Information taken from the Ohio Department of Education
CRITICAL AREA #1: Developing fluency with addition and subtraction of fractions and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions)
Students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators. They develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them. Students also use the meaning of fractions, of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense. (Note: this is limited to the case of dividing unit fractions by whole numbers and whole numbers by unit fractions.)
The standards below relate to this Critical Area:
Number and Operations - Fractions 5.NF
Use equivalent fractions as a strategy to add and subtract fractions.
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4.NF.1
4.NF.2
4.NF.3
4.NF.4a, b
4.NF.5a, b
4.NF.6
4.NF.7a, b, c
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Measurement and Data 5.MD
Represent and interpret data.
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5.MD.2
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CRITICAL AREA #2: Extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations
Students develop understanding of why division procedures work based on the meaning of base-ten numerals and properties of operations. They finalize fluency with multi-digit addition, subtraction, multiplication, and division. They apply their understandings of models for decimals, decimal notation, and properties of operations to add and subtract decimals to hundredths. They develop fluency in these computations, and make reasonable estimates of their results. Students use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal multiplied by an appropriate power of 10 is a whole number), to understand and explain why the procedures for multiplying and dividing finite decimals make sense. They compute products and quotients of decimals to hundredths efficiently and accurately.
The standards below relate to this Critical Area:
Operations and Algebraic Thinking 5.OA
Write and interpret numerical expressions.
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5.OA.1
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Number and Operations in Base Ten 5.NBT
Understand the place value system.
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5.NBT.1
5.NBT.2
5.NBT.3a, b
5.NBT.4
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Number and Operations in Base Ten 5.NBT
Understand the place value system.
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5.NBT.5
5.NBT.6
5.NBT.7
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Measurement and Data 5.MD
Convert like measurement units within a given measurement system.
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5.MD.1
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CRITICAL AREA #3: Developing understanding of volume
Students recognize volume as an attribute of three-dimensional space. They understand that volume can be measured by finding the total number of same-size units of volume required to fill the space without gaps or overlaps. They understand that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume. They select appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume. They decompose three-dimensional shapes and find volumes of right rectangular prisms by viewing them as decomposed into layers of arrays of cubes. They measure necessary attributes of shapes in order to determine volumes to solve real world and mathematical problems.
The standards below relate to this Critical Area:
Measurement and Data 5.MD
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
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5.MD.3a, b
5.MD.4
5.MD.5a, b, c
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Number and Operations - Fractions 5.NF
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
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5.NF.4a, b
5.NF.5a
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Geometry 5.G
Classify two-dimensional figures into categories based on their properties.
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5.G.3
5.G.4
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STANDARDS AND CLUSTERS BEYOND THE CRITICAL AREAS OF FOCUS
Modeling numerical relationships with the coordinate plane
Based on previous work with measurement and number lines, students develop understanding of the coordinate plane as a tool to model numerical relationships. These initial understandings provide the foundation for work with negative numbers, and ratios and proportional relationships in Grade Six and functional relationships in further grades.
The standards below relate to this cluster:
Operations and Algebraic Thinking 5.OA
Analyze patterns and relationships.
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5.OA.3
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Geometry 5.G
Graph points on the coordinate plane to solve real-world and mathematical problems.
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5.G.1
5.G.2
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