FIFTH GRADE MATH SKILLS

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.

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

• 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 ¼ 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.

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

• 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.