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Generate fractions between any two quantities

Generating Fractions between Two number (Fraction Density)
This is a set of steady prompts that will certainly elicit the use of variousstrategies provided to find fractions in between two numbers. The prompts, whenused in sequence, support students in picking a strategy based upon thefractions gift considered. Encourage students to buildmodels/representations and also create contexts to aid in visualization. Thisseries that prompts can be used for a variety of grades and also purposes. Thetime forced will vary depending on the class level and also student readiness.
MathematicsDensity the fractions refers to the important mathematical idea the between any type of two fountain there room infinite number of fractions. Expertise this mathematical reality is a crucial stage in the advance of fraction sense. This is a novel concept for students, because it is not encountered in the totality number system (there are not any type of whole numbers between any two entirety numbers). Students are urged to build a range of various strategies and to usage them strategically, based on the situation. Research shows that it is valuable to spread fraction learning transparent the year and embed it in other strands. Thickness is additionally a key concept in measurement.
Curriculum ConnectionsStudents will:Represent, compare and also order fractional quantities using a range of tools.
Instructional sequence partner students and introduce the task. Short article the selected notice (select from alternatives to the right) on the black/whiteboard or interaction whiteboard, or distribute on a handout. have students define their thinking. Highlight various strategies by intentionally selecting students that addressed the job in various ways. Have students determine the similarities and also differences between the strategies. Prompt 1 recognize three fractions between 2 and also 3. Prompt 2Identify a fraction between 1

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. Prompt 7Select 2 fractions and identify a fraction between them. Prove the your price is correct.
Highlights of college student thinkingStudents may:construct exact models that fractions;rely top top the algorithm for determining identical fractions;consider only the numerators or just the denominators;use benchmarks to make estimates;demonstrate repetitive partitioning to name fractions in between two fractions;create physics partitions however struggle to name the fractional worth represented;identify tantamount fractions (which share a common point on the number line) instead of identifying different points ~ above the line. Key questions just how do you understand that these fractions represent different quantities?What contexts walk you use to visualize the fractions? how did this assist you?What strategy did you use? What perform you like around this strategy? how did it help you?How did her representation aid you to to compare the fractions? What manipulatives can you usage to help you? Materials make tools obtainable such as file and markers, network paper, document strips because that folding, and/or manipulatives such together relational rods.