4th Grade Math : Unit #11 - Place Value : Lesson #9

Understanding the Why of Rounding

Objective: SWBAT round multi-digit numbers using a numberline and place value understanding.
Standards: 4.NBT.A.3
Subject(s): Math
60 minutes
1 What do they know? - 10 minutes

*Before Common Core State Standards, rounding was usually taught by teaching students to just manipulate the numbers and then simply using those rounded numbers to estimate. There wasn't much discussion of why we do it that way.

I can hear the words of lessons past: Take the number needing to be rounded and decide if it is 5 greater and round up if it is. If it isn't, keep it the same and put in your zeros. And then maybe there would be a rhyme attached to help the process. Any student could "do" that. We spoke that language focusing on quickly getting them to just "do it!"

Today with all the cute, great ideas online, I believe we have to be careful not to use language that doesn't support CCSS reasoning and thinking. I have learned to look at resources carefully. This rap uses the words "add one". I avoid that language because that is not what is really going on. Students need to know what is really happening mathematically. The number line shows students the correct concept. I stick with that! That is the whole theme of CCSS!

4.NBT.A.3 is simply stated, but contains the words "place value understanding." This opens a whole different approach. "Understanding." It makes a world of difference to what it means to round and being able the to transfer "why" we do it in the real world.

This lesson gets to the heart of understanding by using a number line and then transfers that to the quick method.

Warm up: I started this lesson with getting to the heart of the matter right away!

I wrote the standard on the board, underlining the word "understand."

I also wrote below it: Why do we round numbers? You can expect students in this transitional stage of CCSS to answer you with reasoning of how.

I turned their attention to the Smart Board and revealed the same question.

Rounding Discussion.pdf  This SB resource was our guide:

To integrate math with Social Studies, we got our student atlases out and looked up the population of our state. The multi-digit numbers in populations are a perfect source of mastering rounding multi-digit numbers. It also sheds light on the idea that we do indeed use rounding to talk about and manipulate numbers in an easier way when it is appropriate. Throughout the lesson, I kept bringing that point out very clearly in my language every chance I got to support the standard.

This atlas was written in 2003, so I took the opportunity to show them how to find out when books are published. We talked about how and why numbers in this book are out of date. I always take the opportunity to talk about number sense any chance I get so students can connect. And, it made them aware that publications need to be up to date for correct data.

They wrote the population number in their notebooks. We then looked up the population of Wisconsin online for 2013. I told them that these were exact numbers. (As exact as possible, anyway.)

They noticed right away that there was an increase in population. We stopped and talked about what it would mean if the population had gone down or stayed the same. We talked about what brings people to our state Again, this was a little opportunity to infuse some math sense, data and how it is connected to social studies. I hope you have the same chance for this discussion.

I waited for the silence and then I questioned them verbally to bring the lesson back to the objective and to keep the discussion going: So if someone asked you about how many people live in Wisconsin now, what would you say? I purposely stressed the word "about."

One of my students offered an exact number.  I realized that they aren't quite warmed up in their thinking yet!

 I wrote the question on the board and underlined the word "about" making it clearly visable in hope that it would dawn on them by seeing it.

*What I saw at this point was the revelation of the mastery level from third grade and it clicked. They could agree that it meant it wasn't an "exact" number. They remembered from mastering 3.NBT.A.1 last year! Yes! We were ready for the lesson! CCSS is working!



2 Core Lesson: Using Learnzillion & Practice - 15 minutes

Rationale: Understanding why a number rounds to the number it does is so important for my students to completely understand so that estimation will be a snap. Using a bent number line is a great way to have students understand the direction the number should be rounded. A flat number line works well, but I find that the bend is what helps students see which way the number should "slide"..

Instead of me teaching this from scratch, I use what resources online I can find to switch it up for my students. Sometimes having another voice or video helps reach students in another way. Using online resources is a way of team teaching. So, I have chosen the to use a Learnzillion lesson for this purpose. During this lesson, I stop the video, elaborate on the areas I think I need to fill in. I personally am not in favor of giving this to my students on their iPads and not being actively involved in teaching it through because the student misses the benefit of me showing them the important parts. I use this resource actively in my classroom. I also am fussy about the resource

I think Ginny Baldwin does a fabulous job teaching students about rounding numbers on the number line. I could design a smart board lesson or a Educreations lesson for my students, but feel that this one that she has done is exactly what I would have designed and recorded. 

Key words: benchmark numbers and midpoint. I wrote these key words on the whiteboard before we started our lesson.

I made sure my students were ready to take notes on this Learnzillion lesson in their notebooks.  Through this lesson, I guided my students to be able to connect benchmark numbers and the midpoint to understand why we round in the direction we do. They drew the numberlines and bent the upward to show their midpoints. I had them practice a few more numbers by rounding it through finding the benchmark numbers first, then the midpoint. I had them draw the bent number line that looks like a big hill. The top of the hill is the midpoint. That way they can see how the number will "slide" to the correct benchmark. I love this visual! The students enjoyed this video lesson resource and they stayed on task, writing their numbers and number lines as we went through the process, practiced and practiced again in the notebooks.

 I think the bent number line to mark the mid point is brilliant! Suddenly the number can visually slide to the benchmark number and rounding makes sense! Suddenly students discover it isn't about a "how" but a "why". They see the way the number will tumble.

Differentiation: If my students don't understand what benchmark numbers are, can't put numbers on a numberline and find a midpoint, then I  needed to back up and go through this lesson. It also serves as a great predecessor to rounding. I can also use it as a fix up strategy later and assign it to my lower students.


3 Practice, Process, Thinking and Review - 20 minutes

I began working with them on the Smart Board and have attached it so you can see how the process, although a little crude, went along. The spontaneous choosing numbers and place values to round was a great way to help them connect. I let them make up the numbers, draw the number lines and I brought forth my lower students to help lead this discussion, making it very hands on instruction. They didn't realize they were being taught because they constructed the practice, with my guidance.

One student saw a pattern and shared. We put it on the Smart Board file under Victor's Idea. Victor noticed that when we round to the tens place, the midpoint has a five in the tens place. If we round to the hundreds place, the five is in the hundreds place, and so forth. I thought it was great that he could see the pattern so students could understand how to set up their midpoints. He made use of understanding structure and patterns.

I didn't even think about this pattern as being a significant point! So when we allow our students to be leaders and help us teach, great things happen! We sometimes learn from them!

We practiced this method for awhile before I introduced the "quick method", using the rhyme and based on "how" to round.

 I then introduced the Take your number..., went back through their created slides and underlined and circled. Some teachers have students draw an arrow. I left it out this time and I think maybe it is better to put it in as well. It gives students direction, but it is too much for some learners. Use your discretion.

Also, as I taught the rhyme: Take your number..., I went back to: Remember why? They chimed in about benchmark numbers and midpoints over and over. It works!

Now, we are mastering the "understanding" part of our standard!

I used the second Smart Board File for a full review and an introduction to estimation to set them up for the next lesson. It was really fun to move the shapes over the answers to reveal them. I highly suggest copying this file to use in class.

4 Assignment IXL or Paper? - 15 minutes

I assigned IXL online  (A.6 Rounding). They must write it all on paper. I know it's a good idea that students copy the rounding exercise on paper, underlining and circling their numbers, or drawing a number line to round showing the benchmarks and midpoints. This way, they prove they understand. Even with the technology paperless driven assignments, students need that paper and pencil experience to strengthen this skill.

Tip: I make sure my students highlight the place value word in the direction and the digit that needs to be rounded. That way, they become conscientious of what they are working with.Highlight those place values!



Developing a Conceptual Understanding

This lesson brings the CCSS to fruition beautifully by getting kids to really understand rounding starting with that bent number line!. The visual of the number line really did that for my students. My student's remarks about the patterns he saw in rounding as place values progressed amazed me! I was so excited to see a student come forth with such thought! Before CCSS, we did not have this thinking process going on in our classroom. It was more like a production line...repeating what I did and not understanding why numbers rounded to the benchmark.

It is wonderful. What a great place to be in our teaching! I find a lot of joy in seeing them truly understand what they are doing and why. This complete absorption of understanding is so rewarding.

My lower end students struggled a little, but with a little extra guidance and that interactive Smart Board lesson, it really tied up their loose ends in understanding. The continual repetition of the bent number line helped them see. Using Victor's idea of the patterns of where the five occurs helped them remember what place value they were rounding to. I tried to focus on the midpoint first with some of them to see if it cleared up their issues with which direction the number would "slide" on the number line, and it worked for two of my students. The other two need more practice.

Overall, I am very pleased with their progress and look forward to teaching them about estimation next! I think it will be easy now!