Gary School Community Corporation Mathematics Department Unit Document

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1 Gary School Community Corporation Mathematics Department Unit Document Unit of Study: 1 Grade: 8 Unit Name: Integer Exponents and Scientific Notation Duration of Unit: 4 Weeks Standards for Mathematical Content UNIT FOCUS 8.C.1: Solve real-world problems with rational numbers by using multiple operations. ***** Standard Emphasis Critical Important Additional 8.AF.1: Solve linear equations with rational number coefficients fluently, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Represent real-world problems using linear equations and inequalities in one variable and solve such problems. ***** 8.C.2: Solve real-world and other mathematical problems involving numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Interpret scientific notation that has been generated by technology, such as a scientific calculator, graphing calculator, or excel spreadsheet. ***** 8.NS.3: Given a numeric expression with common rational number bases and integer exponents, apply the properties of exponents to generate equivalent expressions. ***** 8.NS.4: Use square root symbols to represent solutions to equations of the form x^2 = p, where p is a positive rational number.. Mathematical Process Standards: ******** Mathematical Process Standards: PS.1: Make sense of problems and persevere in solving them. PS.2: Reason abstractly and quantitatively PS.3: Construct viable arguments and critique the reasoning of others PS.4: Model with mathematics PS.5: Use appropriate tools strategically PS.6: Attend to precision PS.7: Look for and make use of structure PS.8: Look for and express regularity in repeated reasoning Vertical Articulation documents for K 2, 3 5, and 6 8 can be found at: (scroll to bottom)

2 Big Ideas/Goals Problem situations can be represented, analyzed and solved with rational numbers. Essential Questions/ Learning Targets In how many different ways can I represent a problem situation? I Can Statements I can evaluate a problem situation, use rational numbers to represent the important facts, and solve the problem. Equations can represent real-world problems. Equation solutions represent valid solutions to the real-world problem being represented. Inequalities can represent realworld problems. Inequality solutions represent valid solutions to the real-world problem being represented. Scientific notation is helpful in representing very large or very small values. Scientific notation is sometimes needed to represent and solve real-world problems. Values can easily be converted from scientific notation to decimals and vice versa. Scientific notation is represented in different ways depending on the technology used. Exponential expressions can be simplified to form equivalent expressions by applying the properties of exponents. How can equations be used to represent and solve real-world problems? How can inequalities be used to represent and solve real-world problems? When is it appropriate to use scientific notation? What are the procedures for converting scientific to decimal notation and decimal to scientific notation? How does technology show us numbers in scientific notation? How do I use properties of exponents to simplify an expression? I can translate a real-world problem into an equation and use the equation to solve the problem. I can solve linear equations fluently. I can translate a real-world problem into an inequality and use the inequality to solve the problem. I can solve linear inequalities fluently. I can use scientific notation to represent very large and very small numbers. I know when it is appropriate to use scientific notation to represent a situation and/or solve a real-world problem. I can convert any number from scientific to decimal notation and from decimal to scientific notation. I can use technology to interpret numbers written in scientific notation. I can apply properties of exponents to simplify an exponential expression to form an equivalent expression. 2

3 Sometimes it is necessary to obtain the square root of a value to reach a solution. Does x 2 = 5 represent a solution for x? When do radical solutions occur? How do I arrive at a radical solution? I can solve problems that have radical solutions. 3

4 UNIT ASSESSMENT TIME LINE Beginning of Unit Pre-Assessment Assessment Name: Size it Up Assessment Type: Worksheet Assessment Standards: 8.C.2 Assessment Description: Students translate scientific to decimal and decimal to scientific notation Assessment Name: Linear Equations Pre-test Assessment Type: short answer Assessment Standards: 8.AF.1 Assessment Description: Students solve linear equations, interpret and solve word problems, and provide short answers to questions about creating and solving equations. Pre-test can be used in its entirety or in part. Assessment Name: TBD Assessment Type: open response word problems Assessment Standards: 8.C.1, 8.NS.3, 8.NS.4 Assessment Description: Pre-assessments should reveal student readiness to represent problem situations using rational numbers and variables as well as ability to understand and work with exponents and radicals. Throughout the Unit Formative Assessment Assessment Name: Measurements to objects comparison Assessment Type: Collaborative Activities (see attached) Card Set A: Measurement Card Set B: Objects Card Set C: Comparisons Assessing Standards: 8.C.1, 8.C.2 Assessment Description: Students estimate using scientific and decimal notation Assessment Name: Exit Ticket Assessment Type: short answer Assessing Standards: 8.AF.1 Assessment Description: Students solve a real-world problem represented in a linear equation. The solution of which will require expanding expressions using the distributive property and collecting like terms 4

5 Assessment Name: TBD Assessment Type: TBD Assessing Standards: 8.NS.3, 8.NS.4 Assessment Description: Students simplify expressions that require application of properties of exponents and use square root symbols to represent solutions. Assessment Name: TBD Assessment Type: TBD Assessing Standards: 8.AF.1, 8.C.1, 8.C.2 Assessment Description: Students develop routines for interpreting real-world scenarios, representing them in equations, and solving them. Students are able to interpret solutions in the context of problems presented. End of Unit Summative Assessments Assessment Name: Resize it Up Assessment Type: Worksheet Assessing Standards: 8.C.2 Assessment Description: Students translate scientific to decimal and decimal to scientific notation Assessment Name: End of Unit Assessment Assessment Type: Combination short answer, open response and performance task Assessing Standards: 8.C.1, 8.AF.1, 8.C.2, 8.NS.3, 8.NS.4 5

6 PLAN FOR INSTRUCTION Unit Vocabulary Key terms are those that are newly introduced and explicitly taught with expectation of student mastery by end of unit. Prerequisite terms are those with which students have previous experience and are foundational terms to use for differentiation. Key Terms for Unit Prerequisite Math Terms scientific notation decimal notation rational numbers exponent integer power base square root radical properties convert decimal exponent base square root expression positive negative estimate Unit Resources/Notes Include district and supplemental resources for use in weekly planning Math Assessment Project Additional assessments and lessons: Carnegie Learning Software - anchor 6

7 Targeted Process Standards for this Unit PS.1: Make sense of problems and persevere in solving them Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway, rather than simply jumping into a solution attempt. They consider analogous problems and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, Does this make sense? and "Is my answer reasonable?" They understand the approaches of others to solving complex problems and identify correspondences between different approaches. Mathematically proficient students understand how mathematical ideas interconnect and build on one another to produce a coherent whole. PS.2: Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. PS.3: Construct viable arguments and critique the reasoning of others Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They analyze situations by breaking them into cases and recognize and use counterexamples. They organize their mathematical thinking, justify their conclusions and communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and if there is a flaw in an argument explain what it is. They justify whether a given statement is true always, sometimes, or never. Mathematically proficient students participate and collaborate in a mathematics community. They listen to or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. 7

8 PS.4: Model with mathematics Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and the workplace using a variety of appropriate strategies. They create and use a variety of representations to solve problems and to organize and communicate mathematical ideas. Mathematically proficient students apply what they know and are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. PS.7: Look for and make use of structure Mathematically proficient students look closely to discern a pattern or structure. They step back for an overview and shift perspective. They recognize and use properties of operations and equality. They organize and classify geometric shapes based on their attributes. They see expressions, equations, and geometric figures as single objects or as being composed of several objects. PS.8: Look for and express regularity in repeated reasoning Mathematically proficient students notice if calculations are repeated and look for general methods and shortcuts. They notice regularity in mathematical problems and their work to create a rule or formula. Mathematically proficient students maintain oversight of the process, while attending to the details as they solve a problem. They continually evaluate the reasonableness of their intermediate results. 8

Extending Place Value with Whole Numbers to 1,000,000

Grade 4 Mathematics, Quarter 1, Unit 1.1 Extending Place Value with Whole Numbers to 1,000,000 Overview Number of Instructional Days: 10 (1 day = 45 minutes) Content to Be Learned Recognize that a digit