Algebra 2 Module 3 Lesson 6

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Eureka Math Grade 6 Module 2 Lesson 15 Example Answer Key

Use Mental Math to Find Quotients

Example 1.Use mental math to evaluate 105 ÷ 35.Answer:\

Example 2.Mental Math and Division of DecimalsEvaluate the expression 175 ÷ 3. 5 using mental math techniques.Answer:\ = 50

Example 3:Mental Math and the Division AlgorithmEvaluate the expression 4,564 ÷ 3. 5 using mental math techniques and the division algorithm.Answer:\

Example 4:Mental Math and Reasonable WorkShelly was given this number sentence and was asked to place the decimal point correctly in the quotient.55. 6875 ÷ 6.75 = 0.825Do you agree with Shelly?Answer:No, I do not agree with Shelly. When I round the dividend to 54 and the divisor to 6, the quotient is 9. I know that 91 is in the ones place, so the decimal should be placed after the 8 in the quotient.

Divide to prove your answer is correct.Answer:

Eureka Math Algebra 2 Module 3 Lesson 6 Problem Set Answer Key

Question 1.The product 4 . 3 . 2 . 1 is called 4 factorial and is denoted by 4!. Then 10! = 10 . 9 . 8 . 7 . 6 . 5 . 4 . 3 . 2 . 1, and for any positive integer n, n! = n 3 . 2 . 1.

a. Complete the following table of factorial values:Answer:

b. Evaluate the sum \.Answer:

c. Evaluate the sum \Answer:2.5

d. Use a calculator to approximate the sum \ to 7 decimal places. Do not round the fractions before evaluating the sum.Answer:\ 2.6666667

e. Use a calculator to approximate the sum \ to 7 decimal places. Do not round the fractions before evaluating the sum.Answer:\ 2.7083333

f. Use a calculator to approximate sums of the form \ to 7 decimal places for k = 5, 6, 7,8,9, 10. Do not round the fractions before evaluating the sums with a calculator.Answer:If k = 5, the sum is \ 2.1766667.

If k = 6, the sum is \ 2.7180556.

1f k = 7,the sum is \ 2. 7182540.

If k = 8, the sum is \ 2.7182788.

If k = 9, the sum is \ 2.7182815.

If k = 10, the sum is \ 2.7182818.

g. Make a conjecture about the sums \ for positive integers k as k increases in size.Answer:It seems that as k gets larger, the sums \ get closer to e.

Question 2.Consider the sequence given by an = )n where n 1 is an integer.

a. Use your calculator to approximate the first 5 terms of this sequence to 7 decimal places.Answer:a1 = )1 = 2a2 = )2 = 2.25a3 = )3 2.3703704a4 = )4 2.4414063a5 = )5 = 2.4883200

c. Use a calculator to approximate the following terms of this sequence to 7 decimal places.Answer:

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Eureka Math Grade 6 Module 3 Lesson 2 Example Answer Key

Example 1:Take It to the BankRead Example 1 silently. In the first column, write down any words and definitions you know. In the second column, write down any words you do not know.

For Tims 13th birthday, he received $150 in cash from his mom. His dad took him to the bank to open a savings account. Tim gave the cash to the banker to deposit into the account. The banker credited Tims new account $150 and gave Tim a receipt. One week later, Tim deposited another $25 that he had earned as allowance. The next month, Tims dad gave him permission to withdraw $35 to buy a new video game. Tims dad explained that the bank would charge a $5 fee for each withdrawal from the savings account and that each withdrawal and charge results in a debit to the account.In the third column, write down any new words and definitions that you learn during the discussion.Answer:

Example 2:How Hot, How Cold?Temperature is commonly measured using one of two scales, Celsius or Fahrenheit. In the United States, the Fahrenheit system continues to be the accepted standard for nonscientific use. All other countries have adopted Celsius as the primary scale in use. The thermometer shows how both scales are related.

a. The boiling point of water is 100°C. Where is loo degrees Celsius located on the thermometer to the right?Answer:It is not shown because the greatest temperature shown in Celsius is 50°C.

ii. The temperature shown on the thermometer in degrees Celsius:Answer:

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Topic C: Making Like Units Numerically

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Engage Ny Eureka Math 2nd Grade Module 3 Lesson 6 Answer Key

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Eureka Math Grade 6 Module 3 Lesson 2 Problem Set Answer Key

Question 1.Express each situation as an integer in the space provided.a. A gain of 56 points in a gameAnswer:

b. A fee charged of $2Answer:

c. A temperature of 32 degrees below zeroAnswer:

d. A 56-yard loss in a football gameAnswer:

e. The freezing point of water in degrees CelsiusAnswer:

Answer:

Question 4.The boiling point of water is 2 12°F. Can this thermometer be used to record the temperature of a boiling pot of water? Explain.Answer:No, it cannot because the highest temperature in Fahrenheit on this thermometer is 120°.

Question 5.Kaylon shaded the thermometer to represent a temperature of 20 degrees below zero Celsius as shown in the diagram. Is she correct? Why or why not? If necessary, describe how you would fix Kaylons shading.Answer:She is incorrect because she shaded a temperature of 20°F. I would fix this by marking a line segment at 20°C and shade up to that line.

Eureka Math Algebra 2 Module 3 Lesson 6 Exercise Answer Key

Exercises 1 3:

Exercise 1.Assume that there is initially 1 cm of water in the tank, and the height of the water doubles every 10 seconds. Write an equation that could be used to calculate the height H of the water in the tank at any time t.Answer:The height of the water at time t seconds con be modeled by H = 2t/10

Exercise 2.How would the equation in Exercise 1 change if

a. the initial depth of water in the tank was 2 cm?Answer:

b. the initial depth of water in the tank was cm?Answer:H = \ . 2t/10

c. the initial depth of water in the tank was 10 cm?Answer:H = 10 . 2t/10

d. the initial depth of water in the tank was A cm, for some positive real number A?Answer:

How would the equation in Exercise 2, part , change if

a. the height tripled every ten seconds?Answer:

b. the height doubled every five seconds?Answer:

c. the height quadrupled every second?Answer:

d. the height halved every ten seconds?Answer:H = A .

Example 1.Consider two identical water tanks, each of which begins with a height of water 1 cm and fills with water at a different rate. Which equations can be used to calculate the height of water in each tank at time t? Use H1 for tank 1 and H2 for tank 2.

Answer:

a. If both tanks start filling at the same time, which one fills first?Answer:Tank 2 fills first because the level is rising more quickly.

c. What is the formula for the average rate of change of the function H1 on an interval ?Answer:\-\boldsymbol_}-\boldsymbol}\)

Exercises 4 8:

Tank 2:

Then b 2.72.

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Eureka Math Grade 6 Module 2 Lesson 15 Exit Ticket Answer Key

Question 1.Evaluate the expression using mental math techniques and the division algorithm. Explain your reasoning.18.75 ÷ 2.5Answer:\I find it easier to divide by 5, so I doubled both the divisor and the dividend. I knew that the dividend would be divisible by 5 since it has a 5 in the hundredths place.18.75 ÷ 2.5 = 7.5

Eureka Math Grade 2 Module 3 Lesson 6 Answer Key

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Topic G: Finding 1 10 And 100 More Or Less Than A Number

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Eureka Math Grade 6 Module 3 Lesson 2 Exit Ticket Answer Key

Question 1.Write a story problem that includes both integers 8 and 12.Answer:Answers may vary. One boxer gains 12 pounds of muscle to train for a fight. Another boxer loses 8 pounds of fat.

Question 2.What does zero represent in your story problem?Answer:Zero represents no change in the boxers weight.

Question 3.Choose an appropriate scale to graph both integers on the vertical number line. Label the scale.Answer:I chose a scale of 1.

Question 4.Graph both points on the vertical number line.Answer:

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Eureka Math Grade 6 Module 3 Lesson 2 Exercise Answer Key

Exercise 1.Read Example 1 again. With your partner, number the events in the story problem. Write the number above each sentence to show the order of the events.For Tims 13 birthday, he received $150 in cash from his mom. His dad took him to the bank to open a savings account.

Tim gave the cash to the banker to deposit into the account. The banker credited Tims new account $150 and gave Tim

a receipt. One week later, Tim deposited another $25 that he had earned as allowance. The next month, Tims dad gave

him permission to withdraw $35 to buy a new video game. Tims dad explained that the bank would charge a $5 fee for

each withdrawal from the savings account and that each withdrawal and charge results in a debit to the account.Answer:

Exercise 2.Write each individual description below as an integer. Model the integer on the number line using an appropriate scale.Answer:

Write each word under the appropriate column, Positive Number or Negative Number.Gain Loss Deposit Credit Debit Charge Below Zero Withdraw Owe ReceiveAnswer:

Write an integer to represent each of the following situations:a. A company loses $345, 000 in 2011.Answer:

b. You earned $25 for dog sitting.Answer:

c. Jacob owes his dad $5.Answer:

d. The temperature at the suns surface is about 5, 500°CAnswer:

e. The temperature outside is 4 degrees below zero.Answer:

f. A football player lost 10 yards when he was tackled.Answer: 10