{"id":12478,"date":"2023-12-17T08:54:54","date_gmt":"2023-12-17T03:24:54","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=12478"},"modified":"2023-12-18T17:15:49","modified_gmt":"2023-12-18T11:45:49","slug":"envision-math-common-core-grade-5-answer-key-topic-15","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-common-core-grade-5-answer-key-topic-15\/","title":{"rendered":"enVision Math Common Core Grade 5 Answer Key Topic 15 Algebra: Analyze Patterns and Relationships"},"content":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 5 Answer Key<\/a>\u00a0Topic 15 Algebra: Analyze Patterns and Relationships<\/strong>\u00a0regularly and improve your accuracy in solving questions.<\/p>\n

enVision Math Common Core 5th Grade Answers Key Topic 15 Algebra: Analyze Patterns and Relationships<\/h2>\n

Essential Questions:<\/strong> How can number patterns be analyzed and graphed? How can number patterns and graphs be used to solve problems?<\/p>\n

\"Envision<\/p>\n

enVision STEM Project: Analyze Patterns<\/strong>
\nDo Research<\/strong> Use the Internet or other sources to find patterns in cities and buildings in other parts of the world.<\/p>\n

Journal: Write a Report<\/strong> Include what you found. Also in your report:
\n\u2022 Describe types of patterns found in nature.
\n\u2022 Describe types of patterns found in cities.
\n\u2022 Make a graph to show relationships between some of the patterns you found.<\/p>\n

Review What You Know<\/strong><\/p>\n

A-Z Vocabulary<\/strong><\/p>\n

Choose the best term from the Word List. Write it on the blank.
\n\u2022 equation
\n\u2022 Expression
\n\u2022 variable
\n\u2022 evaluate
\n\u2022 ordered pair<\/p>\n

Question 1.
\nA numerical _____ is a mathematical phrase that has numbers and at least one operation.<\/p>\n

Answer:
\nA numerical expression is a mathematical phrase that has numbers and at least one operation.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA numerical expression is a mathematical phrase that has numbers and at least one operation.
\nfor example:
\n14 – 8 = 6.
\n21 – 5 + 2.
\n21 – 7 = 14.<\/p>\n

Question 2.
\nA(n) _____ can be used to show the location of a point on the coordinate plane.<\/p>\n

Answer:
\nA(n) ordered pair can be used to show the location of a point on the coordinate plane.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA(n) ordered pair can be used to show the location of a point on the coordinate plane.
\nfor example:
\n(1, 3) is an ordered pair.
\n1 is on the x-axis.
\n3 is on the y-axis.<\/p>\n

\"Algebra<\/p>\n

Question 3.
\nThe letter n in $10 \u00d7 n is called a(n) ___ and is a quantity that can change.<\/p>\n

Answer:
\nThe letter n in $10 x n is called a(n) variable and is a quantity that can change.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe letter n in $10 x n is called a(n) variable and is a quantity that can change.
\nfor example:
\nA factor can be a number, variable, term, or a longer expression.<\/p>\n

Expressions<\/strong>
\nWrite a numerical Expression for each calculation.<\/p>\n

Question 4.
\nAdd 230 and 54, and then divide by 7.<\/p>\n

Answer:
\n230 + 54 \/ 7.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nAdd 230 and 54, and then divide by 7.
\n230 + 54.
\n230 + 54 \/ 7.
\n284 \/ 7 = 40.5.<\/p>\n

Question 5.
\nSubtract 37 from the product of 126 and 4.<\/p>\n

Answer:
\n37 – 126 x 4 = 467.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nSubtract 37 from the product of 126 and 4.
\n126 x 4 – 37.
\n504 – 37.
\n467.<\/p>\n

Solve Equations<\/strong>
\nSolve each equation.<\/p>\n

Question 6.
\n7,200 + x = 13,000<\/p>\n

Answer:
\nX = 5800.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe equation is 7200 + x = 13000.
\n7200 + x = 13000.
\n13000 – 7200 = x.
\nx = 5800.<\/p>\n

Question 7.
\n6,000 = 20 \u00d7 g<\/p>\n

Answer:
\nG = 300.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe equation is 6000 = 20 x g.
\n6000 = 20 x g.
\ng = 6000\/ 20.
\ng = 300.<\/p>\n

Question 8.
\n105 + 45 = w \u00d7 3<\/p>\n

Answer:
\nW = 50.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe equation is 105 + 45 = w x 3.
\n150 = w x 3.
\nw = 150 \/ 3.
\nw = 50.<\/p>\n

Question 9.
\n38 + 42 = 480 \u00f7 b<\/p>\n

Answer:
\nB = 6.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe equation is 38 + 42 = 480 \u00f7 b.
\n80 = 480 \/ b.
\nb = 480 \/ 80.
\nb = 6.<\/p>\n

\"Algebra<\/p>\n

Question 10.
\nJanine has 85 hockey cards in one book and 105 hockey cards in another book. The hockey cards come in packages of 5 cards. If Janine bought all of her hockey cards in packages, how many packages did she buy?
\nA. 21 packages
\nB. 38 packages
\nC. 190 packages
\nD. 195 packages<\/p>\n

Answer:
\nOption D is correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJanine has 85 hockey cards in one book and 105 hockey cards in another book.
\nThe hockey cards come in packages of 5 cards.
\n85 + 105 = 190.
\n190 + 5 = 195.
\nso option D is correct.<\/p>\n

Evaluate Expressions<\/strong><\/p>\n

Question 11.
\nExplain how to evaluate the Expression 9 + (45 \u00d7 2) \u00f7 10.<\/p>\n

Answer:
\n9 + (45 x 2) \/ 10 = 18<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n9 + (45 x 2) \/ 10.
\n9 + (90) \/ 10.
\n9 + 9.
\n18.
\n9 + (45 x 2) \/ 10 = 18.<\/p>\n

Pick a Project<\/strong>
\nPROJECT 15A<\/strong>
\nHow are piano keys arranged on a keyboard?
\nProject: Learn More About Keyboards
\n\"Envision<\/p>\n

PROJECT 15B<\/strong>
\nWhy is it important to protect gopher tortoises?
\nProject: Use Information to Write Problems
\n\"Envision<\/p>\n

PROJECT 15C<\/strong>
\nHow can you use patterns to make art?
\nProject: Create a Work of String Art
\n\"Envision<\/p>\n

3-ACT MATH PREVIEW<\/strong><\/p>\n

Math Modeling<\/strong><\/p>\n

Video<\/strong><\/p>\n

Speed Stacks<\/strong><\/p>\n

\"Envision
\nBefore watching the video, think:
\nStacking cups is a lot less messy when they’re empty.<\/p>\n

Lesson 15.1 Numerical Patterns<\/h3>\n

Activity<\/strong><\/p>\n

Solve & Share<\/strong>
\nEmma has $100 in her savings account. Jorge has $50 in his savings account. They each put $10 in their accounts at the end of each week. Complete the tables to see how much each of them has saved after 5 weeks. What patterns do you notice?
\n\"Envision<\/p>\n

Answer:
\nEmma has $150 and Jorge has $100 after 5 weeks.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nEmma has $100 in her savings account.
\nJorge has $50 in his savings account.
\nThey each put $10 in their accounts at the end of each week.
\n100 + 10 = 110, 110 + 10 = 120, 120 + 10 = 130, 130 + 10 = 140, and 140 + 10 = 150.
\n50 + 10 = 60, 60 + 10 = 70, 70 + 10 = 80, 80 + 10 = 90, 90 + 10 = 100.
\nso Emma has $150 and Jorge has $100 after 5 weeks.<\/p>\n

Look for Relationships to see what is alike and what is different in the two tables.
\n\"Envision<\/p>\n

Answer:
\nBoth of them saved an equal amount of money that is $50.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nEmma has $100 in her savings account.
\nJorge has $50 in his savings account.
\nThey each put $10 in their accounts at the end of each week.
\n100 + 10 = 110, 110 + 10 = 120, 120 + 10 = 130, 130 + 10 = 140, and 140 + 10 = 150.
\n50 + 10 = 60, 60 + 10 = 70, 70 + 10 = 80, 80 + 10 = 90, 90 + 10 = 100.
\nso both of them saved an equal amount of money that is $50.<\/p>\n

Look Back!<\/strong> If the savings patterns continue, will Jorge ever have as much saved as Emma? Explain.<\/p>\n

Visual Learning Bridge<\/strong><\/p>\n

Essential Question<\/strong> How Can You Solve Problems Involving Numerical Patterns?<\/p>\n

A.<\/strong>
\nLindsey has a sage plant that is 3.5 inches tall. She also has a rosemary plant that is 5.2 inches tall. Both plants grow 1.5 inches taller each week. How tall will the plants be after 5 weeks? What is the relationship between the heights of the plants?<\/p>\n

You can create tables to help identify relationships between corresponding terms in the number sequences.
\n\"Envision<\/p>\n

B.<\/strong>
\nYou can use the rule “add 1.5\u201d to complete the tables.
\n\"Envision<\/p>\n

Convince Me! Reasoning<\/strong> If the patterns continue, how can you tell that the rosemary plant will always be taller than the sage plant?<\/p>\n

Guided Practice<\/strong><\/p>\n

Do You Understand?<\/strong><\/p>\n

Question 1.
\nAnthony says, \u201cThe pattern is that the sage plant is always 1.7 inches shorter than the rosemary plant.” Do you agree? Explain.<\/p>\n

Answer:
\nYes, I will agree.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nLindsey has a sage plant that is 3.5 inches tall.
\nShe also has a rosemary plant that is 5.2 inches tall.
\nBoth plants grow 1.5 inches taller each week.
\n5.2 – 3.5 = 1.7.
\nso I will agree.<\/p>\n

Question 2.
\nHow does making tables help you identify relationships between terms in patterns?<\/p>\n

Answer:
\nThe difference for every pattern is 1.7.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nLindsey has a sage plant that is 3.5 inches tall.
\nShe also has a rosemary plant that is 5.2 inches tall.
\nBoth plants grow 1.5 inches taller each week.
\n5.2 – 3.5 = 1.7.
\nso the difference for every pattern is 1.7.<\/p>\n

\"Algebra<\/p>\n

Do You Know How?<\/strong><\/p>\n

Question 3.
\nIf the plants continue to grow 1.5 inches each week, how tall will each plant be after 10 weeks?<\/p>\n

Answer:
\nAfter 10 weeks each plant will be 18.5.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nif the plants continue to grow 1.5 inches each week.
\n11 + 1.5 = 12.5.
\n12.5 + 1.5 = 14.0.
\n14.0 + 1.5 = 15.5.
\n15.5 + 1.5 = 17.0.
\n17.0 + 1.5 = 18.5.<\/p>\n

Question 4.
\nIf the plants continue to grow 1.5 inches each week, how tall will each plant be after 15 weeks?<\/p>\n

Answer:
\nAfter 15 weeks each plant will be 26.0.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nif the plants continue to grow 1.5 inches each week.
\n18.5 + 1.5 = 20.0.
\n20.0 + 1.5 = 21.5.
\n21.5 + 1.5 = 23.0.
\n23.0 + 1.5 = 24.5.
\n24.5 + 1.5 = 26.0.<\/p>\n

Independent Practice<\/p>\n

In 5-7, use the rule “add $0.50” to help you.<\/p>\n

Question 5.
\nTim and Jill each have a piggy bank. Tim starts with $1.25 in his bank and puts in $0.50 each week. Jill starts with $2.75 in her bank and also puts in $0.50 each week. Complete the table to show how much money each has saved after five weeks.
\n\"Envision<\/p>\n

Answer:
\nTim saved $3.75 and Jill saved $5.25.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nTim and Jill each have a piggy bank.
\nTim starts with $1.25 in his bank and puts in $0.50 each week.
\nJill starts with $2.75 in her bank and also puts in $0.50 each week.
\n1.25 + 0.50 = 1.75.
\n1.75 + 0.50 = 2.25.
\n2.25 + 0.50 = 2.75.
\n2.75 + 0.50 = 3.25.
\n3.25 + 0.50 = 3.75.
\n2.75 + 0.50 = 3.25.
\n3.25 + 0.50 = 3.75.
\n3.75 + 0.50 = 4.25.
\n4.25 + 0.50 = 4.75.
\n4.75 + 0.50 = 5.25.<\/p>\n

Question 6.
\nWhat relationship do you notice between the amount Tim has saved and the amount Jill has saved each week?<\/p>\n

Answer:
\nTim has saved $3.75 and Jill saved $5.25.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nTim and Jill each have a piggy bank.
\nTim starts with $1.25 in his bank and puts in $0.50 each week.
\nJill starts with $2.75 in her bank and also puts in $0.50 each week.
\n1.25 + 0.50 = 1.75.
\n1.75 + 0.50 = 2.25.
\n2.25 + 0.50 = 2.75.
\n2.75 + 0.50 = 3.25.
\n3.25 + 0.50 = 3.75.
\n2.75 + 0.50 = 3.25.
\n3.25 + 0.50 = 3.75.
\n3.75 + 0.50 = 4.25.
\n4.25 + 0.50 = 4.75.
\n4.75 + 0.50 = 5.25.<\/p>\n

Question 7.
\nIf Tim and Jill continue saving in this way, how much will each have saved after 10 weeks? Explain how you decided.<\/p>\n

Answer:
\nTim saves $6.25 and Jill saves $7.75.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nTim and Jill each have a piggy bank.
\nTim starts with $1.25 in his bank and puts in $0.50 each week.
\nJill starts with $2.75 in her bank and also puts in $0.50 each week.
\n3.75 + 0.50 = 4.25.
\n4.25 + 0.50 = 4.75.
\n4.75 + 0.50 = 5.25.
\n5.25 + 0.50 = 5.75.
\n5.75 + 0.50 = 6.25.
\n5.25 + 0.50 = 5.75.
\n5.75 + 0.50 = 6.25.
\n6.25 + 0.50 = 6.75.
\n6.75 + 0.50 = 7.25.
\n7.25 + 0.50 = 7.75.<\/p>\n

Problem Solving<\/strong><\/p>\n

For 8-10, use the table.<\/p>\n

\"Envision<\/p>\n

Question 8.
\nenVision\u00ae STEM<\/strong> Bur oak and hickory trees are deciduous, which means that they lose their leaves seasonally. A bur oak is 25\\(\\frac{1}{2}\\) feet tall and grows 1\\(\\frac{1}{2}\\) feet each year. A hickory is 30 feet tall and grows 1\\(\\frac{1}{2}\\) feet each year. Complete the chart to show the heights of the two trees each year for five years.<\/p>\n

Answer:
\nThe heights of the two trees each year for five years = 32 and 37.5.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nBur oak and hickory trees are deciduous, which means that they lose their leaves seasonally.
\nA bur oak is 25\\(\\frac{1}{2}\\) feet tall and grows 1\\(\\frac{1}{2}\\) feet each year.
\nA hickory is 30 feet tall and grows 1\\(\\frac{1}{2}\\) feet each year.
\n25(1\/2) = 51\/2 = 25.5.
\n3\/2 = 1.5.
\n25.5 + 1.5 = 27.0.
\n27.0 + 1.5 = 28.5.
\n28.5 + 1.5 = 30.
\n30 + 1.5 = 31.5.
\n31.5 + 1.5 = 32.
\n30 + 1.5 = 31.5.
\n31.5 + 1.5 = 33.
\n33 + 1.5 = 34.5.
\n34.5 + 1.5 = 36.0.
\n36.0 + 1.5 = 37.5.<\/p>\n

Question 9.
\nIf each tree continues to grow 1\\(\\frac{1}{2}\\) feet each year, how tall will each tree be after 15 years?<\/p>\n

Answer:
\nThe height of each tree after 15 years = 39.5 and 45.0.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA bur oak is 25\\(\\frac{1}{2}\\) feet tall and grows 1\\(\\frac{1}{2}\\) feet each year.
\nHickory is 30 feet tall and grows 1\\(\\frac{1}{2}\\) feet each year.
\n32 + 1.5 = 33.5.
\n33.5 + 1.5 = 35.0.
\n35.0 + 1.5 = 36.5.
\n36.5 + 1.5 = 38.0.
\n38.0 + 1.5 = 39.5.
\n37.5 + 1.5 = 39.0.
\n39.0 + 1.5 = 40.5.
\n40.5 + 1.5 = 42.0.
\n42.0 + 1.5 = 43.5.
\n43.5 + 1.5 = 45.0.<\/p>\n

Question 10.
\nHigher Order Thinking<\/strong> What relationship do you notice between the height of the bur oak and the height of the hickory each year? Explain.
\nAnswer:<\/p>\n

Question 11.
\nReasoning<\/strong> Each small square on the chessboard is the same size. The length of a side of a small square is 2 inches. What is the area of the chessboard? Explain.
\n\"Envision<\/p>\n

Answer:
\nThe area of the chessboard = 4 sq in.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nEach small square on the chessboard is the same size.
\nThe length of a side of a small square is 2 inches.
\narea of the square = side x side.
\narea of the square and area of the chessboard is the same.
\narea = s x s.
\ns = 2 inches.
\narea = 2 x 2.
\narea = 4 sq in.
\nso the area of the chessboard = 4 sq in.<\/p>\n

Assessment Practice<\/strong><\/p>\n

Question 12.
\nJessica has saved $50. She will add $25 to her savings each week. Ron has saved $40 and will add $25 to his savings each week. How much will each person have saved after 5 weeks?
\nA. Jessica: $275; Ron: $225
\nB. Jessica: $250; Ron: $240
\nC. Jessica: $175; Ron: $165
\nD. Jessica: $165; Ron: $175<\/p>\n

Answer:
\nOption C is correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJessica has saved $50.
\nShe will add $25 to her savings each week.
\nRon has saved $40 and will add $25 to his savings each week.
\n$50 + $25 = $75.
\n$25 x 5 = $125.
\n$125 + $50 = $175.
\n$40 + $25 = $65.
\n$65 + $100 = $165.<\/p>\n

Question 13.
\nWhich of the following statements are true?
\n\"Envision Jessica has always saved $25 more than Ron.
\n\"Envision Jessica has always saved $10 more than Ron.
\n\"Envision Ron has always saved $25 less than Jessica.
\n\"Envision Ron has always saved $10 less than Jessica<\/p>\n

Answer:
\nOption B is correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJessica has saved $50.
\nShe will add $25 to her savings each week.
\nRon has saved $40 and will add $25 to his savings each week.
\n$175 – $165 = $10.
\nso option B is correct.<\/p>\n

Lesson 15.2 More Numerical Patterns<\/h3>\n

Activity<\/strong><\/p>\n

Solve & Share<\/strong>
\nDuring summer vacation, Julie read 45 pages each day. Her brother Bret read 15 pages each day. Complete the tables to show how many pages each of them read after 5 days. What relationship do you notice between the terms in each pattern?<\/p>\n

\"Envision<\/p>\n

Find a rule to help you complete each table.
\n\"Envision<\/p>\n

Answer:
\nThe number of pages each of them read after 5 days = 105 and 75.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nDuring summer vacation, Julie read 45 pages each day.
\nHer brother Bret read 15 pages each day.
\n45 + 15 = 60.
\n60 + 15 = 75.
\n75 + 15 = 90.
\n90 + 15 = 105.
\n105 + 15 = 125.
\n15 + 15 = 30.
\n30 + 15 = 45.
\n45 + 15 = 60.
\n60 + 15 = 75.<\/p>\n

Look Back! Reasoning<\/strong> Explain why this relationship Exists between the terms.<\/p>\n

Visual Learning Bridge<\/strong><\/p>\n

Essential Question<\/strong>
\nHow Can You Identify Relationships Between Patterns?<\/p>\n

A.<\/strong>
\nJack is training for a race. Each week, he runs 30 miles and bikes 120 miles. He created a table to record his progress. How many total miles will he run and bike after 5 weeks? Can you identify any relationship between the miles run and the miles biked?<\/p>\n

You can use the rules \u201cadd 30\u201d and \u201cadd 120″ to help you complete the table.
\n\"Envision<\/p>\n

B.<\/strong>
\nSince jack runs 30 miles each week, add 30 to find the nExt term for the total miles run. Add 120 to find each term in the pattern for the total number of miles biked.
\n\"Envision<\/p>\n

C.<\/strong>
\nCompare the corresponding terms in the patterns:
\n30 \u00d7 4 = 120
\n60 \u00d7 4 = 240
\n90 \u00d7 4 = 360
\n120 \u00d7 4 = 480
\n150 \u00d7 4 = 600
\nSo, the total number of miles biked is always 4 times the total number of miles run.<\/p>\n

Convince Me! Generalize<\/strong> Do you think the relationship between the corresponding terms in the table Jack created will always be true? Explain.<\/p>\n

Answer:
\nThe relationship between the corresponding terms in the table Jack created will always be true.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJack is training for a race.
\nEach week, he runs 30 miles and bikes 120 miles.
\nHe created a table to record his progress.
\n30 \u00d7 4 = 120.
\n60 \u00d7 4 = 240.
\n90 \u00d7 4 = 360.
\n120 \u00d7 4 = 480.
\n150 \u00d7 4 = 600.
\nso the relationship between the corresponding terms in the table Jack created will always be true.<\/p>\n

Guided Practice<\/strong><\/p>\n

Do You Understand?<\/strong><\/p>\n

In 1-3, use the table on page 598.<\/p>\n

Question 1.
\nNeko says that the relationship between the terms is that the number of miles run is \\(\\frac{1}{4}\\) the number of miles biked. Do you agree? Explain.<\/p>\n

Answer:
\nYes, it is true.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe number of miles run is 1\/4 the number of miles biked.
\nJack is training for a race.
\nEach week, he runs 30 miles and bikes 120 miles.
\nHe created a table to record his progress.
\n30 \u00d7 4 = 120.
\n60 \u00d7 4 = 240.
\n90 \u00d7 4 = 360.
\n120 \u00d7 4 = 480.
\n150 \u00d7 4 = 600.
\nSo it is true.<\/p>\n

Question 2.
\nHow many total miles will Jack have run and biked after 10 weeks? 15 weeks?<\/p>\n

Answer:
\nThe number of miles will Jack have run and biked after 10 weeks and 15 weeks = 1200 and 1800.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n180 x 4 = 720.
\n210 x 4 = 840.
\n240 x 4 = 960.
\n270 x 4 = 1080.
\n300 x 4 = 1200.
\n330 x 4 = 1320.
\n360 x 4 = 1440.
\n390 x 4 = 1560.
\n420 x 4 = 1680.
\n450 x 4 = 1800.
\nso the number of miles Will Jack have run and biked after 10 weeks and 15 weeks = 1200 and 1800.<\/p>\n

Question 3.
\nMiguel says that he can use multiplication to find the terms in the patterns. Do you agree? Explain.<\/p>\n

Answer:
\nYes, Miguel says that he can use multiplication to find the terms in the patterns.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n180 x 4 = 720.
\n210 x 4 = 840.
\n240 x 4 = 960.
\n270 x 4 = 1080.
\n300 x 4 = 1200.
\n330 x 4 = 1320.
\n360 x 4 = 1440.
\n390 x 4 = 1560.
\n420 x 4 = 1680.
\n450 x 4 = 1800.
\nIndependent Practice<\/strong><\/p>\n

In 4-6, use the rules “add 250” and “add 125\u201d to help you.<\/p>\n

Question 4.
\nMaria and Henry are each starting a savings account. Maria puts $250 into her account each month. Henry puts $125 into his account each month. How much money will each of them have saved after 6 months? Complete the table to solve.
\n\"Envision<\/p>\n

Answer:
\nThe money will each of them have saved after 6 months =<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nMaria and Henry are each starting a savings account.
\nMaria puts $250 into her account each month.
\nHenry puts $125 into his account each month.<\/p>\n

Question 5.
\nWhat relationship do you notice between the total amount Maria has saved after each month and the total amount Henry has saved after each month?
\nAnswer:<\/p>\n

Question 6.
\nIf Maria and Henry continue saving this way for a full year, how much more will Maria have saved than Henry?
\nAnswer:<\/p>\n

Problem Solving<\/strong><\/p>\n

Question 7.
\nSheila and Patrick are making a table to compare gallons, quarts, and pints. Use the rule “add 4” to complete the column for the number of quarts. Then use the rule “add 8” to complete the column for the number of pints.
\n\"Envision
\nAnswer:<\/p>\n

Question 8.
\nPatrick has a 12-gallon fish tank at home. How many quarts of water will fill his fish tank? How many pints?
\nAnswer:<\/p>\n

Question 9.
\nLook for Relationships<\/strong> What relationship do you notice between the number of quarts and the number of pints?
\nAnswer:<\/p>\n

Question 10.
\nHigher Order Thinking<\/strong> At their family’s pizzeria, Dan makes 8 pizzas in the first hour they are open and 6 pizzas each hour after that. Susan makes 12 pizzas in the first hour and 6 pizzas each hour after that. If the pizzeria is open for 6 hours, how many pizzas will they make in all? Complete the table using the rule “add 6” to help you.
\n\"Envision
\nAnswer:<\/p>\n

Question 11.
\nLook for Relationships<\/strong> Compare the total number of pizzas made by each person after each hour. What relationship do you notice?
\nAnswer:<\/p>\n

Assessment Practice<\/strong><\/p>\n

Question 12.
\nMike and Sarah are packing boxes at a factory. Mike packs 30 boxes each hour. Sarah packs 15 boxes each hour. How many boxes will each person have packed after an 8-hour shift?
\nA. Mike: 38 boxes; Sarah: 23 boxes
\nB. Mike: 86 boxes; Sarah: 71 boxes
\nC. Mike: 120 boxes; Sarah: 240 boxes
\nD. Mike: 240 boxes; Sarah: 120 boxes
\nAnswer:<\/p>\n

Question 13.
\nWhich of the following are true statements about the number of boxes Mike and Sarah have packed after each hour?
\n\"Envision Mike has always packed a total of 15 more boxes than Sarah.
\n\"Envision Mike has always packed twice as many boxes as Sarah.
\n\"Envision Sarah has always packed twice as many boxes as Mike.
\n\"Envision Sarah has always packed half as many boxes as Mike.
\nAnswer:<\/p>\n

Lesson 15.3 Analyze and Graph Relationships<\/h3>\n

Activity<\/strong><\/p>\n

Solve & Share<\/strong>
\nA bakery can fit either 6 regular muffins or 4 jumbo muffins in each box. Each box will contain either regular or jumbo muffins. Complete the table to show how many of each muffin will fit in 2, 3, or 4 boxes. Then generate ordered pairs and graph them.
\n\"Envision<\/p>\n

Find rules that describe the relationships between the number of boxes and the number of muffins.
\n\"Envision<\/p>\n

Look Back! Look for Relationships<\/strong> The bakery can fit 12 mini-muffins in a box. How many mini-muffins will fit in 4 boxes? Without Extending the table, what relationship do you notice between the number of mini-muffins and the number of boxes?<\/p>\n

Visual Learning Bridge<\/strong><\/p>\n

Essential Question<\/strong> How Can You Generate and Graph Numerical Patterns?<\/p>\n

You can look for a relationship between the corresponding terms in the patterns.
\n\"Envision<\/p>\n

A.<\/strong>
\nJill earns $5 per hour babysitting. Robin earns $15 per hour teaching ice skating lessons. The girls made a table using the rule “Add 5” to show Jill’s earnings and the rule “Add 15” to show Robin’s earnings. Complete the table, compare their earnings, and graph the ordered pairs of the corresponding terms.
\n\"Envision<\/p>\n

B.<\/strong>
\nCompare the numbers in Jill’s and Robin’s sequences.
\nEach sequence begins with zero. Then each term in Robin’s pattern is 3 times as great as the corresponding term in Jill’s pattern.
\nGenerate ordered pairs from the total amount Jill and Robin have earned after each hour.
\n(0, 0), (5, 15), (10,30), (15,45), (20,60)<\/p>\n

C.<\/strong>
\nGraph the ordered pairs.
\n\"Envision<\/p>\n

Convince Me! Make Sense and Persevere<\/strong> What does the point (0,0) represent?<\/p>\n

Guided Practice<\/strong><\/p>\n

Do You Understand?<\/strong><\/p>\n

Question 1.
\nIn the Example on page 602, what ordered pair would you write for how much Jill and Robin have each earned after 5 hours?<\/p>\n

Question 2.
\nBen says that the relationship is that Jill earns \\(\\frac{1}{3}\\) as much as Robin. Do you agree? Explain.
\nAnswer:<\/p>\n

Do You Know How?<\/strong><\/p>\n

Sam and Eric record the total number of miles they walk in one week. Sam walks 2 miles each day. Eric walks 4 miles each day.<\/p>\n

Question 3.
\nWhat ordered pair represents the number of miles each has walked in all after 7 days?
\nAnswer:<\/p>\n

Question 4.
\nWhat relationship do you notice between the total number of miles Sam and Eric have each walked?
\nAnswer:<\/p>\n

Independent Practice<\/strong><\/p>\n

In 5-8, use the rule \u201cadd 4″ to help you.<\/p>\n

Question 5.
\nMegan and Scott go fishing while at camp. Megan catches 3 fish in the first hour and 4 fish each hour after that. Scott catches 5 fish in the first hour and 4 fish each hour after that. Complete the table to show the total number of fish each has caught after each hour.
\n\"Envision
\nAnswer:<\/p>\n

Question 6.
\nWhat ordered pair represents the total number of fish they each caught after 4 hours?
\nAnswer:<\/p>\n

Question 7.
\nWhat relationship do you notice between the total number of fish each has caught after each hour?
\nAnswer:<\/p>\n

Question 8.
\nGraph the ordered pairs of the total number of fish each has caught after each hour.
\nAnswer:<\/p>\n

Question 9.
\nThe pattern continues until Scott’s total is 29 fish. What ordered pair represents the total number of fish they each caught when Scott’s total is 29 fish?
\nAnswer:<\/p>\n

Problem Solving<\/strong><\/p>\n

In 10-12, use the rules \u201cadd 15″ and “add 10” to help you.<\/p>\n

Question 10.
\nThe Snack Shack made a table to track the amount of money from sales of frozen yogurt and fruit cups for four hours. What are the missing values in the table?
\n\"Envision
\nAnswer:<\/p>\n

Question 11.
\nUse Structure<\/strong> If sales continue in the same manner, what ordered pair would represent the money from sales of yogurt and fruit cups at 1 P.M.? Explain how you know.
\nAnswer:<\/p>\n

Question 12.
\nGraph the ordered pairs for the money from sales of yogurt and fruit cups from 9 A.M. to 1 P.M.
\nAnswer:<\/p>\n

Question 13.
\nA-Z Vocabulary<\/strong> Write two number sequences. Then, circle corresponding terms in the two sequences.
\nAnswer:<\/p>\n

Question 14.
\nHigher Order Thinking<\/strong> Pedro runs 2\\(\\frac{1}{2}\\) miles each day for 5 days. Melissa runs 4 miles each day for 5 days. How many more miles will Melissa run in 5 days than Pedro? Make a table to help you.
\nAnswer:<\/p>\n

Assessment Practice<\/strong><\/p>\n

Question 15.
\nEvery month, Leonard pays $240 for a car payment. He spends $60 each month for a gym membership. Write an ordered pair to represent how much Leonard spends in 12 months for car payments and the gym membership.
\nAnswer:<\/p>\n

Question 16.
\nWhat relationship do you notice between how much Leonard spends in 12 months on car payments and the gym membership?
\nAnswer:<\/p>\n

Lesson 15.4 Make Sense and Persevere<\/h3>\n

Activity<\/strong><\/p>\n

Solve & Share<\/strong>
\nVal is planning a bowling-and-pizza party. Including herself, there will be no more than 10 guests. Val wonders which bowling alley offers the less Expensive party plan.
\nComplete the tables for Leonard’s Lanes and Southside Bowl. On the same grid, graph the ordered pairs in each table. Use a different color for the values in each table. Which bowling alley would be less Expensive? Explain how you know.<\/p>\n

Leonard’s Lanes<\/strong>
\nBowling and Pizza: $25 plus $10 per person
\n\"Envision
\nSouthside Bowl<\/strong>
\nBowling and Pizza: $15 per person Guests 1 2 3 4 5 6 7
\n\"Envision<\/p>\n

Thinking Habits<\/strong>
\nThink about these questions to help you make sense and persevere.
\n\u2022 What do I need to find?
\n\u2022 What do I know?
\n\u2022 What else can I try if I get stuck?
\n\u2022 How can I check that my solution makes sense?
\n\"Envision<\/p>\n

Look Back! Make Sense and Persevere<\/strong> How did the graph help you answer the question?<\/p>\n

Visual Learning Bridge<\/strong><\/p>\n

Essential Question<\/strong> How Can You Make Sense of a Problem Question and Persevere in Solving It?<\/p>\n

A.<\/strong>
\nMake Sense of the Problem<\/strong>
\nOn Aiden’s farm, there are 12 acres of soybeans and 8 acres of corn. Aiden plans to replace his other crops with more acres of soybeans and corn. Will his farm ever have the same number of acres of soybeans and corn? Explain.<\/p>\n

\"Envision<\/p>\n

You can make sense of the problem by answering these questions. What do you know? What are you asked to find?
\n\"Envision<\/p>\n

B.<\/strong>
\nHow can I make sense of and solve this problem?
\nI can
\n\u2022 choose and implement an appropriate strategy.
\n\u2022 use ordered pairs to make graphs.
\n\u2022 identify and analyze patterns.
\n\u2022 check that my work and answer make sense.<\/p>\n

Here’s my thinking…
\n\"Envision<\/p>\n

C.<\/strong>
\nFor each crop, I can write a rule, make a table, and plot the ordered pairs. Then I can see if the number of acres is ever the same.
\nSoybeans
\nRule: Start at 12 and add 3.
\n\"Envision<\/p>\n

\"Envision<\/p>\n

Corn
\nRule: Start at 8 and add 4.
\n\"Envision
\nWhere the lines intersect, at 4 years, Aiden’s farm has 24 acres of each crop.<\/p>\n

Convince Me! Make Sense and Persevere<\/strong> How can you check your work? Does your answer make sense? Explain.<\/p>\n

Guided Practice<\/strong><\/p>\n

Mindy has already saved $20 and plans to save $8 each month. Georgette has no money saved yet but plans to save $5 each month. Will the girls ever have saved the same amount? Explain.
\n\"Envision<\/p>\n

Question 1.
\nWrite a rule and complete each table.
\nRule: _______
\nRule: _______
\nAnswer:<\/p>\n

Question 2.
\nOn the same grid, graph the ordered pairs in each table.
\nAnswer:<\/p>\n

\"Envision<\/p>\n

Question 3.
\nExplain whether the girls will ever have the same amount of money saved.
\nAnswer:<\/p>\n

Independent Practice<\/strong><\/p>\n

Make Sense and Persevere<\/strong>
\nO’Brien’s Landscaping pays employees $15 plus $12 per lawn. Carter’s Landscaping pays $25 plus $10 per lawn. Which company pays more? Explain.
\n\"Envision<\/p>\n

Question 4.
\nWrite a rule and complete each table.
\nRule: _______
\nRule: _______
\nAnswer:<\/p>\n

Question 5.
\nOn the grid, graph the ordered pairs in each table. Explain which company pays more.
\n\"Envision
\nAnswer:<\/p>\n

Problem Solving<\/strong><\/p>\n

Performance Task<\/strong><\/p>\n

Track-a-Thon<\/strong>
\nJordan is running in a track-a-thon to raise money for charity. Who will make a larger donation, Aunt Meg or Grandma Diane? Explain.<\/p>\n

\"Envision<\/p>\n

Question 6.
\nMake Sense and Persevere<\/strong> How can you use tables and a graph to solve the problem?
\nAnswer:<\/p>\n

Question 7.
\nUse Appropriate Tools<\/strong> For each pledge, write a rule and complete the table.
\nRule: ________
\n\"Envision
\nRule: ________
\n\"Envision<\/p>\n

When you make sense and persevere, you choose and implement an appropriate strategy
\n\"Envision<\/p>\n

Question 8.
\nUse Appropriate Tools<\/strong> On the grid, graph the ordered pairs in each table.
\n\"Envision
\nAnswer:<\/p>\n

Question 9.
\nReasoning<\/strong> Explain whose donation will be greater.
\nAnswer:<\/p>\n

Topic 15 Fluency Practice<\/h3>\n

Activity<\/strong><\/p>\n

Follow the path<\/strong><\/p>\n

Solve each problem. Follow problems with an answer of 72,072 to shade a path from START to FINISH. You can only move up, down, right, or left.
\n\"Envision
\n\"Envision<\/p>\n

Topic 15 Vocabulary Review<\/strong><\/p>\n

Glossory<\/strong><\/p>\n

Word List<\/strong>
\n\u2022 coordinate grid
\n\u2022 corresponding terms
\n\u2022 number sequence
\n\u2022 ordered pair \u2022 origin
\n\u2022 x-axis
\n\u2022 x-coordinate
\n\u2022 y-axis
\n\u2022 y-coordinate<\/p>\n

Understand Vocabulary<\/strong>
\nWrite always, sometimes, or never on each blank.<\/p>\n

Question 1.
\nCorresponding terms are ____ in the same position in a pair of number sequences.
\nAnswer:<\/p>\n

Question 2.
\nAn ordered pair can ____ be plotted on the origin of a coordinate grid.
\nAnswer:<\/p>\n

Question 3.
\nThe origin is ____ any other location on a coordinate grid besides (0,0).
\nAnswer:<\/p>\n

Question 4.
\nTwo number lines that form a coordinate grid _____ intersect at a right angle.
\nAnswer:<\/p>\n

Question 5.
\nThe second number of an ordered pair ____ describes the distance to the right or left of the origin.
\nAnswer:<\/p>\n

In 6-8, use the lists of numbers below.<\/p>\n

\"Envision<\/p>\n

\"Envision<\/p>\n

Use Vocabulary in Writing<\/strong><\/p>\n

Question 9.
\nExplain how to identify corresponding terms in two number sequences. Use terms from the Word List in your Explanation.
\nAnswer:<\/p>\n

Topic 15 ReTeaching<\/h3>\n

Set A<\/strong> pages 593-596
\nMaria has $4. She will save $10 each week. Stephen has $9 and will also save $10 each week.
\nMaria uses the rule “add 10” to create tables to see how much each will have saved after each week. What relationship do you notice between the corresponding terms?
\n\"Envision
\nAfter each week, Stephen has $5 more saved than Maria. Or, Maria’s savings are always $5 less than Stephen’s savings.<\/p>\n

Remember<\/strong> to compare corresponding terms to see if there is a relationship.<\/p>\n

Question 1.
\nTwo groups of students went hiking. After 1 hour, Group A hiked 1\\(\\frac{1}{2}\\) miles and Group B hiked 2\\(\\frac{1}{2}\\) miles. After that, each group hiked 2 miles each hour. Complete the tables to show how far each group had hiked after 3 hours.
\n\"Envision
\nAnswer:<\/p>\n

Question 2.
\nWhat relationship do you notice between the corresponding terms?
\nAnswer:<\/p>\n

Set B<\/strong>
\npages 597-600
\nEach week, Andre lifts weights twice and runs 4 times. Andre uses the rules “add 2” and “add 4” to complete the table. What relationship do you notice between the corresponding terms?
\n\"Envision
\nThe number of times Andre went running is always 2 times the number of times he lifted weights.<\/p>\n

Remember<\/strong> to use the rules to help you complete the tables.<\/p>\n

Question 1.
\nA garden center sells 15 trees and 45 shrubs each day for one week. Complete the table to show how many trees and shrubs in all were sold in 4 days. Use the rules \u201cadd 15″ and \u201cadd “45” to help you.
\n\"Envision
\nAnswer:<\/p>\n

Question 2.
\nWhat is the relationship between the corresponding terms of the sequences?
\nAnswer:<\/p>\n

Set C<\/strong>
\npages 601-604
\nKelly uses 3 pounds of nuts and 2 pounds of cereal to make each batch of trail mix. The chart shows how many total pounds of each she will need for 4 batches. Graph ordered pairs of the corresponding terms. What does the point (12, 8) represent?
\n\"Envision
\nThe chart and graph both represent the problem. The point (12,8) shows that when Kelly uses 12 pounds of nuts, she will use 8 pounds of cereal.
\n\"Envision<\/p>\n

Remember<\/strong> to make ordered pairs from corresponding terms.<\/p>\n

Question 1.
\nLauren has $6 and saves $5 each week. Derrick has $3 and saves $5 each week. How much will each have saved after 4 weeks? Use the rule “add 5” to complete the table.
\n\"Envision
\nAnswer:<\/p>\n

Question 2.
\nWhat does the point (26, 23) represent?
\nAnswer:<\/p>\n

Question 3.
\nWhat is the relationship between the corresponding terms?
\nAnswer:<\/p>\n

Set D<\/strong>
\npages 605-608
\nThink about these questions to help you make sense and persevere in solving problems.<\/p>\n

Thinking Habits<\/strong>
\n\u2022 What do I need to find?
\n\u2022 What do I know?
\n\u2022 What else can I try if I get stuck?
\n\u2022 How can I check that my solution makes sense?<\/p>\n

\"Envision<\/p>\n

Remember<\/strong> that you can use patterns, tables, and graphs to represent and solve problems.<\/p>\n

Question 1.
\nSam starts with 5 stamps and buys 10 more each month. Pat starts with 9 stamps and buys 9 more each month. Complete the table using the rules “add 10” and “add 9”.
\n\"Envision
\nAnswer:<\/p>\n

Question 2.
\nMake a graph from the data in the tables. Will Sam ever have more stamps than Pat?
\nAnswer:<\/p>\n

Topic 15 Assessment Practice<\/h3>\n

Question 1.
\nLiz and Fareed each start a new savings account. Liz starts her account with $75. Fareed starts his account with $100. Each month, both save another $50.
\nA. Complete the table to show the total amount each has saved after each month. Use the rule “add 50\u201d.
\n\"Envision
\nB. Select all the ordered pairs that represent amounts Liz and Fareed have each saved.
\n\"Envision (50, 75)
\n\"Envision (75, 100)
\n\"Envision (125, 150)
\n\"Envision (150, 200)
\n\"Envision (275, 300)
\nC. Describe the relationship between the amount each person has saved after each month.
\nAnswer:<\/p>\n

Question 2.
\nThere are 16 pawns and 2 kings in each chess set.
\nA. Complete the table to show how many pawns and kings in all are in different numbers of chess sets. Use the rules \u201cadd 16″ and “add 2”.
\n\"Envision
\nB. Use the total number of pawns and kings to form ordered pairs. Graph the ordered pairs below.
\n\"Envision
\nC. What would the ordered pair (96, 12) represent?
\nAnswer:<\/p>\n

Question 3.
\nLuis kept track of the heights of his basil and chive plants. His basil plant was 15\\(\\frac{1}{2}\\)cm tall and grew 1\\(\\frac{1}{2}\\) cm each week. His chive plant was 18\\(\\frac{1}{2}\\) cm tall and grew \\(\\frac{1}{2}\\) cm each week.
\nA. Complete the table to show the heights of each plant after each week. Use the rules \u201cadd 1\\(\\frac{1}{2}\\)” and “add 1\\(\\frac{1}{2}\\)“.
\n\"Envision
\nB. Will the basil plant ever be taller than the chive plant? If so, when?
\nC. How does the table in A help you answer the question in B?
\nAnswer:<\/p>\n

Question 4.
\nBonnie’s Bakery makes 12 cakes and 36 muffins each hour.
\nA. Complete the table to show how many cakes and muffins in all the bakery has made after each hour. Use the rules “add 12” and “add 36”.
\n\"Envision
\nB. Miles says “the total number of muffins made is always 24 more than the total number of cakes made.” Do you agree? Explain your reasoning.
\nC. Bonnie wants to graph this information. What ordered pair represents the total number of each item made after 6 hours?
\nA. (36,12)
\nB. (18,42)
\nC. (60, 180)
\nD. (72, 216)
\nAnswer:<\/p>\n

Topic 15 Performance Task<\/h3>\n

Butterfly Patterns<\/strong>
\nUse the Butterflies picture to Explore patterns.
\n\"Envision<\/p>\n

Question 1.
\nJessie and Jason use their cell phones to take pictures of butterflies. Jessie had 3 pictures of butterflies stored in her cell phone and Jason had 1 picture in his. On Saturday, they each took a picture of 1 butterfly every hour.<\/p>\n

Part A<\/strong>
\nHow many butterfly wings are in each photo collection after 3 hours? Complete the table.
\n\"Envision
\nPart B<\/strong>
\nWhat is the relationship between the corresponding terms of the two patterns in Part A?
\nPart C<\/strong>
\nWrite rules for the number of butterfly wings in Jessie’s pictures and in Jason’s pictures.
\nAnswer:<\/p>\n

Question 2.
\nCompare the number of wings to the number of legs in different numbers of butterflies.
\n\"Envision
\nPart A<\/strong>
\nComplete the table.
\nPart B<\/strong>
\nWhat is the relationship between the number of wings and the number of legs you found in Part A?
\nAnswer:<\/p>\n

Question 3.
\nTomika has no pictures of butterflies in her cell phone, but Kyle has 3 pictures in his. On Saturday, Tomika takes 2 pictures of butterflies every hour and Kyle takes 1 picture every hour. Answer the following to find whether or not their collections of butterfly pictures will ever have the same number of wings.
\n\"Envision
\nPart A<\/strong>
\nWrite a rule and complete the Tomika’s Pictures table.
\nPart B<\/strong>
\nWrite a rule and complete the Kyle’s Pictures table.
\n\"Envision
\nPart C<\/strong>
\nGraph the ordered pairs from Part A and Part B on the same coordinate grid and draw lines through each set.
\nPart D<\/strong>
\nWill Tomika and Kyle ever have the same number of wings in their pictures? Explain.
\n\"Envision
\nAnswer:<\/p>\n","protected":false},"excerpt":{"rendered":"

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