Graphing Inequalities on a Number Line
Lesson 12 of 20
Objective: SWBAT translate and graph one step inequalities
Students enter silently according to the Daily Entrance Routine. Students are asked to take out their homework from the previous night on solving one step inequalities. The answers are displayed on the SMARTboard and the directions given are as follows:
- Check your answers with your neighbor.
- If you get something wrong, ask your neighbor to find your mistake.
- If you know what it is, don’t tell your neighbor until they try at least one guess.
- If you don’t know what mistake you made, your neighbor should be able to help you find it. If not, raise your hand.
- If you and your neighbor answer every problem correctly, raise your hand and ask for a challenge problem.
Anytime we are working with neighbors on difficult material we are applying MP3 (evaluating neighbor's arguments)to understand difficult problems (MP1) I will be walking around helping students find their errors or giving them the following challenge problem (they can copy it and show their work on the back of their homework sheet):
If a > b, identify the values of c for which the statement is true: a + c > b + c
Answer: all real numbers (other accepted student responses: “all numbers”, “any number”, etc… responses NOT accepted: “all whole numbers”, “any positive number”, or any statement that excludes possible number sets included in the solution).
Partner pairs who answer this question correctly, including correct work and strategies, will have their work put up on the bulletin board for the week. This task presents a great opportunity to practice MP1 with students who can be pushed to higher order thinking levels. While these students are busy on a challenge problem, I am able to work in smaller groups with students who need to master the one-step inequality solutions. These students whom are working on their mastery are using MP7 as they compare the structures and rules of solving inequalities to what they already know about solving equations.
My goal is to get as many students in the room as possible to try the challenge problem and have their work put up on the board. If more than half of the class attempts this problem we can spend the last 5 minutes of class reviewing the answer. But if less than half of the students get to the challenge problem, I will take the last 5 minutes of class to give three more problems students must complete and review to improve our progress toward mastery. Both assignments can also be printed back to back so that students are provided both opportunities.
Students are asked to put away their Do Now and open up to their Class Notes sections in their binders. Class Notes are distributed and student must fill out the heading and copy the aim off the white board. We review the steps for solving inequalities by having students call on one another to fill in the blanks with information they know:
Solve an inequality the same way you would solve an equation.
Step 1: Isolate the variable term.
Step 2: Isolate the variable.
Next, students draw the symbols which represent the inequality statements greater than, greater than or equal to, less than, and less than or equal to. Then I ask students to take 3 minutes to review the phrases in the table with their neighbors by alternating to read the lists. They must also come up with an example that uses one of the phrases and write its corresponding inequality. I give them one sample:
"I always have at least $30 in cash --> Let x represent the amount of cash I could have --> a [is greater than or equal to] 30"
During those 3 minutes I’m checking in with the students I know will struggle with this task either for reasons of difficulty staying on task or difficulty with language fluency. At the end of 3 minutes I follow up with questions to the class:
- What is the unknown?
- Do you know nothing at all about the amount of money I have? What are some amounts I could have?
Next we move on to more translating on the other side. I ask different students to read each line in the “Notes” section out loud. The lines which break down the translation into “word”, “variable” and “inequality” steps must be read using the following stems [filled in with an example]:
- In [words] it is written as [your age is over 12]
- The [variable] is [a for your age]
- The inequality is [a] which represents [your age], [>] represents [is over 12]
Students get 3 minutes to silently complete the 4 examples to the left of the margin. I display the answers, prepared ahead of time on a piece of chart paper.
I then model graphing on a number line with the example x > 3. I show students the difference between the graph of this solution and the graph of all the other three inequality symbols. Then they must graph the solution in their notes, a > 15. They must raise their hand to show me their solution and receive the classwork. Booths will be offered on a first come, first serve basis but students must have shown proper notes and work to earn those spots.
After 15 minutes of Class Notes time students are all given the classwork and allowed to work in groups. Some students will be asked to work with me. I will hold the answers in a basket; students are to come show me their work before taking the answers. They can bring them back to their group to check. This group work time is limited to 15 minutes and then students must return to their seats to complete any work silently, or they will be given their homework to begin early. At this time I will also be asking students to put up their work on the chalk board to display their solutions and draw the graphs. In the last 2 minutes of this section students will be allowed to ask questions out loud about the work that they see on the board.
Students will be given 1 minute to pack up and clear their desks of everything but a pencil. We will end class with a turn and sprint. Students will have 1 minute to complete 10 questions. They will complete 5 initial questions and after 30 seconds I will yell out “turn!” and they must turn the paper whether they are ready or not to solve the other 5 questions. Students who complete the entire sheet on time will be asked to submit their answers for achievement points. Homework will be distributed at the door as students line up for their next class.