# Rangely RE 4 Curriculum Development 4 th Grade Mathematics MA10 GR.4 S.1 GLE.2 MA10 GR.4 S.3 GLE.1

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1 Unit Title Fraction Frenzy Length of Unit 5 weeks Focusing Lens(es) Representation Standards and Grade Level Expectations Addressed in this Unit Inquiry Questions (Engaging Debatable): Unit Strands Concepts MA10 GR.4 S.1 GLE.2 MA10 GR.4 S.3 GLE.1 What would the world be like without fractions? (MA10 GR.4 S.1 GLE.2 IQ.4) Why are fractions useful? (MA10 GR.4 S.1 GLE.2 IQ.3) Number and Operations Fractions, Measurement and Data Increasing, decreasing, numerators, denominators, fractions, factor, equivalence, comparison, referent unit, whole, benchmark fractions, estimation, relative size, common denominator/numerator, decompose, sum, addition, subtraction, properties of operations, relationship, mixed number, equivalent fractions, decimals, word problems, joining, separating, unit fractions, multiple, Generalizations My students will Understand that Factual Guiding Questions Conceptual Equivalent fractions describe the same part of a whole by using different fractional parts (MA10 GR.4 S.1 GLE.2 EO.a.i) Increasing or decreasing both the numerators and denominators of a fraction by the same factor creates equivalent fractions (MA10 GR.4 S.1 GLE.2 EO.a.i) Decisions about the size of a fraction relative to another fraction often involves the comparison of the fractions denominators (if their numerators are equal), or numerators (if their denominators are equal) or the creation of common denominators or numerators for the fractions (MA10 GR.4 S.1 GLE.2 EO.a.iii) As with whole numbers, mathematicians compose fractions by joining/combining fractions (with the same denominator) as sums and decompose/separate fractions (with the same denominator) as differences in multiple ways (MA10 GR.4 S.1 GLE.2 EO.b.i.1) How can you show that ½ and 2/4 are equivalent fractions? How can you justify two fractions are equivalent by using visual fraction models? What happens when you multiply both the numerator and denominator by the same number? What are examples of benchmark fractions and how are they useful in comparing the size of fractions? When do you need to find a common denominator or common numerator? How can you record decompositions of fractions with an equation? How can you justify decompositions of fractions using visual fraction models? Why (or when) are equivalent fractions necessary or helpful? Why are there multiple names for the same fraction? How can different fractions represent the same quantity?(ma10 GR.4 S.1 GLE.2 IQ.1) Why do you need to know equivalent fractions? Why is it possible to compare fractions with either a common denominator or common numerator? Why when you decompose fractions do you only break apart the numerator and not the denominator? How is decomposing fractions similar and different from decomposing whole numbers? December 9, 2013 Page 13 of 23

2 To add and subtract mixed numbers with like denominators requires the use of properties of operations (MA10 GR.4 S.1 GLE.2 EO.b.i.2) Place value (and its understanding) provides an efficient means to express fractions with a denominator of 10 as an equivalent fraction with a denominator of 100 (MA10 GR.4 S.1 GLE.2 EO.a) Word problems and contexts involving joining and separating parts of the same (size) whole require the addition and subtraction of fractions (MA10 GR.4 S.1 GLE.2 EO.b.i.3) The multiplication of a fraction (1/b) by a whole number (a) creates a fraction that is a multiple of the original fraction (MA10 GR.4 S.1 GLE.2 EO.b.i, b.ii.1, 2) Rangely RE 4 Curriculum Development How can you write the number 1 as a fraction? Any whole number? How can you rewrite a mixed number as an equivalent fraction? In a mixed number, what operation is happening between the whole number and the fraction? How can you add two fractions with a denominator of 10 and 100 respectively (e.g. 3/10 + 5/100)? How does solving the problem How much pizza does Thomas have left if gives away half of his pizza at lunch and then eats half of what he has left? require the use of fractions? How can the repeated addition of 1/4, 3 times, show that 3/4 is multiple of 1/4? How can you multiply a whole number by a fraction? What different types of word problems represent the product of a whole number times a fraction? (MA10 GR.4 S.1 GLE.2 EO.b.ii.3) Why might you need to rewrite a mixed number as an equivalent fraction in order to perform addition or subtraction? Why is it easy to change a fraction with a denominator of 10 to 100? How word problems involving the addition and subtraction of fractions similar and different from those of whole numbers? When multiplying a whole number by a unit fraction is the result larger or smaller than the original whole number? Why is every fraction both a multiplication and division problem at the same time? December 9, 2013 Page 14 of 23

6 Critical Language: includes the Academic and Technical vocabulary, semantics, and discourse which are particular to and necessary for accessing a given discipline. EXAMPLE: A student in Language Arts can demonstrate the ability to apply and comprehend critical language through the following statement: Mark Twain exposes the hypocrisy of slavery through the use of satire. A student in can demonstrate the ability to apply and comprehend critical language through the following statement(s): Academic Vocabulary: I can compare two fractions by having first determining if there are smaller or larger than a benchmark fraction like ½ or finding a common numerator or denominator; if two fractions have the same numerator then the fraction with the smaller denominator is larger and vice versa if they have same denominator. Apply, explain, generate, compare, express, understand, increasing, decreasing, estimation Technical Vocabulary: Solve, equivalent, mixed numbers, numerator, denominator, unit fraction, benchmark fraction, whole, part, multiple, equivalent fractions, common numerator, common denominator, decompose, sum, addition, subtraction, joining, separating December 9, 2013 Page 18 of 23

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