How do we know if fractions are equivalent, if not how do we compare their relative sizes? Targeted Content Standard(s): 4. NF.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) 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. 4. NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. Targeted Mathematical Practice(s): 1 Make sense of problems and persevere in solving them 2 Reason abstractly and quantitatively 3 Construct viable arguments and critique the reasoning of others 4 Model with mathematics 5 Use appropriate tools strategically 6 Attend to precision 7 Look for and make use of structure 8 Look for an express regularity in repeated reasoning Supporting Content Standard(s): (optional) 3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Student Friendly Learning Targets I can Purpose of the Lesson: Develop and implement strategies for determining the equivalence and relative size of fractions. Explanation of Rigor: (Fill in those that are appropriate.) Conceptual: Students develop the concept of partitioning wholes into equal sized pieces to generate equivalent fractions and compare fractions sizes. Vocabulary: Numerator Denominator Equivalent Fraction Common Denominator Visual Fraction Model Procedural: Students use a/b= (nxa)/(nxb) to generate equivalent fractions/common denominators and use this tool to compare fractions. Evidence of Learning (): Pre-: Fraction Equivalence and Comparison Pre- Formative (s): Prove the Equivalence, Comparing Fractions, Summative : Generating Equivalent Fractions and Comparing Fractions. Represent equivalent fractions using numbers and visual models. Explain why fractions are equivalent. Compare fractions with a visual model. Compare fractions with symbols. Explain why one fraction is less than, equal to, or greater than another fraction. Application: Self-: Generating Equivalent Fractions and Comparing Fractions (Self-)
How do we know if fractions are equivalent, if not how do we compare their relative sizes? Lesson Segments: 1. Fraction Equivalence and Comparison Pre- 2. Generating Equivalent Fractions 3. Prove the Equivalence 4. Comparing Fractions-Visual Models 5. Comparing Fractions-Benchmarks 6. Comparing Fractions-Common Denominators 7. Unit 2-Lesson 1 -Generating Equivalent Fractions and Comparing Fractions
Grade: 4 Lesson Title: Equivalence and Comparison of Fractions How do we know if fractions are equivalent, if not how do we compare their relative sizes? Lesson Procedures: Segment 1 60 minutes Fraction Equivalence and Comparison Pre- Assess student understanding of the related 3 rd grade fraction standards (3.NF.1 and 3.NF.2). Practice (Homework): 1. Give the Fraction Equivalence and Comparison Pre-
How do we know if fractions are equivalent, if not how do we compare their relative sizes? Segment 2 120 Minutes Building equivalent fractions using physical/visual and symbolic models. MP4 Model with mathematics Students uses models to generate equivalent fractions (area and number lines). MP5 Use appropriate tools strategically Students use tools to represent/generate/identify equivalent fractions (fraction tiles, number lines ). Activity-Fraction Strips Intro (L1-2a) Activity Fractions Strips2 (L1-2b) Handouts: Fraction Strips 2 sheets.(l1-2c) Activity-Visual Fractions (L1-2d) Practice (Homework): 1.
How do we know if fractions are equivalent, if not how do we compare their relative sizes? Segment 3 Visually and numerically proving the equivalence of given fractions, e.g. ¾=6/8. MP3 Construct viable arguments and critique the reasoning of others. Students will explain their reasoning using the models. MP4 Students use models to illustrate/prove a/b=(nxa)/(nxb). Activity- Visual Fractions (L1-2d) Formative -Prove the Equivalence Practice (Homework): 1.
How do we know if fractions are equivalent, if not how do we compare their relative sizes? Segment 4 Compare the size of fractions with visual models. MP4: Model with mathematics Students construct physical models of fractions of varying sizes to illustrate which is larger/smaller. Formative -Comparing Fractions Comparison Overview (L1-4a) Comparison Review (L1-4b) Comparison Review Sheet(L1-4c) Activity-Visual Fractions Students do not recognize fraction comparisons are based on both fractions referring to a common whole. 1. Practice (Homework):
How do we know if fractions are equivalent, if not how do we compare their relative sizes? Segment 5 Benchmark Fraction Talks (L1-5a) Compare fractions based on their relationship to benchmark fractions (1/2, 1, etc.) MP2 & MP3 Reason abstractly and quantitatively Students use their fraction sense/reasoning to compare fractions based on their relationships to benchmarks (1/2, 1, etc) and justify their conclusion. Students do not recognize fraction comparisons are based on both fractions referring to a common whole. 1. Thread Benchmark Fraction Comparison Talks throughout the unit. Practice (Homework):
How do we know if fractions are equivalent, if not how do we compare their relative sizes? Segment 6 Comparison Common Denominator (L1-6a) Comparison Common Denominator Sheet (L1-6b) Comparison Cards (L1-6c) Compare fractions using common denominators. MP7 Look for and make use of structure Students apply a/b= (nxa)/nxb) to generate common denominators to compare fractions with like denominators. Students do not recognize fraction comparisons are based on both fractions referring to a common whole. 1. Practice (Homework):
How do we know if fractions are equivalent, if not how do we compare their relative sizes? Segment 7 Generating Equivalent Fractions and Comparing Fractions. Assess students understanding to explain and generate equivalent fractions and compare fractions using multiple strategies. Practice (Homework): 1. Give Generating Equivalent Fractions and Comparing Fractions.