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5-N-2-4

Page history last edited by Christine Koerner 4 years, 3 months ago

5.N.2.4 Recognize and generate equivalent decimals, fractions, mixed numbers, and fractions less than one in various contexts.


In a Nutshell

This objective requires students to be able to recognize and generate equivalent decimals, fractions (greater than one,) mixed numbers, and fractions less than one.  Not only will they be required to do this within the same form (ex. Decimal to decimal, mixed number to mixed number,) they will be required to find equivalents across forms (ex. Decimal to fraction.)  In fourth grade they find equivalents within the same form by using models, so in fifth grade we will expand on that basic knowledge and move away from using manipulatives.     

Student Actions

Teacher Actions

  • Develop the Ability to Make Conjectures, Model, and Generalize by using manipulatives and models to find equivalent representations of fractions and decimals

  • Develop Strategies for Problem Solving through exploration so they come to understand that parts of whole can be written in either fraction or decimal form.

  • Develop Accurate and Appropriate Procedural Fluency  which allows the ability to convert efficiently between fraction and decimals.

  • Use and connect mathematical representations by providing a variety of fraction and decimal models for students to use to tie their thinking to the correct vocabulary.

  • Build procedural fluency from conceptual understanding by continually finding ways to help  students make connections between fractions and decimals.

  • Pose purposeful questions that will encourage students to ponder on the best strategies for converting between forms.

Key Understandings

Misconceptions

  • Recognize and generate equivalent decimals in various contexts up to the thousandths place

  • Understand that adding zeros to the end of a decimal does not change the value

  • Recognize and generate equivalent fractions using benchmark denominators of halves, thirds, fourths, fifths, sixths, eighths, tenths, and twelfths.

  • Recognize and generate equivalent mixed numbers in various forms

  • Convert fractions to mixed numbers and mixed numbers to fractions

  • Convert between decimals and fractions/mixed numbers

  • Use division to convert fractions to decimal equivalents up to the thousandths place

  • Think that decimals and fractions are different types of numbers therefore, you cannot convert a fraction to a decimal

  • 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.

  • Overgeneralize fraction notation or decimal notation and confuse the two

    • EX. 1/4 = 1.4 or 1/4 = 0.4

  • Restrict interpretation of fractions inappropriately and might not understand that different fractions that name the same amount are equivalent

    • EX. 2/3 and 4/6 cannot name the same amount because they are different fractions

  • Misapply additive ideas when finding equivalent fractions

    • EX. 3/8 + 1/1 = 4/9 because 3 + 1 = 4 and 8 + 1 = 9

  • Overgeneralize results of previous experiences with fractions and associate a specific number with each numerator or denominator when simplifying fractions

    • EX. Prime numbers like 2, 3, or 5 always become 1 when you simplify and even numbers are always changed to one-half of their value. Using “rules” like this the student gets correct answers some of the time, like 2/8 = 1/4 and 4/6 = 2/3 , but not all the time. The student ignores the fact that some of the fractions are already in simplest form.

  • Think that doubling the size of the denominator doubles the size of the fraction

  • Think that dividing the numerator and the denominator by the same number reduces the value of the fraction. 


OKMath Framework Introduction

5th Grade Introduction

 

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