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21st Century Lessons Distributive Property Primary Lesson Designers: Kristie Conners Sean Moran 1 This project is funded by the American Federation of Teachers. 2 21st Century Lessons – Teacher Preparation Please do the following as you prepare to deliver this lesson: • Spend AT LEAST 30 minutes studying the Lesson Overview, Teacher Notes on each slide, and accompanying worksheets. • Set up your projector and test this PowerPoint file to make sure all animations, media, etc. work properly. • Feel free to customize this file to match the language and routines in your classroom. *1st Time Users of 21st Century Lesson: Click HERE for a detailed description of our project. 3 Lesson Overview (1 of 4) Lesson Objective . Lesson Description 4 Students will be able to apply the distributive property to write equivalent expressions. Students will be able explain how to use the distributive property verbally and in writing. This lesson is the second lesson for the standard 6.EE.3. The Distributive Property is a crucial concept in mathematics. The warm up in the lesson is a multiplication problem where the Distributive Property was used. This will trigger students to start to think about multiplication this way to prep them for the Distributive Property. The Launch uses a basketball court to introduce finding the area, which can be solved using two methods, one being the Distributive Property. Students then continue in their groups using divided rectangles to find their areas. Again, students will be asked to use both methods to later connect them as being equivalent; one method being the Distributive Property. The Summary part of the lesson is where students will be given the definition and explanation of the Distributive Property. Students are asked to finish the activity with challenging problems. The lesson finishes with an Exit Slip that contains three terms inside the parentheses. This was designed to push students to think about the process of the Distributive Property. Lesson Overview (2 of 4) 5 Lesson Vocabulary Distributive Property: an mathematical property which helps to multiply a single term and two or more terms inside parenthesis. Expression: numbers and symbols grouped together that show the value of something. Commutative Property: changing the order of numbers does not change the sum or product. Materials Copies of the class work assignment, Exit Slip, and homework. Common Core State Standard 6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Lesson Overview (3 of 4) 6 Scaffolding This lesson is designed around using area models as supposed to an algebraic way to show Distributive Property. Therefore, this lesson tailors to ELL students and students with learning disabilities providing visuals throughout the lesson to access this relatively abstract algebraic concept. Enrichment In the Activity portion of this lesson, there is an opportunity provided for students who seem to have grasped the Distributive Property relatively quickly. These questions challenge students a bit more by writing equivalent expressions using Distributive Property. Online Resources for Absent Students Tutorial: http://learnzillion.com/lessons/372-apply-the-distributive-propertyusing-area-models http://flash.learning.com/ahamath-demo/The-Distributive-PropertyLesson/SCORMDriver/indexAPI.html http://coolmath.com/prealgebra/06-properties/05-propertiesdistributive-01.htm Practice: http://www.ixl.com/math/grade-6/distributive-property Lesson Overview (4 of 4) Before and After Expressions and Equations is a crucial topic for students to become successful in a future Algebra course. This content standard concepts and processes are a critical part in students’ career in mathematics. Thus far in this unit, students have been exposed to writing, reading and evaluating numerical and algebraic expressions. The lessons for this standard continue working on those topics, but taking their understanding of expressions to the next level. The first lesson for this standard deals with the properties of mathematics, where this lesson strictly focuses on the Distributive Property. It is advised that both lessons be used consecutively. With a strong background of the properties and the Distributive Property, students will be successful in continuing their wok in this standard; where students are expected to prove equivalent expressions and then solve equations. Topic Background The link below is a quick reference to the properties in mathematics. This link is a also a helpful resource for students. http://mathforum.org/dr.math/faq/faq.property.glossary.html The link below is an article, “I See It: The Power of Visualization”. This supports the basic idea behind the lesson of using the idea of visuals as means to the lesson. http://www.mathrecap.com/category/conferences/nctm/page/3/ 7 Warm Up Objective: Students will be able to apply the distributive property to write equivalent expressions. Language Objective: Students will be able explain how to use the distributive property verbally and in writing. Ricardo and Keyla are arguing whether the answer to 8(27) can be found by doing the following work. 8 20 160 8 7 56 216 Do you think this is correct? Explain. 8 Agenda Agenda: Objective: Students will be able to apply the distributive property to write equivalent expressions. Language Objective: Students will be able explain how to use the distributive property verbally and in writing. 1) Warm Up Individual 4 minutes 2) Launch 13 minutes 3) Explore High School Vs. College B-ballWhole Class, Pairs Splitting Athletic Fields- Groups 4) Summary The Distributive Property- Whole Class 10 minutes 5) Explore Splitting Athletic Fields– Groups 12 minutes 6) Assessment Exit Slip- Individual 9 17 minutes 4 minutes Launch- High School Vs. College B-ball A standard size high school basketball court is 84ft long and 50ft wide in the shape of a rectangle. 84 ft 50 ft To find the area of the court you can use the formula of A=l w A = 84 ft 50ft 2 A = 4200 ft Agenda 10 Launch- High School Vs. College B-ball Did you know that a college basketball court is usually 10ft longer than a high school basketball court? 84 ft 10 ft 50 ft College Basketball Court Can you think of a method to find the area of the college basketball court? Agenda 11 Launch- High School Vs. College B-ball 84 ft 10 ft 50 ft Why parenthesis? Method 1 50(84+10) 84+10 94 50 2 ft A = 4700 Can you think of a method to find the area of the college basketball court? Method 2 84 50 + 10 50 4200 + 500 2 ft A = 4700 What can we say about these two expressions? 12 12 Agenda Explore- Splitting Athletic Fields Allison lives in a neighborhood with three rectangular fields that all have the same area. The fields are split into different sections for different sports. 20 yds 50 yds 30 yds 120 yds 120 yds 50 yds 80 yds 40 yds Agenda 13 Explore- Splitting Athletic Fields 1. Find the area of this field near Allison’s house. 50 yds 120 yds 6000 yds 2 2. This field is divided into two parts. 20 yds 30 yds 120 yds a. Find the area of each part and record your steps as you go. Prove the area is the same as in the first field? 20 120=2400 2400 yds 2+3600 yds2 6000 yds 2 30 120=3600 Agenda 14 Explore- Splitting Athletic Fields 20 yds 20 120 20 120=2400 30 yds 30 120 120 yds 30 120=3600 b. Write one numerical expression that will calculate the area based on the work you did in part a. 20 120 30 120 c. Find a different way to calculate the area of the entire field and write it as one numerical expression. 120(20 30) 20 yds + 30 yds 120 yds Agenda 15 Explore- Splitting Athletic Fields 3. The field is divided into two parts. 50 yds 80 yds 40 yds a. Write 2 different numerical expressions that will calculate the area of the entire field. 50(80 40) 50 8050 40 4. The field below is split into two parts but are missing the dimensions. 50 ______ 100 20 _________ ______ a. Fill in the missing dimensions of the rectangular field whose area can be calculated using the expression. 50(100 20) b. Write a different numerical expression to calculate the area of the field. 50 10050 20 16 Agenda Summary- The Distributive Property 20 yds 50 yds 30 yds 80 yds 40 yds 120 yds Let’s look at the two equivalent ways of finding the area and connect it to an important property in math. The Distributive Property Agenda 17 Summary- The Distributive Property The Distributive Property 50 yds 80 yds 40 yds 50 (80 40) 50 8050 40 50 80 120+ 40 18 50 80 40 Agenda Summary- The Distributive Property The Distributive Property The Distributive Property is a property in mathematics which helps to multiply a single term and two or more terms inside parenthesis. Check it out! Lets use the distributive property to write an equal expression. 2(35) 2 3 2 5 2 3 + 5 Examples 8(3 x) 8 3 8 x 3a 5a a(35) Formal definition 19 Agenda Explore- Splitting Athletic Fields 5. An algebraic expression to represent the area of the rectangle below is 8 x 8x. 8 x a. Write two different expressions to represent the area of each rectangle below. 5 2 3 x x(52) x 5 x 2 5x 2x x 4 3(x 4) 3x 3 4 3x 12 Agenda 21 Explore- Splitting Athletic Fields 6. Use the distributive property to re-write each expression. You may want to draw a rectangle to represent the area. a) 10( a + 7) = 10 ___________ a10 7 b) 7(x + 3)=________________ 7 x 7 3 c) x( 3 + 10)= ___________ x 3 x 10 d) a(10 + 9)= _______________ a 10 a 9 e) -2(x + 10)=_______ 2 x 2 10 f) 3x(x + 10)= 3x ______________ x 3x 10 Agenda 22 Assessment- Exit Slip Who correctly used the distributive property to write an equivalent expression? Provide evidence to support your answer. Riley 7(4 10 y) 7 4 7 10 y Michael 7(4 10 y) 7 4 7 10 7y Michael did because he correctly distributed the 7 to all terms inside the parenthesis. 23 Agenda 21st Century Lessons The goal… The goal of 21st Century Lessons is simple: We want to assist teachers, particularly in urban and turnaround schools, by bringing together teams of exemplary educators to develop units of high-quality, model lessons. These lessons are intended to: •Support an increase in student achievement; •Engage teachers and students; •Align to the National Common Core Standards and the Massachusetts curriculum frameworks; •Embed best teaching practices, such as differentiated instruction; •Incorporate high-quality multi-media and design (e.g., PowerPoint); •Be delivered by exemplary teachers for videotaping to be used for professional development and other teacher training activities; •Be available, along with videos and supporting materials, to teachers free of charge via the Internet. •Serve as the basis of high-quality, teacher-led professional development, including mentoring between experienced and novice teachers. 31 21st Century Lessons The people… Directors: Kathy Aldred - Co-Chair of the Boston Teachers Union Professional Issues Committee Ted Chambers - Co-director of 21st Century Lessons Tracy Young - Staffing Director of 21st Century Lessons Leslie Ryan Miller - Director of the Boston Public Schools Office of Teacher Development and Advancement Emily Berman- Curriculum Director (Social Studies) of 21st Century Lessons Carla Zils – Curriculum Director (Math) of 21st Century Lessons Brian Connor – Technology Coordinator 32