We then looked at the unit test and decided that we could do it in the traditional way, but no other. That helped set the goal for the day which was learning new ways to solve addition and subtraction problems.
We read and reviewed the mathematical goals in this unit.
In Investigation 1, we worked on place value and adding and subtracting multiples of 10, 100, and 100. Teachers made 1000 books and we talked about out strategies in naming the pages. We expect the students to experience some confusion with this because the numbers that start with 100, such as 134, are on the second page, also called the 200 page. The emphasis is on the students developing and refining strategies for finding numbers efficiently using benchmarks. We played the game Changing Places which adds and subtracts multiples of 10 and 100 from a number students choose. When we worked on the session How Many Miles, we practiced using the number line ourselves. This is usually introduced and used in second and third grade, but we are new to Investigations so the students are unfamiliar with it. We discussed the problems students have with thte US standard algorithm, and generally agreed that the open number line was a useful tool for the kids to have in their repetoire. We then planned Investigation 1 to include: math content, routine, focus question(s), questions to guide student learning, potential problems, and ongoing assesment.
Before we went on to Investigation 2, we spent time looking at the different types of addition strategies. Our goal is that students are able to solve a problem in two different ways using these strategies. These included: breaking the numbers apart, and changing the numbers. We practiced these strategies because we need to be proficient so that our kids may become proficient. We looked at the extended algorithm as a way of fostering understanding of the US Standard Algorithm. Many students want to use the US Algorithm even though they are continually wrong. We will promote use of the new strategies by requiring the students to solve problems two ways. When students are consistently using the US Algorithm incorrectly, we will encourage them to use two other strategies until they understand what is happening in addition and subtraction. We read the Teacher Note: Addition Strategies. Teachers found this a helpful reference that they could go back to when the reached Investigation 2. We also practiced using starter problems in addition. This was an unfamiliar strategy for the teachers, but they understood it quickly after we did a few problems. We played Close to 1000, and looked at strategies to improve students in mental math compution. We discovered that starting from the hundreds place was more helpful than trying to do the algorithm in our heads. We also looked for combinations of nine and ten to further proficiency. I proposed that they get the directions to Close to 100 to do first. Close to 100 could be a good intervention for struggling students.We planned Investigation 2. Session 2.4 reintroduced the US Algorithm with the intent that students learn it using the values of the numbers rather than a procedure. However, we still want students to solve problems two ways.
We spent a rather short amount of time on Investigation 3. Many of the sessions were similar to those in Investigation 1, but used numbers in the thousands. We had a discussion about how to construct the 10,000s chart and where to put it in the room. It needs to be displayed as it is used in other lessons.
We then spent a significant amount of time looking at, dissecting and practicing strategies for subtraction. These included subtracting in parts, adding up and subtracting back, (often using the number line) changing the numbers and subtracting by place. In our experience, the US Algorithm for subtraction is very confusing for students. We talked about typical errors that students might make and what questions we could ask, and what strategies we could suggest instead so that students could understand what was happening in subtraction. We read Teacher Note: Subtraction Strategies.
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| Subtracting back |
We looked at our Ten Minute Math piece. We are familiar with Broken Calculator and many of the teachers reported that it is improving student mathematical fluency. Practicing Place Value is a new routine. In it, students practice reading, writing and saying numbers. Then they add multiples of ten, one hundred and one thousand to a given number. We recognize that this routine prepares students for math that comes later in the unit.
We finished with a quick look at three types of subtraction problems:
Removal:
There were six ice cream bars in the refrigerator. My brother ate four. How many are left for me?
Comparison:
My snake is 16 inches long. Michael's snake is 10 inches long. How much longer is my snake?
Missing part:
There were six ice cream bars in the refrigerator. My brother ate some. There are two left. How many did he eat?
The consensus was that the most valuable part of the day was learning and using the new addition and subtraction strategies. I hope you do well implementing in your class and please post any questions to the blog.
Thank you for your participation on Tuesday and I look forward to our next meeting.
