Grade 5 » Introduction
In Grade 5, instructional time should focus on three critical areas: (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); (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; and (3) developing
understanding of volume.
- 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.)
- 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
- 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
Grade 5 Overview
Operations and Algebraic Thinking
- Write and interpret numerical expressions.
- Analyze patterns and relationships.
Number and Operations in Base Ten
- Understand the place value system.
- Perform operations with multi-digit whole numbers and with decimals to hundredths.
Number and Operations—Fractions
- Use equivalent fractions as a strategy to add and subtract fractions.
- Apply and extend previous understandings of multiplication and division to multiply
and divide fractions.
Measurement and Data
- Convert like measurement units within a given measurement system.
- Represent and interpret data.
- Geometric measurement: understand concepts of volume and relate volume to multiplication
and to addition.
- Graph points on the coordinate plane to solve real-world and mathematical problems.
- Classify two-dimensional figures into categories based on their properties.
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.