Standards
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Explanations and Examples
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1. Make sense of problems and persevere in solving them.
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Mathematically proficient students in grade 5 should solve problems by applying their understanding of operations with wholenumbers, decimals, and fractions including mixed numbers. They solve problems related to volume and measurementconversions. Students seek the meaning of a problem and look for efficient ways to represent and solve it. They may check theirthinking by asking themselves, “What is the most efficient way to solve the problem?”, “Does this make sense?”, and “Can Isolve the problem in a different way?”
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2. Reason abstractly and quantitatively.
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Mathematically proficient students in grade 5 should recognize that a number represents a specific quantity. They connectquantities to written symbols and create a logical representation of the problem at hand, considering both the appropriate unitsinvolved and the meaning of quantities. They extend this understanding from whole numbers to their work with fractions anddecimals. Students write simple expressions that record calculations with numbers and represent or round numbers using placevalue concepts.
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3. Construct viable arguments and critique the reasoning of others.
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In fifth grade mathematical proficient students may construct arguments using concrete referents, such as objects, pictures, anddrawings. They explain calculations based upon models and properties of operations and rules that generate patterns. Theydemonstrate and explain the relationship between volume and multiplication. They refine their mathematicalcommunicationskills as they participate in mathematical discussions involving questions like “How did you get that?” and “Why is that true?”They explain their thinking to others and respond to others’ thinking.
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4. Model with mathematics.
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Mathematically proficient students in grade 5 experiment with representing problem situations in multiple ways includingnumbers, words (mathematical language), drawing pictures, using objects, making a chart, list, or graph, creating equations, etc.Students need opportunities to connect the different representations and explain the connections. They should be able to use allof these representations as needed. Fifth graders should evaluate their results in the context of the situation and whether theresults make sense. They also evaluate the utility of models to determine which models are most useful and efficient to solveproblems.
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5. Use appropriate tools strategically.
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Mathematically proficient fifth graders consider the available tools (including estimation) when solving a mathematical problemand decide when certain tools might be helpful. For instance, they may use unit cubes to fill a rectangular prism and then use aruler to measure the dimensions. They use graph paper to accurately create graphs and solve problems or make predictions fromreal world data.
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6. Attend to precision.
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Mathematically proficient students in grade 5 continue to refine their mathematical communication skills by using clear andprecise language in their discussions with others and in their own reasoning. Students use appropriate terminology whenreferring to expressions, fractions, geometric figures, and coordinate grids. They are careful about specifying units of measureand state the meaning of the symbols they choose. For instance, when figuring out the volume of a rectangular prism they recordtheir answers in cubic units.
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7. Look for and make use of structure.
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In fifth grade mathematically proficient students look closely to discover a pattern or structure. For instance, students useproperties of operations as strategies to add, subtract, multiply and divide with whole numbers, fractions, and decimals. Theyexamine numerical patterns and relate them to a rule or a graphical representation.
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8. Look for and express regularity in repeated reasoning.
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Mathematically proficient fifth graders use repeated reasoning to understand algorithms and make generalizations about patterns.Students connect place value and their prior work with operations to understand algorithms to fluently multiply multi-digitnumbers and perform all operations with decimals to hundredths. Students explore operations with fractions with visual modelsand begin to formulate generalizations
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