Lines Around the World: Combining and Graphing Integers on a Number Line
Lesson 9 of 20
Objective: SWBAT combine two or more integers by writing numerical expressions and plotting them on a number line
Students enter the class and find a “Do Now – Pop Quiz” on their desk that will include 5 integer combination questions. The questions will assess student knowledge of combining integers with opposite signs and integers with the same sign(i.e. 16 + (-5) and -6 + (-8)). The pop quiz will help me generate a list of students still struggling with integer addition. Students who have not mastered this concept will be encouraged to work in groups so that I can work with them more closely. There are two forms of the quiz, A and B. The letters are indicated at the top right hand corner of each quiz. I will have answers ready to check as students finish.
Students are instructed to take out their homework from the previous night. They are also instructed to fill out their heading in their notes and to copy the aim off the power point.
We begin by reviewing the answers to the homework assignment from the previous night. That assignment included 6 word problems. Students were responsible for writing and evaluating addition expressions to represent each word problem (i.e. a “plane descends 1200 feet and then ascends 500 feet”; Glencoe Workbook online, pg 18). I review the answers to the homework by asking students to read each word problem. After a student reads a portion that could be represented using an integer I ask them to stop and I show everyone which integer represents that part of the problem. Some students may ask about the relationship between adding the inverse and subtracting. I simply state that their number sentence gives the same result, but they must write an addition sentence because of the directions. We discuss the answers to each expression by thinking about the use of counters we explored the previous day. I stop when we get to the golf problem to explain the rules of golf. Many students do not understand the idea of “par”, so I make sure to make time to explain golf, how it is played, and the meaning of “par”. To check for understanding, I ask a volunteer to explain what “0 par” would mean, as well as “1 over par” and “1 under par”. I also point out that in golf you want to get a negative score or zero, not a positive score. Students are asked to explain why one would want a negative or zero score.
After the homework has been reviewed, we fill out the Cornell Notes. I review the position of negative and positive integers in relation to zero for both horizontal and vertical lines. Then, we complete two sample problems together: one that asks students to draw the “arrow annotation” given an expression and another that gives the arrow notation and asks students to write an expression. If there is time, I also show students how to draw arrow notation for combining two negatives. Student questions are answered if there are many, or if there are only a few, they are encouraged to ask their questions during the game.
I explain the structure of the game to students: it is called “Around the World” because they will be moving around the room to complete the problems at different stations. The first station includes 4 problems like the examples in the Cornell notes: two will ask them to draw the arrow notation on a number line and two will ask them to write expressions given number line arrow notations. The second station includes two word problems like the examples in the homework. Students will be writing expressions to illustrate the word problem. The third station includes one problem about combining integers along the number line, but one of the numbers is a variable. The last station is a puzzle station. Two puzzles are given, students are to choose one. If they answer correctly, they will receive a free homework pass. Additionally, students will receive achievement points for clearing stations. One achievement point will be awarded for completing each station if a student chooses to work independently. If a student chooses to work with a partner, they will each receive two achievement points after completing each station. MP1 and MP2 are being used to explore integer addition in these three different formats (skill level problems, world problems, algebra, and puzzles).
When 5 minutes are left for class, students come back to their seats. They are instructed to use a sticky note to write one question they still have about combining integers and stick it on a piece of chart paper before exiting the room.