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5-N-2-3

Page history last edited by Brenda Butz 6 years, 2 months ago

5.N.2.3 Compare and order fractions and decimals, including mixed numbers and fractions less than one, and locate on a number line.

In a Nutshell

This objective requires students to be able to compare and order fractions and decimals, including mixed numbers and fractions less than one. In fourth grade they ordered and compared fractions to fractions, decimals to decimals, and benchmark fractions and decimals. They will now compare and order a combination of decimals and fractions without models and also locate them on a number line.

Student Actions	Teacher Actions
Develop Mathematical Reasoning by discussing and explaining when to convert between fractions and decimals in order to make comparisons more efficiently. Develop the Ability to Make Conjectures, Model, and Generalize when utilizing manipulatives such as unifix cubes, empty number lines, fraction tiles to find equivalent representations of fractions and decimals. Develop the Ability to Communicate Mathematically when discussing solutions by using appropriate mathematics vocabulary. Develop Mathematical Reasoning when making sense of a real world problem by ordering a set of numbers (using number lines, models, representations) that includes fractions, decimals, and mixed numbers	Pose purposeful questions which provide students opportunities to illustrate their thinking. Facilitate meaningful mathematical discourse by urging students to continually evaluate the reasonableness of their results in their work and their peers. Build procedural fluency from conceptual understanding by providing appropriate physical and/or digital tools to represent, explore and deepen student understanding.
Key Understandings	Misconceptions
Compare and order decimals, fractions, and mixed numbers Find appropriate increments between whole numbers to locate decimals, fractions, and mixed numbers on a number line Use benchmark numbers (0,¼, ⅓, ½, ⅔, ¾, 1) to help them compare and order fractions, and mixed numbers Understand place value to help them compare and order decimals Read a number line segment even if it doesn’t show 0	Think that mixed numbers are larger than fractions greater than one because mixed numbers contain a whole number part and whole numbers are larger than fractions EX. 3 ½ > 9/2 Think fractions have to be less than 1 Misapply rules for comparing whole numbers in fraction situations Overgeneralize the idea that “the bigger the denominator, the smaller the part” by ignoring numerators when comparing fractions Not use benchmark numbers like 0, ¼, 1/2, ¾, and 1 to compare fractions because they have restricted their understanding of fractions to part-whole situations and do not think of the fractions as numbers Think that decimals are bigger than fractions because fractions are really small things Misapply rules for comparing whole numbers in decimal situations EX. 0.058 > 0.21 because 58 > 21 or 2.04 > 2.5 because it has more digits Believes that two decimals can always be compared by looking at how many digits they have Misuse the use of zero as a placeholder EX. 1.5 is the same as 1.05 Think that decimals with more digits are smaller because tenths are bigger than hundredths and thousandths EX. .845 is smaller than .5 Think that decimals with more digits are larger because they have more numbers EX. 1,234 is larger than 34 so 0.1234 is larger than 0.34 Mistake applying what they know about fractions EX. 1/204 > 1/240 , so 0.204 > 0.240 Mistake applying what they know about whole numbers EX. 600 > 6, so 0.600 > 0.6 Not use a zero as a placeholder when ordering numbers or finding numbers