Student Interactive Plan (SIP)

Transcription

1 Student Interactive Plan (SIP) Bundle 1: Unit 2 Equations and Inequalities Estimated Duration: 20 Days Unit Overview This unit will provide knowledge of writing and solving one-variable equations using rational number coefficients and constants. It includes modeling in order to solve the equations. Students will also be able to write inequalities that represent a given situation and a situation that represents a given inequality. Students will need to be fluent in rational number operations in order to effectively solve the one-variable equations. TEKS NOTES WRITING EXPRESSIONS AND EQUATIONS 8.8 Expressions, equations, and relationships The student applies mathematical process standards to use one-variable equations or inequalities in problem situations. The student is expected to: 8.8A (SS) 8.1G (PS) Performance: write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants Content: one variable equations or inequalities Vocabulary 8 th Grade Math Bundle 1, Unit 2 Page 1 of

2 Specificity / Examples: Student must be able to identify the variable of a problem, determine the differences between equations and inequalities and represent relationships algebraically. This TEKS also notes that the coefficients and constants are rational numbers. There will be decimals and fractions involved in the problems. Every time Sarah and Joey visit their grandmother, she always gives them money for ice cream. She makes sure they get the same amount. Grandma only had a few ones and a roll of coins. Joey was given 3 dollar bills and 4 coins, while Sarah was given 1 dollar bill and 12 coins. Write an equation to determine c, the value of the coin where they were given? Self Assessment: I can write an equation to represent a real world situation. I can write an inequality to represent a real world situation. Mary has decided to make and sell personalized tote bags as a side job. The cost to make the bags is $15 in addition to the cost of the machine which is $150. She can sell the bags for $25. Write an inequality to represent the number of bags she must sell to make a profit. Points of Confusion??? Maria and Alex are opening savings accounts. Maria deposits $50 and plans to add $10 each week. Alex deposits $30 and plans to add $15 each week. 1. Write an equation to find the number of weeks until both accounts have the same amount. 2. Write an inequality to show when Maria has more money in her account than Alex. 3. Write an inequality to show when Alex has more money in her account than Maria. 8 th Grade Math Bundle 1, Unit 2 Page 2 of

3 TEKS NOTES WRITING REAL-WORLD SITUATIONS TO REPRESENT AN EQUATION/INEQUALITY 8.8 Expressions, equations, and relationships The student applies mathematical process standards to use one-variable equations or inequalities in problem situations. The student is expected to: 8.8B (SS) 8.1A (PS) Performance: write a corresponding real-world problem when given a one variable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants Content: a corresponding real world problem Vocabulary 8 th Grade Math Bundle 1, Unit 2 Page 3 of

4 Specificity / Examples: Students must understand how to interpret parts of an algebraic expression including the difference between an equation and inequality. The equal sign or inequality separates two facts (or sets of information) and compares them. Students must represent each fact with a defined variable and show the relationship. Mrs. Johnson wrote the following equation on the board. this equation? 3x + 20 = 5x Which situation is modeled by A Jessie charges 3 dollars per hour plus a 20 fee for babysitting. Joey charges 5 dollars per hour with a 10 gas charge to mow yards. When, in hours, will they earn the same amount of money? B Maria is 20 feet from her house and walking away at a rate of 3 feet per second. Jill started 10 feet from the house and is walking at a rate of 5 feet per second. At what time, in seconds, is Maria ahead of Jill? C Donald reads a magazine at a rate of 3 pages per minute but started on page 20. Daisy started reading on page 10 and reads at 5 pages per minute. When, in minutes, will they be on the same page? D At the beginning of soccer season, Jackson had already scored 20 goals. He is now scoring 3 goals per game. Nicholas is scoring 5 goals per game but started with only 10 goals. If x represents the game number, which game(s) will Nicholas have scored more total goals than Jackson? Self Assessment: I can write a real-world situation to represent an equation. I can write a real-world situation to represent an inequality. Points of Confusion??? Write a real-world example for the following equation Write a real-world example for the following inequality 2x + 3 = x + 5-3x + 15 < -x th Grade Math Bundle 1, Unit 2 Page 4 of

5 TEKS NOTES MODELING EXPRESSIONS AND EQUATIONS 8.8 Expressions, equations, and relationships The student applies mathematical process standards to use one-variable equations or inequalities in problem situations. The student is expected to: 8.8C (RS) 8.1D (PS) Performance: model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real world problems using rational number coefficients and constants Content: one variable equations or inequalities Vocabulary 8 th Grade Math Bundle 1, Unit 2 Page 5 of

6 Specificity / Examples: Students use manipulatives and drawings to model equations and the algorithms to solve those equations. Variables will be on both sides of the equation. After modeling and solving equations with integer coefficients and constants, rational numbers can be used in solving equations by algorithm. Write an equation for each model below then solve for x. A. B. C. Self Assessment: I can model one-variable equations that include rational numbers. I can solve one-variable equations that include rational numbers. I can add, subtract, multiply, and divide rational numbers. Points of Confusion??? Explain two ways you could solve the following problem. 20 = 5(-3 + x) 20 = 5(-3 + x) 8 th Grade Math Bundle 1, Unit 2 Page 6 of

7 Misconceptions/Distractors 1. The student may not understand that an action is replicated on both sides of the equal sign to maintain equality when solving an equation. The value of the expression does not change throughout the solving of equation process. 2. Students may treat unlike terms as if the terms are like terms (i.e. 2x + 3 may be misrepresented as 5x). 3. Students may confuse the inverse operation for addition/subtraction and the inverse operation of multiplication/division yielding the incorrect usage of signs (i.e. -3x = 6; -3X/3 = 6/3; x = 2). 1. What is equivalence? 2. Why is writing equations important in math? Essential Questions 3. What is the difference in an inequality and equality? 4. When solving equations, how do you know which operation to use to solve for x? McGraw Hill textbook Virtual Manipulative Lab 3-a Additional Resources Parts of Equations Step-by-Step Example of Writing Equation from Word Problem Writing Inequalities from Word Problem with Keywords Writing Algebraic Expressions From Word Problems Solving Equations 8 th Grade Math Bundle 1, Unit 2 Page 7 of