Cluster: Extend understanding of fraction equivalence and ordering 4.NF.2 Compare two fractions with different numerators and different denominators, e.g. by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols <, >, =, and justify the conclusion, e.g. by using a visual fraction model. Knowledge Targets “I Can” Statements Standard Interpretations Benchmark fractions include common fractions Recognize fractions as being greater than, I can compare two fractions with between 0 and 1 such as halves, thirds, fourths, less than, or equal to other fractions. different numerators and different fifths, sixths, eighths, tenths, twelfths, and Record comparison results with symbols: <, denominators by creating common hundredths. >, = denominators or numerators or by Use benchmark fractions such as ½ for comparing them to a benchmark Fractions can be compared using benchmarks, common denominators, or common numerators. comparison purposes. fraction like ½ Symbols used to describe comparisons include <, Make comparisons based on parts of the I can recognize that comparisons of >, =. same whole. fractions are valid only when the Reasoning Targets two fractions refer to the same Fractions may be compared using as a benchmark. whole Compare two fractions with different numerators, e.g. by comparing to a I can compare fractions using Possible student thinking by using benchmarks: symbols and support the benchmark fraction such as ½. is smaller than because when 1 whole comparison by using models Compare two fractions with different is cut into 8 pieces, the pieces are denominators, e.g. by creating common much smaller than when 1 whole is cut into 2 pieces. denominators, or by comparing to a benchmark fraction such as ½. Possible student thinking by creating common Justify the results of a comparison of two denominators: > because = and > fractions, e.g. by using a visual fraction model. Fractions with common denominators may be compared using the numerators as a guide. < < Fractions with common numerators may be compared and ordered using the denominators as a guide. < <
Cluster: Extend understanding of fraction equivalence and ordering 4.NF.2 Compare two fractions with different numerators and different denominators, e.g. by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols <, >, =, and justify the conclusion, e.g. by using a visual fraction model. Knowledge Targets “I Can” Statements Standard Interpretations Recognize fractions as being greater than, less than, or equal to other fractions. Record comparison results with symbols: <, >, = Use benchmark fractions such as ½ for comparison purposes. Make comparisons based on parts of the same whole. I can compare two fractions with different numerators and different denominators by creating common denominators or numerators or by comparing them to a benchmark fraction like ½ I can recognize that comparisons of fractions are valid only when the two fractions refer to the same whole I can compare fractions using symbols and support the comparison by using models Benchmark fractions include common fractions between 0 and 1 such as halves, thirds, fourths, fifths, sixths, eighths, tenths, twelfths, and hundredths. Fractions can be compared using benchmarks, common denominators, or common numerators. Symbols used to describe comparisons include <, >, =. Fractions may be compared using as a benchmark. Possible student thinking by using benchmarks: is smaller than because when 1 whole is cut into 8 pieces, the pieces are much smaller than when 1 whole is cut into 2 pieces. Possible student thinking by creating common denominators: > because = and > Fractions with common denominators may be compared using the numerators as a guide. < < Fractions with common numerators may be compared and ordered using the denominators as a guide. < < Reasoning Targets Compare two fractions with different numerators, e.g. by comparing to a benchmark fraction such as ½. Compare two fractions with different denominators, e.g. by creating common denominators, or by comparing to a benchmark fraction such as ½. Justify the results of a comparison of two fractions, e.g. by using a visual fraction model.