Lesson Overview Objective Materials Needed Key Vocabulary ...
Lesson Overview Unit
Real Numbers
Subject
Algebra 1
Lesson Description
How to solve for the absolute value of real numbers in real world scenarios
Common Core State Standard(s)
CCS.6.NS7c: Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value in a real-world situation
RK12 Online Lesson
Absolute Value of Real Numbers
Objective Students will understand the definition of absolute value and how to solve for absolute value equations in a real-world situation
Materials Needed Markers and flash cards for vocabulary word wall and guided practice activity Images of thermometers with a range of temperatures for anticipatory set M& M Chocolate mini bags of candy for guided practice activity Exit slips prepared in advance with similar type questions from the RK12 online lesson (A sample exit slip is provided below in the Check for Understanding section and can be duplicated for classroom use) Copies of extra practice/extension problems (provided below in the Closure section) Absolute Value Real-World Scenario Card (can be duplicated or projected on the board for whole class instruction)
Key Vocabulary Opposites: Two numbers that are the same distance from 0 on a number line, but on opposite sides of 0 Absolute value: The distance a number is from 0 on a number line.
Standards for Mathematical Practice Addressed x 1: Make sense of problems and persevere in solving them. x 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 and express regularity in repeated reasoning.
Methods Anticipatory Set
Bring in a thermometer to class or show images generated from the Interpret displaying sub zero temperatures versus temperatures in the upper 80's. Ask students how would they dress for school if it was 5 below zero versus 95 degrees Farenheit. Discuss the importance of the negative sign on the number line. Ask students to brainstorm other real world scenarios when understanding of real numbers, positive and negative integers, comes in handy. Introduce today's topic on absolute value and how it will expand their understanding of real numbers as it relates to positive and negative integers in the real world context.
Direct Instruction
In previous lessons, students learned how to place integers on a number line. Now they will find the distance between a point and zero on the number line to find the opposite of a number or the absolute value of a number in a real world scenario. Ask the students what absolute value means. Define it the distance from zero. Illustrate it by drawing a number line and showing the absolute value of +4 and -4. Emphasize that the distance from zero is always positive. Whole Class Instruction: Explain this idea by showing a problem using a number line. Introduce the sample problem. Demonstrate the steps to solve for absolute value by displaying the sample problem: |2x + 3| = 9 Because the expression “2x + 3” is in the absolute value bars, we know that when we solve this part of the equation we will be 9 units away from zero. We could be at positive 9 or we could be at negative 9. Therefore we must set up our problem using two different equations, one in which we would end 9 units away from zero on the positive side, 2x + 3 = 9, and the other in which we would end 9 units away from zero on the negative side, 2x + 3 = -9. Show students that in the first case we find that by subtracting 3 and dividing by 2 on each side, we get an answer of 3. In the second case, we find that by subtracting 3 and dividing by 2 on each side, we get an answer of -6. Therefore x = 3 and -6. Either answer would work because |2(3) + 3| = 9 and |2(-6) + 3| = 9. If we have a coefficient in front of the absolute value bars, we want to divide by that number first in order to isolate the absolute value expression. In a problem such as 4|5x + 1| = 44, we divide the entire equation by 4 first to isolate the absolute value expression and see that: |5x + 1| = 11. We then solve this equation twice, once in which 5x + 1 = 11 and once in which 5x + 1 = -11. Solving these two-step equations, we find that x = 2 and -2.4. We want to first divide by the coefficient just in case the coefficient is negative. If the initial expression had been -4|5x + 1| = 44, we would have divided 44 by -4 and found that |5x + 1| = -11. We know that an absolute value expression must have a positive value, so this problem could not be solved.
Guided Practice
Divide students into groups with peer tutors. Advanced and proficient students should be paired with underperforming students and those needing more assistance. Use a real world situation using mini M&M bags of chocolates to show how this works in the problem outlined below. Tell students they are not allowed to eat the chocolates until the exercise below is completed. M&Ms snack packs should way 2 ounces, but their weight can vary by 0.5 ounces and still be acceptable. What are the greatest and least weights that are acceptable? Ask students to work with a partner to turn this scenario into a mathematical statement reflecting absolute value. We can put this into a problem to show that |x – 2| = 0.5. x – 2 = 0.3 and x – 2 = -0.5 Now have students collaborate with their partner to write two additional math problems involving absolute value. They will write these problems on blank flashcards and quiz other groups. The teacher will provide support as needed to each group. Once the exercise has been completed, students can eat the chocolate with permission from the teacher.
RK12 Mentor Session In-Class Guided Instruction: Access your student view of the Revolution K12 Algebra 1 program (by selecting "Online Course" from the teacher login.) Select the Syllabus and find the unit on Real Numbers in Algebra I. Go to the first question in the RK12 mentor session entitled, Real World Scenario:Absolute Value. Using your SmartBoard, Promethean, or LCD projector, display this image from the RK12 Real -World Scenario Card for in-class instruction:
Begin to engage students in the math by asking in-depth, process oriented questions about the problem. What are the key steps involved to answer the problem? What is the question asking you to do? What are the math rules that apply to absolute value that will need to be taken into consideration to accurately solve this problem? Intentionally answer the first question incorrect ly to work through the provided scaffolded support in the embedded mini-diagnostics. At all steps, discuss the procedures with students. Now, students will work independently to complete the rest of the real-world applications based mentor session on their own computer. Independent Practice
Students will work on the RK12 mentor session , "Absolute Value of Real Numbers" in conjunction with their math journal. All questions, correct or incorrect, will be recorded in the journal to encourage accountability and process- based learning.
Formative/Summative Assessment Assign students the RK12 mentor session Absolute Value of Real Numbers . If students receive a score below 70%, the student will be expected to meet with a peer tutor for
support. If a student receives lower than a 50%, then they will receive an extra practice mentor session related to absolute value. Review the assignment report from the RK12 online teacher Gradebook after students have completed working on the computer to go over specific skill gaps. Assign the Real Numbers Post Test online assignment in the RK12 program .
Closure Check for Understanding
Provide exit slips for each student to assess for content mastery. A sample exit slip for this lesson is provided below: Absolute Value Exit Slip: Checking for Understanding
Extension Activities
Option 1 (proficient/advanced students): Students will create 5 additional word problems related to absolute value in the real world scenario. Option 2: Provide the following extra practice problems (#1-25) as an extension lesson or homework practice.
Accessibility for All EL Learners
The use of repetition and paraphrasing is an important modification for all EL/Special Needs and under-performing students. Ask students to rephrase the definition of absolute value and provide assistance when needed. Repeat the definition until each student is able to explain it to their peer in their own words.
Special Needs
Math manipulatives, such as a magnetic number line or a number line board with an adjustable slider, is a powerful modification for students with special needs as it provides for kinesthetic and experiential learning to support the learning process.
Under Performing Students
Utilize the word wall to define key words to assist with memory retention and understanding. Highlight additional key words and provide simple definitions for additional scaffolding. Research shows that the use of direct, physical objects and/or visual images, such as bringing in an actual thermometer in this case, helps to dramatically increase engagement and concept mastery of all students, particularly the EL, SPED, and under-performing student population.
Advanced-
Engage advanced students by increasing the level of difficulty of informal assessments. Vary the questioning format to include higher levels of abstract thinking. Provide real-world based problem-solving opportunities related to absolute value to extend learning.
Real Numbers
Subject
Algebra 1
Lesson Description
How to solve for the absolute value of real numbers in real world scenarios
Common Core State Standard(s)
CCS.6.NS7c: Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value in a real-world situation
RK12 Online Lesson
Absolute Value of Real Numbers
Objective Students will understand the definition of absolute value and how to solve for absolute value equations in a real-world situation
Materials Needed Markers and flash cards for vocabulary word wall and guided practice activity Images of thermometers with a range of temperatures for anticipatory set M& M Chocolate mini bags of candy for guided practice activity Exit slips prepared in advance with similar type questions from the RK12 online lesson (A sample exit slip is provided below in the Check for Understanding section and can be duplicated for classroom use) Copies of extra practice/extension problems (provided below in the Closure section) Absolute Value Real-World Scenario Card (can be duplicated or projected on the board for whole class instruction)
Key Vocabulary Opposites: Two numbers that are the same distance from 0 on a number line, but on opposite sides of 0 Absolute value: The distance a number is from 0 on a number line.
Standards for Mathematical Practice Addressed x 1: Make sense of problems and persevere in solving them. x 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 and express regularity in repeated reasoning.
Methods Anticipatory Set
Bring in a thermometer to class or show images generated from the Interpret displaying sub zero temperatures versus temperatures in the upper 80's. Ask students how would they dress for school if it was 5 below zero versus 95 degrees Farenheit. Discuss the importance of the negative sign on the number line. Ask students to brainstorm other real world scenarios when understanding of real numbers, positive and negative integers, comes in handy. Introduce today's topic on absolute value and how it will expand their understanding of real numbers as it relates to positive and negative integers in the real world context.
Direct Instruction
In previous lessons, students learned how to place integers on a number line. Now they will find the distance between a point and zero on the number line to find the opposite of a number or the absolute value of a number in a real world scenario. Ask the students what absolute value means. Define it the distance from zero. Illustrate it by drawing a number line and showing the absolute value of +4 and -4. Emphasize that the distance from zero is always positive. Whole Class Instruction: Explain this idea by showing a problem using a number line. Introduce the sample problem. Demonstrate the steps to solve for absolute value by displaying the sample problem: |2x + 3| = 9 Because the expression “2x + 3” is in the absolute value bars, we know that when we solve this part of the equation we will be 9 units away from zero. We could be at positive 9 or we could be at negative 9. Therefore we must set up our problem using two different equations, one in which we would end 9 units away from zero on the positive side, 2x + 3 = 9, and the other in which we would end 9 units away from zero on the negative side, 2x + 3 = -9. Show students that in the first case we find that by subtracting 3 and dividing by 2 on each side, we get an answer of 3. In the second case, we find that by subtracting 3 and dividing by 2 on each side, we get an answer of -6. Therefore x = 3 and -6. Either answer would work because |2(3) + 3| = 9 and |2(-6) + 3| = 9. If we have a coefficient in front of the absolute value bars, we want to divide by that number first in order to isolate the absolute value expression. In a problem such as 4|5x + 1| = 44, we divide the entire equation by 4 first to isolate the absolute value expression and see that: |5x + 1| = 11. We then solve this equation twice, once in which 5x + 1 = 11 and once in which 5x + 1 = -11. Solving these two-step equations, we find that x = 2 and -2.4. We want to first divide by the coefficient just in case the coefficient is negative. If the initial expression had been -4|5x + 1| = 44, we would have divided 44 by -4 and found that |5x + 1| = -11. We know that an absolute value expression must have a positive value, so this problem could not be solved.
Guided Practice
Divide students into groups with peer tutors. Advanced and proficient students should be paired with underperforming students and those needing more assistance. Use a real world situation using mini M&M bags of chocolates to show how this works in the problem outlined below. Tell students they are not allowed to eat the chocolates until the exercise below is completed. M&Ms snack packs should way 2 ounces, but their weight can vary by 0.5 ounces and still be acceptable. What are the greatest and least weights that are acceptable? Ask students to work with a partner to turn this scenario into a mathematical statement reflecting absolute value. We can put this into a problem to show that |x – 2| = 0.5. x – 2 = 0.3 and x – 2 = -0.5 Now have students collaborate with their partner to write two additional math problems involving absolute value. They will write these problems on blank flashcards and quiz other groups. The teacher will provide support as needed to each group. Once the exercise has been completed, students can eat the chocolate with permission from the teacher.
RK12 Mentor Session In-Class Guided Instruction: Access your student view of the Revolution K12 Algebra 1 program (by selecting "Online Course" from the teacher login.) Select the Syllabus and find the unit on Real Numbers in Algebra I. Go to the first question in the RK12 mentor session entitled, Real World Scenario:Absolute Value. Using your SmartBoard, Promethean, or LCD projector, display this image from the RK12 Real -World Scenario Card for in-class instruction:
Begin to engage students in the math by asking in-depth, process oriented questions about the problem. What are the key steps involved to answer the problem? What is the question asking you to do? What are the math rules that apply to absolute value that will need to be taken into consideration to accurately solve this problem? Intentionally answer the first question incorrect ly to work through the provided scaffolded support in the embedded mini-diagnostics. At all steps, discuss the procedures with students. Now, students will work independently to complete the rest of the real-world applications based mentor session on their own computer. Independent Practice
Students will work on the RK12 mentor session , "Absolute Value of Real Numbers" in conjunction with their math journal. All questions, correct or incorrect, will be recorded in the journal to encourage accountability and process- based learning.
Formative/Summative Assessment Assign students the RK12 mentor session Absolute Value of Real Numbers . If students receive a score below 70%, the student will be expected to meet with a peer tutor for
support. If a student receives lower than a 50%, then they will receive an extra practice mentor session related to absolute value. Review the assignment report from the RK12 online teacher Gradebook after students have completed working on the computer to go over specific skill gaps. Assign the Real Numbers Post Test online assignment in the RK12 program .
Closure Check for Understanding
Provide exit slips for each student to assess for content mastery. A sample exit slip for this lesson is provided below: Absolute Value Exit Slip: Checking for Understanding
Extension Activities
Option 1 (proficient/advanced students): Students will create 5 additional word problems related to absolute value in the real world scenario. Option 2: Provide the following extra practice problems (#1-25) as an extension lesson or homework practice.
Accessibility for All EL Learners
The use of repetition and paraphrasing is an important modification for all EL/Special Needs and under-performing students. Ask students to rephrase the definition of absolute value and provide assistance when needed. Repeat the definition until each student is able to explain it to their peer in their own words.
Special Needs
Math manipulatives, such as a magnetic number line or a number line board with an adjustable slider, is a powerful modification for students with special needs as it provides for kinesthetic and experiential learning to support the learning process.
Under Performing Students
Utilize the word wall to define key words to assist with memory retention and understanding. Highlight additional key words and provide simple definitions for additional scaffolding. Research shows that the use of direct, physical objects and/or visual images, such as bringing in an actual thermometer in this case, helps to dramatically increase engagement and concept mastery of all students, particularly the EL, SPED, and under-performing student population.
Advanced-
Engage advanced students by increasing the level of difficulty of informal assessments. Vary the questioning format to include higher levels of abstract thinking. Provide real-world based problem-solving opportunities related to absolute value to extend learning.
