 pesos and 75 centavos deducted from her pay. The script outlines how to calculate her actual monthly pay and annual earnings by using multiplication and subtraction. The solution shows that her monthly pay after tax is 4,472 pesos and 25 centavos, and her annual pay is 536,000 pesos, considering a 12-month year. The teacher emphasizes the importance of verifying the calculations to ensure accuracy.

15:05

🍌 Fruit Sales and Customer Payments

The lesson continues with a scenario where a customer buys bananas and grapes from a market. Bananas cost 25 pesos per kilogram, and grapes cost 180 pesos per kilogram. The customer buys 5.25 kilograms of bananas and 3.75 kilograms of grapes. The solution involves calculating the total cost for each fruit using multiplication and then adding them to find the total payment the customer must make, which is 806 pesos and 25 centavos. The teacher encourages students to check their work to ensure the calculations are correct.

20:07

📝 Creating and Solving Custom Math Problems

In the final part of the script, Teacher F challenges students to create their own math problems using given data and solve them. The teacher provides an example involving the sale of pineapples, where 80 pineapples are bought at 15 pesos and 25 centavos each, and three get rotten. The remaining pineapples are sold at 20 pesos each, and the teacher asks students to calculate the profit. This activity aims to develop students' critical thinking and problem-solving skills by applying what they've learned in a creative way.

Keywords

💡Multi-step problem

A multi-step problem is a complex mathematical problem that requires more than one operation or step to solve. In the context of the video, these problems involve operations such as multiplication and addition or subtraction of decimals and whole numbers, including money. The video aims to teach viewers how to approach and solve these problems using a systematic four-step method. For example, calculating Mr. Fernandez's total earnings involves multiplying his hourly rate by the number of regular and overtime hours worked.

💡Whole numbers

Whole numbers are the set of natural numbers including zero, used to count objects. In the video, whole numbers are used to represent quantities such as hours worked, rates of pay, and the number of items in a calculation. They are fundamental to the multi-step problems discussed, as they form the basis for calculations involving decimals and money.

💡Decimals

Decimals are numbers that represent a part of a whole, expressed using a decimal point to separate the integer and fractional parts. In the video, decimals are used to represent precise amounts of money, such as Mr. Fernandez's hourly rate of 28 pesos and 50 centavos. The script emphasizes the importance of handling decimals in calculations involving money and other real-world applications.

💡Word problems

Word problems are mathematical problems presented in a narrative or real-world context, requiring the solver to interpret the situation and apply mathematical operations to find a solution. The video focuses on word problems that involve multi-step calculations with whole numbers and decimals. These problems are designed to improve viewers' problem-solving skills and understanding of mathematical concepts in practical scenarios.

💡Problem-solving strategies

Problem-solving strategies refer to the methods or approaches used to tackle and solve complex problems. In the video, a four-step strategy is introduced to solve multi-step word problems: understanding the problem, planning the approach, solving the problem, and checking the answer. This structured approach helps viewers organize their thoughts and actions to effectively solve mathematical problems.

💡Higher order thinking skills

Higher order thinking skills (HOTS) are cognitive processes that involve analysis, synthesis, evaluation, and problem-solving. The video aims to develop these skills by encouraging viewers to think deeply and critically when solving multi-step problems. HOTS are essential for understanding and applying mathematical concepts in complex, real-world situations, as demonstrated in the various word problems presented.

💡Money

Money is a medium of exchange that is used to purchase goods and services. In the video, money is represented in pesos and centavos, and calculations involving money are used to illustrate the application of mathematical operations in real-world contexts. The script includes problems where viewers must calculate earnings, savings, and payments, emphasizing the practical importance of mathematical skills in financial situations.

💡Overtime pay

Overtime pay is additional compensation given to employees for hours worked beyond the standard or regular working hours. In the video, Mr. Fernandez's earnings are calculated based on his regular hourly rate and an overtime rate, which is 1.75 times his regular rate. This concept is used to demonstrate how to calculate total earnings for a week, including both regular and overtime hours.

💡Percentage

A percentage is a way of expressing a number as a fraction of 100. It is used to describe proportions, discounts, tax rates, and more. In the video, Lucy's savings are calculated as a percentage of her weekly earnings, demonstrating how to apply percentages in financial calculations. The script uses the concept of percentage to teach viewers how to calculate a part of a whole amount, such as savings from a weekly income.

💡Withholding tax

Withholding tax is an income tax that is deducted from an employee's salary by the employer and remitted to the government. In the video, Mrs. Bionz's monthly pay is reduced by a withholding tax, and the script uses this concept to illustrate how to calculate an employee's actual take-home pay after taxes. This teaches viewers about the financial implications of taxes on income.

💡Profit

Profit is the financial gain or excess of revenues over expenses. In the video, the concept of profit is used in a problem where a mother sells pineapples at a higher price than she bought them, after accounting for some that got rotten. The script helps viewers understand how to calculate profit in a simple business transaction, which involves subtracting the cost from the revenue.

Highlights

Introduction to multi-step problems involving whole numbers and decimals.

Explanation of four steps to solve word problems: understand, plan, solve, and check.

Mr. Fernandez's earnings calculation with regular and overtime pay.

Calculation of Lucy's annual savings based on her weekly earnings and savings rate.

Mrs. Bionz's annual actual pay after withholding tax deductions.

Clerk's pay calculation for overtime and holiday work with different rates.

Sarah's weekly earnings based on her daily work hours and hourly rate.

Customer's total payment for buying bananas and grapes at different prices and quantities.

Encouragement for students to think deeply and improve higher order thinking skills.

Emphasis on using appropriate problem-solving strategies and tools.

Importance of checking answers to ensure they make sense.

Practical application of mathematical operations in real-life scenarios.

Guidance on creating one's own word problems using given data.

Teacher's feedback and encouragement for students to learn and apply the lesson.

Invitation for students to subscribe, like, share, and follow for latest updates.

Use of music and visual cues to engage students and mark transitions in the lesson.

Transcripts

[Applause]

math

6 quarter

1 week

six milk

base let's learn

about multi-step problem involving whole

numbers and

decimals hello kids it's me teacher F

don't forget to

subscribe like

and

share and hit the notification Bell for

the latest video you can also follow my

Facebook page Teacher frel

[Music]

TV for today's lesson in math 6 we will

discuss about multi-step problem

involving whole numbers and

decimals for most essential learning

competencies so multi-step problems

involving multiplication and addition or

subtraction of decimals mixed decimals

and whole numbers including money using

appropriate problem solving strategies

and

tools after going through this lesson

you are expected to solve multi-step

problems involving multiplication and

addition or subtraction of decimals

mixed decimals and whole numbers

including m money using appropriate

problem solving strategies and

tools let us now proceed to our first

activity Learning test one enumerate the

four steps in solving simple problems

write the hidden questions for every

step what are the four steps in solving

word problems very good step one is to

understand first know what is asked

and second know what are the given

facts step two is to

plan know what operation to be used and

what is the number

sentence step three is to

solve what will be the solution and

write the answer and step four check and

look back see if your answer makes sense

write the complete answer so these are

the four steps in solving word

problems multi-step word problems are

combination of fundamental operations

which includes hidden

questions here you will be able to think

deeply and improve your higher order

thinking skills to solve the

problems learning test two solve the

given problems use the four steps in

solving word problem s a hidden question

should be incorporated in your answer

Write Your solution in your

notebook number one Mr Fernandez earns

28 pesos 50 centavos per hour as an

office clerk he earns 1 and 7500 times

as his regular rate for overtime his

regular work is 40 hours per week he

gets overtime pay if he works more than

40 hours how much is his total earning

if he works 45 hours in one week step

one understand the problem letter A what

is as in the problem the total earning

of Mr Fernandez for working 45 hours in

one week the hidden questions are his

total earning in working 40 hours and

the total overtime earning in 5

hours letter B what are the given facts

the given facts are 28 pesos 50 centavos

per hour 1 and 7500s times 40 hours per

week and 45 hours in 1 week second step

is to plan what operation to be used the

operation to be used are multiplication

and

addition what is the number sentence the

number sentence is 28 pesos 50 centavos

time 40 hours plus 1 and 7500 * 28 pesos

50 centavos * 5 days equal

n step three sove for the solution the

regular working hour is 28 pesos and 50

centavos * 40

equal

1,140 pesos

for overtime rate multiply

17500 times 28 PES and 50 centavos

equals 49 pesos 87 centavos Time 5 equal

249 pes4

centavos then add the earnings for

regular working hours in 5 days is

1,140 pesos plus the the overtime rate

the overtime rate is 249 pesos 40

centavos equals

1,389 pes4

centavos then write the answer the

answer is Mr Fernandez earned

1,389 pesos 40

centavos this is his total earning if he

works 45 hours in one week step four

check and look back so the regular

working hours is

1,140 pesos divided by 28 pesos 50

centavos equals 40 which is 40 hours the

overtime rate is 249 pesos 40 centavos

divided by 5 days equals 49 pesos and88

centavos 49 pesos and8 8 centavos ided

28 pesos 50 centavos equals

17500 then add

1,389 pes4 centavos minus 249 pesos 40

centavos

equals

1,140 pesos 40 centavos this answer is

the regular working hours for Monday to

Friday

number two Lucy earns

1,525 pesos a week she sets aside 15% of

this for savings how much does she save

in a year the hint is one year is

equivalent to 52 weeks step one

understand what is ask in the problem

the amount of her savings in a

year the hidden question is the amount

of her savings in a week what are the

given facts the given facts are

1,525 pesos a week

15% or equivalent to

1500s and one year is equivalent to 52

weeks step two plan what operation to be

used the operation to be used is

multiplication and what is the number

sentence the number sentence is

1,525 pesos *

1500s multip by 52 weeks equals

n now step three solve solution Savings

in a week

1,525 pesos * 1500

equal 228 pesos and 75

centavos now the Savings in a year 22 8

pesos 75 centavos multip by 52 weeks

equals

11,895 pesos now write the answer in a

Year Lucy saves

11,895

pesos step four check and look back

Savings in a week 228 pesos 75 cavos

divided by 1500s equal 1

1,525 pesos and the Savings in a year

11,895 pesos divided by 52 weeks

equals 228 p75

cavos number three Mrs bionz has a

monthly pay of 15,000 Pesos the

withholding tax from her monthly salary

is

5,275 p75

tabos what is the actual pay she

receives in a year step one understand

what is asking the problem the actual

pay of Mrs bones receives in a year the

hidden question the actual pay of Mrs

bionz in a month what are the

given 50,000 a month and

5,275 pesos 75 centavos withh holding

tax a month

step two plan what operation to be used

the operation to be used are

multiplication and

subtraction what is the number sentence

50,000 pesos minus

5,275 pesos and 75 centavos ultip by 12

= n now solve

solution monthly pay is 50,000 pesos

minus

5,275 p PES 75 cavos equals

44724 p25 centavos this is her monthly

pay the actual pay in a year is

44724 pesos 25 centavos multip by 12

months

equals 536,000

the actual pay she receives in a year is

536,000 pesos 25 centavos plus

5,275 p75 centavos equals 50,000 pesos

this is the monthly pay for Mrs

bionz next the pay in a year is 536,000

[Music]

[Music]

hours per week one and 1500s times the

regular rate for overtime and double the

regular for a holiday how much does the

clerk get if he works overtime for 3

hours and 5 hours on a holiday step one

understand what is as in the problem the

total amount of money the clerk gets for

working overtime in a holiday what are

the given 45 pesos and 50 per hour 40

hours per week 1 and 00s overtime rate

step two plan what operation to be used

the operation to be used are

multiplication and

addition what is the number

sentence 45 pesos 50 centavos * 40 plus

45 pesos 50 centavos Time 1 and 1500 * 3

+ 45 pesos 50 cavos * 2 * 5 =

n step three solve

solution 45 pesos 50 centavos * 40 equal

1,820 pesos next 45 PES and 50 centavos

* 1 and 1500s * 3 equal 2 204 p75

centavos this is the overtime pay and 45

pesos and 50 centavos * 2 * 5 = 455

pesos this is the holiday pay add the

following add

1,820 pesos + 204 pesos 75 Centos plus

455 pesos

equal 2,4 79 pesos 75 centavos now write

the answer the clerk will get the amount

of

2,479 p75

centavos now check and look back

2,479 p75 centavos minus 455 pesos equal

2,24 pesos 75

cavos then 224 pesos 75 centavos minus

204 p75 centavos equal

1,820

pesos number two Sarah works 8 and 510

hours a day from Monday to Friday and 6

and 7500s hours on Saturday if she paid

55 pesos and 25 centavos per hour how

much does she earn in a week step step

one understand what is say in the

problem the amount of money Sarah earn

in a week what are the given facts 55

pesos and 25 centavos per hour 8 and 510

hours Monday to Friday 6 and 75 hours on

Saturday step two is to

plan what operation to be used the

operation to be used are multiplication

and addition

what is the number sentence 8 and 51 * 5

+ 6 and

7500s multip by 55 pesos and 25 centavos

equal n step three solve the problem

solution 8 and 510 * 5 + 6 and 7500s =

49 and 2500 hours in a week now multiply

49 and 2500 hours * 55 pesos 25 centavos

equals

2,721 pesos and 625 centavos round this

up to the nearest hundreds now write the

answer Sarah earns

2721 pesos and6 centavos in a

week now check and look back

2721 1 pesos and6 centavos divided by 49

and

2500

equals 55 pesos and 25

centavos number three Mr paron sells

fruits in the market banana cost 25

pesos per kilog and grapes cost 180

pesos per kilg a customer bought 5 and

2500 kilos of banana and 3 and 7500 kog

of grapes how much will the customer pay

step one is to understand what is as in

the problem the total amount of customer

pay what are the given facts the given

facts are 25 pesos per kilog of banana

180 pesos per kilog of

grapes 5 and 2500 kilos of banana bot

and 3 and 75 100 kilos of grapes both

step two is to plan what operation to be

used the operation to be used are

multiplication and

addition what is the number sentence the

number sentence is 25 pesos * 5 and

2500s plus 180 pesos * 3 and

7500s equal n step three solve solution

25 pesos * 5 and 2500

equal 131 pesos and 25 centavos cost of

banana 180 pesos * 3 and 7500 equal

675 pesos cost of grapes then add 131

PES 25 cavos plus

675 pesos equal 86 pesos 25

centavos now write the

answer the customer will pay 8006 pesos

and 25

centavos step four check and look back

8006 pesos and 25 centavos minus 675

pesos

equal 131 pesos and 25 centavos for

banana next 86 pesos and 25 centavos

minus 131 pesos 25 centavos

equals

675 pesos for

grapes when the time that you have

mastered on how to solve problems and

can be able to analyze it you can an

problems as fast as you can without

using the steps if you can solve

problems critically we can also create

our own problem

and for learning task 4 Create a simple

problem using the given data solve and

write your answer in your notebook I'll

give you an example for number one for

number one the given data is 80

pineapples at 15 pesos and 25 centavos

each three pineapple got rotten sold the

rest at 20 pesos each amount of gain and

here is my

example mother bought 80 pieces of

pineapples at 15 pesos 25 centavos each

Tre pineapple got rotten she sold the

rest at 20 pesos each how much does she

gain if she sold the rest of the

pineapples create your own problem based

on the given data for number two 3 four

and five so kids do you understand our

lesson for today

wow good

job kids I hope you learn a lot from

this lesson until our next topic bye-bye

kids thanks for watching

[Music]