7th Grade Math Lesson Plans with Sample Problems
Math for 7th grade students covers a number of new or expanded areas, including ratios, proportions, fractions, decimals, circumference, area and negative numbers. Below is an example of a lesson plan for adding and subtracting negative numbers with sample problems.
Negative Number Lesson Plan for 7th Grade
Before writing a lesson plan, it can be helpful to determine what you want students to learn by the end of the class period. For this lesson, students will be able to:
- Verbally describe the logic for adding and subtracting negative and positive numbers
- Solve problems requiring addition and subtraction of both negative and positive numbers
Materials can include any worksheets you will pass out as well as visual aids. A number line is the only visual needed for this lesson.
Students need to know how to add and subtract positive numbers. To activate this prior knowledge, consider starting the lesson with a quick review game.
To introduce this lesson, show the students a large number line that has both positive and negative numbers on it. Tell them that the numbers to the right of zero are called positive numbers and could be written with a + in front of them to show that they are positive numbers.
The numbers to the left of zero are called negative numbers. They are written with a - (minus sign) in front of them. Ask if anyone has any idea how you add numbers when one of them is smaller than zero (a negative number). If anyone gives a correct answer, tell them they are 'right on' and you'll explain why in a moment. If they are close, praise them for being close and that you will show them why it wasn't quite right.
As motivation for learning about positive and negative numbers, you might now tell a few real-world stories, such as the one below. Word problems can be challenging for students, but they demonstrate how negative numbers are present in the world outside the classroom.
Your sister just got a note from the bank saying that her account was overdrawn. In other words, she doesn't have any money in her account! In fact, she owes the bank $25, which means that her bank account shows -$25. She thought that she'd had $15 left in the account. How much money does she need to put into the bank to show that she has $15 in the account? In other words: (-$25) + ? = $15?
Review addition and subtraction using the number line. When adding, move right on the number line; when subtracting, move left on the number line. This physical demonstration may help kids visualize and internalize the concept.
Teach New Information
- 1) To add two positive numbers, follow the same process as usual. The addition they've done so far has always been adding two positive numbers, so they know this process well. Example: 3 + 5 = 8
- 2) When adding two negative numbers, it's just like adding two positive numbers, except you keep the negative sign in front of the answer. Example: (-3) + (-5) = -8
- A trick for adding numbers that are either both positive or both negative is to add the numbers together and keep the sign they both had.
- 3) To add a positive number and a negative number, subtract the smaller number from the larger one and keep the sign of the larger number. Examples: (-3) + 5 = 2; 3 + (-5) = -2
- 1) Subtracting a positive number from a negative number is the same as if you added two negative numbers. Add the numbers and keep the negative sign. Example: (-5) - 3 = (-5) + (-3) = -8
- 2) When demonstrating how to subtract a negative number from a positive or negative number, point out that 5 - 8 is not the same as 5 - (-8). It is easy to show 5 - 8 on a number line. However, the logic for 5 - (-8) is may be best explained with a drawing.
For all problems that subtract a negative number turn the '- (-' part of the equation into a big '+' sign to show that subtracting a negative number is the same as adding a positive number. Examples: 5 - (-8) = 5 + 8 = 13; (-5) - (-8) = (-5) + 8 = 3
As a class, give the students practice by telling another story that involves several sample problems. The following example is an extended story that can be engaging, funny and a great way to give students individual practice.
- Joe was a loyal soldier; Rauf was not so loyal, and he did his best to get Joe in trouble. The sergeant finally told Joe that he would give him a chance to prove that he was trying to obey his superiors. Every time he was caught doing something that showed obedience, he would get four points. If he disobeyed a rule, four points would be taken away. If he earned 40 points, they would no longer have to keep track. If he earned -40 points he would be discharged.
- Joe started the second week with eight points. Rauf told the sergeant that Joe had not saluted a superior, so the sergeant took away four points. (8 - 4 = 4) The superior, John, said that Joe had saluted him so the sergeant 'undid' the penalty. (4 - (-4) = 4 + 4 = 8 You are adding points back in, so subtracting a negative is actually adding.)
- The following week, Joe had 16 points. His shoes were spit-shined to perfection, so he got four more points. (16 + 4 = 20) But Rauf told the sergeant that Pete had shined Joe's shoes for him, so the points were removed. (20 - (+4) = 20 - 4 = 16) When Pete said he hadn't shined Joe's shoes, the points were added back. (16 - (-4) = 16 + 4 = 20)
- Joe made his bed perfectly and the sergeant successfully bounced a quarter on it, thus earning Joe another four points. (20 + (+4) = 20 + 4 = 24 ) Rauf tripped Joe in the food line and Joe spilled coffee on the sergeant's clean uniform. Another four points were lost. (24 + (-4) = 24 - 4 = 20 Adding a negative is the same as subtracting the number.) Finally, several of Joe's buddies told the sergeant about all the things Rauf had done to get Joe in trouble. Rauf was given a dishonorable discharge; Joe re-enlisted and was a model soldier.
If there is time, students can do some worksheets or they can take them for homework. If students have access to computers, you can find numerous interactive games online for practicing the addition and subtraction of negative numbers.
Hold a short class discussion giving students opportunity to express what they liked about negative numbers. Some may express still having confusion about certain points; if there is not time to go over the issues at this point, they can be addressed during the next lesson.
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