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HMH Algebra 1, Grade: 8 Publisher: Houghton Mifflin Harcourt
Hmh algebra 1, title : hmh algebra 1, publisher : houghton mifflin harcourt, isbn : not available, isbn-13 : 9780544102156, use the table below to find videos, mobile apps, worksheets and lessons that supplement hmh algebra 1..
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Into Math Grade 7 Module 1 Lesson 2 Answer Key Recognize Proportional Relationships in Tables
We included H MH Into Math Grade 7 Answer Key PDF Module 1 Lesson 2 Recognize Proportional Relationships in Tables to make students experts in learning maths.
HMH Into Math Grade 7 Module 1 Lesson 2 Answer Key Recognize Proportional Relationships in Tables
I Can identify proportional relationships in tables and equations, identify the constant of proportionality, and write the associated equation.
Spark Your Learning
Turn and Talk What characteristic of the table allows you to predict the cost of any number of items?
Build Understanding
Connect to Vocabulary Two quantities have a proportional relationship if the ratio of one quantity to the other is a constant. In a proportional relationship, the constant unit rate is called the constant of proportionality and is usually represented by the letter k.
A. Show that the ratio of dogs walked to amount earned is a constant ratio. _____________________________ B. Show that the ratio of amount earned to dogs walked is a constant ratio. _____________________________ C. What is the unit rate of dogs walked per dollar earned? Does it make sense? Explain. _____________________________ D. What is the unit rate of dollars earned per dog walked? Does it make sense? Explain. _____________________________ E. What is the constant of proportionality k in this situation? _____________________________ F. Describe what the unit rate k represents in this situation. _____________________________ Answer: A) The ratio of dogs walked to amount earned = 2/7 = 0.28 4/14 = 0.28 6/21 = 0.28 Therefore the ratio of dogs walked to the amount earned is a constant ratio.
B) The ratio of amount earned to dogs walked = 7/2 = 3.5 14/4 = 3.5 21/6 = 3.5 The ratio of the amount earned to dogs walked is a constant ratio.
C) The unit rate of dogs walked to amount dollar earned = 2/7 = 0.28 4/14 = 0.28 6/21 = 0.28 The unit rate is 0.28 dogs walked/dollar.
D) The unit rate of dollar earned to dogs walked = 7/2 = 3.5 14/4 = 3.5 21/6 = 3.5 The unit rate is 3.5 dollar/dogs walked.
E) The constant of proportionality k = 3.5.
F) The unit rate k = 3.5 dollar/dog walked.
Turn and Talk In a table of values that represents a proportional relationship, how can you find the constant of proportionality?
Step It Out
Turn and Talk When would it be better to use an equation to represent a proportional relationship? When would it be better to use a table? Answer: The equation is better to represent a proportional relationship.
Check Understanding
B. Is this a proportional relationship? If so, identify k and explain what it represents. If not, explain why not. Answer: Given that, 4 quarters in $1.00 The equation is y = 4x If x = 1 then y = 4(1) =4 If x = 2 then y = 4(2) = 8 If x = 3 then y = 4(3) = 12 If x= 4 then y = 4(4) = 16. If x = 5 then y = 4(5) = 20. The ratio of Quarters and dollars is k = y/x = 4/1 = 4 8/2 = 4 12/4 = 4 16/4 = 4 20/4 = 4 All ratios in the table are equal. So, it is a proportional relationship. The value of the k = 4.
C. Write an equation for the situation. _____________________________ Answer: Given that, 4 quarters in $1.00 The equation is y = 4x If x = 1 then y = 4(1) =4 If x = 2 then y = 4(2) = 8 If x = 3 then y = 4(3) = 12 If x= 4 then y = 4(4) = 16. If x = 5 then y = 4(5) = 20.
On Your Own
Tell whether each table represents a proportional relationship. If it does, identify the constant of proportionality.
Model with Mathematics For Problems 10-12, use the description of a proportional relationship to make a table. Then identify the constant of proportionality, and write an equation for the situation.
I’m in a Learning Mindset!
What strategies do I use to decide if a relationship displayed in a table is proportional? How do I know when I am finished? Answer: You decide all the ratios of the table are equal and find the constant proportionality then the relationship displayed on the table is proportional.
Lesson 1.2 More Practice/Homework
Recognize Proportional Relationships in Tables
Model with Mathematics Use the description of a proportional relationship in each table. Identify the constant of proportionality, then write an equation to represent the situation in the table.
A. Write an equation for the relationship. _____________________________ Answer: The equation for the relationship is y = 16x If x = 2 then y = 16(2) = 32 If x = 4 then y = 16(4) = 64 If x = 8 then y = 16(8) = 128.
B. There are 4 quarts in a gallon and 4 cups in a quart. How many cups are in one serving? Answer: Given that, 4 quarts in a gallon and 4 cups in a quart. The number of cups in the serving is 4 x 4 =16 cups there are 16 cups in one serving
C. There are 8 fluid ounces in a cup. How many fluid ounces are in one serving? Answer: Given that, 8 fluid ounces in a cup. There are 8 fluid ounces in one serving.
Question 10. Describe a method for determining whether a table represents a proportional relationship. _____________________________ _____________________________ _____________________________ Answer: Yes, the table represents the proportional relationship. Because in the table all the ratios are equal.
Question 11. Kevin uses \(\frac{2}{3}\) cup of flour to make 2 servings of biscuits. How many cups of flour are there per serving? How many cups of flour should Kevin use to make 7 servings? A. \(\frac{1}{3}\) cup; 2\(\frac{1}{3}\) cups B. \(\frac{2}{3}\) cup; 2\(\frac{1}{3}\) cups C. \(\frac{2}{3}\) cup; 4\(\frac{2}{3}\) cups D. 1\(\frac{1}{3}\) cups; 4\(\frac{2}{3}\) cups Answer: Given that, Kevin uses \(\frac {2}{3} \) cup of flour to make 2 servings of biscuits. \(\frac {2}{3} \) = 2/3. Divide cups by servings. 2/3 ÷ 2 = 1/3 1/3 cup of flour to make 1 serving of biscuit. For 7 servings = 1/3 x 7 = 7/3. Therefore the answer is \(\frac {1}{3} \) cup; 2\(\frac {1}{3} \) cups Option A is the correct answer.
Spiral Review
Question 12. Donya ran a 3k race at a constant speed in 21 minutes 30 seconds. At this speed, how long does it take her to run 1k? _____________________________ Answer: Given that, Donya ran a 3k race at a constant speed in 21 minutes 30 seconds. 1 minute = 60 seconds 21 minutes 30 seconds = 21 + (30/60) = 21.5 minutes. Donya ran a 1k race at a constant speed is 21.5/3 = 7.17 minutes. 7.17 minutes = 7 + (0.17 x 60) = 7 minutes 10 seconds. Therefore Donya run 1k in 7 minutes 10 seconds.
Question 13. It costs $20 for 4 play tickets and $35 for 7 play tickets. Is cost per ticket constant? Why or why not? _____________________________ Answer: Given that, The cost of 4 play tickets is $20. The cost of 7 play tickets is $35. 1 Play ticket cost = $20 ÷ 4 = $5. 7 Play ticket is $5 x 7 = $35. The cost of the ticket for play is not changed so, it is a constant. Therefore the cost per ticket is constant.
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