Oklahoma 6th Grade Math Chapter 1

Chapter 1: Numerical Expressions and Factors Big Idea of the Chapter: Analyze Mul ples and Factors Suggested Pacing: Chapter Opener - 1 Day See Co-Author Notes in the Teaching Edition for suggestions on how to effectively implement this lesson plan. Launch the Chapter with the Career Discuss the q...

Chapter 1: Numerical Expressions and Factors Big Idea of the Chapter: Analyze Mul ples and Factors Suggested Pacing: Chapter Opener - 1 Day See Co-Author Notes in the Teaching Edition for suggestions on how to effectively implement this lesson plan. Launch the Chapter with the Career Discuss the ques ons about astronomers on the student page. This discussion should spark students’ interest and promote thinking about astronomers and the work they do. Have you ever thought about what astronomers study? What can astronomers learn from studying space? How might astronomers use math when studying the universe? Big Idea of the Chapter Extension: “If all five cicada species emerged this year, when do you next expect all the species to emerge at the same me?” 7,735 years from this year Review the defini on of prime number. “Do you think that the number of prime numbers is finite? Explain your reasoning.” Chapter Vocabulary: power, base, exponent, perfect square, numerical expression, evaluate, order of opera ons, equivalent expressions, prime number, composite number, factor pair, prime factoriza on, factor tree, Venn diagram, common factors, greatest common factor, common mul ples, least common mul ple Ge ng Ready for the Chapter Students used divisibility rules to find factor pairs in Grade 4, but they will benefit from a quick review of the rules. A er working through the second example, ask, “Is there a Commuta ve Property of Subtrac on or Division?” Have students share and discuss their answers and reasoning. “Is there an Associa ve Property of Subtrac on or Division?” Have students share and discuss their answers and reasoning. Lesson 1.1: Whole Number Opera ons Oklahoma State Standards: Mathema cs: 6.N.4.1 WIDA English Language Development Standards: ELD-MA.6-8.Explain.Expressive, ELD-MA.6-8.Argue.Expressive Learning Target: Perform opera ons on whole numbers. Success Criteria: Determine which opera on to perform. Add, subtract, mul ply, and divide whole numbers. Use es ma on to check answers. Vocabulary: No new vocabulary Suggested Pacing: 2 Days See Co-Author Notes in the Teaching Edition for suggestions on how to effectively implement this lesson plan. Warm Up Goal: Students will review a prerequisite skill needed for this lesson. Mo vate Goal: Students will explore dividing whole numbers. Inves gate Goal: Students will use a real-life context to explore choosing opera ons to perform on whole numbers. Example 1 and Example 2 “In Example 1, how can you find the total atendance for the art fes val?” Find the sum of the daily atendances. “How can you find the increase in atendance from Day 1 to Day 2?” Find the difference of the atendances on Day 2 and Day 1. As you demonstrate Example 1, be sure to emphasize the importance of lining up place values. “In Example 2, how can you es mate the total number of chicken nuggets served?” Sample answer: 12 × 100 = 1,200 chicken nuggets “When finding the product of 95 and 12, does the order of the factors mater? Explain.” No, mul plica on is commuta ve. Example 3 In Example 3, the context of money helps students make sense of division. Ask a volunteer to read the problem aloud. “Should the answer be greater than $1,380 or less than $1,380?” less than $1,380 “How do you know?” Listen for understanding that dividing a whole-number quan ty by a whole number greater than 1 will result in a lesser amount. Be sure to discuss the reasonableness of the answer and demonstrate the Check. Example 4 - Connec ng to Real Life It is important for students to problem-solve in class, where they can receive support from you and their peers. A Problem-Solving Guide can be found in the back of the book. “What experiences have you had with amusement park rides? What types of rides do you enjoy? What rides do you avoid?”  Search the Internet for a video of a roller coaster ride. If possible, show a video of Skyrush at Hersheypark because it is referenced in the Closure. Have students discuss the mathema cs involved in an amusement park. Ask a volunteer to read Example 4 aloud. Then have students restate the problem in their own words. Work through the solu on as shown, making references to the Problem-Solving Plan. In this problem, simplifying the remainder is unnecessary and may cause students to incorrectly think that 5 people are on the last ride. Closure Exit Ticket: “At Hersheypark in Pennsylvania, there is a roller coaster called Skyrush. About 1,350 people can ride Skyrush each hour. Skyrush has 2 trains that each hold 32 riders. The two trains take turns comple ng the course. About how many mes does each train complete the course in one hour?” about 21 mes Lesson 1.2: Powers and Exponents Oklahoma State Standards: Mathema cs: 6.N.2.4, 6.GM.2.1 WIDA English Language Development Standards: ELD-MA.6-8.Explain.Expressive, ELD-MA.6-8.Explain.Expressive Learning Target: Write and evaluate expressions involving exponents. Success Criteria: Write products of repeated factors as powers. Evaluate powers. Vocabulary: power, base, exponent, perfect square Suggested Pacing: 2 Days See Co-Author Notes in the Teaching Edition for suggestions on how to effectively implement this lesson plan. Warm Up Goal: Students will review a prerequisite skill needed for this lesson. Mo vate Goal: Students will explore powers. Inves gate Goal: Students will explore paterns to write and evaluate expressions involving exponents. Example 1 Engage students with the Key Vocabulary and the table of powers to acclimate them with words that are commonly used to describe powers. Example 1: Point out the two different symbols that are used to indicate mul plica on (⋅ and ×). Encourage students to be precise when using a dot to represent mul plica on so that it is not mistaken as a decimal point (e.g., 2 ⋅ 2 versus 2.2). Also point out that the × symbol can some mes be mistaken for a variable. Example 2 and Example 3 Example 2: Have students read each power and its value using precise language. You should hear “7 squared is 49” and “5 cubed is 125.” As an introduc on to the defini on of perfect square, write the numbers 1, 4, 9, 16, 25, 36 on the board. “What are the next three numbers in this sequence?” 49, 64, 81 “What is the patern?” Some students may recognize that the coun ng (natural) numbers are being squared, while others may describe the patern as adding 3, adding 5, adding 7, and so on. Model: Have students use square les to create a square array to model each perfect square in Example 3. Example 4 - Connec ng to Data It is important for students to problem-solve in class, where they can receive support from you and their peers. By the end of the school year, you want all students to be comfortable with the Problem- Solving Plan. “Do you like to watch movies? What type of movie do you prefer to watch?” Closure “You have a dozen boxes of protein bars. Each box holds a dozen protein bars, and each protein bar contains a dozen almonds. Write and evaluate an expression involving an exponent to find the total number of almonds in all the boxes.” 123 = 1,728 almonds Lesson 1.3: Order of Opera ons Oklahoma State Standards: Mathema cs: 6.A.2.1, 6.GM.2.1 WIDA English Language Development Standards: ELD-MA.6-8.Explain.Interpre ve, ELD-MA.6-8.Explain.Expressive Learning Target: Write and evaluate numerical expressions using the order of opera ons. Success Criteria: Explain why there is a need for a standard order of opera ons. Evaluate numerical expressions involving several opera ons, exponents, and grouping symbols. Write numerical expressions involving exponents to represent a real-life problem. Vocabulary: numerical expression, evaluate, order of opera ons Suggested Pacing: 2 Days See Co-Author Notes in the Teaching Edition for suggestions on how to effectively implement this lesson plan. Warm Up Goal: Students will review a prerequisite skill needed for this lesson. Mo vate Goal: Students will explore a need for a standard order of opera ons to evaluate numerical expressions. Inves gate Goal: Students will explore evalua ng numerical expressions and why there is a need for a standard order of opera ons. Key Concept, Example 1, and Example 2 Engage students with the Key Concept. Students should recall the order of opera ons from the previous grade. The rules are now extended to include evalua ng numbers with exponents. Example 1(a): “How many opera ons are in the expression?” 2 “Which opera on should be performed first?” mul plica on Example 1(b): Discuss the two grouping symbols, parentheses and brackets. “How do you think this expression should be evaluated? Write your ideas on your whiteboard.” Example 3 Discuss the different ways that mul plica on can be represented. For example, 3 times 4 can be represented as 3 × 4, 3 · 4, 3(4), or (3)(4). Example 3(b): “Remember that you can interpret a frac on as division. You can rewrite an expression that contains a frac on bar by using a division symbol and parentheses. You can think of the frac on bar as a grouping symbol.” Example 4 - Connec ng to Real Life “Have you ever seen a skydiver? Where were you? What was that experience like?” Allow students to share their experiences with the class. Engage students with the Problem-Solving Plan. Support students in making sense of the problem and looking for entry points to its solu on. “Look at the expression for the area of Zone 2. What do the values 402 and 202 represent in the context of problem?” Closure Write the following expressions on the board and have students evaluate each expression. a. 52 + 5 − 10 20 b. 25 − 12 + 8 21 c. (22 + 16) − 4 + 5 21 Lesson 1.4: Proper es of Opera ons Oklahoma State Standards: Mathema cs: 6.A.2.1 WIDA English Language Development Standards: ELD-MA.6-8.Argue.Expressive, ELD-MA.6-8.Argue.Interpre ve Learning Target: Apply proper es of opera ons to write and evaluate equivalent expressions. Success Criteria: Iden fy equivalent expressions. Use proper es of opera ons to rewrite expressions. Evaluate expressions. Vocabulary: equivalent expressions Suggested Pacing: 2 Days See Co-Author Notes in the Teaching Edition for suggestions on how to effectively implement this lesson plan. Warm Up Goal: Students will review a prerequisite skill needed for this lesson. Mo vate Goal: Students will explore equivalent expressions. Inves gate Goal: Students will explain the meanings of various proper es of opera ons. Key Concept and Example 1 Reinforce the defini on of equivalent expressions and engage students with the Key Concept. Make connec ons to the Inves gate. As you work through Example 1, point out that mental math strategies o en u lize the Commuta ve and Associa ve Proper es. Key Concept and Example 2 Engage students with the Key Concept. Students o en say that these proper es are simple or obvious. Explain that they will revisit these proper es when they study equa ons. Example 2: Have students discuss how the value of each expression was found and the proper es that were used. Key Concept and Example 3 Discuss the Key Concept. Display the equa ons and their related models on the board. For each equa on, ask, “How is each value in the equa on represented in the model? Discuss your ideas with a partner.” Explain that the blue arrows remind you to distribute the 3 to each number in the expression inside the parentheses. Example 4 - Test Prep: Connec ng to Real Life “Do you have a tablet at home? Why is the size of a tablet important?” Allow me for students to discuss their ideas with a partner. Select a student to read the problem aloud.  Review the Problem-Solving Plan with students. It is important to allow me for students to prac ce using the Problem-Solving Plan in class. “What do you know? What do you need to find?” “How is the expression related to the verbal model? How does a verbal model help you solve a real- life problem?” Closure “In this sec on, you applied proper es of opera ons to write and evaluate equivalent expressions. With a partner, discuss the proper es of opera ons that you used and write an example of each property on your whiteboard.” Lesson 1.5: Prime Factoriza on Oklahoma State Standards: Mathema cs: 6.N.2.5 WIDA English Language Development Standards: ELD-MA. 6-8.Argue.Expressive Learning Target: Write a number as a product of prime factors and represent the product using exponents. Success Criteria: Find factor pairs of a number. Explain the meanings of prime and composite numbers. Create a factor tree to find the prime factors of a number. Write the prime factoriza on of a number. Vocabulary: prime number, composite number, factor pair, prime factoriza on, factor tree Suggested Pacing: 1 Day See Co-Author Notes in the Teaching Edition for suggestions on how to effectively implement this lesson plan. Warm Up Goal: Students will review a prerequisite skill needed for this lesson. Mo vate Goal: Students will revisit divisibility rules to explore factors of a number. Inves gate Goal: Students will explore wri ng numbers as products of factors. Example 1 Define factor pair and have students generate addi onal examples. “Does every number have a factor pair? Explain.” Yes, every number can be writen as 1 mes itself. Model: Distribute 30 square les to each pair of students. Tell them to use all the les to form a rectangle. The dimensions of the different possible rectangles are the factor pairs found in Example 1. “How can you be sure that you have not missed any factor pairs of a number?” Listen for understanding of how factor pairs can be listed in an organized manner. Key Concept and Example 2 Write the defini on of prime factorization and work through the example in the Key Concept. Remind students that although 15 is odd, it is not prime. If me allows, ask students to name a factor pair of 60 that does not include a prime number. Have students work in pairs to find the prime factoriza on by beginning the factor tree with the factor pair they named. Then have them compare their work to the example. “Use the terms factors, prime, and composite to explain the features of a factor tree.” Example 2: Work through the two different factor trees for 48. It is important for students to understand that the trees may look different, but they result in the same prime factoriza on because every composite number has only one prime factoriza on. Example 3 Example 3 provides an opportunity for students to use prime factoriza on to inves gate special characteris cs of a number.  “What factor pair would you use to begin a factor tree for 1,575?” Have students use whiteboards to record and share their answers. Discuss similari es in answers. “How do you know that 25 is a factor of 1,575?” Relate 25 to a quarter and 1,575 to $15.75. “How do you know that only 9, 25, and 225 are perfect square factors of 1,575?” Closure Exit Ticket: “The class ended, and your friend did not finish finding the prime factoriza on of a number. Your friend’s first step was 8 × 24. What was the original number? What is the prime factoriza on of the number?” 192; 26 × 3 Lesson 1.6: Greatest Common Factor Oklahoma State Standards: Mathema cs: 6.N.2.6 WIDA English Language Development Standards: ELD-MA.6-8.Explain.Expressive Learning Target: Find the greatest common factor of two numbers. Success Criteria: Explain the meaning of factors of a number. Use lists of factors to iden fy the greatest common factor of numbers. Use prime factors to iden fy the greatest common factor of numbers. Vocabulary: Venn diagram, common factors, greatest common factor Suggested Pacing: 2 Days See Co-Author Notes in the Teaching Edition for suggestions on how to effectively implement this lesson plan. Warm Up Goal: Students will review a prerequisite skill needed for this lesson. Mo vate Goal: Students will explore a real-life problem that involves the greatest common factor of two numbers. Inves gate Goal: Students will use Venn diagrams to explore and iden fy common factors. Example 1 and Example 2 Examples 1 and 2 present two different strategies for finding the greatest common factor of two numbers: using lists of factors and using prime factoriza ons. Have students work in pairs to discuss and define the Key Vocabulary and connect the terminology to the mathema cs shown in Example 1. Example 1: “What are the factors of 24? 40? What are the common factors of 24 and 40? What is the greatest common factor of 24 and 40?” Example 2: Have students make a factor tree for each number and then write the prime factoriza ons of the numbers without using exponents. Then have students circle the common prime factors and find the product of the common prime factors. Example 3 Example 3: Have students discuss the ques on and the reasoning for elimina ng Choices A and C. When students are speaking, be aten ve to the language and vocabulary they use. Big Idea: The GCF of two numbers will always be less than or equal to the lesser of the two original numbers. Example 4 - Connec ng to Real Life “Have you been to a party that involved a piñata? Describe your experience.” Allow me for students to share. Have students whisper read the problem to themselves and then tell a partner what the problem is about. Discuss what it means to have iden cal groups of gi s in each piñata with no gi s le over. Closure Exit Ticket: “Use any method to find the greatest common factor of 24 and 36.” 12 Sort students’ responses based on strategy. What paterns do you see emerging in their work? Lesson 1.7: Least Common Mul ple Oklahoma State Standards: Mathema cs: 6.N.2.6 WIDA English Language Development Standards: ELD-MA.6-8.Explain.Expressive, ELD-MA.6-8.Explain.Expressive Learning Target: Find the least common mul ple of two numbers. Success Criteria: Explain the meaning of mul ples of a number. Use lists of mul ples to iden fy the least common mul ple of numbers. Use prime factors to iden fy the least common mul ple of numbers. Vocabulary: common mul ples, least common mul ple Suggested Pacing: 2 Days See Co-Author Notes in the Teaching Edition for suggestions on how to effectively implement this lesson plan. Warm Up Goal: Students will review a prerequisite skill needed for this lesson. Mo vate Goal: Students will explore a real-life problem that involves the least common mul ple of two numbers. Inves gate Goal: Students will use Venn diagrams to explore and iden fy common mul ples. Example 1 and Example 2 Remember to dis nguish between LCM and GCF when demonstra ng the two methods in Examples 1 and 2. Students must fully understand the defini ons of multiple and factor. Begin Example 1 by engaging in a whole-class choral count. Skip count by 4s: 4, 8, 12, 16, 20, 24, 28, 32, 36. Then skip count by 6s: 6, 12, 18, 24, 30, 36, 42, 48, 54. Reinforce mathema cal terminology by saying, “When we skip count by 4s, we are lis ng the mul ples of 4. When we skip count by 6s, we are lis ng the mul ples of 6.” In Example 2, explain that each different factor that appears in either prime factoriza on is used to find the LCM. Use the Venn diagram in the Check to help students make sense of why you do not circle the 2s in the prime factoriza on of 20. Example 3 Example 3: Using prime factoriza ons to find the LCM of three numbers can be challenging for students. Have students use lists of mul ples to check their answer. “When might it be more efficient to find the least common mul ple of numbers using prime factoriza ons instead of lists of mul ples?” Example 4 - Connec ng to Real Life “Have you ever seen a firefly? Does a firefly always glow?” Make sure students understand that a firefly flashes light but does not constantly glow. Consider showing a short video about fireflies. Engage students with Example 4 and review the Problem-Solving Plan. Select a volunteer to read the problem aloud. “Tell a partner what the problem is asking and discuss a strategy for solving the problem.”  Have students solve the problem independently and then compare solu ons with their partner. “Why did you need to find the least common mul ple of 8 and 10 to answer the ques on?” The LCM of the numbers of seconds between flashes represents the number of seconds it will take for both fireflies to flash at the same me. Closure Exit Ticket: “Explain how to find the least common mul ple of 8 and 15.” End of Chapter 1: Numerical Expressions and Factors Pacing: 3 Days See Co-Author’s Notes in the Teaching Edition for suggestions on how to effectively implement this lesson plan. Day 1 Chapter Review An Informa on Frame can be used to help students organize and remember concepts. Students write the concept in the middle rectangle. Then students write related categories in the spaces around the rectangle. Related categories may include words, numbers, algebra, example, defini on, non-example, visual, procedure, details, or vocabulary. Students can place their Informa on Frames on note cards to use as a quick study reference. Chapter Prac ce Students will review what they learned in the chapter. Prac ce Test Remind students to quickly look over the en re test before they start so that they can budget their me. When students receive their tests, they should jot down simple examples of finding the greatest common factor and the least common mul ple of two numbers. This will alleviate confusion when students are under pressure. Teach students to use the Stop and Think strategy before answering. Stop to carefully read the problem and Think about what the answer should look like. Day 2 Chapter Test Students will complete an assessment for the chapter. Day 3 Performance Task Students will apply their understanding of numerical expressions and the least common mul ple of numbers to a real-life situa on.