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Generate fountain between any two quantities

Generating Fractions in between Two numbers (Fraction Density)
This is a collection of progressive prompts that will certainly elicit the usage of variousstrategies provided to find fractions between two numbers. The prompts, whenused in sequence, support students in selecting a strategy based upon thefractions gift considered. Encourage students come buildmodels/representations and create contexts to help in visualization. Thisseries the prompts can be used for a selection of grades and also purposes. Thetime compelled will vary relying on the great level and student readiness.
MathematicsDensity of fractions refers to the vital mathematical idea the between any type of two fractions there are infinite variety of fractions. Expertise this mathematical truth is a critical stage in the advancement of fraction sense. This is a novel principle for students, since it is no encountered in the entirety number system (there space not any kind of whole numbers between any two entirety numbers). Students are encouraged to develop a variety of various strategies and also to use them strategically, based upon the situation. Research shows that it is beneficial to spread portion learning transparent the year and also embed that in various other strands. Density is also a vital concept in measurement.
Curriculum ConnectionsStudents will:Represent, compare and also order fractional amounts using a variety of tools.
Instructional sequence companion students and introduce the task. Post the selected prompt (select from options to the right) on the black/whiteboard or interactive whiteboard, or distribution on a handout. have actually students describe their thinking. Highlight various strategies by intentionally picking students that fixed the task in various ways. Have students recognize the similarities and 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 two fractions and identify a fraction between them. Prove that your answer is correct.
Highlights of college student thinkingStudents may:construct precise models the fractions;rely ~ above the algorithm because that determining equivalent fractions;consider only the numerators or only the denominators;use benchmarks to make estimates;demonstrate recurring partitioning to name fractions in between two fractions;create physics partitions however struggle to surname the fractional value represented;identify equivalent fractions (which share a common suggest on the number line) instead of identifying different points on the line. Key questions just how do you recognize that these fractions represent different quantities?What contexts go you use to visualize the fractions? exactly how did this assist you?What strategy did girlfriend use? What execute you like about this strategy? how did it help you?How did her representation assist you to to compare the fractions? What manipulatives might you use to aid you? Materials do tools available such as file and markers, grid paper, record strips for folding, and/or manipulatives such as relational rods.