Observe a mathematical concept being reviewed, taught, or practiced in your classroom. Please describe it in detail, or add a picture of it here. Explain the five different modes in which a mathematics concept may be represented and give an example of each for the concept you have observed in your lab classroom.

The mathematical concept currently being taught in Mrs. Cook’s 2nd grade classroom is place value. The students are expected to know that the three separate digits of a three-digit number represents the amount in hundreds, tens, and ones. For example, 482 equals 4 hundreds, 8 tens, and 2 ones. The children are also expected read and write numbers up to 1,000 using base-ten numerals, number names, and expanded form. With the use of drawings or objects, students must further their understanding of the knowledge by explaining why addition and subtracting strategies work using place value.

An example piece of work that the students had in their Math folders was a matching worksheet that required the students to pair a written numeral to its corresponding number. On one side of the sheet you could find *seven thousand, four hundred seventy-three * or *four thousand, seven hundred seventy-seven. *On the other side you could find 7,473 and 4,777.

Mathematical concepts can be represented in a variety of ways. A representation may be visible (a number sentence, display, or graph), or strictly an internal form of thinking carried out by an individual.

Written Symbols – A written symbol is a certain character or mark used to designate something. With place value, there isn’t a specific written symbol that is used, however I have come up with a few that could possibly be used to assist in understanding. The thousands place could be abbreviated (th), or four separate lines can be drawn (_ _ _ _). The same goes for the hundreds place (h) (_ _ _), tens place (t) (_ _), and ones (o) (_).

Pictures – Pictures are similar to manipulative models but lack the actual color/texture/size. In Mrs. Cook’s classroom, pictures are frequently used for place value with the use of worksheets and white board work. Cubes

Manipulative Models – Manipulative models are are significant for visual learners. Using cubes, students are able to either use a mat or simply use their imagination and a flat surface to create numbers using place value.

Oral Language – Oral language is important because not always are we handed problems written on paper. Oral language can be related to real world situations even. By stating a number and requiring students to write the number down in numerals, they are learning to think of the number in the minds and determine the number without the use of objects which may not always be available.