Understand a fraction 1/𝑏 𝐚𝐬 𝐭𝐡𝐞 𝐪𝐮𝐚𝐧𝐭𝐢𝐭𝐲 𝐟𝐨𝐫𝐦𝐞𝐝 𝐛𝐲 𝟏 𝐩𝐚𝐫𝐭 𝐰𝐡𝐞𝐧 𝐚 𝐰𝐡𝐨𝐥𝐞 𝐢𝐬 𝐩𝐚𝐫𝐭𝐢𝐭𝐢𝐨𝐧𝐞𝐝 𝐢𝐧𝐭𝐨 𝒃 𝐞𝐪𝐮𝐚𝐥 𝐩𝐚𝐫𝐭𝐬 (𝐮𝐧𝐢𝐭 𝐟𝐫𝐚𝐜𝐭𝐢𝐨𝐧); 𝐮𝐧𝐝𝐞𝐫𝐬𝐭𝐚𝐧𝐝 𝐚 𝐟𝐫𝐚𝐜𝐭𝐢𝐨𝐧 𝑎/𝑏 𝐚𝐬 𝐭𝐡𝐞 𝐪𝐮𝐚𝐧𝐭𝐢𝐭𝐲 𝐟𝐨𝐫𝐦𝐞𝐝 𝐛𝐲 𝒂 𝐩𝐚𝐫𝐭𝐬 𝐨𝐟 𝐬𝐢𝐳𝐞 1/𝑏 . 𝑭𝒐𝒓 𝒆𝒙𝒂𝒎𝒑𝒍𝒆, 3/4 𝒎𝒆𝒂𝒏𝒔 𝒕𝒉𝒆𝒓𝒆 𝒂𝒓𝒆 𝒕𝒉𝒓𝒆𝒆 1/4 𝒑𝒂𝒓𝒕𝒔, 𝒔𝒐 3/4 = 1/4 + 1/4 + 1/4 .

Understand a fraction as a number on the number line; represent fractions on a number line diagram. a. Represent a fraction 1/𝑏 𝐨𝐧 𝐚 𝐧𝐮𝐦𝐛𝐞𝐫 𝐥𝐢𝐧𝐞 𝐝𝐢𝐚𝐠𝐫𝐚𝐦 𝐛𝐲 𝐝𝐞𝐟𝐢𝐧𝐢𝐧𝐠 𝐭𝐡𝐞 𝐢𝐧𝐭𝐞𝐫𝐯𝐚𝐥 𝐟𝐫𝐨𝐦 𝟎 𝐭𝐨 𝟏 𝐚𝐬 𝐭𝐡𝐞 𝐰𝐡𝐨𝐥𝐞 𝐚𝐧𝐝 𝐩𝐚𝐫𝐭𝐢𝐭𝐢𝐨𝐧𝐢𝐧𝐠 𝐢𝐭 𝐢𝐧𝐭𝐨 𝒃 𝐞𝐪𝐮𝐚𝐥 𝐩𝐚𝐫𝐭𝐬.𝐑𝐞𝐜𝐨𝐠𝐧𝐢𝐳𝐞 𝐭𝐡𝐚𝐭 𝐞𝐚𝐜𝐡 𝐩𝐚𝐫𝐭 𝐡𝐚𝐬 𝐬𝐢𝐳𝐞 1/𝑏 . 𝐑𝐞𝐜𝐨𝐠𝐧𝐢𝐳𝐞 𝐭𝐡𝐚𝐭 𝐚 𝐮𝐧𝐢𝐭 𝐟𝐫𝐚𝐜𝐭𝐢𝐨𝐧 1/𝑏 𝐢𝐬 𝐥𝐨𝐜𝐚𝐭𝐞𝐝 1/𝑏 whole unit from 0 on the number line.

Represent a non-unit fraction 𝑎/𝑏 𝐨𝐧 𝐚 𝐧𝐮𝐦𝐛𝐞𝐫 𝐥𝐢𝐧𝐞 𝐝𝐢𝐚𝐠𝐫𝐚𝐦 𝐛𝐲 𝐦𝐚𝐫𝐤𝐢𝐧𝐠 𝐨𝐟𝐟 𝒂 𝐥𝐞𝐧𝐠𝐭𝐡𝐬 𝐨𝐟 1/𝑏 (𝐮𝐧𝐢𝐭 𝐟𝐫𝐚𝐜𝐭𝐢𝐨𝐧𝐬) 𝐟𝐫𝐨𝐦 𝟎.𝐑𝐞𝐜𝐨𝐠𝐧𝐢𝐳𝐞 𝐭𝐡𝐚𝐭 𝐭𝐡𝐞 𝐫𝐞𝐬𝐮𝐥𝐭𝐢𝐧𝐠 𝐢𝐧𝐭𝐞𝐫𝐯𝐚𝐥 𝐡𝐚𝐬 𝐬𝐢𝐳𝐞 𝑎/𝑏 𝐚𝐧𝐝 𝐭𝐡𝐚𝐭 𝐢𝐭𝐬 𝐞𝐧𝐝𝐩𝐨𝐢𝐧𝐭 𝐥𝐨𝐜𝐚𝐭𝐞𝐬 𝐭𝐡𝐞 𝐧𝐨𝐧 − 𝐮𝐧𝐢𝐭 𝐟𝐫𝐚𝐜𝐭𝐢𝐨𝐧 𝑎/𝑏 on the number line.

Explain equivalence of fractions through reasoning with visual fraction models. Compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

Recognize and generate simple equivalent fractions with denominators of 2, 3, 4, 6, and 8, e.g., 1/2 = 2/4 , 4/6 = 2/3 . Explain why the fractions are equivalent, e.g., by using a visual fraction model.

Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 6/2 (𝟑 𝒘𝒉𝒐𝒍𝒆𝒔 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝒔𝒊𝒙 𝒉𝒂𝒍𝒗𝒆𝒔); 𝒓𝒆𝒄𝒐𝒈𝒏𝒊𝒛𝒆 𝒕𝒉𝒂𝒕 3/1 = 𝟑; 𝒍𝒐𝒄𝒂𝒕𝒆 4/4 and 1 at the same point of a number line diagram.

Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model

Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units – whole numbers, halves, or quarters.