Lesson 4 ­ Equivalent_Ratios_Part_2_Math_6_WP_Summary.notebook
August 23, 2014
Lesson 4: Equivalent Ratios (Part 2)
In this lesson, we learned that you can determine if two ratios are equivalent by identifying whether there is a constant, c. In the example above, the ratios are not equivalent because the quantity in the first ratio is not multiplied by the same number in the second quantity. This can be fixed by changing the second ratio to 42:77 so that the constant is 7 (c = 7). It can also be fixed by changing the second ratio to 48:88 so that the constant is 8 (c = 8). CONTINUED on next page...
Jan 8­8:18 AM
Lesson 4 ­ Equivalent_Ratios_Part_2_Math_6_WP_Summary.notebook
August 23, 2014
Lesson 4: Equivalent Ratios (Part 2)
We also learned how to justify whether ratios in a tape diagram were equivalent using this method.
In a bag of mixed walnuts and cashews, the ratio of number of walnuts to number of cashews is 5:6. Determine the amount of walnuts that are in the bag if there are 54 cashews. Use a tape diagram to support your work. Justify your answer by showing that the new ratio you created of number of walnuts to number of cashews is equivalent to 5:6. Jan 8­8:18 AM
Lesson 4 ­ Equivalent_Ratios_Part_2_Math_6_WP_Summary.notebook
Learning Targets By the end of this lesson, you will be able to answer the following questions:
(1) How can tape diagrams be used to determine if two ratios are equivalent?
(2) How can you determine if two ratios are equivalent using a constant, c?
Jan 8­8:18 AM
August 23, 2014
Lesson 4 ­ Equivalent_Ratios_Part_2_Math_6_WP_Summary.notebook
Learning Targets Why do you need to know this?
Ratios can be used to solve all types of real world problems. We use ratios to decide what items have the best price when we shop, which cars get the best gas mileage, and many other real world problems.
Jan 8­8:18 AM
August 23, 2014
Lesson 4 ­ Equivalent_Ratios_Part_2_Math_6_WP_Summary.notebook
August 23, 2014
Example 1
The morning announcements said that two out of every seven 6th graders in the school have an overdue library book. Jasmine said, “That would mean 24 of us have overdue books!” Grace argued, “No way. That is way too high.” How can you determine who is right? You can determine who is right if you know the total number of students in sixth grade. Then you can make a tape diagram to figure out if the ratios are equivalent. If there are 84 total sixth graders, then Jasmine if correct. If there aren't 84 total sixth graders, then she is not correct. Grace is correct if there are fewer than 84 sixth graders. Aug 11­6:09 PM
Lesson 4 ­ Equivalent_Ratios_Part_2_Math_6_WP_Summary.notebook
August 23, 2014
Exercise 1
Decide whether or not each of the following pairs of ratios is equivalent.
If the ratios are not equivalent, find a ratio that is §
equivalent to the first ratio.
If the ratios are equivalent, identify the positive number, §
, that could be used to multiply each number of the first ratio by in order to get the numbers for the second ratio. Aug 11­6:09 PM
Lesson 4 ­ Equivalent_Ratios_Part_2_Math_6_WP_Summary.notebook
August 23, 2014
Exercise 2
In a bag of mixed walnuts and cashews, the ratio of number of walnuts to number of cashews is 5:6. Determine the amount of walnuts that are in the bag if there are 54 cashews. Use a tape diagram to support your work. Justify your answer by showing that the new ratio you created of number of walnuts to number of cashews is equivalent to 5:6. Aug 11­6:20 PM
Lesson 4 ­ Equivalent_Ratios_Part_2_Math_6_WP_Summary.notebook
August 23, 2014
Learning Targets Answer the following questions:
(1) How can tape diagrams be used to determine if two ratios are equivalent?
Create a tape diagram and figure out what number to put in each of the unit boxes after you are given one of the quantities in the equivalent ratio. If the totals pass the "justification test" where the number in each box is the same, then the two ratios are equivalent.
(2) How can you determine if two ratios are equivalent using a constant, c?
If you can multiply each number in the first ratio by a constant, c, to get the second ratio, then the two ratios are equivalent. If the number multiplied is not the same, then there is no constant, c, and the ratios are not equivalent. Jan 8­8:18 AM
Lesson 4 ­ Equivalent_Ratios_Part_2_Math_6_WP_Summary.notebook
Homework
Problem Set Lesson 4
Aug 10­6:42 PM
August 23, 2014