So Many Solutions - Inequalities

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Objective

SWBAT translate and solve one step inequalities

Big Idea

students work in pairs and groups of 4 to solve inequalities and identify possible integer value answers

Do Now

10 minutes

Students enter silently according to the Daily Entrance Routine.. Do Now are handed at the door as I narrate students getting right to work and praising those who are immediately ready and beginning their work. This is a strategy touted by Lee Canter. It is meant to motivate other students to do the same as their peers, who are being praised publicly. After 5 minutes of independent work, students with correct work and answers will be asked to copy their work on the board and the rest will be asked to discuss their solutions and the ones at the board with their neighbors. I will be observing students work during those first 5 minutes to flag or target a group that will debrief solutions with me during the last 5 minutes of this section.   

The three problems included on the worksheet reflect problems most commonly missed by students on the last unit test. Students continue to struggle with order of operations involving absolute value, solving equations that require distribution and combining like terms. The last problem in the Do Now ties in the previous lesson, translating word problems in t equations to solve. I review the previous lesson’s strategy, using bar models to translate, in the video included.

The most common errors made by students for each question are listed below:

Question 1:

  • Not understanding what an exponent of three means; some students will multiply by 3
  • Adding and subtracting before multiplying
  • Not understanding absolute value; thinking that -3 means subtract three

 

 

Question 2:

  • Not distributing the negative correctly; specifically the -2 to the second term of -6
  • Combining terms that are not alike
  • Issues with solving equations

 

 

Question 3:

  • Lack of use of a strategy (i. e. bar models, verbal models)
  • Decimal operations errors

 

It's important to be able to identify these errors to better place students into pairs and groups around the room for the upcoming paired work time. 

Class Notes

10 minutes

After debriefing on solutions, all students will be asked to return to their seats and class notes will be distributed. The problems on the back are additional practice that students who move quickly through the notes can complete, or extra samples for students to study before the quiz this week. Anything in red font in the notes document is meant for students to copy off the board. I have a SMARTboard document displayed at the front that looks like students’ papers (this document is attached as a pdf file). I begin with translations of word problems to inequality statements to gauge students’ prior knowledge. I anticipate common issues such as not knowing how to read the symbols < vs >, or getting confused when there are variables on the right side. First I have a student read the statements. The first statement is modeled as follows and then I ask students to help me with the second statement:

The number of points a basketball team scores is greater than 80.

I model:

  • What is the unknown? # of points
    • Let’s give it a variable à p
  • What is the short inequality statement? Greater than 80  
  • Summarize in the furthest column to the right:
    • # of points is greater than 80
  • This is another way to state the same fact:
    • 80 is less than # of points

This other way tends to confuse many kids, so it could be useful to use whole number values to prove it:

3 < 5  three is less than five

5 > 3  five is greater than three

 

Next, another student/s model(s) the next question while I lead them through the same cycle of questions:

  • What is the unknown? What variable should we give it?
  • What is a shorter way to say the inequality statement?
  • What is another way to say this fact? How do you say it if the variable is on the right side?
  • What are some possible values for a (the unknown)?

When a student struggles to answer the question correctly I may call on (or ask the student who is stuck to call on) another student to continue where the initial one left off. This may continue until the question is answered correctly and fully. It’s a great way to keep participation positive and team based and it’s most useful when reviewing short response questions.

All students are given 3-4 minutes to complete the two left over statements in pairs. We discuss how these statements are different from the first two. This is how I develop the idea of inclusion. These last two examples can be checked for understanding by posing different values, positive negative, rational, as solutions to the set. Drawing a number line is a visual strategy that should be used for all students.  

Independent Practice

20 minutes

Students work independently and silently for 15 minutes to complete the worksheet. During this time I am walking around to provide help if students are getting stuck and noting those who are struggling to master the skill. At the end pf 15 minutes those who were struggling will be asked to form a small group with me to review the answers and I’ll give them a problem to complete independently once again. Other students will be asked to pair up to check their answers or complete their work. Any student who was unable to complete at least 6 of the problems will be asked to be in my group.

The common errors I anticipate are mostly with the last 4 questions. Some students may forget how to solve one step equations with a variable in the numerator. As for the number lines, I am not asking students to graph, simply to circle possible integer values. This class work also presents a good opportunity to use MP6, attention to precision. Question 2utilizes this practice through the operations with decimals, a skill some of my students continue to improve.  Questions 7 and 8 utilize this skill when drawing the number line. It will be informative to see how students scale their lines or where they choose to place their positive and negative integers. 

Closing

10 minutes

During the last 10 minutes of class students are asked to make groups of 4. Each group will be responsible for displaying the solution to one problem on the board or a piece of char paper. I work to show the answers to two other problems. They are only given 5 minutes to do this so they must hurry to display their solution. Achievement points are awarded to groups that are successful in getting all of the work on the board/chart paper. During the last 5 minutes of this section we discuss whether or not the solutions are correct and why. Homework is distributed at the end and students are dismissed.