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 4 know that doing mathematics involves solving problems and
discussing how they solved them. Students explain to themselves the
meaning of a problem and look for ways to solve it. Fourth graders may
use concrete objects or pictures to help them conceptualize and solve
problems. They may check their thinking by asking themselves, “Does
this make sense?” They listen to the strategies of others and will try
different approaches. They often will use another method to check their
answers.
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2. Reason abstractly and quantitatively.
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Mathematically proficient fourth graders
should recognize that a number represents a specific quantity. They
connect the quantity to written symbols and create a logical
representation of the problem at hand, considering both the
appropriate units involved and the meaning of quantities. They extend
this understanding from whole numbers to their work with fractions and
decimals. Students write simple expressions, record calculations with
numbers, and represent or round
numbers using place value concepts.
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3. Construct viable arguments and critique the reasoning of others.
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In fourth grade mathematically
proficient students may construct arguments using concrete referents,
such as objects, pictures, and drawings. They explain their thinking
and make connections between models and equations. They refine their
mathematical communication skills 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 fourth grade
students experiment with representing problem situations in multiple
ways including numbers, 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
all of these representations as needed. Fourth graders should evaluate
their results in the context of the situation and reflect on whether
the results make sense.
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5. Use appropriate tools strategically.
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Mathematically proficient fourth graders
consider the available tools (including estimation) when solving a
mathematical problem and decide when certain tools might be helpful.
For instance, they may use graph paper or a number line to represent
and compare decimals and protractors to measure angles. They use other
measurement tools to understand the relative size of units within a
system and express measurements given in larger units in terms of
smaller units.
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6. Attend to precision.
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As fourth graders develop their
mathematical communication skills, they try to use clear and precise
language in their discussions with others and in their own reasoning.
They are careful about specifying units of measure and state
the meaning of the symbols they choose. For instance, they use
appropriate labels when creating a line plot.
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7. Look for and make use of structure.
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In fourth grade mathematically
proficient students look closely to discover a pattern or structure.
For instance, students use properties of operations to explain
calculations (partial products model). They relate representations of
counting problems such as tree diagrams and arrays to the
multiplication principal of counting. They generate number or
shape patterns that follow a given rule.
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8. Look for and express regularity in repeated reasoning.
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Students in fourth grade should notice
repetitive actions in computation to make generalizations Students use
models to explain calculations and understand how algorithms work. They
also use models to examine patterns and generate their own algorithms.
For example, students use visual fraction models to write equivalent
fractions.
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