Benchmark fractions

Learning Objectives Identify the benchmark fractions 0, 1/2, and 1 on a number line. Determine if a given fraction is less than, equal to, or greater than 1/2. Compare two fractions by reasoning about their position relative to the benchmark of 1/2. Compare two fractions with the same numerator or denominator by reasoning about their distance from the benchmarks 0 or 1. Use the symbols <, >, and = to correctly record the results of fraction comparisons. Explain their comparison strategy using the language of benchmark fractions. Would you rather have 1/3 of a giant cookie or 5/6 of it? 🍪 Using special 'benchmark' fractions can help you choose the bigger piece every time! In this lesson, you will learn about special, easy-to-picture fractions called benchmar...

TermDefinitionExample Benchmark FractionA common, easy-to-understand fraction that you can use to measure or compare other fractions. The most important benchmarks for Grade 3 are 0, 1/2, and 1.To compare 4/10, you can think, 'I know 5/10 is 1/2, so 4/10 must be a little less than the benchmark 1/2.' FractionA number that shows a part of a whole or a part of a group. It has a numerator (top) and a denominator (bottom).The fraction 3/4 means we have 3 parts out of a whole that is split into 4 equal parts. NumeratorThe top number in a fraction. It tells you how many equal parts you have.In the fraction 5/8, the numerator is 5. DenominatorThe bottom number in a fraction. It tells you how many equal parts the whole is divided into.In the fraction 5/8, the denominator is 8. Equivalen...

The 'Compare to 1/2' Rule For a fraction \frac{a}{b}: If a < (b ÷ 2), then \frac{a}{b} < \frac{1}{2}. If a > (b ÷ 2), then \frac{a}{b} > \frac{1}{2}. If a = (b ÷ 2), then \frac{a}{b} = \frac{1}{2}. Use this rule to quickly check if a fraction is smaller or larger than one-half. First, find half of the denominator. Then, compare the numerator to that number. The 'Distance from 1' Rule To compare two fractions close to 1, like \frac{7}{8} and \frac{9}{10}, find the 'missing piece' for each. The fraction with the smaller missing piece is the larger fraction. This is useful when both fractions are greater than 1/2. For 7/8, the missing piece is 1/8. For 9/10, the missing piece is 1/10. Since 1/10 is smaller than 1/8, 9/10 is closer to 1...