Standard: MACC.4.NF.1.1 Depth of Knowledge Level 3: Strategic Thinking Explain why a fraction a/b is equivalent to a fraction & Complex Reasoning by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Explanations and Ideas to Support: Sample Test/Task Item(s): This standard refers to visual fraction models. This includes area models, linear models (number lines) or it could be a collection/set models. This standard extends the work in third grade by using additional denominators (5, 10, 12, and 100). Students can use visual models or applets to generate equivalent fractions. Students’ initial experience with fractions began in Grade 3. They used models such as number lines to locate unit fractions, and fraction bars or strips, area or length models, and Venn diagrams to recognize and generate equivalent fractions and make comparisons of fractions. Conceptual: Students will understand a fractional quantity can be subdivided into an infinite number of equal pieces while maintaining the original fractional quantity, e.g., 1/2 can be subdivided into 2/4, 4/8 and so on. Those subdivisions are called equivalent fractions. Students will understand the identity property of multiplication and its relationship to fractions (1/1, 2/2, 3/3, 4/4,… n/n = 1) Students will understand how the identity property of multiplication is employed to create equivalent fractions [(n*a)/(n*b) = na/nb] Procedural: Students can identify differences in two equivalent fractions, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Students can identify how the identity property of multiplication transforms a fraction into its fraction. Representational: Students can represent equivalency of fractions pictorially (a/b is equivalent to (n x a)/(n x b)). Students can construct models of equivalent fractions using manipulatives such as paper, color tiles, fraction bars, and fraction circles. Using a fraction model, students can subdivide both numerator and denominator by multiplying with the same factor (a/b is equivalent to (n x a)/(n x b), because both a and b were changed by the same factor n), e.g. 1/2 = 2/4 because (2 x 1)/(2 x 2) = 2/4, or, pictorially. Aisha, Sara, and Brendan have 20 pencils. Aisha says 4 of the pencils are hers. Sara says of the pencils are hers. Brendan says of the pencils belong to him. Explain how they all could be right. Use words or drawings. My mom left ½ of a cake on the counter. The doorbell rang and one of my friends came over. If we cut what’s left into equal parts, what fraction of the whole cake did we each eat? If 3 of my friends came over and we cut ½ cake that’s left into equal parts, what fraction of the whole cake did we each eat? (Ask the child to extend this reasoning as far as he/she is able.) Mrs. Caha asked her class to write fractions on their whiteboards that were equivalent to . Tell if each student’s fraction is equivalent to Mrs. Caha’s fraction and show how you know. Connections: SMPs to be Emphasized Critical Area Critical Area 2: Developing an understanding of MP2- Reason abstractly and quantitatively. fraction equivalence, addition and subtraction of MP4- Model with mathematics. fractions with like denominators and multiplication MP7- Look for and make use of structure. of fractions by whole numbers. MP8- Look for and express regularity in repeated th 4 Grade Related Standards: reasoning. MACC.4.NF standards MA.4.A.2.3, MA.4.A.2.4, MA.4.A.6.3, MA.4.A.6.4, MA.4.A.6.5 Foundational Skills for 5th Grade: Use equivalent fractions as a strategy to add and subtract fractions. FCAT 2.0 Connections: Related NGSSS Standard(s) MA.4.A.6.3- Generate equivalent fractions and simplify fractions. Related NGSSS Standard(s) MA.4.A.6.4- Determine factors and multiples for specified whole numbers. FCAT 2.0 Test Item Specification Benchmark Clarification: Students will find equivalent fractions or simplify fractions to lowest terms. Students will rename fractions as mixed numbers or vice versa. Content Limits: All common factors of the numerator and denominator must be less than or equal to 10. Items will not include graphical representations of fractions FCAT 2.0 Test Item Specification Benchmark Clarification: Students will determine factors and/or multiples for whole numbers. Content Limits: All common factors of the numerator and denominator must be less than or equal to 10. Items will not include graphical representations of fractions Common Misconceptions: Students think that when generating equivalent fractions they need to multiply or divide either the numerator or denominator, such as, changing 1/2 to sixths. They would multiply the denominator by 3 to get 1/6, instead of multiplying the numerator by 3 also. Their focus is only on the multiple of the denominator, not the whole fraction. It’s important that students use a fraction in the form of one such as 3/3 so that the numerator and denominator do not contain the original numerator or denominator.
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