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## Eureka Math Grade 7 Module 5 Lesson 4 Answer Key

Engage ny eureka math 7th grade module 5 lesson 4 answer key, eureka math grade 7 module 5 lesson 4 example answer key.

Example 1. Based on the 20 trials, estimate for the probability of a. Choosing a yellow cube b. Choosing a green cube c. Choosing a red cube d. Choosing a blue cube Answer: a. Answers will vary but should be approximately \(\frac{5}{20}\), or \(\frac{1}{4}\). The probability in the sample provided is \(\frac{5}{20}\), or \(\frac{1}{4}\) .

b. Answers will vary but should be approximately \(\frac{5}{20}\), or \(\frac{1}{4}\). The probability in the sample provided is \(\frac{6}{20}\), or \(\frac{3}{10}\).

c. Answers will vary but should be approximately \(\frac{5}{20}\), or \(\frac{1}{4}\). The probability in the sample provided is \(\frac{4}{20}\), or \(\frac{1}{5}\).

d. Answers will vary but should be approximately \(\frac{5}{20}\), or \(\frac{1}{4}\). The probability in the sample provided is \(\frac{5}{20}\), or \(\frac{1}{4}\).

Example 2. If there are 40 cubes in the bag, how many cubes of each color are in the bag? Explain. Answer: Answers will vary. Because the estimated probabilities are about the same for each color, we can predict that there are approximately the same number of each color of cube in the bag. Since an equal number of each color is estimated, approximately 10 of each color are predicted.

Example 3. If your teacher were to randomly draw another 20 cubes one at a time and with replacement from the bag, would you see exactly the same results? Explain. Answer: No. This is an example of a chance experiment, so the results will vary.

Example 4. Find the fraction of each color of cubes in the bag. Yellow Green Red Blue Answer: Yellow \(\frac{10}{40}\), or \(\frac{1}{4}\) Green \(\frac{10}{40}\), or \(\frac{1}{4}\) Red \(\frac{10}{40}\), or \(\frac{1}{4}\) Blue \(\frac{10}{40}\), or \(\frac{1}{4}\) Present the formal definition of the theoretical probability of an outcome when outcomes are equally likely. Then, ask → Why is the numerator of the fraction just 1? Since the outcomes are equally likely, each one of the outcomes is just as likely as the other. Define the word event as “a collection of outcomes.” Then, present that definition to students, and ask

→ Why is the numerator of the fraction not always 1? Since there is a collection of outcomes, there may be more than one favorable outcome. Use the cube example to explain the difference between an outcome and an event. Explain that each cube is equally likely to be chosen (an outcome), while the probability of drawing a blue cube (an event) is \(\frac{10}{40}\).

Each fraction is the theoretical probability of choosing a particular color of cube when a cube is randomly drawn from the bag. When all the possible outcomes of an experiment are equally likely, the probability of each outcome is P(outcome) = \(\frac{1}{\text { Number of possible outcomes }}\)

An event is a collection of outcomes, and when the outcomes are equally likely, the theoretical probability of an event can be expressed as P(event) = \(\frac{\text { Number of favorable outcomes }}{\text { Number of possible outcomes }}\).

The theoretical probability of drawing a blue cube is P(blue) = \(\frac{\text { Number of blue cubes }}{\text { Total number of cubes }}\) = \(\frac{10}{40}\). Answer:

Example 5. Is each color equally likely to be chosen? Explain your answer. Answer: Yes. There are the same numbers of cubes for each color.

Example 6. How do the theoretical probabilities of choosing each color from Exercise 4 compare to the experimental probabilities you found in Exercise 1? Answer: Answers will vary.

## Eureka Math Grade 7 Module 5 Lesson 4 Exercise Answer Key

Exercises 1–4 Exercise 1. Consider a chance experiment of rolling a six-sided number cube with the numbers 1–6 on the faces. a. What is the sample space? List the probability of each outcome in the sample space. b. What is the probability of rolling an odd number? c. What is the probability of rolling a number less than 5? Answer: a. Sample space: 1, 2, 3, 4, 5, 6 Probability of each outcome is \(\frac{1}{6}\).

b. \(\frac{3}{6}\), or \(\frac{1}{2}\)

c. \(\frac{4}{6}\), or \(\frac{2}{3}\)

Exercise 2. Consider an experiment of randomly selecting a letter from the word number. a. What is the sample space? List the probability of each outcome in the sample space. b. What is the probability of selecting a vowel? c. What is the probability of selecting the letter z? Answer: a. Sample space: n, u, m, b, e, r Probability of each outcome is \(\frac{1}{6}\).

b. \(\frac{2}{6}\), or \(\frac{1}{3}\)

c. \(\frac{0}{6}\), or 0

## Eureka Math Grade 7 Module 5 Lesson 4 Problem Set Answer Key

Question 1. In a seventh-grade class of 28 students, there are 16 girls and 12 boys. If one student is randomly chosen to win a prize, what is the probability that a girl is chosen? Answer: \(\frac{16}{28}\), or \(\frac{4}{7}\)

Question 4. Seventh graders are playing a game where they randomly select two integers 0–9, inclusive, to form a two-digit number. The same integer might be selected twice. a. List the sample space for this chance experiment. List the probability of each outcome in the sample space. b. What is the probability that the number formed is between 90 and 99, inclusive? c. What is the probability that the number formed is evenly divisible by 5? d. What is the probability that the number formed is a factor of 64? Answer: a. Sample space: Numbers 00–99 Probability of each outcome is \(\frac{1}{100}\). b. \(\frac{10}{100}\), or \(\frac{1}{10}\) c. \(\frac{20}{100}\), or \(\frac{1}{5}\) d. \(\frac{7}{100}\) (Factors of 64 are 1, 2, 4, 8, 16, 32, and 64.)

Question 5. A chance experiment consists of flipping a coin and rolling a number cube with the numbers 1–6 on the faces of the cube. a. List the sample space of this chance experiment. List the probability of each outcome in the sample space. b. What is the probability of getting a heads on the coin and the number 3 on the number cube? c. What is the probability of getting a tails on the coin and an even number on the number cube? Answer: a. Sample space: H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6 The probability of each outcome is \(\frac{1}{12}\). b. \(\frac{1}{12}\) c. \(\frac{3}{12}\), or \(\frac{1}{4}\)

## Eureka Math Grade 7 Module 5 Lesson 4 Exit Ticket Answer Key

An experiment consists of randomly drawing a cube from a bag containing three red and two blue cubes. Question 1. What is the sample space of this experiment? Answer: Red, blue

Question 2. List the probability of each outcome in the sample space. Answer: Probability of red is \(\frac{3}{5}\). Probability of blue is \(\frac{2}{5}\).

Question 3. Is the probability of selecting a red cube equal to the probability of selecting a blue cube? Explain. Answer: No. There are more red cubes than blue cubes, so red has a greater probability of being chosen.

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Engage NY Eureka Math 5th Grade Module 4 Lesson 7 Answer Key Eureka Math Grade 5 Module 4 Lesson 7 Problem Set Answer Key Solve using a tape diagram. a. of 18 Answer: 6 Explanation: ... Eureka Math Grade 5 Module 4 Lesson 7 Homework Answer Key. Question 1. Solve using a tape diagram. a. \(\frac{1}{4}\) of 24. b. \(\frac{1}{4}\) of 48.

Multiply any whole number by a fraction using tape diagrams, common core, fraction of a number, simplify fractions, help teachers, help students, help parents

Multiplication and Division of Fractions and Decimal Fractions. Eureka Essentials: Grade 5. An outline of learning goals, key ideas, pacing suggestions, and more! Fluency Games. Teach Eureka Lesson Breakdown. Downloadable Resources. Teacher editions, student materials, application problems, sprints, etc. Application Problems.

Multiply whole numbers by fractions using tape diagrams

Module 4: 5. 12 gal. 3. 24. bags of nuts, 20 bags. 24 bags of dried fruit. Multiplication and Division of Fractions. Answer Key. ka Math® Grade 5 Module 4TEKS EDITIONSpecial thanks go to the Gordon A. Cain Center and to the Department of Mathematics at Louisiana State University for their supp. 5.

Unit 5: Module 5: Addition and multiplication with volume and area. 0/1400 Mastery points. Topic A: Concepts of volume Topic B: Volume and the operations of multiplication and addition Topic C: Area of rectangular figures with fractional side lengths. Topic D: Drawing, analysis, and classification of two-dimensional shapes.

Addition and Multiplication with Volume and Area. Eureka Essentials: Grade 5. An outline of learning goals, key ideas, pacing suggestions, and more! Fluency Games. Teach Eureka Lesson Breakdown. Downloadable Resources. Teacher editions, student materials, application problems, sprints, etc. Application Problems.

Eureka Essentials: Grade 4. An outline of learning goals, key ideas, pacing suggestions, and more! Fluency Games. Teach Eureka Lesson Breakdown. Downloadable Resources. Teacher editions, student materials, application problems, sprints, etc. Application Problems. Files for printing or for projecting on the screen.

These Helpers explain, step by step, how to work problems similar to those found in Eureka Math assignments. There is a homework helper to go with every homework assignment. There are other valuable resources for families at eureka-math.org. 4th Grade Links ... Grade 4 Module 5. Comments (-1) Grade 4 Module 6. Comments (-1) Grade 4 Module 7 ...

This book may be purchased from the publisher at eureka-math.org 10 9 8 7 6 5 4 3 2 1 Eureka Math™ Grade 5, Module 4 Student File_A Contains copy-ready classwork and homework as well as templates (including cut outs) A Story of Units®

Eureka Math™ Grade 4, Module 7 Student File_A Contains copy-ready classwork and homework as well as templates (including cut outs) Published by Great Minds ... Lesson 11: Solve multi-step measurement word problems. 11 Problem Set 4 ...

1x 4 = 4. 4 x 3 = 12. 4/12. Eureka Math Grade 4 Module 5 Lesson 7 Homework Answer Key. Each rectangle represents 1. Question 1. The shaded unit fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. The first one has been done for you. a. b. Answer: 1/4 = 4/8. Explanation:

10 9 8 7 6 5 4 3 2 1 Eureka Math™ Grade 4, Module 6 Student File_A ... Lesson 1 Homework 4 6 L =L 0.3 L Name Date Shade the first 4 units of the tape diagram. Count by tenths to label the number line using a fraction and a decimal for each point. Circle the decimal that represents the shaded part. ...

1. + 4 = 4f. 17 =11 + 27Lesson 1: Decompose fractions as a sum of unit f. 512b. 103c. 2Lesson 2:Decompose fractions as a sum of unit f. ac. 2. 156b. 87c. 10Lesson 2:Decompose fractions as a sum of unit f. d. agrams.Lesson 2 Homework2. Step 1: Draw and shade a tape d.

Eureka Math Grade 7 Module 4 Lesson 5 Exit Ticket Answer Key. Question 1. A tank that is 40% full contains 648 gallons of water. Use a double number line to find the maximum capacity of the water tank. Answer: I divided the percent line into intervals of 20% making five intervals of 20% in 100%.

Lesson 5 Video Page. Lesson PDF Page. Homework Solutions File. Google Slideshow ... Grade 4 Module 7. Topic A: Measurement Conversion Tables. Lesson 1. Lesson 2. Lesson 3. Lesson 4. ... This work by EMBARC.Online based upon Eureka Math and is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

It's Homework Time! Help for fourth graders with Eureka Math Module 5 Lesson 7.

Eureka Math. Print Materials. As the creator of Engage NY Math and Eureka Math, Great Minds is the only place where you can get print editions of the PK-12 curriculum. Our printed materials are available in two configurations: Learn, Practice, Succeed, or student workbooks, teacher editions, assessment and fluency materials.

Courses. Grade 5. Eureka Math and EngageNY resource for 5th grade. Grade 5 General Resources. A 5th grade resource for teachers using Eureka Math and EngageNY. G5M1: Place Value and Decimal Fractions. A 5th grade resource for teachers using Eureka Math and EngageNY. G5M2: Multi-Digit Whole Number and Decimal Fraction Operations.

Eureka Math Grade 5 Module 5 Lesson 7 Homework Answer Key. Wren makes some rectangular display boxes. Question 1. Wren's first display box is 6 inches long, 9 inches wide, and 4 inches high. What is the volume of the display box? Explain your work using a diagram. Answer: Volume = length x width x volume. V = 6 x 9 x 4. V = 216 cubic inches

Module 7: Exploring Measurement with Multiplication Lesson 4 Answer Key 4• 7 Lesson 4 Problem Set 1. 240 minutes 4. 66,000 mL 2. 112 ounces 5. 86 ounces 3. 36 feet Exit Ticket 8 ounces Homework 1. 360 minutes 5. 14 2. 56 ounces 6. a. 45 quarts (or equivalent) 3. 1,350 mL b. No; answers will vary 4. 12 feet 9 A STORY OF UNITS

Sample: I can change the side length of 6 cm to 7 cm. Then the sum of any two side lengths will be greater than the third side length. 14. Find the value of the expression shown. (−1.2) ( 2 _ ) ÷ ( 2 _. 3 5 ) (−5) (3) The value of the expression is 30.

Answer: a. Sample space: Numbers 00-99 Probability of each outcome is 1100. b. 10100, or 110. c. 20100, or 15. d. 7100 (Factors of 64 are 1, 2, 4, 8, 16, 32, and 64.) Question 5. A chance experiment consists of flipping a coin and rolling a number cube with the numbers 1-6 on the faces of the cube. a.