Checking the Reasonableness of Addition
Lesson 3 of 16
Objective: SWBAT round in order to check for reasonableness when adding multi-digit numbers.
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 modeled and encouraged students to experiment with decomposing.
Task 1: 4,283 + 1,429
For the first task, students showed their thinking in a variety of ways: Decomposing, Decomposing 2, and Decomposing 3. However, most students decomposed 4,283 into 4000 +200 + 80 + 3 and 1,429 into 1000 + 400 + 20 + 9. Then, they added the thousands, hundreds, tens, and ones separately.
Task 2: 4,283 - 1,429
The next task was certainly more challenging. For example, students had to figure out how to take 9 ones away from 3 ones. Here's a student who had Problems with Subtraction. After this little conference together, she was then able to explain her thinking using Negative Numbers. Here are other examples of student work: Example A and Example B.
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.
Goal & Vocabulary
I began this lesson by reviewing the goal and key vocabulary from the past two lessons: Fourth graders, over the past couple of days, we have reviewed addition and subtraction. We have also learned to check for reasonableness by rounding numbers and by finding compatible numbers. Today, we are going to continue checking for reasonableness when adding by rounding and finding compatible numbers. But first, I'd like to make sure you are using high-level math vocabulary when you are turning and talking today. We then reviewed the meanings of addend, sum, minuend, subtrahend, difference, checking for reasonableness, and compatible numbers. By teaching math vocabulary, students will have the tools to truly practice MP 3 (Constructing Viable Arguments).
In order to continue teaching the process of checking for reasonableness and provide students with opportunities to put their mathematical reasoning into words, I created a Google Presentation using Google Drive Documents called Checking Addition prior to the lesson. Here are specific directions explaining How to Create a Google Presentation for Student Practice. Next, I was able to share this presentation with students using their student Google email accounts.
Students then copied the shared presentation and saved it in their math folders under the Google Drive. Once all students were successful at copying the presentation and making it their own,we discussed the first slide together, which was the Goal of the lesson: I can check for reasonableness when adding multi-digit numbers. This was also the page that students took ownership of their presentation by adding, "By: First & Last Name." This is important as student ownership always translates into higher motivation and learning.
We then moved on to Slide 2 and Slide 3 and discussed the importance of checking answers for reasonableness. I explained, Sometimes when I buy a couple items at the grocery store, I'll think in my head, "Okay, this item is about $5 and this item is about $3 so the ten dollar bill in my pocket will be a reasonable amount to pay with. Later on, when I pay for my two items, I think, "Okay, $2 would be a reasonable amount to get back because $10-$8 = $2." If the the cashier might accidentally hand me $5 bill. I would immediately know that the amount is unreasonable and that I should say something.
Modeling: Algorithm & Checking for Reasonableness
I then used the Teacher Model Slide to show students how to use the grid to complete the given algorithm. Next, I modeled how to answer the question: Is your answer reasonable? Students were ready to give this a try themselves!
I asked students to continue on to the next slide with me. We solved the algorithm, 50 + 82 together. Students showed their work in their own presentations while I modeled using a projection of my presentation. Then, instead of writing the explanation in paragraph form, we used a bulleted list. It was at this moment that I realized that a bulleted list would better match my students' computer skills. Also, I knew that my students would lose excitement and motivation quickly if expected to write a complete paragraph on each slide!
By asking students to provide an explanation, students would be further developing practice MP 3 (Constructing Viable Arguments).
Assigning partners is always quick and easy as I already have students strategically placed in groups of 4-5 students throughout the room (based on abilities, behavior, communication skills, etc.). I simply divided these larger groups into smaller groups of 2-3 students. During partner work, sometimes students choose to work alone, but they frequently check answers with each other.
Right to Work!
Many students completely understood what to do and got to work right away. Others needed a little more guided practice (in the areas of technology and math). I took this time to roam about the room and provide extra support.
Although the technology seemed to slow students down, I loved watching students take the time necessary to truly think about every step of the algorithm and their explanations: Solving 6050 + 2782.
Here, a student who is often unsure of himself simply needs a little encouragement: Adding 861 + 529. You'll see that there are a few technology struggles, but students quickly adapt. This is a great opportunity to discuss the importance of perseverance (Math Practice 1). He frequently struggles with providing written explanations. However, once I provided with support and encouragement, he was able to complete the explanation on his own, Developing an explanation.
As students completed more and more slides, their computer, math, reasoning, and explanatory skills were noticeably developing. This student explained her thinking beautifully: 600,861+ 429,509.
Here is what a student's completed presentation looked like: Example Student Presentation.