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3.3 TeachingBy the end of grade 2, children should know the basic addition and subtraction combinations, should be fluent in adding two-digit numbers, and should have methods for subtracting two-digit numbers. NCTM Standards 2000, page 33The use of calculators is becoming more common in schools, but the NCTM Standards 2000 recommends that students know the basic addition and multiplication facts for single digit numbers. Discuss some reasons why it is important to know these facts and to be able to do these computations quickly without the use of a calculator. 3.3 Concepts Two students were discussing their lesson on different number bases for positional numeration systems. One student said there is an advantage in using our base ten system because to multiply by ten, just put a zero at the end of the number. The other student said the same thing was true when multiplying by five in base five, eight in base eight, or twelve in base twelve. Give examples in these three bases to show that the second student is correct. Write a general statement about multiplying numbers in base n by the number n. 3.3 Concepts When students leave grade 5, . . . they should be able to solve many problems mentally, to estimate a reasonable result for a problem, . . . and to compute fluently with multidigit whole numbers. NCTM Standards 2000, page 149When estimating the product of two whole numbers by rounding one number up and the other number down, the estimation might be equal to or larger or smaller than the actual product (see section 3.3). Devise a method in these cases, without computing the actual product, for determining if the estimation from rounding is too large or too small. Use the rectangular array model to explain how and why your method works. |