In this lesson plan, we will explore addition and subtraction with 0. We'll begin with familiar first-then-now addition stories and gradually introduce scenarios where zero is one of the addends. Through various examples and equations, your learner will grasp the concept that adding or subtracting zero leaves the original number unchanged. Then we'll explore the notion of subtracting a number from itself resulting in zero.
Key Concepts for Addition and Subtraction with 0
Here are the main concepts that will be covered in this lesson:
Adding Zero: When you add 0 to any number, the result is the same number. This is because zero represents nothing being added. For example, 5 + 0 = 5. In future lessons, this will be defined as the Identity Property of Addition.
Subtracting Zero: When you subtract 0 from any number, the result remains the same number. This is because nothing is being taken away. For example, 7 - 0 = 7.
Subtracting a Number from Itself: When you subtract a number from itself, the result is always 0. This is because you are taking away all of the quantity that you started with. For example, 6 - 6 = 0.
Teaching Plan
The following activities will help your learner become confident in addition and subtraction with 0. Be sure to work at a pace that is comfortable for your learner.
Examples and visuals to support the lesson:
1. Addition Stories with Zero
Start with reviewing a familiar first-then-now addition story that does not have zero as either addend. Have your learner write an equation with the addends and the sum.
For example: First, there were four children on the bus. Then three more children got on. Now there are seven children on the bus." The equation for this scenario is 4 + 3 = 7.
Then build on the same type of story problem but this time look at situations where one of the addends is zero.
Here is an example where the second addend is zero: "First there were six children on the bus. Then no more children got on the bus. Now there are still six children on the bus." The equation is 6 + 0 = 6.
This story has zero as the first addend: "First there were no children on the bus. Then three children got on the bus. Now there are three children on the bus." Have your learner write the equations for these equations as well. The equation is 0 + 3 = 3.
Skill Check
I can solve addition stories that have zero as an addend.
2. Exploring Zero as an Addend
Continue to provide your learner with various contexts with zero as an addend. You can also explore part-part-whole diagrams where one of the parts is zero.
Work towards the generalized statement: "When zero is added to a number, the number remains the same."
Note that sometimes children think that adding zero gives a result of zero. Address this misconception with an example such as: "Peter says that five plus zero is zero because adding zero means you don't have anything. Explain why he is wrong."
Next, provide your learner with addition equations that have zero as an addend. Have them find the sum for each equation.
Provide a mixture of equations that have zero as the first addend and as the second addend.
I know that when zero is added to a number, the number stays the same.
3. Subtraction Stories with Zero
Now move on to subtraction of zero. Provide your learner with a familiar first-then-now subtraction story that does not have zero as the subtrahend.
For example: "Harry has a basket of six eggs. He drops three eggs. Now he has three eggs left." Have your learner write an equation to represent the story. The equation for this example is 6 - 3 = 3.
Build on the context of the story to explore situations where the subtrahend is zero. For example: "Harry has a basket of six eggs. He doesn't drop any. Now he still has six eggs in the basket." Have your learner write the equation which is 6 - 0 = 6 for this example.
Point out to your learner that if we subtract zero, there is no change to our starting quantity and the total remains the same.
Skill Check
I can solve subtraction stories with zero as the subtrahend.
4. Exploring Zero as a Subtrahend
Provide additional story problems and part-part-whole diagrams to reinforce subtraction of zero. Work towards the generalized statement: "When zero is subtracted from a number, the number remains the same."
Similar to the misconception about adding zero, some children mistakenly think that subtracting zero results in zero. You can address the misconception with an example such as: "Sara says that seven minus zero is zero because if you take away zero it means everything is all gone so the answer is zero. Explain why she is wrong."
Next, provide your learner with subtraction equations that have zero as the subtrahend (the number being subtracted). Have them find the difference for each equation. Begin with 10 - 0, 9 - 0, and so on until you reach 0 - 0.
Continue to practice with a variety of addition and subtraction problems in the form of missing number equations, part-part-whole diagrams, and story problems.
Skill Check
I know that when zero is subtracted from a number, the number stays the same.
5. Subtraction with a Difference of Zero
Once your learner is confident with adding and subtracting zero, explore contexts where the difference is zero.
For example: "Harry has a basket of six eggs. He drops six eggs. Now he has no eggs in the basket." Have your learner write an equation to represent the story. For this example, the equation is 6 - 6 = 0.
Use a variety of story problems and part-part-whole diagrams to model scenarios that have a difference of zero. Work towards the generalized statement: "Subtracting a number from itself gives a difference of zero."
Have your learner practice solving missing number equations that have a difference of zero. Begin with 10 - 10, 9 - 9, and so on until you reach 0 - 0.
When they are confident with those equations, provide a mix of subtraction problems that have zero as the subtrahend and ones that have a difference of zero.
Skill Check
I know that subtracting a number from itself gives a difference of zero.
Summary
By the end of this lesson, your learner will have a thorough understanding of the impact of zero in addition and subtraction. They will know that adding zero to a number leaves the number unchanged, and that subtracting zero from a number also leaves it unchanged. They will also realize that subtracting a number from itself always results in zero. Through a series of story problems, equations, and part-part-whole diagrams, we have reinforced these key concepts and addressed common misconceptions. This foundational knowledge about zero will enhance your learner's overall number sense and prepare them for more problem-solving concepts.
With over 12 years of experience as a classroom teacher, tutor, and homeschool parent, my specialty is easing math anxiety for students of all ages. I'm committed to empowering parents to confidently support their children in math!
Skill Check