Lesson 15 | Understanding and Representing Ratios | 6th Grade Mathematics | Free Lesson Plan (2024)

FAQs

What grade do you learn about ratios? ›

The heart of middle school mathematics, and a key part of algebra readiness, is understanding ratios and rates. The overview and lessons below are tools to prepare students, usually in Grades 6 and up, who are ready to learn about these concepts.

Ratios and proportions are foundational to student understanding across multiple topics in mathematics and science. In mathematics, they are central to developing concepts and skills related to slope, constant rate of change, and similar figures, which are all fundamental to algebraic concepts and skills.

Unit rate is the ratio of two different units, with denominator as 1. For example, kilometer/hour, meter/sec, miles/hour, salary/month, etc. Arithmetic is probably the most basic and ancient branch of mathematics and is quite commonly used in our day-to-day life.

Ratios compare two numbers, usually by dividing them. If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B. For example, if A is five and B is 10, your ratio will be 5/10.

Begin by explaining to students that a ratio expresses the relationship between two quantities. Ratios compare two measures of same types of things (use an example from the classroom here: boys to girls, teacher to students) Allow time for students to come up with a few on their own.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls)

Ratio tells us how much of one thing there is in relation to another thing. For example, 'For every 2 apples we have 3 bananas'. Proportion tells us about how much of one thing there is in relation to the whole amount of something. For example, 'There are 50 pieces of fruit, and 1 in every 5 of those is an apple.

Often times students struggle with ratios and proportional reasoning because of misconceptions, which were established in earlier grades. Mathematical misconceptions are faulty and incorrect ideas resulting from students' misunderstanding about a mathematical idea or concept.

The first number in the ratio is the numerator; the second number is the denominator. Ratios written as a common fraction are read as a ratio, not as a fraction. Say “2 to 5,” not “two-fifths.”

A unit rate is a ratio between two different units with a denominator of 1. To calculate the unit rate, divide the numerator by the denominator. The resulting decimal number is the unit rate. The unit price is a type of ratio where the numerator is the price and the denominator is the quantity of a good or product.

What are three examples of a rate? ›

Three examples of rates are speed, hourly pay, and price per pound for groceries. These are all rates because they measure a per b, where a and b are quantities with different types of units, such as miles and hours.

A ratio shows how much of one thing there is compared to another. Ratios are usually written in the form: a:b. If you are making orange squash and you mix one part orange to four parts water, then the ratio of orange to water will be 1:4 (1 to 4).

For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."

A ratio can be expressed in its lowest form. For example, ratio 60 : 24 is \frac { 60 }{ 24 } in the form of a fraction. In its lowest form \frac { 60 }{ 24 } = \frac { 5 }{ 2 } = 5 : 2. thus, in its lowest form ratio 60 : 24 is treated as 5 : 2.