Subtracting from Nines

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Objective

SWBAT use the subtract from nines method to solve addition and subtraction problems.

Big Idea

Students will subtract from multiples of 10 by changing all the digits into nines.

Opening

20 minutes

Today's Number Talk

For a detailed description of the Number Talk procedure, please refer to the Number Talk Explanation. For this Number Talk, I will encourage students to represent their thinking using the subtract from nines method on their white boards.

 

Task 1: 100 - 76

For the first task, I asked students to solve 100 - 76 on their white boards. Some students used transformation while others used a number line, decomposing, or compensation. I modeled each of their Strategies on the Board. I then said: I am just so impressed with all of you! Look at all of your amazing strategies! I can think of another really neat strategy we could use to solve this problem! Would anyone like to see it?! Students excitedly responded, "Yes!" I then modeled How to Subtract from Nines on the board. Before moving on, I asked a student volunteer to explain the model once more just in case anyone missed my explanation! I also introduced the Subtract from Nines Poster to help support my visual learners. 

 

Task 2: 100 - 48 

During the next task, many students solved 100 - 4 by turning the 100 into 99 + 1. Then they subtracted 48 from 99 to get 51. Finally, they added the one back in to get 52 as answer: 100 - 48

 

Task 3: 1,000 - 152

During the next task, I continued to encourage students to use the subtract from nines method: 1000 - 152. Many students used a second strategy to check their work. 

 

Task 4: 1,000 - 789

For this task, most students quickly turned the 1000 into a 999 + 1 to subtract: 1000 - 789. At times, students would forget to "add the one back in," but many of them realized this mistake through turning and talking with nearby peers. 

 

Task 5: 10,000 - 1,305

For the final task, the majority of students turned the 10,000 into 9,999 + 1 before continuing on with subtraction: 10000 - 1305. At this point, students LOVED this strategy and were disappointed that this was our last task! 

Teacher Demonstration

40 minutes

Reasoning for Teaching Multiple Strategies

During this Addition and Subtraction Unit, I truly wanted to focus on Math Practice 2: Reason abstractly and quantitatively.  I knew that if students learned multiple strategies of adding and subtracting numbers, I wouldn’t only be providing them with multiple pathways to learning, but I would also be encouraging students to engage in “quantitative reasoning” by “making sense of quantities and their relationships in problem situations.” By teaching students how to use a variety of strategies, such as using number lines, bar diagrams, decomposing, compensating, transformation, and subtracting from nines, I hoped students would begin to see numbers as units and quantities that can be computed with flexibility. 

PowerPoint Presentation 

In order to provide students with guided practice using the "subtract from nines" method, I created a PowerPoint presentation called, Bathroom Remodel. This way, I could provide students with an actual real-life scenario in which the subtracting across nines method would be helpful. This way, I would also be supporting Math Practice 4 (Model with mathematics).

Goal & Bathroom Remodel Introduction  

At this point in the lesson, I asked students to join me on the front carpet with their white boards. To begin, I showed students the first slide, which was the Goal: Today we are going to continue using the same strategy that you have already practiced using during our number talk. I can subtract from zeros by subtracting from nines. I heard a few students respond positively with a "Yes" or "Yay!" Students were excited to continue using a strategy that they had already become comfortable with.  

Moving on to the next slide, Bathroom Remodel Example, I explained: Aaron (my husband) and I moved into a house about a year ago and we are planning on remodeling our bathrooms. Here's an example of a bathroom remodel. Let's say that you just bought a house and it has a Pink Bathroom. Who would want to remodel this bathroom? Who would want to keep it pink? (Of course a few of my boys raised their hands with a giggle.) 

Let's say that you have a Budgeted Amount of Money. It looks like you have 3 thousand dollar bills and 6 hundred dollar bills. How much money do you have in your budget? Students responded, "3,600!" 

Purchasing a Mirror

I then showed students the Mirror and asked: What if you walked into the hardware store and you bought this mirror for $29? What if you paid with a hundred dollar bill? How much money would you have left over? I wrote 100 - 29 vertically on the board. Then, I modeled how to solve this problem by "subtracting from nines" and asked students to complete the same problem on their white boards with me. I first turned the 100 into 99 + 1. Then I subtracted: 99-29 = 70. Next, I added the 1 back in to get 71. 

Extra Challenge

To add an extra challenge for students, I said: Now, if you want to be high-level today, you could keep track of how much money we will have left over from our budgeted amount. How much did we save on the mirror? Students responded, "Seventy-one dollars!" I wrote this amount off to the side. Almost all students began keeping track as well! 

Purchasing Other Remodel Items

We then moved on to the next remodel item, a Toilet. Many students couldn't help but snicker. Who knew that a toilet would be a high-interest topic?! This time, I asked students to try solving the problem on their own: 100 - 88. During this time, I monitored student learning. Once in a while, students forgot to "add the one back in," and I would simply ask, "What do you need to do next?" They would often retrace their steps and respond, "Oh yeah, I've got to add the one back in." This was a reminder of how multiple-step strategies are always more difficult. 

Before moving on to the next slide, I asked students: So we saved $71 on the mirror and $12 on the toilet. How much have we saved altogether? Students responded, "Eighty-three dollars!" 

We then discussed and figured the leftover amounts for each of the  Faucet and Shower Faucet. Here's an example of a student's calculations: 100 - 74

Multi-Step Problems

To provide students with a couple of multi-step problems, I included two scenarios in which another calculation would be required. For the Flooring, students would have to calculate the total cost of two cases and then subtract from 100: Flooring Calculations. For the Light, students would have to take into consideration a $5 coupon: Light Calculations. Most students completed the first steps using mental math. 

Subtracting From $1000 

To gradually increase the complexity of tasks, we then purchased Shower Doors, a Vanity, and a Bath Tub, each time using a thousand dollar bill. Here are examples of student calculations: 1000-286. and 1000-729.. Some students even Showed All Calculations on their white boards! 

Determining the Total Left Over

After purchasing our final remodel item, students immediately went to work finding the amount of money left over. Some students subtracted each amount left over from $3,600 (our original budgeted amount). Others added all of the left over amounts together. Some students also calculated as we solved each problem while others waited until the end to solve. Also, some students immediately wanted to get a calculator out. I asked them to first solve the problem on their white boards and then to use the calculator as a tool to check their work. About half of the students arrived at the correct answer: $1,733 extra! 

Student Practice

50 minutes

For our student practice time, I wanted to continue increasing the complexity of the tasks. Instead of subtracting from 100 or 1000, I wanted students to apply the "subtract from nines" strategy using numbers such as 6,005. So I provided students with a Practice Page from CommonCoreSheets.com

I began by modeling the first three problems (Problem #1Problem #2, and Problem #3) while students completed these problems on their own papers. Then, students continued working with partners. I simply asked students to work with students within their groups as I have students strategically seated throughout the room already. 

During this time, I conferenced with students, checked for understanding, and asked probing questions: 

  • How is this strategy helpful to you?
  • Have you figured out any tricks?
  • Have you found any mistakes that are easy to make? 
  • How might this strategy help you in real life?

 

Other times, I encouraged student-to-student collaboration instead of teacher-stduent collaboration: 90,006-15,630.