**NUMBER AND OPERATION**

The student will identify, represent, order, and compare
numbers and compute and solve problems.

The following skills would be introduced in Fifth Grade:

• Explain why one form of a number might be more useful
for computation than another form.

The following skills would be developing in Fifth Grade.

• Order and compare (<, >, or =) whole numbers, fractions,
mixed numbers, and decimals using models (e.g., number lines,

base ten blocks, Venn diagrams, and hundreds boards).

• Demonstrate knowledge and understanding of grade level mathematical terms.

• Represent proper fractions, improper fractions, and mixed numbers using
concrete objects, pictures, and the number line.

• Identify and change improper fractions to mixed numbers and vice versa.

• Recognize relationships among commonly used fractions and decimals.

• Explain and demonstrate the inverse nature of addition and subtraction.

• Explain and demonstrate the inverse nature of multiplication and division.

• Explain how addition, subtraction, multiplication, and division affect the
size and order of numbers.

• Select appropriate methods and tools for computations (e.g., mental
computation, estimation, calculators, and paper and

pencil).

• Identify missing information and/or too much information in real-world
problems.

• Solve real-world problems using decimals (including money), fractions, and
percents.

The following skills would be mastered in Fifth Grade.

• Use commutative, associative, and identity properties.

The following skills would be assessed in Fifth Grade by the Tennessee Comprehensive Assessment Program:

• Read and write numbers from millions to thousandths.

• Identify the place value of a given digit from millions to thousandths.

• Represent whole numbers and two-place decimals in expanded form.

• Represent, compare, and order whole numbers and decimals to thousandths.

• Compare and order fractions using the appropriate symbol (<, >, and =).

• Connect symbolic representations of proper and improper fractions to models of
proper and improper fractions.

• Represent numbers as both improper fractions and mixed numbers.

• Generate equivalent forms of commonly used fractions, decimals, and percents
(e.g., 1/10, 1/4, 1/2, .75, 50%).

• Multiply a fraction by a multiple of its denominator (denominator less than or
equal to 10).

• Use estimation to determine a reasonable solution to a whole number
computation.

• Add, subtract, multiply, and divide whole numbers (multipliers and divisors no
more than two-digits).

• Add, subtract, and multiply decimals.

• Add and subtract commonly used fractions.

• Solve one- or two-step real-world problems involving addition, subtraction,
and/or multiplication of whole numbers and

decimals.

**ALGEBRA**

The student will sort and classify objects; create,
extend, and describe patterns; and represent number sentences with words,

objects, and pictures.

The following skills would be developing in Fifth Grade:

• Generalize and extend or complete patterns involving
geometric figures or numbers.

• Represent and analyze patterns and functions using words, tables, and graphs.

• Determine or apply a function rule involving data in a function table.

• Represent the idea of a variable as an unknown quantity using a letter or a
symbol.

• Investigate how a change in one variable relates to a change in a second
variable.

• Use methods to compare and describe situations involving constant and/or
varying rates of change and to solve real-world

problems (e.g., extending rate charts).

The following skills would be mastered in Fifth Grade:

• Demonstrate understanding that an equation is a number
sentence stating two quantities are equal.

• Apply commutative, associative, zero, distributive, and identity properties.

• Show that division is not commutative.

The following skills would be assessed in Fifth Grade by the Tennessee Comprehensive Assessment Program:

• Extend numerical patterns.

• Extend geometric patterns.

• Generalize numerical patterns using a variable.

• Apply basic function rules.

• Solve open sentences involving addition, subtraction, multiplication, and
division.

• Connect open sentences to real-world situations.

• Select an equation that represents a given mathematical relationship.

• Extend rate charts to solve real-world problems.

**GEOMETRY**

The student will identify, describe, and create basic
shapes and describe relative positions and directions.

The following skills would be introduced in Fifth Grade:

• Make and test hypothesis about geometric properties.

• Explore similarity and how the sides and angles of similar triangles are
related.

• Describe and identify line and rotational symmetry in two-dimensional figures.

• Use visualization and spatial reasoning (e.g., geometric models) to solve
problems.

The following skills would be developing in Fifth Grade:

• Identify, compare, and analyze attributes of two- and
three-dimensional figures.

• Use the attributes of geometric figures to develop definitions of the figures.

• Identify and draw points, lines, line segments, rays, and angles.

• Draw circles and label diameter, circumference, radius, and center.

• Investigate and describe the results of subdividing and combining geometric
figures.

• Recognize, name, compare, and contrast congruent and symmetrical geometric
figures.

• Describe the relationships between lines and the characteristics of angles
(e.g., parallel, perpendicular, intersecting, right,

acute, obtuse, and straight).

• Describe location and movement using appropriate mathematical language.

• Identify, predict, and describe the results of transformations of
two-dimensional figures (i.e., slides, flips, and turns).

• Describe a motion or a series of motions that will show that two shapes are
congruent.

• Construct and draw two- and three-dimensional geometric figures.

• Create and describe mental images of objects, patterns, and paths.

• Recognize and build a 3-dimensional object from a 2-dimensional representation
(net) of that object (e.g., cube,

rectangular prism, pyramid, cone, or cylinder).

The following skills would be assessed in Fifth Grade by the Tennessee Comprehensive Assessment Program:

• Identify lines of symmetry in two-dimensional geometric
figures.

• Identify two- or three- dimensional shapes given defining attributes.

• Identify lines, line segments, rays, and angles.

• Classify geometric figures using properties.

• Locate and specify a point in Quadrant I of a coordinate system.

• Use spatial reasoning to predict the result of sliding, flipping, or turning a
two-dimensional shape.

• Use spatial reasoning to identify the three-dimensional figure created from a
two-dimensional representation (net) of that

figure (i.e., cube, rectangular prism, pyramid, cone, or cylinder).

**MEASUREMENT**

The student will apply measurement concepts of time,
length, weight, capacity, and temperature.

The following skills would be introduced in Fifth Grade:

• Understand how differences in units affect precision of
measurements.

• Develop informal strategies to determine the surface area and volume of
rectangular solids.

The following skills would be developing in Fifth Grade:

• Demonstrate understanding of the concepts of length,
perimeter, circumference, area, weight, capacity, volume, elapsed

time, and angle measure.

• Demonstrate understanding that measurements are approximations.

• Demonstrate understanding of the relationships among the units within both
customary and metric systems of

measurement.

• Explore what happens to measurements of a two-dimensional shape when the shape
is changed in some way (e.g.,

perimeter, area).

• Select and use appropriate standard units to measure length, perimeter, area,
capacity, volume, weight, time, temperature,

and angles.

• Select and use appropriate tools for measuring in real-world situations.

• Explain and demonstrate how scale in maps and drawings shows relative size and
distance.

• Connect simple units of measurement within the same
system of measurement.

• Use estimation to determine if a length or volume measurement is reasonable.

• Select appropriate standard units to measure length, perimeter, area,
capacity, volume, weight, time, temperature, and

angles.

• Use strategies to estimate perimeter and area of rectangles.

• Use a ruler to measure to the nearest centimeter and ΒΌ inch.

• Solve real-world problems involving addition and subtraction of measurements.

• Solve real-world problems involving perimeter and area of rectangles.

• Solve real-world problems involving elapsed time.

• Read temperatures on a thermometer using Fahrenheit and Celsius scales.

• Apply formulas to find the area of parallelograms and triangles.

**DATA ANALYSIS AND PROBABILITY**

The student will make simple graphs using concrete objects
and pictures and describe events as likely or unlikely.

The following skills would be introduced in Fifth Grade:

• Find the range of a data set.

• Explain the importance of sample size in investigations.

The following skills would be developing in Fifth Grade:

• Collect data using observations, surveys, and
experiments.

• Understand how data-collection methods could affect the results.

• Represent data using pictographs, bar graphs, tables, circle graphs, and line
graphs.

• Interpret data displayed in pictographs, bar graphs, tables, circle graphs,
and line graphs.

• Use measures of central tendency (i.e., mean, median, and mode).

• Make predictions and justify conclusions based on data.

• Design investigations to address a question.

• Examine various graphical representations of data to evaluate how accurately
the data is depicted.

• Describe the likelihood or chance of events as likely, unlikely, certain,
equally likely, or impossible.

• Use a sample space to predict the probability of an event.

• Represent and interpret data in bar graphs and
pictographs.

• Determine the mean, median, and mode of a data set.

• Make predictions based on data.

• Determine the most likely, least likely, or equally likely outcomes in simple
experiments.

• Represent the likelihood of an event using a fractional number from zero to
one.