Geometry
We will begin our Geometry unit shortly. In this unit we will be working on finding perimeter using U.S. standard and metric units. We will find the area of a given shape by counting square units and partial units. We will identify triangles as three-sided closed figures with three vertices and three angles. Our work will also cover identifying right angles and recognizing if angles are larger or smaller than right angles. Geometry is a topic that has a large amount of vocabulary for us to learn and use. Working on this unit this early in the year will give us more time for review and practice.
Addition & Subtraction
We are completing our unit on addition and subtraction. Students expanded their work in place value to adding and subtracting 3 digit numbers, reaching into 4 digit numbers. Our work focused on clear ways to show how we combine or break apart numbers. Students have worked with using a series of equations to add numbers together and used a number line. Most of our work with subtraction has been with a number line or adding on to the known addend to reach the total (finding the missing addend). The number line has been a very powerful tool for us to cross over those tricky or confusing points in our work.
It is important to note that we are not focused on learning the traditional algorithm at this time. The tradtional algorithm is when we stack numbers and carry the tens or hundreds into the next column. In subtraction it would the borrowing that we were all taught to do when we were in school. Our current way of working requires a solid understand of place value, and we will only move on to the algorithm when students show they have the readiness skills for it. Long ago we did teach the algorithm much quicker and students often didn't truly understand why they were borrowing or carrying and it really limited their thinking mathematically. Students are truly showing deeper thinking about numbers and are capable to doing incredible mental math with our more in depth approach.
We will continue to reinforce and practice our work with addition and subtraction for the rest of the year. So while this unit is "official" finishing our practice is not. We will expand into working with 4 digit numbers as we become stronger in our work. We are constantly reviewing the work we done all year long.
Place Value & Graphing
We have been focused on working with two and some three digit numbers and recognizing the value of each digit within a number. Students have also worked on different ways to represent the same number. For example, they have shown multiple ways to show the number 137 by using one hundred, three tens, and seven ones. They know they could do with one hundred, two tens, and seventeen ones. Understanding these different ways to represent the same number is the foundation for our later work with addition or subtraction that requires regrouping (the borrowing or trading technique from when we were in school).
We have worked heavily with addition and subtraction with two digit numbers with a strong focus on how we found our answers. Students could show their thinking (their work) with pictures, equations, or number lines. We are working to find more efficient ways than using pictures. As we work with larger numbers, heading towards 4 digit numbers, we do not want to be bogged down with drawing large numbers. Students are transitioning to more efficient methods. We have also focused on writing equations that match the problem. This means we are showing our understanding of what the problem is asking of us. At this point in our work, most of our subtraction problems are written as addition equations with a missing addend. For example, 100 - 25 = ____ if often written as 25 + ___ = 100. Later, students will become more fluent with using either equation.
An interesting note about equations! Two of Muddy Brook's teachers (Jessic Redman, 4th grade and Mary Berle, 3rd grade) are part of a state committee to work on the math MCAS. We have learned that the state is not accepting the vertical alignment of numbers as an equation. It could be a strategy to work with numbers; however, if a problem asks for an equation to be written it must be written horizontally. We have carried over this expectation in our classrooms in effort to better prepare students for both the MCAS and their future in math.
We have been working with pictographs and line plots. Pictographs can be challenging because students often forget to look at the key to see what the value is of each picture used in the graphing. Pictographs usually use one picture to represent 2, 5, or 10 items in 3rd grade. The value of the picture is not limited to those numbers, it just the common place for our work at this age. Line plots are a way to graph numerical data. We have collected data on how many pockets we were wearing on a given day, then taken that data and displayed it in a line plot. The line plot allows us to analyze the data more easily because the data in organized sequentially and visually. The challenge is in using precise, accurate language to describe the data.
Math Fact Practice!We began the year reviewing our addition facts. Many students will be finishing their review and will begin the process of memorizing their subtraction facts. Some children master their facts much easier than others. For those who have to work harder, it is important that time is spent working on this. I highly recommend the use of flash cards or some math games to do so. Many families just use the worksheets we quiz with. This is not the better route; students can end up memorizing the sequence of answers instead of the facts themselves. When using flash cards or math games, there is no repetitive order; thus, more of a focus on memorizing the fact. The sequence of memorization of addition facts (and subtraction) is available on the "Tools to Download" page.
For those of you who have a child that has easily memorized facts do not rush into multiplication facts. We have found in the past that students memorize the facts before they are taught the concept end up struggling with the concept. There is more to multiplication than facts. If you are looking for an alternative until we teach this until you can practice counting by 2s, 3s, 4s, 6s, 7s, 8s, 9s, and so on. This is not the same as memorizing facts but will make the memorizing easier when we are ready.