Monday, January 15, 2024

UNDERSTANDING PARTITIVE PROPORTION FOR GRADE 6 STUDENTS.


Hey there, Grade 6 friends! Today, we're diving into the world of partitive proportion – a fancy term for sharing things fairly. Imagine you have a bag of candies, and you want to split them among friends. That's where partitive proportion comes in handy!

Now, let's solve a real-world problem using partitive proportion. We have $56 to share among friends Udandie, Tahir, and Nazhir. Udandie gets $4, Tahir gets $2, and Nazhir gets $1. How do we split the money?

**Step-by-Step Solution:**

1. **Understand the Ratios:**

   Udandie:Tahir:Nazhir = $4:$2:$1

2. **Find the Total Parts:**

   Add up the parts in the ratio: $4 + $2 + $1 = $7

3. **Determine the Value of Each Part:**

   Divide the total money by the total parts: $56 / $7 = $8

4. **Calculate Individual Shares:**

   - Udandie's share: $8 per part * 4 parts = $32

   - Tahir's share: $8 per part * 2 parts = $16

   - Nazhir's share: $8 per part * 1 part = $8

And there you have it, Grade 6 pals! Udandie gets $32, Tahir gets $16, and Nazhir gets $8. Partitive proportion made sharing money a piece of cake! Keep rocking those math skills! 🌟

Try this example:  The ratio of boys to girls in a class is 3:5. If there are 48 students in the class, how many boys and girls are there?

Look out for your quizz on partitive proportion in the next post.

Saturday, January 13, 2024

WHY IS YOUR GRADE 6 CHILD IS FAILING MATH: THE CRUCIAL LINK BETWEEN GRADE 6 PERFORMANCE AND MASTERING THE TIMES TABLES

Poor performance in grade 6 mathematics can be directly correlated with inadequate mastery of times tables

Mathematics is a fundamental skill that lays the groundwork for various academic pursuits. One critical aspect that significantly influences a student's performance in grade 6 is the mastery of basic multiplication tables. This foundational knowledge not only fosters numerical fluency but also enhances problem-solving abilities. Unfortunately, a considerable number of students face challenges in mathematics, and often, the root cause can be traced back to a lack of proficiency in times tables.

Poor performance in grade 6 mathematics can be directly correlated with inadequate mastery of times tables. These tables serve as building blocks for more complex mathematical concepts, and a deficiency in this fundamental knowledge can create a cascading effect on a student's overall mathematical aptitude.

One contributing factor to this issue is suboptimal teaching strategies. Traditional rote learning methods often focus on memorization without emphasizing the practical application of times tables. This can result in a superficial understanding that hinders students when confronted with problem-solving tasks. Teachers should adopt interactive and engaging techniques, incorporating real-life scenarios to demonstrate the relevance of times tables.

Moreover, the responsibility does not solely rest on educators. Parents play a crucial role in supporting their child's mathematical development. Encouraging regular practice of times tables at home through games, flashcards, or interactive apps can reinforce classroom learning. Parents should collaborate with teachers to identify areas of improvement and provide a conducive learning environment.

Recommendations for educators include integrating technology into the curriculum, leveraging educational apps, and incorporating hands-on activities that make learning times tables enjoyable. Additionally, periodic assessments can identify struggling students early on, allowing for targeted interventions.

Parents should actively participate in their child's learning journey by fostering a positive attitude toward mathematics. Establishing a routine for practicing times tables, offering praise for effort, and seeking additional resources when needed can make a significant impact.

In conclusion, the relationship between poor performance in grade 6 mathematics and the mastery of times tables is undeniable. By addressing teaching strategies and fostering a collaborative effort between teachers and parents, we can empower students to build a solid foundation in mathematics, unlocking their full potential for future academic success.

Thursday, January 11, 2024

Partitive Proportion Practice Test - Grade 6

1. If 8 apples cost $4, how much will 12 apples cost?


2. A recipe calls for 2 cups of flour to make 24 cookies. How many cups of flour are needed to make 36 cookies?


3. A car travels 180 miles in 3 hours. How far will it travel in 5 hours at the same speed?


4. If 5 books cost $20, how much will 8 books cost?


5. In a school with 120 students, if 40% are girls, how many boys are there?


6. If 15 workers can complete a task in 6 days, how many days will it take for 10 workers to complete the same task?


7. A train travels 240 miles in 4 hours. How long will it take to travel 360 miles at the same speed?


8. A recipe calls for 3 cups of sugar to make 36 muffins. How many cups of sugar are needed to make 24 muffins?


9. If 6 bottles of juice cost $9, how much do 9 bottles cost?


10. In a garden with 80 flowers, if 25% are roses, how many flowers are not roses?

INDIRECT OR INVERSE PROPORTION - MORE IS LESS


Welcome, young mathematicians, to an exciting journey into the world of proportions! Today, we'll dive into the fantastic realm of indirect. Think about Indirect or inverse proportion as a relation between two quantities where an increase in one leads to a decrease in the other, and vice-versa. 

Get ready to explore these mathematical adventures and discover how these relationships are all around us. So, grab your math tools and let's embark on a proportion-filled learning adventure together!

  1. Consider a task that needs to be completed, such as painting a wall. The more workers you assign to the job, the less time it will take to finish. Conversely, if you reduce the number of workers, the time it takes to complete the task increases. Here, the number of workers and the time to complete the task are in an indirect proportion.

In a construction company, a supervisor claims that 5 men can complete a task in 30 days. In how many days will 10 men finish the same task?

The answer to this type of problem we need to apply the concept of Inverse Proportion

But what is an Inverse Proportion?

  • When an increase in one quantiy causes the decrease of the other quantity. 
  • When the decrease in one quantity causes an increase of the other quantity.

Inverse means opposite  -  what happens in one quantity affect the other quantity in the opposite way. This is the ooposite of Direct Proportion where when on quantity increases the other increse or if it decreases so does thr other.

 Lets look at the problem - 5 men can complete a task in 30 days. In how many days will 10 men finish the same task?

If 5 men can do the work in 10 days what do you think will happen if 10 men do the job. Will it take more or less men? It will take less time of course.

 Solution:- 

 1. The number of workers is inversely proportional to the time need to finish the job

 2. The more men work together, the faster the work will be done.

 3. The lesser men work together, the slower the work will be done.

 Solution: 

                                 MEN

                     TIME (days)

                                  5

                         30 

                                 10

                         15

  Multiply the quanties on the same row:

          5 x 30       =   10 x N 

          150           =   10N

          150/10     =   N

           15             =   N

 Answer: It will take 15 days for 10 men to finish the same job.

 2.  Travel Time and Speed: Think about a car trip. If you maintain a constant speed, the time it takes to reach your destination will be inversely proportional to your speed. If you drive faster, you'll cover more distance in less time. On the other hand, if you slow down, it will take more time to cover the same distance. So, in this case, travel time and speed are in an indirect proportion.

The time taken by a vehicle is 3 hours at a speed of 60 miles/hour. What would be the speed taken to cover the same distance at 4 hours

                              SPEED (mph)

                     TIME (hrs)

                                    60

                          3

                                    45

                          4

 Solution:

Multiply the quantities in the same line

60  x  3  =  N  x  4

180        =   4N

180/4    =  N

45          =   N

Answer. One will have to drive at 45mph to take 4 hours to complete the trip.


Try this example:   20 men can pave a stretch of road in 15 days. How many  days will 30 men take to do this same job?

 Hint: Start with your table

 

 

 

 

 

 

 Look out for the quiz on  Friday!

Wednesday, January 10, 2024

QUIZ ON PROPORTION

                          

Quiz for Ratio and Proportion

Question 1.   Unit of ratio

a)            m

b)            m/s²

c)            kg

d)            none of the above

Question 2.  What is the most important character that signifies that the number is a ratio?

a)            .

b)            :

c)            @

d)            *

Question 3. The value of {-8/13 × 26/-3} is _____

a)            -8/13

b)            7/26

c)            -4/13

d)            16/3

Question 4.   To find the ratio of two numbers it is necessary that:

a)     The numbers should have unequal units

b)     The numbers should be equal

c)      The numbers have the same unit

d)      None of the above

Question 5. The product of two numbers is 20/9. If one of the numbers is 4, find the other.

a)       5/9

b)       3/11

c)       12/39

d)       9/11

Question /6    Fill in the blank: - 19:25___25:19.

 a)         ::

b)        ₌

c)         ≠

d)        none of the above

Question 7.   Express 19kg and $38 in a ratio.

a)            19:38

b)            1:02

c)            38:19

d)            Cannot be expressed as a ratio

Question 8.   Express 8m and 6m in a ratio.

a)            4:03

b)            8:06

c)            6:08

d)            3:04

Question 9.   Find the ratio of 8 months to 3 years.

a)            3:8

b)            8:3

c)            9:2

d)            2:9

Question 10. A man earns $200 as his weekly earnings. He spends $20 on his food, he gives $15 to his wife, he puts $60 in his savings, and the rest he spends on daily expenditure. Calculate the ratio of money spent on food.

a)            1:10

b)            3:40

c)            3:10

d)            21:40


GOOD LUCK!!

Monday, January 8, 2024

QUIZ ON INDIRECT OR INVERSE PROPORTION

Hello my Mathematics friends! Hope you grasped the concept of Indirect Proportion.

Here is the quizz to test your knowledge:

Indirect Proportion Quiz          Total questions: 16            Worksheet time: 30 mins 

Instructor name: Dedan Baptiste.

1. If 4 workers can build a wall in 10 days, how many days will it take for 5   workers to build the same wall? 

a) 12 days b) 8 days c) 6.67 days d) 5 days

 2. If Nazir wants to buy 20 cartoon books, and each book costs $3, how much will he have to pay in total? 

a) $80 b) $60 c) $70 d) $50 

3. If Tahir, Udanie, and Nazir work together, they can complete a project in 8 hours. How long will it take for Tahir, Udanie, Nazir, and Louann to complete the same project working together? 

a) 2 hours b) 6 hours c) 3 hours d)4 hours 

4. If 5 workers can paint a house in 8 days, how many workers are needed to paint the same house in 4 days? 

a) 10 workers b) 3 workers c) 20 workers d) 15 workers 

5. If Louann, Tahir, Nazir, and Udanie can eat 48 pizzas in 6 hours, how many pizzas can Louann, Tahir, Nazir, and Udanie eat in 4 hours? 

a) 16 b) 20 c) 45 d) 32 

6. If Tahir, Nazir, and Louann are using 3 trucks to transport 120 boxes in 5 trips, how many trips will it take for Tahir, Nazir, Louann, and Udanie to transport the same boxes using 5 trucks? 

a) 7 trips b) 2 trips c) 10 trips d) 3 trips 

7. If Louann, Tahir, and Nazir can complete a project in 20 days, how many days will it take for Udanie and Tahir to complete the same project?

 a) 30 days b) 7.5 days c) 20 days d) 5 days 

8. If 6 machines can produce 300 units in 9 hours, how many units can 9 machines produce in 6 hours?

 a) 400 b) 600 c) 300 d) 500 

9. If Udanie, Nazir, and Tahir can mow a lawn in 12 hours, how many hours will it take for Louann, and Tahir to mow the same lawn? 

a) 8 hours b) 6 hours c) 10 hours d) 18 hours 

10. If Tahir, Louann, and Nazir can finish a test in 45 minutes, how many minutes will it take for Udanie to finish the same test? 

a) 60 minutes b) 90 minutes c) 30 minutes d) 15 minutes

11. A farmer has enough food to feed 20 animals at his farm for 6 days. How long the food lost if there were 10 more animals in the farm?

a) 4 days b) 6 days c) 3 days d) 5 days 

12. 6 pipes fill a tank in 120 minutes, then 5 pipes can fill it in _______ minutes 

a) 144 b) 108 c) 100 d) 174 

13. If 15 men can do a work in 12 days, how many men will do the same work in 6 days? 

a) 15 b) 8 c) 25 d) 30 

14. 15 men can build a wall in 42 hours, how many workers will be required for the same work in 30 hours? 

a) 13 b) 23 c) 20 d) 21 

15. The social worker thought he had enough food to feed 18 children for 6 days. If there were 27 children, how long would the food last? 

Ans.............................................................. 

16. If four carpenters can build a fence in 14 days, how many carpenters are needed to do the job iin 8 days?

Ans.............................................................

 

 


PROPORTION - YOUR SUPERHERO SIDEKICK


Hello, Grade 6 friends!
Today, we're going to dive into the exciting world of proportions—a magical concept in mathematics that helps us compare and relate different quantities in a balanced way. Imagine you have a delicious recipe for making cookies, and you want to adjust the ingredients to make more or fewer cookies while keeping the same tasty flavor.

 Proportions are like your recipe's secret code, ensuring that the right balance is maintained. As we explore proportions, think of them as the superhero sidekicks that help us keep things in harmony and maintain the perfect balance between different values. Get ready to embark on a proportional adventure in the world of math!

A proportion is a name which we give to any statement that two ratios are equal. It can be written in two ways, two equal fractions, or, using a colon, a: b = c: d or a/b : c/d.

It is obvious that if the two ratios are not equal then they are definitely not in proportion.

In any proportion the first and fourth term are called as extreme terms and the second and third as mean terms.

Example 1: Are the terms 20, 30, 40, 60 in proportion?

Solution: The ratio of first two terms is 20:30 = 2:3.

The ratio of the next two terms is 40:30 = 4:6= 2:3.

Since both the ratios are equal and hence the terms are in proportion.

                                                         Unitary Method

The method in which we first find out the value of one unit and then the value of required number of units is called as Unitary method.

10 apples = $40

1 apple = 40/10 = $4

 6 apples = 4 x 6 = $24

Example 2: If the cost of 6 notebooks is $72. Then what will be the cost of 4 notebooks?

Solution: Cost of 6 notebooks = $72

Hence the cost of one notebook will be = $72/6 = $12

Hence the cost of 4 notebooks =

Cost of one notebook x 4 = $12 x 4 = $48

Practice Questions

Q1)      Udanie made 63 runs in 7 overs and Tahir made 72 runs in 8 overs. Who made more run per over?

Q2)    The cost of 4kg wheat is $48. Find the cost of 10 kg of wheat.

Q3)    State True or False

           a) $40: $200 = 80kg : 400kg

           b) 23 litre : 69 litre = 12g:36g

Q4)    Determine the proportion

           a)      30, 40, 90, 360.

           b)      1,2,4,8

           c)       4,6,8,12

Q5)  The cost of 5 dozen bananas is $60.Find how many dozens of bananas one will get for $40.

Recap

  1. For comparison by ratio, the two quantities must be in the same unit. If they are not, they should be expressed in the same unit before the ratio is taken.
  2. The order in which quantities are taken to express their ratio is important.
  3. Two ratios are equivalent, if the fractions corresponding to them are equivalent. Thus, 3 : 2 is equivalent to 6 : 4 or 12:8.
  4. The method in which we first find the value of one unit and then the value of the required number of units is known as the unitary method.
  5. In ratio and proportion the order is very important because as the order changes the ratio also changes.
                                                    Wrap-up with this video on proportion
CHECK BACK TOMORROW FOR YOUR QUIZ ON PROPORTION!!!