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EAST ALLEN COUNTY SCHOOLS Bundle 2 Grade 6 Math Integers, Number Line Big Idea: Perception Enduring Understandings Essential Questions Positive and negative integers are reflections based upon the value of zero at the center. Adding and subtracting positive and negative integers demonstrates the inverse relationship of addition and subtraction. Absolute value is the distance of a number from zero on a number line. Measuring temperatures near zero, altitudes near sea level, or any values above or below a set standard are real-world applications of integers. CC/Learning Targets *6.1.1 *6.1.2 *6.1.3 *6.2.2 6.7 6.NS.5 6.NS.7 6.EE.5 6.EE.7 6.EE.8 6.EE.9 What is absolute value? In what ways can a number line represent real-world situations or calculations? What is a consistent way of remembering the rules for adding, subtracting, multiplying, and dividing positive and negative integers? How can you represent multiplication and division on a number line? Core Vocabulary absolute value integers Links to Technology -Math!!! (app) -Whiteboard (app) -Show Me (app) -SAS Flashcards (app) Bundle Performance Task(s) Using this hyperlink: Indiana Temperature Extremes, the students will create a table (include city, year, and temperature) which shows twenty of the record low temperatures that occurred in January. They will also make a table (include city, year, and temperature) which shows twenty of the record high temperatures which occurred in July. Students will calculate how much colder absolute zero is than at least five of the record low temperatures (absolute zero is about -459 degrees Kelvin). Students will also calculate how much hotter the boiling point of water is than at least five of the record high temperatures. (The boiling point of water is 212 degrees Fahrenheit.) As an extension, students may create a table which shows at least ten of the record high temperatures for each of the following months: June, July, August. They will then analyze where most of the record high temperatures occurred. Were they mostly found in the northern, middle, or southern part of Indiana? They may also find the five record high temperatures and five record low temperatures which occurred closest to the current year. Are there any noticeable trends? There is also a 2nd extension activity located at the end of this bundle. Grade 6 Math Bundle 2 Quarter 1 Sept.-Oct. Recommended Read-Alouds Title Big Idea: Perception Author Relates to… Little Numbers Edward Packard Numbers Less Than One Math Curse Jon Scieszka Perception Math Man Teri Daniels Percentage/ Fractions The Wishing Club Donna Jo Napoli Fractions Math Appeal Harry Briggs Problem Solving Math for All Season Greg Tang Problem Solving Piece=Part=Portion: Fractions=Decimals=Percents Scott Gifford Fractions/Decimals/Percents Less Than Zero Stuart Murphy Integers/Graphs Dinosaur Deals Stuart Murphy Equivalency L.A. Bundle 2 Read-Alouds Page 2 of 5 Math G6 - Bundle 2 CC/Learning Targets 6.1.1 6.1.2 6.1.3 a. Define negative numbers. Include the definition of integers and their opposites. b. Represent given situations using positive and negative numbers. c. Solve problems involving the concept of integers (e.g., on a number line, in counting, in temperature, in "owing"). My bank account is overdrawn by $15. How much money must I deposit to have a balance of $20? a. Define and model the concept of absolute value for any integer, positive or negative fraction, and positive or negative decimal. b. State and write the absolute value of any integer, positive or negative fraction, and positive or negative decimal. a. Compare positive fractions, decimals and mixed numbers using the symbols <, >, or =. Students may use conversions or their number sense of the relative size of numbers to compare. b. Plot points on a number line to represent positive fractions, mixed numbers and decimals. c. Plot the approximate location of positive fractions, decimals and mixed numbers on a number line. d. Compare integers and plot them on a number line. Resource of Ideas -Holt Middle School Math, Lesson 9-1 Evidence of Learning -Apply negative numbers to a number line for real life situations: (extreme temperatures, elevation below sea level, etc.) -Less Than Zero by Stuart Murphy (integers/graphs) -Dinosaur Deals by Stuart Murphy (equivalency) -Absolute value quiz (interactive) -Absolute value quiz (interactive) -Lobster Dive (app) -Holt Math Corresponding Lesson Resources -Absolute value lesson (interactive practice at bottom of page) -Absolute value lesson (interactive practice at bottom of page) -Holt Middle School Math, Lesson 9-1 -Math Man by Teri Daniels (percentage/fractions) -The Wishing Club by Donna Jo Napoli (fractions) -Little Numbers by Edward Packard (fractions) -Inequalities on a number line lesson (interactive practice at bottom of page) -Integers on a number line lesson -Number lines lesson (interactive practice at bottom of page) -Decimals on number lines(interactive practice at bottom of page) -“Don’t be Negative About Negative Signs,” integers rap song -Holt Middle School Math, Lessons 3-1, 9-4, 9-5 -Holt Math Corresponding Lesson Resources -Integers on a number line quiz (interactive) -Number lines quiz (interactive) -Decimals with number lines quiz (interactive) Math G6 - Bundle 2 e. Compare integers, positive and negative fractions, positive and negative decimals, and positive and negative mixed numbers. f. Plot integers, positive and negative fractions, positive and negative decimals, and positive and negative mixed numbers. g. Plot the approximate location of integers, positive and negative fractions, positive and negative decimals, and positive and negative mixed numbers on a number line. 6.2.2 (6.NS.2) a. Using models, determine the results of using multiplication on integers by doing the following: multiplying two positives, multiplying two negatives, multiplying a positive and a negative. b. Analyze the results of multiplication on integers; state and justify the rules for multiplying integers. c. Using models, determine the results of using division on integers by doing the following: dividing two positives, dividing two negatives, and dividing a positive and a negative. d. Analyze the results of division on integers; state and justify the rules for dividing integers. Fluently divide multi-digit numbers using the standard algorithm. (Notes: Sufficient practice and support throughout the year are needed to help students meet this fluency.) -Add, subtract, multiply, and divide visually on a number line (interactive) -Positive and negative integer multiplication visually (interactive) -Holt Middle School Math, Lessons 9-6, 9-7 -Holt Middle School Math, pp. 667 -Holt Math Corresponding Lesson Resources Math 6.7 G6 - Bundle 2 Problem Solving -Five Easy Steps to a Balanced Math Program for Secondary Grades, pp. 29-73 -The Problem Solver 6: Activities for Learning Problem-Solving Strategies -Problem Solver Activities -See Problem Solving Template in Appendix. -Math Appeal by Harry Briggs (problem solving) -Math for All Seasons by Greg Tang (problem solving) 6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. 6.NS.7 Understand ordering and absolute value of rational numbers. a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For -Holt Middle School Math, pp. 451-455 -Holt Math Corresponding Lesson Resources -Holt Middle School Math, pp. 451, 454-457, 463 -Holt Math Corresponding Lesson Resources Math 6.EE.5 6.EE.7 6.EE.8 example, write –3 0C > –7 0C to express the fact that –3 0C is warmer than –7 0C. c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; G6 - Bundle 2 -Holt Middle School Math, pp. 76-77 -Holt Math Corresponding Lesson Resources -Holt Middle School Math, pp. 604-605 -Problem Solver Activities -See Problem Solving Template in Appendix. -Holt Middle School Math, pp. 76-77 -Holt Math Corresponding Lesson Resources Math 6.EE.9 represent solutions of such inequalities on number line diagrams. independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Correlating CC/Learning Targets 6.1.4 6.1.5 6.2.1 6.2.5 G6 - Bundle 2 -Variables (independent/dependent -Independent and Dependent Variables - YouTube -Problem Solver Activities -See Problem Solving Template in Appendix. Teacher Notes -Problem Solving indicators need to be embedded in each Bundle -Nlvm.usu.edu (huge library of virtual manipulatives for all standards!) -Studyzone.com (huge library of process and content activities; many are interactive) -Onlinemathlearning (huge library of online videos for all standards) -Study Jams (huge resource of interactive lessons and activities) -Five Easy Steps to a Balanced Math Program for Secondary Grades, pp. 75-100 -All embedded apps included in this curriculum are free.