For our warm up today, I quickly reviewed, whole class:
1. We can round to other place values other than the lead number, but the lead number makes it easier to do the math in our head.
2. We use rounding to check our exact answers and it is important to consider what place value we had rounded to to get a closer figure.
We began by remembering estimating skills to check exact answers for subtraction.
One student asked: If we round to the nearest thousand, does it matter to be so close? I was really happy to see such thinking going on! I think CCSS has started to take hold and that I am starting to see richer discussions as this unit has progressed.
I led the discussion by presenting examples different situations that we have in life with such large numbers and that the size of the number might make a difference if we were spending money like buying a car, improving a home, or living expenses, such as grocery shopping. If we were just estimating how much money to spend at Subway, it wouldn't matter so much. We would use the lead digit only. But, I pointed out that sometimes, we would need to round the hundreds or tens place to arrive at estimated numbers that produced a number which was closer to the exact number.
I moved ahead quickly because I wanted to get them going with picking up on their writing where we left off yesterday. All students were instructed to get out their materials.
Before students start to write, I believe it is a good thing to have a rubric ready so that they completely understand what is expected and also have an opportunity to set goals. Writing about math and math thinking is just about the hardest thing they can write about for my students. I realize it must be taught step by step if they are going to be successful at writing on the Smarter Balance or PARCC tests. My CCSS transitioning students simply are not used to writing at this level.
I created this rubric Estimation Rubric for them on a Google Drive spreadsheet and shared it on their iPad for convenience. I love not having to have the paper that they can lose! I asked them to bring up their Google Drive and check out what I had just sent them. I brought the same document on the Smart Board for reference.
"It looks like a chart!" One student piped in. I knew they were on task. They were so fascinated with the document there was too much chatter about it immediately. One of my students noticed that it was a grading "thing."
"How can you tell?' I asked. He proceeded to tell me that it looked like he needed to score all fours in order to get a good grade.
We proceeded to discuss each and every square so that they understood that it was a goal setting resource. I emphasized that they should aim high and be honest with themselves as they use it to check their writing. I want my students to be proficient at writing about math and I realize that if I don't show them exactly what is expected, they will be lost since it is not like anything they have written before.
Think: To get their minds ready for the writing task, I instructed: Before you begin, I want you to think about your purpose for writing this. Why are you writing this?
I ask this question of my students for every writing piece in language arts, so it is imperative to me that I ask it when writing in math too. If they value the reason for writing, they will write well!
The answers came in correctly: We are writing to tell someone how to estimate. Someone chimed that we were also writing about the "why" about math. I smiled. That is the kind of engagement I wanted to see with writing.
I told them that they were correct! I also told them that I could see the mastery of their rounding standard and fluency in subtraction. I asked them to remember we discussed accurate and precise language. I flipped over to the Smart Board Lesson from the day before. Estimation in Math served as a good resource to help as I asked these questions:
Why is accurate and precise language important in this essay? One student responded that he understood that it was important to use precise words to help other people know that he knew what he was talking about.
What are some accurate words to use? I asked these questions to help them think about focusing on their word choice. We listed: lead number, rounding, nearest, thousands place, estimate, and subtract on the board together. That way, they could see the words as they wrote. I told them I expected to see these words within their explanation. I set the expectation and told them to focus on using their rubric.
Next, we listed on the board the " hows" of estimation in subtraction. Students shared their lists and we created. I wrote "HOW" above this list on the board.
1: Round the numbers you are subtracting to the lead number.
2. Subtract. Subtract the smaller number from the larger. ( Added at last minute.)
3. Your answer is your estimation.
We moved into thinking about how we write about "why" we are estimating this number. I formed a second column next to the HOW list and wrote WHY above in order to compare the two lists. I reminded them that they needed to look at their rubric. Estimation Rubric I directed them to the square: "Explanation of why." We read the first square in that category and they caught on right away.
1. I round to the lead number to help make the number easier to work with.
2. I can subtract these rounded numbers by easily using mental math and my basic facts.
3. I can use this estimated number for a quick understanding of the value and make decisions using this estimated number.
This part is difficult, but so important as we plan further. It is just so foreign yet! I know it will be really tough to move their thinking in this direction.
Can we see how the "how" and "why" are related?. I asked it if they could see how our lists helped us understand how we needed to write. I suggested sentences could be written like: We round the numbers we are subtracting because...
Next, I asked them to write my list of notes in sentences like this: I placed the numbers from the number sentence with the total on top because I will need to subtract the smaller number from it. Second, I rounded the numbers I am subtracting to make them easier to work with. I rounded the numbers to the nearest thousands place, which is the lead number.
And I continued to write the sample list ( plan) in front of them until all the steps of estimating the problem were listed. This direct instruction helps guide them and omits some anxiety. I was hoping it will produce quality math writing!
Who is our audience? I told them that they need to write to their audience and imagine that they are explaining the process to their classmate who doesn't know how to estimate.
Teacher Write Aloud: I proceeded to write the paragraph from the notes as they watched me. I talked about a good opening hook. I was more concerned about them explaining the procedure of estimation than I was about the opening, so I simply wrote: "Estimating a subtraction problem is easy!" as my first sentence. I told them they could use this for their first sentence if they wanted to or something similar. I did this because my students need exact examples of what is expected in an expository paragraph in order to know how to write one.
After my example was done, I asked them to go ahead and use their planned list and write. They could add anything that was on the board into their plan, if it was missing. I reminded them to continually look at their rubric and then put it back up on the SB for a visual reminder.
RTI: Students set to work. I roved around and conferred with them as needed. Three of mybelow grade level achieving students needed conferencing and step by step guidance. I sat a table with them and worked step by step through the process. They were struggling with language and so I worked at starting each step for them as they worked together to produce the same writing plan. Word for word, they were the same when we finished, but they all seemed to understand. I asked them to bring up the rubric on their iPad and we would check each step to see if the procedures were in order, correct and that we had included "why". They could see they were now prepared to write. They went back to their desks to try independently. After 10 minutes passed, they were well on their way to being able to write the paragraph from the revised plan!
After I felt confident that my below grade level achieving students were comfortable, I now had time to work with everyone else.
I worked with individual students conferencing with them on their finished rough copies quickly. I continually had them refer back to the rubric to check spelling reminding them that their goal was a 4 in each category. I asked them to look back at their plan and see if their steps were in order according to their plan. Some struggling student's thought that the plan was a mini paragraph in the first place and simply put their plan sentences together. Student sample work. I guided them to work on making their sentences more interesting. My above grade level achieving students extended their thinking beyond my expectations. A student explains his work very well. He used the inverse to explain how to check his subtraction. I coached him to explain more about the "why" of the process.
I let them write until the end of the period and they were to finish at home. I was confident, because I had roved around the room and been so thorough in my expectations, that they would succeed at whatever level they were at.
I gathered students to talk about how they were feeling about this rigorous assignment. One student said that he knew he really didn't know how to round numbers to the lead number yet because he couldn't explain it, even though he could do it by saying the rounding rhyme and rounding. I explained that he just needed to focus on making sure he was thinking about the "why". I told him I thought that most students were struggling with it. I asked for a show of thumbs. Many thumbs were sideways to indicate that they were struggling.
I asked them to take home their writing and finish with the notes they had and to be sure to check their rubric. The plan for this writing would be to share a few and then place them in our writing working portfolios for future lessons in revision.
I told them how proud I was of their accomplishments. This was the hardest writing they have done! I saw growth in thinking and they all worked hard to prove they understood the rounding standard.
(I will collect them and read them to assess for understanding as well as for the writing standards.)