![]() The discussion above suggests that cubes, counters, or base-ten blocks help students see ideas. In turn, this enables them to easily learn a mental or written method to divide.Ĭlick on the ORIGO ONE video for more about how grouping and sharing mats can be used to model multiplication and division. The process of division on the grouping and sharing mat helps students to visualize and describe a sequence of steps that is logical. So, it is necessary to regroup as shown in the second picture. For this example, students quickly see, that it is not possible to share and give a hundred to each of the 4 groups. In the situation below, the quickest way to share (divide) is to start with the blocks in the hundreds place. In order to reinforce the link between the operations, these graphic organizers are often called “grouping and sharing” mats.Ī grouping and sharing mat is a very useful tool for greater numbers. ![]() Here, a total is shared among 3 groups (equally). The most useful aspect of the grouping mat is the link to division when the “after” picture is rotated. The equivalent size of the smaller groups on the mat implies equality. ![]() In particular, the answer in a multiplication situation is a total that is a result of joining several parts by pushing the counters down. If he tips the 3 bags into an empty basket, how many apples will be in the basket?” The answer can be obtained with counters without a graphic organizer, but with a “grouping mat” like the example pictured below, the before and after features help to show more about the concept. For example, “Jacque had 3 bags with 4 apples in each bag. The first everyday situations that are used to introduce multiplication usually involve equal groups. Multiplication and Division Math Graphic OrganizersĪ graphic organizer also helps to show the relationship between multiplication and division. The “after” picture using the mat helps students see that 6 plus 2 is 8 as well as 8 subtract 2 is 6. More importantly, the cubes on the mat make it much easier to see the connection between subtraction and addition. The 2 dots on the mat that are not covered form the other part. But, using a number mat, the 6 cubes are now on the “8 mat” which shows all of the key features for subtraction. Like the first example, 2 cubes are removed. Students place 8 cubes on the number mat to show the starting amount. All of the features linked to the idea of subtraction are easier to see if a simple graphic organizer, like a number mat, is used. In fact, the focus is solely on the answer rather than the overall idea of subtraction. The second picture does not clearly show a part of any total. However, the second picture above is the usual result and the students see only one number (6 blocks). If the blocks are carefully managed, students can see the total, part, part. Using blocks, students usually begin with 8 blocks, remove 2 blocks and see the 6 blocks that remain. How much money does she now have in her wallet?” If the aim is to build understanding, we want students to see the total, the part that was spent, and the part that remains in the wallet. When the idea of subtraction is taught, blocks are often used to act out the situation. Addition and Subtraction Math Graphic Organizers When these materials are used, there is an assumption that students are seeing the concept or strategy that is the aim of the lesson. Math visual models such as counters, cubes, base-ten blocks, number lines, and a wide range of measurement and geometry materials are now common in elementary classrooms. Part 4: Graphic organizers for math that accelerate learning – this post Part 3: Visual Models in Mathematics: The Importance of a Number Line (Part 3) Part 2: Visual Models in Mathematics: The First Classroom Examples (Part 2) Part 1: Visual Models in Mathematics: The First Images (Part 1) ![]() Read this post and check out the other articles in our series: This article is the last of a four-part series on Visual Models in Mathematics. Graphic organizers build powerful ideas in the mathematics classroom
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