Unit 3
Ratios
Ratios
Notebook:
What are the differences between these two volleyball games?
What are the similarities?
I want to introduce you to what I like to call "A Useful One."
We can all agree that when you multiply a number by one, you will get the same number.
In other words:
In other words:
We can take the ratio 3 students to 1 teacher and multiply it by one to get the same ratio.
2 divided by 2 equals 1. Therefore: 1 equals 2 divided by 2.
Let's multiply the ratio of 3 students to 1 teacher by the ratio 2 to 2:
Let's multiply the ratio of 3 students to 1 teacher by the ratio 2 to 2:
Top times top, bottom times bottom.
Multiply the ratios... THERE. You got 'em.
Multiply the ratios... THERE. You got 'em.
There are an infinite number of Useful One. Here are some others:
We can keep track of equivalent ratios in what is called a ratio table.
3 students to 1 teacher is the same comparison as 300 students to 100 teachers.
(though the gym would be awfully crowded)
This relationship between numbers is known as a proportion.
In the next lesson, we are going to look at a special type of ratio, the rate. Then we're really going to get running...
Classwork & Homework:
-- EngageNY
State Test Practice:
California Standards:
CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them.
CCSS.Math.Practice.MP2 Reason abstractly and quantitatively.
CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others.
CCSS.Math.Practice.MP4 Model with mathematics.
CCSS.Math.Practice.MP5 Use appropriate tools strategically.
CCSS.Math.Practice.MP6 Attend to precision.
CCSS.Math.Practice.MP7 Look for and make use of structure.
CCSS.Math.Practice.MP8 Look for and express regularity in repeated reasoning.
CCSS.Math.Content.6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
CCSS.Math.Content.6.RP.A.3.a
Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
CCSS.Math.Practice.MP2 Reason abstractly and quantitatively.
CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others.
CCSS.Math.Practice.MP4 Model with mathematics.
CCSS.Math.Practice.MP5 Use appropriate tools strategically.
CCSS.Math.Practice.MP6 Attend to precision.
CCSS.Math.Practice.MP7 Look for and make use of structure.
CCSS.Math.Practice.MP8 Look for and express regularity in repeated reasoning.
CCSS.Math.Content.6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
CCSS.Math.Content.6.RP.A.3.a
Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.