RATIO & PROPORTION | GRADE 6

Sheena Doria

13 Jan 202113:20

EducationalLearning

32 Likes 10 Comments

TLDRIn this lesson, students learn about the concepts of ratio and proportion using concrete examples. The teacher explains the three ways to write ratios: word form, colon form, and fraction form. Simplification of ratios and the concept of equivalent ratios are also covered. The lesson includes practical examples, such as comparing apples to mangoes and determining proportions using cross-multiplication. Students are taught to find missing terms in proportions, enhancing their understanding of these mathematical concepts through engaging, step-by-step instructions.

Takeaways

🍎 The concept of ratio is introduced as a way to compare two or more quantities.
📝 Three methods of expressing ratios are discussed: word form (e.g., 'three is to six'), colon form (e.g., '3:6'), and fraction form (e.g., '3/6').
🔍 Ratios can be simplified to their lowest terms by dividing both quantities by their greatest common factor.
🍩 Equivalent ratios are explained as ratios that represent the same comparison, regardless of their original form.
📚 The script demonstrates how to find equivalent ratios by multiplying or dividing both terms by the same factor.
📈 Proportion is defined as a statement of equality between two ratios or fractions.
🔢 The importance of the product of the means and extremes in determining if two ratios are in proportion is highlighted.
🔄 The script shows how to use cross-multiplication to check if two ratios are equivalent or in proportion.
🕵️‍♂️ The method of solving for a missing term in a proportion using cross-multiplication is explained with examples.
📝 The script provides practical examples, such as determining the amount of flour needed for baking multiple cakes based on a given ratio.
🎓 The lesson concludes with a summary of the key concepts learned about ratios and proportions.

Q & A

What is the definition of a ratio?
-A ratio is a way of comparing two or more quantities.
How do you write a ratio in word form?
-In word form, a ratio is written as 'a is to b'.
What is the ratio of apples to mangoes in the example provided?
-The ratio of apples to mangoes is 3 is to 6.
What are the three ways to write a ratio?
-The three ways to write a ratio are in word form (a is to b), colon form (a:b), and fraction form (a/b).
How can you simplify the ratio 3 is to 6?
-You can simplify the ratio 3 is to 6 by dividing both quantities by their greatest common factor, which is 3, resulting in 1 is to 2.
What are equivalent ratios?
-Equivalent ratios are ratios that make the same comparison of numbers, such as 1 is to 2 being equivalent to 2 is to 4 or 3 is to 6.
What is the definition of proportion?
-Proportion is a statement of equality between two ratios or fractions.
How can you determine if two ratios are proportional?
-Two ratios are proportional if the product of their means equals the product of their extremes.
What method can be used to solve for a missing term in a proportion?
-The cross multiplication method can be used to solve for a missing term in a proportion.
How many cups of flour does the baker need to make three cakes if the ratio of cups of flour to cakes is 2 is to 1?
-The baker needs 6 cups of flour to make three cakes.

Outlines

00:00

🎓 Introduction to Ratios and Proportions

The lesson introduces the concept of ratios and proportions, explaining how to define and illustrate them using concrete or pictorial models. The example given involves buying three apples and six mangoes and determining the ratio of apples to mangoes. The ratio is defined as a comparison of two or more quantities, and different ways to write ratios are explained: word form (three is to six), colon form (3:6), and fraction form (3/6). The concept of simplifying ratios to their lowest terms is introduced, using the greatest common factor to show that 3:6 simplifies to 1:2. Equivalent ratios, which make the same comparison, are also discussed, with examples given to illustrate how to find them by multiplying or dividing both quantities by the same number.

05:00

🔄 Understanding Equivalent Ratios and Proportions

The section delves into equivalent ratios and proportions, providing examples of how to find equivalent ratios by multiplying or dividing both quantities by their factors. It explains that equivalent ratios make the same comparison of numbers and introduces the concept of proportion as a statement of equality between two ratios or fractions. Examples are given to illustrate how to determine if two ratios are proportional using the cross-multiplication method. The process involves multiplying the means and the extremes and checking if their products are equal. An example with donuts and a drink is used to show that equivalent ratios can be simplified or expanded to find their proportions.

10:01

🧮 Solving Proportion Problems with Missing Terms

This part of the lesson focuses on solving proportion problems where a term is missing. The process involves setting up a proportion and using cross-multiplication to find the missing value. An example with a baker making cakes is given, demonstrating how to determine the number of cups of flour needed for a given number of cakes. The cross-multiplication method is used to solve for the unknown term, and additional examples are provided to reinforce the concept. The section concludes with a summary of the key points learned in the lesson, emphasizing the importance of understanding ratios and proportions in practical situations.

Mindmap

Keywords

💡Ratio

A ratio is a way of comparing two or more quantities. In the video, it is defined as comparing the quantity or number of items, like apples to mangoes. For example, the ratio of 3 apples to 6 mangoes can be written as 3:6, 3 is to 6, or 3/6.

💡Proportion

Proportion is a statement of equality between two ratios or fractions. It is used to show that two ratios are equivalent. For example, in the video, the proportion 1:3 is equivalent to 3:9, meaning their ratios are equal when cross-multiplied.

💡Equivalent Ratios

Equivalent ratios are ratios that express the same relationship between quantities. In the video, 3:6 is simplified to 1:2, showing that for every one apple, there are two mangoes. Equivalent ratios can be found by multiplying or dividing both terms by the same number.

💡Fraction Form

The fraction form of a ratio expresses the first quantity as the numerator and the second quantity as the denominator. In the video, the ratio 3:6 is written as 3/6, which can be simplified to 1/2. This form helps in comparing two quantities directly.

💡Cross Multiplication

Cross multiplication is a method used to determine if two ratios are proportional by multiplying the numerator of one ratio by the denominator of the other. In the video, it is used to check if ratios like 1/2 and 3/6 are equivalent by comparing the products of the means and extremes.

💡Greatest Common Factor (GCF)

The greatest common factor is the largest number that divides both quantities of a ratio without leaving a remainder. In the video, the GCF of 3 and 6 is used to simplify the ratio 3:6 to 1:2 by dividing both terms by 3.

💡Means and Extremes

In a proportion, the means are the inner terms and the extremes are the outer terms. Their products should be equal to prove the proportion. For instance, in the video, for 1:3 and 3:9, the means are 3 and 3, and the extremes are 1 and 9.

💡Simplifying Ratios

Simplifying ratios involves reducing them to their smallest form by dividing both terms by their GCF. In the video, the ratio 3:6 is simplified to 1:2, illustrating how equivalent ratios can be made simpler.

💡Concrete or Pictorial Models

Concrete or pictorial models are visual representations used to illustrate mathematical concepts. The video uses examples like apples and mangoes to visually explain ratios, helping students understand the concept better.

💡Missing Term

A missing term in a proportion can be found using cross multiplication. In the video, an example is given where the ratio of cups of flour to cakes is 2:1, and students learn how to find the number of cups needed for 3 cakes by setting up and solving a proportion.

Highlights

Introduction to the concepts of ratio and proportion.

Definition of ratio as a way of comparing two or more quantities.

Illustration of ratio using three apples and six mangoes.

Explanation of three ways to write a ratio: word form, colon form, and fraction form.

Simplifying ratios into their lowest terms.

Definition and examples of equivalent ratios.

Introduction to the concept of proportion as a statement of equality between two ratios.

Explanation of means and extremes in a proportion.

Verification of proportions using the cross multiplication method.

Example of using proportion to find a missing term.

Application of proportion in real-life scenario: calculating the amount of flour needed for baking multiple cakes.

Multiple examples of solving proportions with missing terms using cross multiplication.

Summary of the lesson emphasizing the key learnings about ratios and proportions.

Interactive examples and exercises to reinforce the understanding of the concepts.

Conclusion encouraging students to apply the concepts in various scenarios.

Transcripts

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Takeaways

Q & A

What is the definition of a ratio?

How do you write a ratio in word form?

What is the ratio of apples to mangoes in the example provided?

What are the three ways to write a ratio?

How can you simplify the ratio 3 is to 6?

What are equivalent ratios?

What is the definition of proportion?

How can you determine if two ratios are proportional?

What method can be used to solve for a missing term in a proportion?

How many cups of flour does the baker need to make three cakes if the ratio of cups of flour to cakes is 2 is to 1?