Common Core State Standards


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1 Common Core State Standards Common Core State Standards 7.NS.3 Solve realworld and mathematical problems involving the four operations with rational numbers. Mathematical Practices 1, 3, and 4 are aspects of mathematical thinking that are emphasized in every lesson. Students are given opportunities to be persistent in their problem solving, to express their reasoning, and apply mathematics to realworld situations. Exercise 13 focuses on Mathematical Practice 5 Use appropriate tools strategically. Exercises 14 and 16 focus on Mathematical Practice 3 Construct viable arguments and critique the reasoning of others. Exercises 15 and 17 focuse on Mathematical Practice 1 Make sense of problems and persevere in solving them. Exercises 20 and 21 focus on Mathematical Practice 4 Model with mathematics. Printed by: Nicole Sladich Page 1 of 12 Printed on 11/04/ :06 PM
2 1 Launch the Lesson Focus narrowing the scope Objective Read and write integers, and find the absolute value of an integer. Preparation for 7.NS.3 Coherence Previous Students used the order of operations to evaluate expressions. connecting within and across grades Now Students evaluate expressions involving absolute values. Next Students will add integers with the same sign and add integers with different signs. Rigor pursuing concepts, fluency, and applications See the Levels of Complexity chart in the Practice and Apply section. Materials/Manipulatives Number Lines Master Lesson Vocabulary integer negative integer positive integer graph absolute value As students enter the classroom, have them complete the Common Core Quick Check to review and assess the skills presented in the previous lesson. Engage Explore Explain Elaborate Evaluate Ideas for Use You may wish to launch the lesson using a whole group, small group, thinkpairshare activity, or independent activity. ThinkPairShare Have students work in pairs to complete the Vocabulary StartUp. Introduce the word integer and give students time to think about the word. Have them share their responses with their partner. Then have one student or pair share their responses with the class to start a discussion. 1, 6 Alternate Strategy Have students research and report on how integers are used in daily life such as bank deposits, temperatures, and golf scores. 1, 2 Resources Common Core Quick Check: Integers and Absolute Value Manipulative Masters: Number Lines Printed by: Nicole Sladich Page 2 of 12 Printed on 11/04/ :06 PM
3 2 Teach the Concept Focus: Mathematical Background Integers (whole numbers, their negatives, and zero) can be graphed on a number line. Integers are used to represent many quantities in everyday life such as elevations, temperatures, and bank deposits. The McGrawHill Professional Development Video Library provides short videos that support Glencoe Math. The featured videos for mathematical content in this lesson are: Absolute Value Integers on a Number Line Positive and Negative Integers For classroom presentation, use the StepbyStep Examples to demonstrate the examples from the Student Edition. Engage Explore Explain Elaborate Evaluate Ask the scaffolded questions for each example to differentiate instruction. 1. Write an integer. What symbol is used to represent negative and positive integers? () and (+) What is the number of degrees? 5 Does below represent a positive or negative amount? negative In 200 feet below sea level, does below have the same representation as in Example 1? Explain. Yes; below is represented as being negative. Need Another Example? Write an integer to represent a loss of 12 yards Write an integer. What is the number of inches? 5 Does above represent a positive or negative amount? positive In 85 F above normal, does above have the same representation as in Example 2? Explain. above is represented as being positive. Need Another Example? Write an integer to represent 4 inches above normal Graph an integer. Yes; Are positive integers left or right of zero on a number line? right Are negative integers left or right of zero on the number line? left Printed by: Nicole Sladich Page 3 of 12 Printed on 11/04/ :06 PM
4 Where should you graph 4? 6? 4 units to the right of zero; 6 units to the left of zero Would the integers 8, 6, and 4 be to the left of the zero? Explain. No; 4 will be on the right of the zero. Need Another Example? Graph the set of integers {1, 3, 2} on a number line. 4. Evaluate expressions. What integer is used in the expression? 4 How many units is 4 from zero? 4 What is the absolute value of 4? 4 Is the absolute value of a negative integer always negative or positive? Explain. positive; Sample answer: Absolute value represents a distance and distance is always positive. Need Another Example? Evaluate Evaluate expressions. What is the absolute value of 5? 5 What is absolute value of 2? 2 What operation is between the two absolute value signs? subtraction Evaluate the expression Need Another Example? Evaluate Evaluate expressions with absolute value. What do you need to find? how many feet Nick climbs How could you find the answer? Evaluate the given expression. In the expression, why is 30 positive? It represents the distance he climbs upward. In the expression, why is 22 negative? It represents the distance he climbs downward. Nick descended another 42 feet. How many total feet did he climb? 94 feet Need Another Example? The number of pounds Megans's dog gained and then lost is represented by the expression How many pounds did Megan s dog gain and lose? 9 pounds Alternate Teaching Strategy If students have trouble writing an integer for a situation, Printed by: Nicole Sladich Page 4 of 12 Printed on 11/04/ :06 PM
5 1. 2. Then use one of these reteach options: Quick Review Math Handbook, pp Working with a partner, one student will give a situation such as down 3. The other gives the integer, 3. Then they reverse roles. Formative Assessment Use these exercises to assess students' understanding of the concept of the lesson. If they need more help use the Personal Tutors available online. below. If some of your students are not ready for assignments, use the differentiated activities Paired Heads Together Have students work in pairs to solve Exercises 1 7. Students first complete the exercises individually then turn to their partners to discuss their answers. For Exercise 7, students should pay close attention when graphing integers. Students should check to make sure the dot is at the correct location on the number line. 1, 5 TradeaProblem Have students create their own problems, similar to Example 6, using negative integers, positive integers, and a number line as part of their answers. Students will trade their problems, solve each other s problems, and compare solutions. If the solutions do not agree, students should work together and discuss to find the errors. 1, 4 Resources Virtual Manipulatives Write an Integer Write an Integer Graph Integers Evaluate Expressions Evaluate Expressions Evaluate Expressions with Absolute Value Evaluate Expressions with Absolute Value RealWorld Example: Represent Situations with Integers Graph Integers on a Number Line Use a Number Line to Evaluate Expressions with Absolute Value Write Integers RealWorld Example: Solve Problems with Absolute Value etoolkit Hot Topic 14: Integer Operations Absolute Value Integers on a Number Line Positive and Negative Integers Printed by: Nicole Sladich Page 5 of 12 Printed on 11/04/ :06 PM
6 3 Practice & Apply Engage Explore Explain Elaborate Evaluate Independent Practice and Extra Practice The Independent Practice pages are meant to be used as the homework assignment. The Extra Practice page can be used for additional reinforcement or as a secondday assignment. Levels of Complexity The levels of the exercises progress from 1 to 3, with Level 1 indicating the lowest level of complexity. Suggested Assignments You can use the table below that includes exercises of all complexity levels to select appropriate exercises for your students' needs. Differentiated Homework Options Approaching Level 1 11, 13, 14, 16, 29, 30 On Level 1 11 odd, 12 14, 16, 29, 30 Beyond Level 12 17, 29, 30 practice. can provide additional remediation support with personalized instruction and Create Your Own Homework Online esolutionsmanual can be used to create worksheets for the suggested assignments above, or to create your own worksheets for differentiated homework or review. The following worksheets are also available for additional homework practice: The Skills Practice editable worksheet provides students with additional practice in the skills taught in this lesson. The Homework Practice editable worksheet helps students practice skills in this lesson and use those skills to solve problems. The ProblemSolving Practice editable worksheet helps students become better problem solvers by providing frequent opportunities to solve realworld problems. The Extra Practice worksheet provides additional practice for the skills taught in this lesson. The StepbyStep Solutions provide a worked out solution for selected exercises from the Independent Practice in the Student Edition. Printed by: Nicole Sladich Page 6 of 12 Printed on 11/04/ :06 PM
7 Common Error Students may confuse the term opposite with absolute value. Remind them that absolute value is a distance and therefore never negative. Resources Step by Step Solutions: Integers and Absolute Value Skills Practice: Integers and Absolute Value Skills Practice Answers: Integers and Absolute Value Homework Practice: Integers and Absolute Value Homework Practice Answers: Integers and Absolute Value ProblemSolving Practice: Integers and Absolute Value ProblemSolving Practice Answers: Integers and Absolute Value Extra Practice: Integers and Absolute Value Extra Practice Answers, Chapter 3 Homework Practice: Integers and Absolute Value ProblemSolving Practice: Integers and Absolute Value Skills Practice: Integers and Absolute Value Extra Practice: Integers and Absolute Value esolutions, Glencoe Math Course 2 Printed by: Nicole Sladich Page 7 of 12 Printed on 11/04/ :06 PM
8 Additional Activities for Differentiated Instruction Differentiated Instruction activities for Approaching Level, On Level, and Beyond Level Learners can also be found at pointofuse in the Launch the Lesson and Teach the Concept sections. The following are additional activities that can be used with this lesson. Option 1: Kinesthetic Learners Materials: masking tape, index cards Many students think that the absolute value of a number is the opposite of that number. Make a number line on the floor using masking tape, with units a comfortable stride length apart. Use index cards to label the number line. Have students take turns finding the absolute value of different integers by finding how many steps or units the number is from zero. The Reteach Worksheet provides additional examples and practice for students who may have difficulty in grasping the math concepts in this lesson. Option 2: Naturalistic Learners Have students complete an individualized study by researching water levels in their state or community. Have them research the water levels in each month for a specific year. They should use integers to show the gains and losses. Have them make note of any weatherrelated event, such as flooding or dry season, that would have affected the water level. Option 3: Logical Learners Materials: newspapers Have students work in groups to research how integers are used in journalism. Assign each group a different section of a newspaper, including Sports, Weather, News, and Business. Ask a volunteer from each group to describe how integers are used in their section and give examples. The Enrich Worksheet provides students with valuable opportunities for extending this lesson. Resources Reteach: Integers and Absolute Value Reteach Answers: Integers and Absolute Value Enrich: Jaime Escalante Enrich Answers: Jaime Escalante Reteach: Integers and Absolute Value Enrich: Jaime Escalante Printed by: Nicole Sladich Page 8 of 12 Printed on 11/04/ :06 PM
9 Additional Activities for English Learners Differentiated Instruction activities for English Learners can also be found at pointofuse in the Launch the Lesson and Teach the Concept sections. The following are additional activities that can be used with this lesson. Option 1: Use Chapter 3, from the Interactive Guide for English Learners. Option 2: Verbal/Linguistic Learners Have students create a list of words that represent opposites and organize the list according to words that represent a positive concept or a negative math concept. For example, up represents a positive concept and down represents a negative concept. Other examples include forward/backward, above/below, and deposit/withdrawal. Option 3: Verbal/Linguistic Learners Materials: index cards Have students write on an index card a sentence describing a positive or negative integer situation such as the following: Have students exchange cards and write the integer described on the other side of the card. Word Wall Printable English/Spanish Word Wall cards are available for the following vocabulary words in this lesson: absolute value graph integer negative integer positive integer Resources Word Wall Cards Interactive Guide for English Learners, Student Edition, Course 2, Lesson 31: Integers and Absolute Value Interactive Guide for English Learners, Teacher Edition, Course 2, Lesson 31: Integers and Absolute Value Interactive Guide for English Learners, Course 2, Teacher Edition Interactive Guide for English Learners, Course 2, Student Edition Visual Kinesthetic Vocabulary, Course 2, Student Edition Visual Kinesthetic Vocabulary, Course 2, Teacher Edition Printed by: Nicole Sladich Page 9 of 12 Printed on 11/04/ :06 PM
10 Assessment Formative Assessment Use this activity as a closing formative assessment before dismissing students from your class. Have students describe a realworld situation in which integers are used. See students' work. The online SelfCheck Quiz for this lesson allows students to review concepts from each lesson. Exercises 29 and 30 prepare students for more rigorous thinking needed when taking the CCSS assessment. 29. This test item requires students to reason abstractly and quantitatively when problem solving. Depth of Knowledge CCSS Content Standard Mathematical Practices Online Experience DOK1 7.NS.3 MP1, MP3 Students will be required to click on the bubbles to select all answers that are correct. Scoring Rubric 1 point Students correctly answer all parts of the question. 30. This test item requires students to analyze and solve complex realworld problems through the use of mathematical tools and models. Depth of Knowledge CCSS Content Standard Mathematical Practices Online Experience DOK2 7.NS.3 MP1, MP4 Students will click on the number line to plot the integers and also type their response in a box. Scoring Rubric 2 points Students correctly plot 6 points and correctly answer the question. 1 point Students correctly plot 6 points but fail to answer the question OR students correctly plot 4 5 points and correctly answer the question based on the points they have plotted. Quick Check Are students continuing to struggle with finding the absolute value of integers? If Yes Printed by: Nicole Sladich Page 10 of 12 Printed on 11/04/ :06 PM
11 If No Reteach Worksheet Differentiated Instruction Option 1 Skills Practice Worksheet Differentiated Instruction Option 2 Enrich Worksheet Differentiated Instruction Option 3 Resources SelfCheck Quiz: Integers and Absolute Value Printed by: Nicole Sladich Page 11 of 12 Printed on 11/04/ :06 PM
12 Printed by: Nicole Sladich Page 12 of 12 Printed on 11/04/ :06 PM
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