To set the tone for this lesson, I want students to be looking at inequalities right away. We deal with inequalities on a daily basis, we just haven’t called them anything. So, I’ve chosen 2 problems for the students to work with. First, they will be writing out in words what the inequality represents. I’m going to have them write it two ways. (this is important because students will read and write the inequalities two different ways and they need to know that both are correct).
I should see: Three is greater than one or one is less than three. They have been working on these inequalities for a long time, we just need to deepen the understanding.
Then I should see: You can ride the ride if you are 54 inches, 55 inches, 56 inches. You cannot ride the ride if you are 50 inches, 49 inches etc.
When students have completed writing this down in their notes, I will give them time to share their responses with their tablemates. Then, I will ask “what do you notice about the solutions for problem #2?” I want students to say that there is more than one solution. Then, I will ask “can you be 52 inches to ride the ride and how do you know?”
I will explain to students that both problems represent inequalities. The second problem is an inequality that we encounter in our daily lives. If we think logically about what they mean, it will be no trouble at all to write an inequality, read an inequality and find the solutions to an inequality.
Tools: Do NOW problem
Students will be following along in their notes as I go over the symbols, words, and graphing points for inequalities. The vocabulary is out of context, but I wanted to show them ahead of time so we can use them in the next section. The graphing points will be used in the next lesson, but I wanted to make sure they have it all in one place.
While I go over the symbols, I tell the students that can tell the difference between the < ,> symbols and the because the line under the symbol looks like part of an equal sign. When we start graphing, I tell them the second line rolled itself into a ball and colored in the circle to represent greater than and equal to and less than and equal to.
Tools: Vocabulary words
I’ve chosen two real-world inequalities to help students make sense of the solutions.(SMP 1) For each of these problems, the students are going to give me sample solutions first. Once that is done, they will make a connection between the number and a word (SMP 2). So in the first example, children under 12 eat for free. I will ask “who eats for free”? Then I will ask, “what do you notice about the solutions”? Then, I will say “ what symbol represents less than”?, then we get to write the inequality.
Writing the inequality is tricky because students like to flip the variable around, but not flip the symbol. So, I ask “what does the variable represent”? They should say the variable represents the solutions. Then I say, “we always read with the side of the variable”. So in this case a stands for ages.
a < 12, which is read all the ages are less than 12.
12 > a, which is still read with the side of the variable, we just read it backwards. Point out to the students that the symbol still represents the same information. I tell them, you see the point is still pointing to a.
I will do this same type of guided questioning for the next problem too. This problem does have the solution included so the symbol will be different. Ask the students “how did you know 65 was included” or “can you drive 65 without getting a ticket”.
Tools: Inequality examples
Before showing students the completed slide about the words of inequalities, have them write down as many words as they know for each of the symbols. Tell them to think logically about the symbols and their meanings. For example: “how would you know that something means less than”?
Have the students partner share at their tables and then show them the slide to add to their lists.
Students have a difficult time with minimum and maximum. I tell them that if the word maximum is used it means that is the most, it’s like a limit, it can’t go any higher. If they hear the word minimum, it means the least, it can’t go any lower.
Tools: Inequality words
Have students use whiteboards to practice writing inequalities. I like to use whiteboards because you can formally assess a large group all at once. Do as many problems as you feel are necessary for your group. If you feel that they have it, then move on to the Around the Room. If you feel they need more practice, then continue working as a whole group.
I will be looking for students to use a variable, symbol and a number to represent the given problem. Students can write the inequality either way a < 12 or 12 > a. If students have written it the different ways, ask the students if they answer are the same? (SMP 7: students will understand why both representations are the same)
Tools: Practice Problems
The students will be working in pairs for this Around the Room activity. Students will be writing inequalities from real-life situations. This will help them make sense of their solutions. (SMP 1 and 2). They will work independently, but share their responses with a partner to justify their solutions. (SMP 3)
Watch that students are writing the inequality correctly and if they are writing it with the variable on the right, that the symbol is correct.
Tools: ATR problems
The students will be completing a connect 3 using the words solutions, inequalities and equations. Students will have a difficult time deciphering between when it is an inequality and when it is an equation, so I attached it to the word solution as this is the most identifying trait. I should see students understanding that equations have one solution and inequalities have many. The connection between inequalities and solutions are that they both use variables to represent numbers.
Connect 3 supports mathematical practice 6 by getting the students to use precise mathematical language in their explanation.
Tools: Connect 3