Navigating a Table of Equivalent Ratios: IM 6.2.12
[url=https://im.kendallhunt.com/MS/teachers/1/2/12/preparation.html]“Navigating a Table of Equivalent Ratios”[/url] from IM Grade 6 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson 6.2.12
- IM 6.2.12 Lesson: Navigating a Table of Equivalent Ratios
- Practice 6.2.12
- IM 6.2.12 Practice: Navigating a Table of Equivalent Ratios
IM 6.2.12 Lesson: Navigating a Table of Equivalent Ratios
Find the following products mentally.
[math]\frac{1}{3}\cdot21[/math]
[math]\frac{1}{6}\cdot21[/math]
[math]\left(5.6\right)\cdot\frac{1}{8}[/math]
[math]\frac{1}{4}\cdot\left(5.6\right)[/math]
Use the table to help you solve the problems below. Explain or show your reasoning.
Noah bought 4 tacos and paid $6. At this rate, how many tacos could he buy for $15?
Jada’s family bought 50 tacos for a party and paid $72. Were Jada’s tacos the same price as Noah’s tacos?
Lin is paid $90 for 5 hours of work. She used the table to calculate how much she would be paid at this rate for 8 hours of work.
What is the meaning of the 18 that appears in the table?
Why was the number [math]\frac{1}{5}[/math] used as a multiplier?
Explain how Lin used this table to solve the problem.
At this rate, how much would Lin be paid for 3 hours of work? For 2.1 hours of work?[br][br]
In 2016, 128 gigabytes (GB) of portable computer memory cost $32. Here is a double number line that represents the situation:
[size=150][size=100]One set of tick marks has already been drawn to show the result of multiplying 128 and 32 each by [math]\frac{1}{2}[/math]. Label the amount of memory and the cost for these tick marks.[br][br]Next, keep multiplying by [math]\frac{1}{2}[/math] and drawing and labeling new tick marks, until you can no longer clearly label each new tick mark with a number.[/size][/size]
Here is a table that represents the situation. Find the cost of 1 gigabyte. You can use as many rows as you need.
Did you prefer the double number line or the table for solving this problem? Why?
[size=150]A kilometer is 1,000 meters because kilo is a prefix that means 1,000. The prefix mega means 1,000,000 and giga (as in gigabyte) means 1,000,000,000. One byte is the amount of memory needed to store one letter of the alphabet. About how many of each of the following would fit on a 1-gigabyte flash drive?[/size][br][br]letters
pages
books
movies
songs
IM 6.2.12 Practice: Navigating a Table of Equivalent Ratios
Priya collected 2,400 grams of pennies in a fundraiser. Each penny has a mass of 2.5 grams. How much money did Priya raise? If you get stuck, consider using the table.
Kiran reads 5 pages in 20 minutes. He spends the same amount of time per page. How long will it take him to read 11 pages? If you get stuck, consider using the table.
Mai is making personal pizzas. For 4 pizzas, she uses 10 ounces of cheese.
How much cheese does Mai use per pizza? At this rate, how much cheese will she need to make 15 pizzas?
At this rate, how many seconds does it take for her to earn 25 cents?
Clare is paid $90 for 5 hours of work. At this rate, how many seconds does it take for her to earn 25 cents?
A car that travels 20 miles in [math]\frac{1}{2}[/math] hour at constant speed is traveling at the same speed as a car that travels 30 miles in [math]\frac{3}{4}[/math] hour at a constant speed. Explain or show why.
Lin makes her favorite juice blend by mixing cranberry juice with apple juice in the ratio shown on the double number line. Complete the diagram to show smaller and larger batches that would taste the same as Lin's favorite blend.
Each of these is a pair of equivalent ratios. For each pair, explain why they are equivalent ratios or draw a representation that shows why they are equivalent ratios.
[math]600:450[/math] and [math]60:45[/math]
[math]60:45[/math] and [math]4:3[/math]
[math]600:450[/math] and [math]4:3[/math]