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Unit: Creating a Community of Mathematical Thinkers

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Unit: Creating a Community of Mathematical Thinkers Curriculum Map: Grade 6 Pre-Algebra Course: PreAlgebra Sub-topic: Algebra Grade(s): None specified Course Description This course is designed to complete the 6th grade standards of Ratio and Proportional reasoning, Geometry and Statistics and Probability. The course will also complete 7th grade standards of developing understanding of and applying proportional relationships; developing understanding of operations with rational numbers and working with expressions and linear equations. It will solve problems including scale, area, surface area, and volume. Statistics and Probability will include drawing comparative inferences from random sampling, and investigating chance. Unit: Creating a Community of Mathematical Thinkers Subject: Mathematics Timeline: Week 1 Purpose: The purpose of the Establishing a Community of Mathematical Thinkers Module is to launch the important mathematical processes and practices that will support the growth and independence of our students as mathematical thinkers in a learning community. Stage One - Desired Results Enduring Understandings:What will students understand (about Essential Questions:What arguable, recurring, and thought- what big ideas) as a result of the unit? "Students will understand provoking questions will guide inquiry and point toward the big ideas that..." of the unit? Mathematical thinkers effectively use their understanding, Why problem solve (or why think mathematically)? knowledge and skills. How does participation in a community of learners support Mathematical thinkers learn through collaboration and problem thinking and learning? solving. How do structures, strategies, and routines in problem solving support thinking and learning? How does productive mathematical thinking support critical thinking, growth and independence? Learning Targets: I can attack a math problem and solve it (MP1) I can make sense of a problem (MP2) I can prove my answer (MP3) I can assist others when I do not agree with their answer (MP3) I can use the appropriate vocabulary and symbols to represent a problem or solution (MP4) I can use math tools to help me solve/show how I solved a problem (MP5) I can explain the steps I used to solve a problem, and I am careful in my calculations (MP6) I can use what I already know to help me solve a new problem (MP7) I can use multiple ways to find a solution to a problem (MP8) STANDARDS Unit: Unit 1 - Compacted 5/6 Review Subject: Mathematics Timeline: Week 2 to 3 Purpose: The purpose of this learning unit is for students to develop a learning path of previously taught 6th grade skills and concepts in a differentiated workshop model. Stage One - Desired Results Enduring Understandings:What will students understand (about Essential Questions:What arguable, recurring, and thought- what big ideas) as a result of the unit? "Students will understand provoking questions will guide inquiry and point toward the big ideas that..." of the unit? Computational fluency includes understanding not only the What makes a strategy both effective and efficient? meaning, but also the appropriate use of numerical operations. How do you know if your solution is reasonable? Mathematical rules and expressions depict mathematical How do you determine what algorithm( including relationships operations,GCF, LCM, and distributive property) is There are multiple representations for any number. appropriate when solving a word problem. How can models and representations depict mathematical relationships? Learning Targets: I can use the distributive property to find the sum of two numbers that share a common factor. (example:36 + 8= 4(9 + 2). I can solve problems involving operations (+, -, x, ÷) with whole numbers, decimals, straight computation, or word problems. I can write, graph, interpret and or explain relationships between rational numbers in real-world contexts. STANDARDS STATE: PA Core Standards (2014) CC.2.1.6.E.1 (Practiced) Apply and extend previous understandings of multiplication and division to divide fractions by fractions. CC.2.1.6.E.2 (Practiced) Identify and choose appropriate processes to compute fluently with multi-digit numbers. CC.2.1.6.E.3 (Practiced) Develop and/or apply number theory concepts to find common factors and multiples. CC.2.1.6.E.4 (Practiced) Apply and extend previous understandings of numbers to the system of rational numbers. CC.2.2.6.B.1 (Practiced) Apply and extend previous understandings of arithmetic to algebraic expressions. CC.2.2.6.B.2 (Practiced) Understand the process of solving a one-variable equation or inequality and apply it to real-world and mathematical problems. CC.2.2.6.B.3 (Practiced) Represent and analyze quantitative relationships between dependent and independent variables. Unit: Unit 3 - Computation with Rational Numbers Subject: Mathematics Timeline: Week 7 to 10 Purpose: The purpose of this learning unit is for students to solve problems with rational numbers including fractions, decimals, and integers and to develop an understanding of how to use representations to model solutions. Stage One - Desired Results Enduring Understandings:What will students understand (about Essential Questions:What arguable, recurring, and thought- what big ideas) as a result of the unit? "Students will understand provoking questions will guide inquiry and point toward the big ideas that..." of the unit? Rational numbers can be represented in multiple forms How can the properties of whole numbers help us to perform (fraction, decimal, percent). operations of fractions and decimals? The same properties that were used to add, subtract, multiply, divide whole numbers can be applied to operations with all How can representations be used to model the solutions when rational numbers. adding and subtracting rational numbers? Learning Targets: I can apply properties of operations to add, subtract, multiply & divide rational numbers, including real-world contexts. I can represent addition & subtraction on a horizontal or vertical number line. STANDARDS STATE: PA Core Standards (2014) CC.2.1.7.E.1 (Practiced) Apply and extend previous understandings of operations with fractions to operations with rational numbers. Unit: Unit 4 - Expressions and Equations Subject: Mathematics Timeline: Week 11 to 15 Purpose: The purpose of this learning unit is for students to write and solve equations and inequalities, with an emphasis on real-world applications. Stage One - Desired Results Enduring Understandings:What will students understand (about Essential Questions:What arguable, recurring, and thought- what big ideas) as a result of the unit? "Students will understand provoking questions will guide inquiry and point toward the big ideas that..." of the unit? How do algebraic representations relate to one another? The properties of numbers can be applied to expressions, How can variables, expressions, equations and inequalities help equations and inequalities, to expand, simplify or solve. us solve problems? Learning Targets: I can apply properties of operations to add, subtract, factor and expand linear expressions with rational coefficients. I can apply properties of operations to calculate with numbers in any form and convert between forms as appropriate. I can use the distributive property to solve word problems with rational numbers. I can translate a word problem or real-world situation into an algebraic equation or inequality, solve that equation/inequality, and graph the solution set. I can reason about my answer, and determine if it is reasonable in the context of the problem. STANDARDS STATE: PA Core Standards (2014) CC.2.2.7.B.1 (Focus) Apply properties of operations to generate equivalent expressions. CC.2.2.7.B.3 (Focus) Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations. Unit: Unit 5 - Ratios and Proportional Reasoning Subject: Mathematics Timeline: Week 12 to 15 Purpose: The purpose of this unit is for students to develop an understanding of ratios and proportional relationships, with an emphasis on solving problems including unit rates, percents, and scale and reasoning through them. Stage One - Desired Results Enduring Understandings:What will students understand (about Essential Questions:What arguable, recurring, and thought- what big ideas) as a result of the unit? "Students will understand provoking questions will guide inquiry and point toward the big ideas that..." of the unit? Ratios can be represented in numerous ways. How can ratios be represented? An understanding of proportional relationships provides the How are proportional relationships used in the real world? basis for solving many types of problems. Learning Targets: I can find the unit rate a/b associated with a ratio a:b (with b ≠0) and use rate language in the context of a ratio relationship. I can make tables of equivalent ratios showing quantities with whole-number measurements and use them to find missing values, plot coordinates on a graph, and compare ratios. I can find a percent of a quantity as a rate per 100; solve problems involving find the whole, given a part and the percentage. I can use ratios to convert measurements from one unit to another and solve problems that involve multiplying and dividing quantities in more than one unit of measurement. I can solve unit rate problems, including those involving unit price and constant speed. I can determine whether 2 ratios are proportionally related. I can identify and interpret the constant of proportionality (unit rate) in tables, graphs,
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