Unit 3
Ratios
Ratios
Notebook:
A rate is a ratio with two different measurable units.
I would like you to measure your heart rate for 15 seconds and express the ratio in heartbeats to seconds.
We are going to compare the number of your heartbeats to the amount of time that passes.
Let's create a ratio table with heartbeats on top and time (in seconds) on the bottom:
Let's create a ratio table with heartbeats on top and time (in seconds) on the bottom:
Measure how many times your heart beats in 15 seconds. Fill in the number of heartbeats in the appropriate section in the ratio table,
Can you create equivalent rates for the rest of the table?
Can you create equivalent rates for the rest of the table?
This was a problem from our homework:
Poor Dominique! Those mean ol' meanies who wrote the book didn't let her get the job. I sure hope one of us writes a new word problem where Dominique gets the job. Maybe you can write one?
If you compare distance to time, you get a special rate we call velocity (or speed).
This toy car goes 4 feet in 6 seconds.
How long will it take to go 6 feet?
Classwork & Homework:
-- EngageNY
State Test Practice:
California Standards:
CCSS.Math.Practice.MP2 Reason abstractly and quantitatively.
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.2
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger."1
CCSS.Math.Content.6.RP.A.3.d
Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
CCSS.Math.Content.6.EE.C.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
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.2
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger."1
CCSS.Math.Content.6.RP.A.3.d
Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
CCSS.Math.Content.6.EE.C.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.