Targeted Content Standard(s): 6.NS.7 Understand ordering and absolute value of rational numbers. a) Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret 3 > - 7 as a statement that 3 is located to the right of -7 on a number line oriented from left to right. b) Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3 C > -7 C to express the fact that -3 C is warmer than - 7 C. c) Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of 30 dollars, write -30 = 30 to describe the size of the debt in dollars. d) Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than 30 dollars represents a debt greater than 30 dollars. Targeted Mathematical Practice(s): 1 Make sense of problems and persevere in solving them 2 Reason abstractly and quantitatively 3 Construct viable arguments and critique the reasoning of others 4 Model with mathematics 5 Use appropriate tools strategically 6 Attend to precision 7 Look for and make use of structure 8 Look for an express regularity in repeated reasoning Supporting Content Standard(s): (optional) 6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Student Friendly Learning Targets I can Identify the absolute value of a number as the distance from zero. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. Use inequalities to order integers relative to their position on the number line. Write statements of order for rational numbers in real-world contexts. Interpret statements of order for rational numbers in real-world contexts. Explain statements of order for rational numbers in real-world contexts. Represent the absolute value of a rational number as the distance from zero and recognize the symbol x. Interpret absolute value as magnitude for a positive or negative quantity in a realworld situation. Distinguish comparisons of absolute value from statements about order. (Compare rational numbers using absolute value in real-world situations. For negative numbers, as the absolute values increases, the value of the number decreases.) 1
Purpose of the Lesson: In this lesson students use the statements of inequalities to compare numbers gaining a sense of ordering on the expanded number line. The students learn that comparing negative numbers requires closer attention to the relative positions on the number line rather than the magnitude of the number. Furthermore, students use context such as temperature, sea level, money and stocks to compare values and magnitudes of numbers in a real world context. Explanation of Rigor: (Fill in those that are appropriate.) Conceptual: Students are developing the concepts of signed numbers using relative positions on the expanded number and absolute value. 6.NS.7 Vocabulary: Absolute value distance Evidence of Learning (): Formative (s): Jeopardy Game, Integer War Summative : Ordering and Absolute Value Procedural: Students will use their understanding of the relative positions of numbers on the number line to write inequality statements comparing numbers both as values and in real world contexts. (6.NS.7b) Application: Self-: Ordering and Absolute Value Self- Skeleton, Jeopardy Game Self- Rubric 2
Lesson Procedures: Segment 1 Assessing prior learning Approximate Time Frame: 30 minutes Focus: The focus of this segment is to assess students knowledge of concepts of comparing numbers (positive and negative) and absolute value. Lesson Format: Whole Group Small Group Independent Modeled Guided Collaborative Math Practice Look For(s): MP 1: Look for students to make sense of the problem in their own way. MP 6: Look for students to pay attention to the precise language of times as much to MP 4: Differentiation for Remediation: Resources: Ordering and Absolute Value Modalities Represented: Concrete/Manipulative Picture/Graph Table/Chart Symbolic Oral/Written Language Real-Life Situation Differentiation for English Language Learners: Real context problems will be reread and rephrased as needed. Differentiation for Enrichment: Potential Pitfall(s): Independent Practice (Homework): The teacher should give the students the assessment but keep the time to 30 minutes. Teacher Tip: Because this is new material for 6 th graders, we are using the same pre and post summative assessments. If the students cannot complete the test within the time frame, then they have not mastered the concepts or are not fluent. 3
Segment 2 Conceptual understanding of positions of integers on the number line Approximate Time Frame: 80 minutes Focus: The focus of this segment is to have students conceptually develop the idea of comparing numbers based on their relative position on the number line. Lesson Format: Whole Group Small Group Independent Modeled Guided Collaborative Math Practice Look For(s): MP1: Look for students to make sense of the problem in their own way. MP.2: Students demonstrate abstract reasoning about rational numbers with their visual representations. Students consider the values of these numbers in relation to distance (number lines). MP4: Students use number lines to compare numbers using inequality symbols. Potential Pitfall(s): Students may have problems choosing an appropriate scale. They may also be looking at the magnitude of the number rather than the relative position on the number line. Steps: 1. Previous knowledge of the number line: a. Give students a number line and have them place positive numbers such as 3 and 6. Then, have students write an inequality Resources: Conceptual understanding of positions of integers on the number line Integer War Differentiation for Remediation: Integer War Observational Check List Modalities Represented: Concrete/Manipulative Picture/Graph Table/Chart Symbolic Oral/Written Language Real-Life Situation Teacher may work in small group. First using a number line from 0 to 10. The teacher would then ask the students what happens to the value of the number lines as they move from left to right. For Integer War, you may need to play a game with the small group. Differentiation for English Language Learners: Students will be paired with an English-speaking study buddy. Real context problems will be reread and rephrased as needed. Visual pictures will be used to depict the context of the story. Differentiation for Enrichment: Give students an inequality and then have them to create a context for the problem. Independent Practice (Homework): 4
and justify why one number is larger than another using the number line. b. Next, have students compare positive integers, fractions and decimals. 2. Have students explain what they know about using the number line to compare positive rational numbers. 3. Introduce the Conceptual understanding of positions of integers on the number line. Students should work through problem 1 on the Conceptual understanding of positions of integers on the number line in pairs. After problem 1, the teachers should have students share their thoughts and answers and then answer question 2 independently. Teacher Tips: As students are working on problem one, the teacher may need to ask questions such as: What happens on to the value of the number as you move from 2 to 6 on the number line? On the thermometer, what are the coldest temperatures? 2. Students should work through problems 3-6 on the Conceptual understanding of positions of integers on the number line in pairs. After problem 6, the teachers should have students compare their answers. Teacher Tip: The teacher might have the students draw their number line from problem 5 on large poster paper or white boards. 3. Students should work through problems 7 and 8 on the Conceptual understanding of positions of integers on the number line in pairs. Let the pairs discuss and write down their thoughts. Teacher Tip: The teacher could place Always, Never and Sometimes in three of the corners of the room. Ask questions based on students placement 4. Give each group of 3 students a copy of the directions to Integer War. The students should play through both level 1 and level 2. The group should demonstrate with the teacher that they understand Level 1 before they. 5
move to level 2. You will need a deck of cards for each group of 3 students. 6
Segment 3 Connecting Positive and Negative Numbers to Real World Context Approximate Time Frame: 120 minutes Focus: In this segment the students connect words such as loss, gain, credit, below zero, owed to the value of numbers. Lesson Format: Whole Group Small Group Independent Modeled Guided Collaborative Math Practice Look For(s): MP1: Look for students to make sense of the problem in their own way. MP2: Students demonstrate abstract reasoning about rational numbers by using positive and negative numbers to represent real world contexts. MP3 Students construct and critique arguments regarding number line representations and the use of inequalities to represent real-world contexts. Potential Pitfall(s): Students may be unfamiliar with some of the terms. Resources: Real World Context to Positive and Negative numbers Understanding Sea Level Write, Interpret and Explain Sea Level Exit Ticket Modalities Represented: Concrete/Manipulative Picture/Graph Table/Chart Symbolic Oral/Written Language Real-Life Situation Differentiation for Remediation: The teacher may put the words on index cards and have students sort them. Also, the teacher may need to give examples of loss, gain, etc. Differentiation for English Language Learners: Also, the teacher may need to give examples of loss, gain, etc. Students will be paired with an English-speaking study buddy. Real context problems will be reread and rephrased as needed. Visual pictures will be used to depict the context of the story. Differentiation for Enrichment: The students add more words to the list and share them with the class. Independent Practice (Homework): Use some of the questions like 9, 10 and 11 on Understanding Sea Level. Sea Level Exit Ticket 7
Steps: 1. Real World Context to Positive and Negative a. Students should work on Real World Context to Positive and Negative numbers question 1. They should independently sort the words and then meet with a partner to discuss and share answers. b. Students should work on problem 2 on Real World Context to Positive and Negative numbers. They should independently answer the question and then meet with a partner to discuss and share answers. The class should then come together to discuss the answers. c. The students should complete problem 3 Real World Context to Positive and Negative numbers. They should independently answer the question and then meet with a partner to discuss and share their ideas. Teacher Tip: The teacher may have the students write the words for the word sort on index cards so that student can move them around. 2. Understanding Sea Level a. Students should discuss the picture in understanding Sea Level in partners. The class should then come together to discuss the answers. b. Students should work through the problems on 2-8 with a partner. The class should then come together to discuss the answers. c. Problems 9-11 from Understanding Sea Level can be given as homework or solved independently. The teacher also should listen for students discussions and correct misconceptions as needed. Teacher should pose questions to the class and define elevation. 3. Students should work through the problems on Write, Interpret and Explain with a partner. The class should then come together to discuss the answers. 8
Segment 4 Conceptual development of Absolute Value Approximate Time Frame: 80 minutes Focus: In this segment, students develop a conceptual understanding of absolute value as magnitude of a number. Math Practice Look For(s): Lesson Format: Whole Group Small Group Independent Modeled Guided Collaborative MP. 2 Reason abstractly and quantitatively. Students consider the values of these numbers in relation to distance (number lines). MP.3 Students construct and critique arguments regarding absolute values of numbers. MP.5 Students model absolute value using two colored counters. Potential Pitfall(s): Students will have trouble differentiating the magnitude of the number compared to its value. Steps: 1. Conceptual Development of Absolute Value a. Students should work through problems 1-4 with a partner. Then discuss as a class. b. Students should then work through problem 5. They should independently answer the question and then meet with a partner to discuss and share answers. The class should then come together to discuss the answers. c. The students should complete problem 6 with a partner. d. As a class, the definition of Absolute Value should be discussed. Then the student pairs should complete problem 7. The class should then come together to discuss the answers. e. Problems 8 and 9 should be answered Resources: Differentiation for Remediation: Conceptual Development of Absolute Value Absolute Value Magnitude Modalities Represented: Concrete/Manipulative Picture/Graph Table/Chart Symbolic Oral/Written Language Real-Life Situation Teacher may put a number line on the floor so that the students can walk the distance on the number line. Differentiation for English Language Learners: Students will be paired with an English-speaking study buddy. Problems will be reread and rephrased as needed. Differentiation for Enrichment: Independent Practice (Homework): 9
independently. 2. Absolute Value Magnitude-In this part of the segment, we are laying the foundation for students to add and subtract integers in 7 th grade. We are having the students compare the values of the numbers and then actually find the absolute value by looking at the magnitude (number of chips). When we are comparing the absolute values of numbers, we eliminate the zero pairs if there are more negatives then the absolute value of the negative number is greater, if there are positive numbers left, then the absolute value of the positive number is greater. a. The students should think about what a zero pair is with the 2 colored chips. They can use the number line and use their prior knowledge from lesson 1 about opposite numbers. b. With a partner the students should use the chips to model comparing integers and then absolute value. Segment 5 Interpretation of absolute value Approximate Time Frame: 120 minutes Focus: In this lesson, students will apply the concepts of absolute value and interpret positive and negative numbers and zero in the context of the real world. Lesson Format: Whole Group Small Group Independent Modeled Guided Collaborative Resources: Credit-debit Calendar Social Media Earth s Global Temperature Modalities Represented: Concrete/Manipulative Picture/Graph Table/Chart Symbolic Oral/Written Language Real-Life Situation 10
Math Practice Look For(s): MP.2 Reason abstractly and quantitatively. Students demonstrate abstract reasoning about rational numbers with their visual representations. Students consider the values of these numbers in relation to distance (number lines). MP.3 Construct viable arguments and critique the reasoning of others. Students construct and critiques arguments regarding number line representations and the use of inequalities to represent real-world context MP.4 Model with mathematics. Students use number lines to compare numbers and represent inequalities in mathematical and real-world contexts. Differentiation for Remediation: Teacher may need to work in small groups to help students to interpret the meaning of zero in each situation. Differentiation for English Language Learners: Students will be paired with an English-speaking study buddy. Problems will be reread and rephrased as needed. Differentiation for Enrichment: Students may research and analyze: Budgets Stocks Global Warming MP.6 Attend to precision. Students attend to the language of real-world situations to determine if positive or negative quantities/distances are being represented. Potential Pitfall(s): Students may not be sure which situations to represent as positive and negative. Students may also struggle with interpreting what the zero represents in the context of the problems. Steps: 1. Credit-debit Calendar Students should work through the problem with a partner. Partners should then compare answers. The class should then come together to discuss the answers. 2. Social Media Students should work through the problem with a partner. Partners should then compare answers. The class should then come together to discuss the answers. 3.Earth s Global Temperature Students should work through the problem with a partner. Partners should then compare answers. The class should then come together to discuss the answers. Teacher Tip: The teacher may have the students use a ruler to find the Independent Practice (Homework): 11
numbers on the graph. Segment 6 Assessing Learning Approximate Time Frame: 80 minutes Focus: This segment s focus is to formatively assess students learning and then to measure students overall understanding of the concepts of ordering and absolute value. Math Practice Look For(s): Lesson Format: Whole Group Small Group Independent Modeled Guided Collaborative MP.2 Reason abstractly and quantitatively. Students demonstrate abstract reasoning about rational numbers with their visual representations. Students consider the values of these numbers in relation to distance (number lines). MP.3 Construct viable arguments and critique the reasoning of others. Students construct and critiques arguments regarding number line representations and the use of inequalities to represent real-world context Resources: Jeopardy Game Differentiation for Remediation: Skeleton Jeopardy Game Self- Rubric Ordering and Absolute Value Ordering and Absolute Value Self- Modalities Represented: Concrete/Manipulative Picture/Graph Table/Chart Symbolic Oral/Written Language Real-Life Situation Teacher may need to work with students in small groups depending on the results of Jeopardy. Differentiation for English Language Learners: Students will be paired with an English-speaking study buddy. Problems will be reread and rephrased as needed. Differentiation for Enrichment: MP.4 Model with mathematics. Students use number lines to compare numbers and represent inequalities in mathematical and real-world contexts. MP.6 Attend to precision. Students attend to the language of real-world situations to determine if positive 12
or negative quantities/distances are being represented. Potential Pitfall(s): Independent Practice (Homework): Steps: 1. Jeopardy Game Students should work in partners/small groups to discuss answers to questions. Teachers and/or students can decide the rules. Students should fill out the Skeleton Jeopardy Game Self- Rubric as they play the game. 2. Students will complete the summative assessment, Ordering and Absolute Value. After the assessment, the students should complete the Ordering and Absolute Value Self-. 13