The student recognizes, identifies, and names equivalent fractions and decimals without concrete or pictorial models. The student recognizes, identifies, and names equivalent fractions and decimals with concrete or pictorial models. 75 would appear at the same point on a number line, take up the same amount of space on an area model, and be shown similarly in a set or measurement model. Naming an equivalent fraction and decimal means that the quantities are the same even though they are represented differently. For example, although one can use division with the fraction to find the decimal equivalent, another way is to find an equivalent decimal fraction with 10 or 100 in the denominator to find the decimal equivalent (e.g. 16 of Van de Walle text) are useful models to connect decimals and fractions as one moves beyond common fractions to continue the development of fraction-decimal equivalence (Van de Walle et al., 2018).Īny number can be represented in an infinite number of ways that have the same value (Charles, p.10).ĭecimal to fraction equivalents can be named not just through procedures but through sense-making with our base-ten system (e.g. A double number line, decimal grids, and rational numbers wheel (see chap. For example using a decimal grid and shading ½ and 50/100=. Students should begin to identify equivalence among fractions and decimals starting with common fractions such as halves, thirds, fourths and eighths as decimal fractions. How would your answer change if you rounded to a different place value? What do you look at when rounding to the nearest tenth? To the nearest hundredth? To the nearest whole number? How did you decide which location to round to on your number line? Why did you decide to round in that direction? How did you determine the relative location of your decimal? How did you determine the start, end, and midpoint of your number line? The student determines numbers that round or do not round to a given benchmark. In other words, the student can determine the consecutive whole numbers/tenths/hundredths between which a given number lies. The student locates a number on the number line, determines the closest multiples of whole numbers, tenths, or hundredths that it lies in between, and identifies which it is closer to. The student uses a number line to round a decimal. The student uses base-10 models to support their reasoning for rounding. The student writes the decimal quantity accurately, placing the decimal point correctly. For example 5.65 lies between 5.6 and 5.7 as well as whole numbers 5 and 6. This number may be read as “zero and one hundred twenty-five thousandths” or as “one hundred twenty-five thousandths.”Ī decimal number lies between other decimal places and/or whole numbers. In mathematics, decimals can be written correctly by remembering that any decimal less than one can include a leading zero (e.g., 0.125). Place values extend infinitely in two directions from a decimal point. This ability to rename and decompose decimals can help students round to the nearest whole number, tenth or hundredth.Ī decimal point separates the whole number and decimal places. 57 as 5 tenths and 7 hundredths as well as 57 hundredths (Common Core Standards Writing Team, 2019, p. For example, it is important to deepen understanding and fluency with decimals in the different forms, seeing. The base-ten system helps students see a relationship between adjacent place values which in turn helps them compare decimals and thus supports their ability to round them.
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