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CONSTRUCTING AND DECONSTRUCTING FOR ALGEBRA READINESS Andrea Tamarazio & Steve Graser , Erie 1 BOCES April 9, 2013 Algebra Warm Up Complete the Frayer Model independently then create a final table version. Post the table Frayer Model along the wall. Algebra Vocabulary Brainstorm Does This Help? Does This Help? Will This Help? How Can This Help? Will This Help? Nomials 2 3xy 5x - 1 3 x + 5y2 - 3 Expression vs. Equation 2x – 6 2x – 6 = 5 Write Algebraic Expressions for The Word Phrases A number s plus 2 A number decreased by 1 31 less than a number A number b increased by 7 The sum of a number and 6 Scott’s brother is two years younger than Scott Write Algebraic Expressions for These Word Phrases A number s plus 2 s+2 A number decreased by 1 n-1 31 less than a number n - 31 A number b increased by 7 b+7 The sum of a number and 6 n+6 Scott’s brother is two years younger than Scott s-2 Show Me eighteen Compare 24 and 15 One less than thirteen Two numbers that make 20 Three numbers that make thirty-seven The sum of nine and twelve Bar Diagrams / Tape Diagrams Part Whole Model Comparison Why Learn Algebra Learning Algebra All students should learn algebra beginning in pre-kindergarten “By viewing algebra as a strand in the curriculum from pre-kindergarten on, teachers can help students build a solid foundation of understanding and experiences as preparation for more sophisticated work in algebra in the middle grades and high school.” NCTM, 2000 Primary algebra should not be a watered-down version of the standard high school course that most of us took; instead the goal in Grades K - 2 is to develop students’ understanding for the order and situations, predict beyond the information at hand, and make generalizations. from Lessons for Algebraic Thinking Grades K- 2 by von Rotz and Burns Algebra Experience? Students in Grades K - 2 have knowledge about and are developing comfort with number patterns Patterns provide a useful foundation on which teachers can develop students’ algebraic thinking Students need experience creating, recognizing, and extending patterns Relating to items in which they are familiar with This foundational skill leads to the conceptual understanding of functions in future years. from Lessons for Algebraic Thinking Grades K- 2 by von Rotz and Burns Connecting to CCLS Looking at your Grade Level CCLS, identify and list which standards connect to foundational skills within algebra. On Chart Paper, make a grade level list. NYSED Recommended Models for Algebra Readiness Area Model / Arrays Number Bonds Bar Diagrams / Tape Diagrams Number Towers Show me how many groups of four make 24. Write and solve an equation aligned to the prompt above. Area Model / Array Example 6 24 Array Model Video X Area Model X 48 Area Model Video y Number Bonds Number Bond Video Number Bonds Number Bonds Bar Diagrams / Tape Diagrams Part Whole Model Comparison Bar Diagram Video Bar Diagram / Tape Diagram # 1 Sara has 5 stamps. Mark brings her 4 more stamps. How many stamps does Sara have now? Bar Diagram / Tape Diagram #2 Sara has 16 stamps. Mark brings her 4 more stamps. How many stamps does Sara have now? Bar Diagram / Tape Diagram #3 Sara brought 4 apples to school. After Mark brings her some more apples, she has 9 apples altogether. How many apples did Mark bring her? Bar Diagram / Tape Diagram #4 Matteo has 5 toy cars. Josiah has 2 more than Matteo. How many toy cars do Matteo and Josiah have altogether? Bar Modeling – Key Points When building proficiency in tape diagraming skills start with simple accessible situations and add complexities one at a time. Develop habits of mind in students to reflect on the size of bars relative to one another. Part-whole models are more helpful when modeling situations where you are given information relative to a whole. Compare to models are best when comparing quantities. Writing Word Problems with Tape Diagrams Tape diagrams are well suited for problems that provide information relative to the whole or comparative information of two or more quantities. Visual fraction models includes: tape diagrams, number line diagrams, and area models. When designing a word problem that is well supported by a tape diagram, sketch the diagram for the problem before or as your write the problem itself. Key Points – Tape Diagrams Use of tape diagrams, as described in the progressions documents provides visualization of relationships between quantities thereby promoting conceptual understanding, provides coherence through standards from Grade 1 through Grade 7, and supports standards for mathematical practice. Proficiency in the tape diagram method can be developed in students and teachers new to the process through a natural development of problems and representations. Content knowledge directed by the standards and the progressions is required to provide coherent and balanced instruction. Bar Diagram / Tape Diagram #5 Jasmine had 328 gumballs. Then, she gave 132 gumballs to her friend. How many gumballs does Jasmine have now? Bar Diagram / Tape Diagram #6 Jose has 4 paper clips. Harry has twice as many paper clips as Jose. How many paper clips does Harry have? Bar Diagram / Tape Diagram #7 Jose has 4 paper clips. Harry has twice as many paper clips as Jose. How many paper clips do they have altogether? Bar Diagram / Tape Diagram #8 William’s weight is 40 kg. He is 4 times as heavy as his youngest brother Sean. What is Sean’s weight? Bar Diagram / Tape Diagram #9 Jamal has 8 more marbles than Thomas. They have 20 marbles altogether. How many marbles does Thomas have? Bar Diagram / Tape Diagram #10 The total weight of a football and 10 tennis balls is 1 kg. If the weight of each tennis ball is 60 g, find the weight of the football. Bar Diagram / Tape Diagram #11 Two pears and a pineapple cost $2. Two pears and three pineapples cost $4.50. Find the cost of a pineapple. Bar Diagram / Tape Diagram #12 David spent 2/5 of his money on a storybook. The storybook cost $20 how much did he have at first? Bar Diagram / Tape Diagram #13 Alex bought some chairs. One third of them were red and one fourth of them were blue. The remaining chairs were yellow. What fraction of the chairs were yellow? Bar Diagram / Tape Diagram #14 Jim had 360 stamps. He sold 1/3 of them on Monday and ¼ of the remainder on Tuesday. How many stamps did he sell on Tuesday? Bar Diagram / Tape Diagram #15 Max spent 3/5 of his money in a shop and ¼ of the remainder in another shop. What fraction of his money was left? If he had $90 left, how much did he have at first? Bar Diagram / Tape Diagram #16 Henry bought 280 blue and red paper cups. He used 1/3 of the blue ones and ½ of the red ones at a party. If he had an equal number of blue cups and red cups left, how many cups did he use altogether? Bar Diagram / Tape Diagram #17 A club had 600 members. 60% of them were males. When 200 new members joined the club, the percentage of male members was reduced to 50%. How many of the new members were males? Bar Diagram / Tape Diagram #18 The ratio of the length of Tom’s rope to the length of Jan’s rope was 3:1. The ratio of the length of Maxwell’s rope to the length of Jan’s rope was 4:1. If Tom, Maxwell and Jan have 80 feet of rope altogether, how many feet of rope does Tom have? Exit Ticket Create a model to represent the CCLS aligned standards that you previously identified at your grade level. Contact Information If you have any questions, please do not hesitate to contact us: Andrea Tamarazio [email protected] Steven Graser [email protected]