Signed Number Word Problems Lesson Plan- 7th Grade Math

Warm-Up

Because students should already be familiar with signed number operations, give students a few minutes to try this signed number word problem independently.

When students have an answer, they should discuss their work with a partner. Listen to the strategies students used to better understand where students’ current levels of understanding are. Many students are inclined to jump directly into an operation without truly understanding the problem. Encourage all students to draw a number line to make sense of the problem.

The number line helps them to see that the distance between `20` and `-10` is `30` and that we went back from `20` to `-10`; so the answer must be `-30`.

• If students are struggling, ask what the given numbers tell them about the situation. Students should be able to recognize that they are given a starting value and a final value. Help students recognize if the change is positive or negative. From there, encourage students to draw an open number line.
• If students are more advanced, challenge them by asking them to think of a general rule or formula that can be used when a problem includes a starting value, some change, and a final value. Students may develop a similar informal equation; however, they may use different words: starting value `+` change `=` final value

Finding the change

With the next example, students will have to use the initial and final values to find the change between values. It is important to note that “change” will include a positive or negative sign as needed because it includes direction, unlike “difference” which is always positive.

Students have likely seen similar problems before; however, they may make errors with the signs of the numbers or the change. To help make connections to the warm up, draw an open number line with `-5, 0,` and `7` labeled.

From there, show the jumps on the number line from `-5` to `0`, and then from `0` to `7`. This can help students determine which value is the starting value, as well as recognize that they are finding the change between values instead of finding the final value.

Series of changes

With the next example, students have to find the final amount after they are given an initial amount and a series of changes. Give students time to try this problem and check their work with a partner.

Students may use different strategies to solve this problem. Some will find the total change, and then add it to the starting value. Other students may start with the initial value and then add each change individually to get to the final value. 

Describing changes

When reviewing with students, highlight the different methods students choose. Make sure students are able to verbally describe what is happening in the scenario with each change. For example, students should recognize that `-10` feet indicates that the penguin’s elevation went down. If students chose to add all of the change values together, they should recognize that `-24` means the penguin’s elevation decreased by `24` feet overall. 

Finding the initial value

For the next examples, students will have to calculate the initial amount. These types of problems tend to give students the most issues; however, still give students a chance to solve this problem on their own to see what methods they use.

Using number lines

You may notice that students may question what operation they have to use with the given numbers. It may help students to draw open number lines to recognize that they do not know the starting value. This can help give students more context to recognize that the amount of money Ruben had was less than what he still owed. 

Series of changes to find the initial

With this final example, students have to find the initial amount again; however, there are a series of changes. Give students time to try this problem and check it with a partner. As students work, listen to the strategies they use.

This problem is quite tricky for students and most students will add all the changes to `-20` as if they are finding the final amount. Students might want to use an equation to solve a problem like this; for example: `x + 1 + 3 + (-4) + (-5) = -20`. Some students might choose to work their way backwards by undoing what was done. Some students might find the total change with this problem first and then subtract it from the final amount.