Comparing and Ordering Integers
Lesson 3 of 10
Objective: SWBAT compare and order integers on the number line.
In order to refresh their minds about comparing numbers, I’m going to have students work through 4 inequality statements. The directions for the students are to make the statement true by using the <,> symbols (SMP 2) and then to say how they know their statement is true. I’m looking for students to say that I know __________ is larger because it means more money, or it’s farther on the number line, or that they compare place value. As easy as this activity seems, it will be a bit of a stretch for students to decide how they know. When students are done working the problems, have them do a HUSUPU to share their solutions and justifications with a partner (SMP 3)
Students need to know that comparing means greater than, less than, or equal to. I will be showing the students that a number line is a useful tool to use when comparing integers.(SMP 5 and 6) The farther right on the number line indicates larger numbers. Or you can say, the farther left on the number line indicates smaller numbers. So, when comparing integers, you can put the numbers on a number line and decide the largest or smallest number by its location on the number line.
When doing the examples together, I’m going to have students place their numbers on a number line. The number line needs to be drawn in by the students. They need to become familiar with using and drawing this tool. There is space in their notes to draw a number line. First, have them draw the number line, next place the points on the number line, finally put in the appropriate symbol.(SMP 2) Once they have decided on the correct inequality, have them answer the question “how do you know it’s true?” (SMP 3) Students should say, for example, I know that -2 is greater than -3 because -2 is closer to zero (farther right) then -3. As students work through these problems, they can check with their solutions with a tablemate or two.
Students will be working on an illustrative math problem involving comparing integers. This is very similar to the format I was using during their direct instruction. First students need to place two numbers on a number line that is not completely marked. This is difficult for students to do. Remind them that zero is the symmetry point or our starting point. Students should use reasoning for their placement of the numbers. For example, they could say that they know that -3 means 3 units to the left or 3 units to the left of zero. They can do the same for the next number. Once the numbers are located, they are to tell whether the inequality statements are true or false and how they know. They will use the statement: this answer is true or false because ______ is closer to zero or farther right on the number line. This is what I will be looking for as they work through this problem. As students are working through this problem, I will be walking around checking for understanding. When all students are done, we will go over this as a whole group.
Students need to know that ordering numbers needs to be a least to greatest or a greatest to least statement and knowing which one to use will be found in the directions. Again, I will be using a number line to show students how to order numbers. In the slide for ordering integers, two points are left out. I did this so students could see how to place them on the number line. As students practice ordering, I will want them to make several inequality statements to support their answer. For example, if I’m ordering the numbers -5, -8, 10, and 1, my final supporting statement should look like this: -8 < -5, -5 < 1, 1 < 10. (SMP 2) Students should notice that the inequality symbols will be all facing the same way and this is a good indication that your numbers are ordered correctly.
I’m using another problem from illustrative math to support their learning. Students will need to draw a number line and plot the points on the number line to put them in the correct order. I liked this problem because it is dealing with temperatures. Students will need to make the connection that colder temperatures move left on a number line whereas warmer temperatures move right. This type of thinking will help them justify their answers in parts b and c. As students are working through this problem, I will be walking around checking for understanding. When all students are done, we will go over this as a whole group.
The closure will be turned in so I can assess understanding and plan for any re-teaching the next day. Students can complete the questions in their notes and then cut along the dotted line to turn this portion in. Questions are a summation of today’s learning and should be completed with ease.