By A. Ya. Khinchin

Elementary-level textual content by way of famous Soviet mathematician deals extraordinary advent to positive-integral components of conception of endured fractions. homes of the gear, illustration of numbers through endured fractions, extra.

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Extra resources for Continued Fractions

Sample text

25500500 < 25500400; 865328 > 865000 Insert a digit in the square so that these numbers are in increasing order: 32,249,677 32,2 □ 9,687 32,299,637 Make these true: 372 > 3 □ 3, 11111 > 1111 □ Are these true? 400 - 205 = 450 - 250; 1320 x 10 < 1320 ^ 10 Compare: 420 - 6 and 420 ^ 60; 1400 - 685 and 1400 - 554 Summary and Comments. There is evidence that children can quite easily discover the rules for ordering whole numbers (Sowder & Wheeler, 1987). It would therefore seem pedagogically sound to allow (and guide) this discovery rather than to give rules.

Is 5 closer to 6 or to 9? , estimate 1,886 -i- 2,491 -i- 2,970 18 SOWDER [Grade 9]). Predictions formulated from Case’s theory of cognitive growth were remarkably accurate. One extrapolation made by the authors is that educators should not to be in too much of a hurry to teach computational estimation, but rather should first focus on number size concepts, on men­ tal computation skills, and on estimation-type problems that do not re­ quire the coordination of complex skills. A fourth grader who can tell whether 352 + 486 is less than or more than 1,000 might not be able to find an estimate of 352 + 486.

28 (10 + 6) = 280 + 25 X 6 + 3 X 6 = 280 + 150 + 18 = 430 + 18 = 448. 28 doubled four times is 56, 112, 224, 448. Exploration of this problem depends on being able to decompose the numbers 28 and 16 in several different ways. Comparing the Sizes of Whole Numbers Comparing two numbers by size begins in Grade 1 in CAPl, where students are given the rule that to compare two two-digit numbers, they need only to compare the tens. The symbols for the relations greater than and less than are introduced in Grade 1, and students compare one- and two-digit numbers.