Free preview Module 1: Ratios and proportional relationships

Topic B: Unit rate and constant of proportionality

▶ Intro to rates

Rates are essential in understanding everyday situations, such as speed, wages, and food consumption. They help us measure and compare quantities, like miles per hour or calories per serving. Rates are closely related to ratios and play a significant role in math subjects like algebra and calculus, making them crucial for problem-solving and analysis.

⏱ 5:30 💾 6.6 MB License: cc-by-nc-sa Streaming via CDN

▶ Solving unit rate problem

Jayda delivers newspapers on her paper route, taking 3 hours to distribute 189 newspapers. To calculate her rate per hour, divide the total newspapers (189) by the hours taken (3). This results in Jayda delivering 63 newspapers per hour, showcasing her efficiency and speed.

⏱ 2:31 💾 2.2 MB License: cc-by-nc-sa Streaming via CDN

▶ Solving unit price problem

Nierria earns $75 for tutoring 4 hours. To find her hourly rate, we divide her total earnings by the number of hours worked. By calculating 75 divided by 4, we discover that Nierria makes $18.75 per hour for her tutoring services.

⏱ 1:56 💾 2.9 MB License: cc-by-nc-sa Streaming via CDN

▶ Constant of proportionality from equation

Sal identifies the constant of proportionality from equations.

⏱ 2:23 💾 2.4 MB License: cc-by-nc-sa Streaming via CDN

▶ Identifying constant of proportionality graphically

The video explains the concept of the constant of proportionality in graphs. It shows how to calculate it using the formula Y = KX or Y/X = K, where K is the constant. It also demonstrates how to identify lines with specific constants on a graph.

⏱ 4:37 💾 6.6 MB License: cc-by-nc-sa Streaming via CDN

▶ Constant of proportionality from table (with equations)

Sal identifies the constant of proportionality from table.

⏱ 1:45 💾 1.7 MB License: cc-by-nc-sa Streaming via CDN

▶ Comparing proportionality constants

Sal compares constants of proportionality in various forms, such as graphs, equations, contexts, diagrams, and tables.

⏱ 5:33 💾 6.7 MB License: cc-by-nc-sa Streaming via CDN

▶ Interpret proportionality constants

Sal interpret what the constant of proportionality means in a context.

⏱ 3:20 💾 3.8 MB License: cc-by-nc-sa Streaming via CDN

▶ Worked example: Solving proportions

Learn the reasoning behind solving proportions. We'll put some algebra to work to get our answers, too.

⏱ 7:20 💾 6.6 MB License: cc-by-nc-sa Streaming via CDN

▶ Writing proportions example

Some examples of writing two ratios and setting them equal to each other to solve proportion word problems.

⏱ 5:51 💾 4.4 MB License: cc-by-nc-sa Streaming via CDN

▶ Proportion word problem: cookies

A recipe for oatmeal cookies calls for 2 cups of flour for every 3 cups of oatmeal. How much flour is needed for a big batch of cookies that uses 9 cups of oatmeal?

⏱ 5:48 💾 5.6 MB License: cc-by-nc-sa Streaming via CDN

▶ Proportion word problem: hot dogs

Mika can eat 21 hot dogs in 66 minutes. She wants to know how many minutes it would take her to eat 35 hot dogs if she can keep up the same pace.

⏱ 4:58 💾 7.5 MB License: cc-by-nc-sa Streaming via CDN

▶ Equations for proportional relationships

Learn how to write a proportional equation y=kx where k is the so-called "constant of proportionality".

⏱ 5:01 💾 5.4 MB License: cc-by-nc-sa Streaming via CDN

▶ Writing proportional equations from tables

Writing an equation to describe the relationship between the number of scoops in an ice cream cone and the price

⏱ 2:47 💾 2.3 MB License: cc-by-nc-sa Streaming via CDN

▶ Interpreting graphs of proportional relationships

Learn how to read and understand graphs of proportional relationships

⏱ 7:32 💾 30.3 MB License: cc-by-nc-sa Streaming via CDN

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