Make A Ten To Subtract
Lesson 4 of 5
Objective: SWBAT round numbers and place value for subtracting mentally.
The focus of the opening of the lesson is to cue students into using subtraction in this lesson. I open by connecting students to their prior learning with subtracting numbers. I review a subtraction strategy students have already learned, called break it apart.
To practice this strategy I give them a word problem that requires subtracting two digit numbers with regrouping. For example, A bakery has 64 cookies to sell. A customer comes in to buy 39 cookies. How many cookies does the bakery have left to sell. To solve this problem, I want the students to subtract by breaking apart 39 into 34 and 5 to subtract. This would change the problem to 64 - 34 = 30, and 30 - 5 = 25. This type of review includes the math skill they will be using, and it also allows me to connect the same problem to the new subtraction strategy being taught in this lesson.
I explain there is another way to handle numbers, that are closer to a tens or hundreds number, especially if they end in with a nine in ones place. I ask the students to talk with their partner about the rule for rounding numbers ending with a nine. Students learned about rounding numbers earlier in the school year, and I have students regularly use this skill to evaluate their work to see if it is a reasonable answer. Their responses should be that they need to round 39 to 40.
I use connecting cubes to demonstrate a subtraction problem where an even number of tens is subtracted from the whole amount. I do this as a review because I know this is a concept my students have already learned. This also increases their confidence. I think this attitude is important because I know the next steps will be somewhat challenging for them.
Next, as a demonstration problem, I write 60 - 19 = ______
I ask the students to identify which number would need to be rounded.
I show the students how adding a connecting cube (of a different color to) change the 19 into 20 makes it easier to subtract.
The new model shows 60 - 20 = 40.
Then I ask if that was the amount I really wanted to subtract in the beginning problem. The students identify that I had subtracted one too many, and I need to give it back.
I focus on the idea that the amount that we started with did not change, we had only changed the amount we subtracted, and we still had cubes left. We had to put the one extra cube with the amount remaining and determine the new difference.
I move the different colored cube to the remaining amount, and ask the students to determine how many are left now.
I repeat this with the information: Add 1 to make a ten, and then subtract. You subtracted one too many, so you have to add one back to the amount left over to get the answer.
Additional problems are demonstrated, using the cubes and questioning students to guide my modeling.
Because this is a new strategy for my students the students, we create an anchor chart to reinforce the concept. The chart is titled "Make a Ten or Hundred". Writing this chart together connects the new concept with the learning at that moment.
I use one of same number sentences from the demonstration with the connecting cubes, and I have my students write the anchor chart in their math journal at the same time I write on it on the chart paper. This allows students to repeat a problem that has already been demonstrated, and they write down the information they already know. This repetition of a problem allows students to focus on the strategy rather than on finding the difference between the numbers. The students already know the answer, so now they are working on the process and anchoring their learning.
To keep myself organized, I write out the chart myself on paper before presenting it to students. I also try to create the title of the chart in advance. This chart can be reused throughout the school year with your students, but it should be created with each new group of students from year to year, or even if you teach multiple classes in the same year.
It is important to focus on the idea of rounding up meaning, in this context, that you are subtracting (taking away) one more (to make it easy), and that one has to be added back in to the amount remaining.
Using color to demonstrate +1 when subtracting, and then +1 on the difference helps the students identify where to put the one back.
Using their individual whiteboards, students practice the strategy of making a ten. I put the numbers into a word problem context, and I demonstrate how to round to ten, subtract, and then add the one added to make the friendly ten back in to the difference.
Because the Common Core math practice of reasoning abstractly and quantitatively is used throughout all areas of math, I taught this practice earlier in the year with rounding numbers and using estimation for adding and subtracting. This skill is one that needs to be practiced repeatedly and not in isolation or in only one area of math. Students use the strategy of rounding to check if their computations are reasonable. It may be helpful to use a number line to show how to round numbers for students if needed.
A few of the students understand the strategy and ask if the original number ended in an 8 would it mean you can add 2 to make 10, subtract, and then add 2 to the difference. I ask them to try it, and see if it works. Other students are not ready for this, and continue to practice with just adding one.
Try It Yourself
I give the students a blank piece of paper for their individual work. I have the students fold the paper into 6 sections like a brochure.
In the first box, the students rewrite the anchor chart information for reference. Each section on the paper has a different problem to solve. I challenge the students to change one of the numbers to end with an 8 if they felt confident.
As students work on the problems, I question students about the steps they are using to solve the problems. These questions include:
- What is your first step?
- Explain how you rounded the number?
- What number are you going to change?
- Describe what you have done so far. What will be your next step?
- Which step is the easiest for you?
- Which step is the most difficult for you?
To close this lesson, students work with a partner to write and explain the steps of this number sentence 52 - 19 = _________.
- Round 19 to the nearest 10, which is 20
- Discuss this is taking away one more than the number sentence indicates, and it will need to be added back in.
- Subtract 52 - 20 = 32
- Add one back to the difference of 32; 32 + 1 = 33
- Rewrite the number sentence 52 - 19 = 33
The students repeat this process with their own original number sentence.
The concept of understanding the taking away too many because of the rounding step, can be confusing for the students. This step of discussing and explaining this taking away too many and it needs to be added back to the difference is crucial for students to develop the conceptual understanding of subtraction with regrouping.