Prep for CCSS Assessments: Explaining Estimation in Writing Part 1

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SWBAT show understanding of place value through writing about rounding and estimation.

Big Idea

Integration of Math and Writing: Students will plan a thorough explanation of how they solved a subtraction problem involving estimation as they prepare for CCSS tests.

Warm up.

10 minutes

We warmed up today by gathering around the Smart Board to review concepts of place value and tens. I simply picked a few random expressions involving multiplying by 10's to get them going.

I asked what 30 x 10 was. I got the right response from about half to the class.  I kept them moving in their thinking and reasoning with multiples of tens using 30 to practice mental math. I asked what 10x10 was to shift gears for those students who looked a little dazed at this point. This familiar factor pair brought them all back because everyone shouted 100! I said: So what's 12x10. One boy said 200. Oops. Something is missing here.

To redirect, I went to the white board and started to diagram the patterns of tens. Another student shared the idea that another zero was "added", I simply corrected the language to say; "You don't really mean added do you? I think you mean that the zero becomes the placeholder for the idea that the number has just been grouped by tens. Knowing that, if we have 12 groups of tens, we can't have 200"... I got interrupted by the boy and he said, "No, that would be 20 groups...its 200." 

To continue: I pointed to my series of 30 x10, 30 x100, 30 x 1000 etc on the board and asked: What do these zeros do? One boy's hand shot up. "The zero holds the place for all the other places!"

My last opening question was:  Do you realize, that 10 is 10x the ones place? 100 is 10x the tens place? ( I was addressing standard 4.NBT.A.1)

 I told them that Zero is my Hero! and played the clip from Multiplication Rock on my Smart Board.

Plan Like This: Teacher Think Aloud

20 minutes

To bridge the movie topic over to starting my lesson, I asked: What do zeros mean when we round a number?  I continued very smoothly by connecting the idea of zeros being placeholders to talking about how the zeros work in rounding.  I complimented the student who explained what zeros mean. I told them that we were going to write a piece that explained rounding in estimation using subtraction. It was time for me to reveal the Smart Board Lesson Writing in Math and opened with the questions on the first page. I chose a note taker for the board as we discussed each question. I was happy to hear them connect their sentence types they had been learning in language arts. One interesting point arose with two of my students.  They pointed out that describing and explaining were different, but describing was part of explaining. 

I explained that Common Core Writing standards expected us to be able to explain procedures and write well in every subject. The second slide helped us discuss why this was important. We listed a few good reasons why we need to write explanations well and moved on. The third slide got us to the meat of the lesson, but it was very important to me to set up their thinking carefully.  If I could get them to value the writing, even those who struggle would do well. I pointed out that we had talked about audience and author's purpose for writing. What would be our purpose?

When I turned to the third slide, it funneled their thinking into the purpose of writing the problem listed. My question was: What is our purpose as authors to write a procedure? Many of them could pinpoint that it was to explain how to do something. 

I told them that good expository writing explains how to do something needs to also explain why. Explaining why gives meaning to the procedure. I told them that people will remember the procedure if they understand why they are doing it. 

We talked about the many times in this past unit we were expected to explain why; why we regroup, why we line up numbers to add and subtract, why we round to the nearest benchmark number, etc. A lot of examples were offered up, and I explained that just the how would not be enough. I told them that their writing needed to tell why as well.

We read the problem together and turned to the fourth slide. I chose to use a simple subtraction problem because it was quick. There weren't too many steps. Then, we discussed the past strategies we had learned and put our number sentence on the page to examine our thinking. Would any of the strategies help us explain? 

One student said he liked the Start, Change and Result strategy because it set up the solution in his mind. He said he knew where to put the numbers in the equation right away. Another student liked the KWS and making the equation right away. He said he would use a variable. We all decided that the math mountain was not as effective. It didn't get our minds wrapped around an explanation very well. I told them that next we would make a list of the procedure for subtracting and solving this problem. I turned to the next page to start a list of the procedure. 

We kept going through the slide and decided that a "list method" for a plan fit best. The web is more for description, but I explained that if it was more comfortable,  they should please feel free to  use it. 

* If you look at Start, Change and Result strategy, students can easily see where numbers go in the equation and won't confuse the order of the numbers in the algorithm. It sets them up for good thinking about equations. I really like it!




The Task: We Plan Our Writing First

20 minutes

I turned to the last page of the Smart Board Lesson. We read it together. A student passed out the attached worksheet: Estimate the following equation. I told them that I expected them to be able to plan their explanation about estimating the problem. That is All we will do today! 

We went over the steps of estimation in subtraction.  If they could not remember how to estimate a subtraction problem, they needed to look up their notes from the lesson last week and review them. They had the tools to review independently. Most of them were able to do that on their own and it helped them to see that note taking from days before served as a tool today.

I announced that when the plan was done, they should show me. I had to approve their plan before they could write! This way, I can be sure they have set themselves up for a good foundation to write from. I conferred with students and helped them to work on improvement.

Through one on one reviews, it was revealed that they needed guidance in planning to write. I referred back to the Smart Board list once again. I told those struggling:Lets make a list that starts with " First, I do this...because... "For example: " First,  I round the lead number because it makes the numbers more simple to subtract."

Suddenly plans looked better! Conferring one on one helped them to plan and get over the hurdle of thinking the steps through in their mind first.  Student example of first attempt to improve plan shows how this progress happened.


5 minutes

In our closure time, I asked students what they learned about planning. Several shared that they didn't ever know that they had to plan math writing. They also shared that they have never written a  a math essay. I have the opportunity to forge a new path in a writing experience that has implications on how well they can adjust to the new standardized tests. Finally, I asked them if the planning made them think through estimation,how to do it and why we do each step. They responded with comments about having to think about it. It forced them to think through the process. I told them that tomorrow we would complete the writing lesson.