Minds On
Relational proportions
Consider the following situations:
- Person 1 has a total of $20 and donates $10 to charity.
- Person 2 has a total of $50 and donates $20 to charity.
Who has donated the largest portion of their money, Person 1 or Person 2? How did you decide?
Person 3 has a total of $500 and donates $100 to charity.
Select a method for recording your thinking such as in print, digitally, or with an audio recording. What were some of your reasons for choosing Person 1 or Person 2?
Now consider the following new scenarios:
- Person 3 has a total of $500 and donates $100 to charity.
- Person 4 has a total of $100,000 and donates $100 to charity.
Who has donated the largest portion of their money, Person 3 or Person 4? How did you decide?
Again, select a method for recording your thinking such as in print, digitally, or with an audio recording. What were some of your reasons for choosing Person 3 or Person 4?
Brainstorm
Brainstorm
Out of all four people, who do you think donated the largest portion of their money?
Pick only one person and select a method of your choice for recording your thinking such as in print, digitally, or with an audio recording. How did you decide who donated the most?
Action
Who donated most?
Let’s revisit the scenarios from the Minds On section to explore who donated the largest portion of their money.
- Person 1 has a total of $20 and donates $10 to charity.
- Person 2 has a total of $50 and donates $20 to charity.
- Person 3 has a total of $500 and donates $100 to charity.
- Person 4 has a total of $100,000 and donates $100 to charity.
One way of deciding whom donated the largest portion of their money might be by considering one person at a time and comparing the total amount of money that person has to the amount they donate.
If we compare the amount of money a person has to the amount of money they donate, we are examining a proportional amount.
Proportional amounts help us compare different amounts relative to one another.
Two examples of proportional amounts are rates and ratios.
Rates
Through the use of multiplication or division, a rate compares two different, but related, types of measurements. The different types of measurements compared in a rate have different units.
Press the following tabs to explore some different examples of rates.
Speed is an example of a rate.
Speed compares the amount of distance covered in a certain amount of time.
The units usually used to measure the rate of speed are kilometers per hour, or in symbols km/hr.
A rate does not have to always involve comparing amounts to time.
We can measure the flow of a river by measuring the volume of water travelling through an imaginary chosen cross-sectional area.
We can often find rates in different sports.
Some examples include:
- the number of assists in a game
- the number of goals in a game
- the number of passes in a game
- the number of penalties in a game
- the number of saves made by a goalie in a game
Rates are usually expressed as a fraction. They are communicated as “unit per unit”, such as kilometers per hour, or assists per game.
Ratios
A ratio is another proportional amount that compares two categories of quantities.
Ratios often compare a part to another part of the same whole, or a part to the entire whole.
We often express ratios by providing a ratio title that describes what each amount represents and then the ratio below the title.
Press the following tabs to access some examples of ratios.
The number of gingerbread cookies to the number of shortbread cookies in a cookie tin
5 : 9
The number of students to the number of teachers in a school
300 : 40
The number of red pattern blocks to the number of blue pattern blocks in a bin
15 : 25
Practice: equivalent rates
Let’s practice creating equivalent rates!
Explore the following scenario:
Species disappearing over time
In 2015, The Yale School of the Environment examined data for the (estimated) rate of species extinction on Earth. At that time the rate was 8700 species disappear per a year.
In your notebook or using the following document, find the equivalent rates of species disappearing over 2-year, 3-year, 4-year, and 5-year periods of time.
Complete Species disappearing over time in your notebook or using the following fillable and printable document. If you would like, you can use speech-to-text or audio recording tools to record your thoughts.
Press the ‘Activity’ button to access Species Disappearing Over Time.
Practice: equivalent ratios
Next, let’s practice creating equivalent ratios!
Explore the following scenario:
Comparing cookie quantities
If the number of gingerbread cookies to the number of shortbread cookies in a cookie tin is 1 to 2, that means for every 1 gingerbread cookie there are 2 shortbread cookies. The ratio is 1∶2. Another way to think of this is we have double the amount of shortbreads as we do gingerbreads.
To find an equivalent ratio when we increase the number of gingerbread cookies to 2, we must scale up the proportion of gingerbreads to shortbreads. So, the equivalent ratio would be 2 to 4 (2∶4). If we have 3 gingerbread cookies the equivalent ratio becomes 3 to 6 (3∶6).
In your notebook or using the following document, find the equivalent ratios for the given number of cookies.
Complete Ratio of Gingerbread Cookies to Shortbread Cookies in your notebook or using the following fillable and printable document. If you would like, you can use speech-to-text or audio recording tools to record your thoughts.
Press the ‘Activity’ button to access Ratio of Gingerbread Cookies to Shortbread Cookies.
Consolidation
Finding equivalencies
Can you determine some equivalent ratios for the following scenario?
Complete Ratio of Farm Animals to other Animals in your notebook or using the following fillable and printable document. If you would like, you can use speech-to-text or audio recording tools to record your thoughts.
Press the ‘Activity’ button to access Ratio of Farm Animals to other Animals.
Student Success
Planning for sustainability
In a specific community, the ratio of cyclists to vehicles during morning traffic is 10 to 200 (10∶200).
Consider the following questions:
- What is the equivalent ratio for one cyclist to vehicles?
- What ratio do you think would be most ideal to promote a greener, more sustainable future
Record your thinking in print, digitally, or using an audio recording. If possible, share your thinking with a partner.
I feel...
Now, record your ideas using a voice recorder, speech-to-text, or writing tool.