![]() They may still count by one, instead of by groups of ten or hundreds. When students do not have a solid grasp or understanding of the base-ten number system, it can prevent students from developing sophisticated counting strategies. The numbers of the base-ten system can be added to determine the total value of the number. This is known as the Multiplicative Principle. A 4 in the second position to the right of the decimal point would have the value of 4/100 or 0.04. For example, a four in the second spot to the left of the decimal point would be (10 x 4), or in other words, would have the value of 40. Each position to the right of the decimal point is 1/10the position to the right. Each position to the left is ten times the positional value of the previous position. Starting from the position directly to the right of the decimal point and going left, the value is (1 x the numeral), (10 x the numeral), (100 x the numeral), and so on. The value of a numeral in this system is determined by multiplication. It holds a position when there is nothing to be placed in a particular position. The base-ten numeration system consists of ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and groups numbers into ten. Fingers are very easily assessable as counting tools. No one knows exactly why the number ten was chosen as the base for this system, but it is theorized that it is due to the number of fingers that humans possess. The base-ten numeration system is the system that most of the world uses today. The position to the right would hold up to four of the number before it would then be grouped as numbers of up to four times four, and then groups of four times four times four, and so forth. The base number is how the numbers are grouped. The value of a number is determined by its position. The number of digits in the place-value numeration system is the same number as the base of that system and must include a place-holder. The base of a system is the highest number to which you can count without repeating any previous digit. Place-value numeration systems have limited numbers of digits which need to be repeated in order to represent larger numbers. all whole numbers, integers, or real numbers), give every number represented a unique representation (or at least a standard representation), reflect the algebraic and arithmetic structure of the numbers” (Wikipedia, the free encyclopedia-numeral system). Under ideal circumstances a numeration system will: “represent a useful set of numbers (e.g. Particular symbols used to represent numbers are known as the digits of the system. Otherwise, confusion as to which number was intended would be a frequent occurrence. Each number must be represented by a different symbol. ![]() So, if we as teachers are expected to teach our students about the base-ten number system, what exactly is it and what is the best way to teach it for understanding?Ī numeration system is a way of representing numbers using symbols. It also expects that “In grades 3-5 all students should understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals” (p 148). ![]() SwitchDemoFallThrough shows statements in a switch block that fall through.The National Council of Teachers of Mathematics states that “In prekindergarten through grade 2 all students should use multiple models to develop initial understandings of place value and the base-ten number system” (p. The break statements are necessary because without them, statements in switch blocks fall through: All statements after the matching case label are executed in sequence, regardless of the expression of subsequent case labels, until a break statement is encountered. Control flow continues with the first statement following the switch block. Each break statement terminates the enclosing switch statement. An if-then-else statement can test expressions based on ranges of values or conditions, whereas a switch statement tests expressions based only on a single integer, enumerated value, or String object.Īnother point of interest is the break statement. You could also display the name of the month with if-then-else statements:ĭeciding whether to use if-then-else statements or a switch statement is based on readability and the expression that the statement is testing. The switch statement evaluates its expression, then executes all statements that follow the matching case label. A statement in the switch block can be labeled with one or more case or default labels. The body of a switch statement is known as a switch block. In this case, August is printed to standard output.
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