Fifth Grade - Math Indicators

Numbers, Number Sense and Operations 

Number and Number Systems
  • Use models and visual representation to develop the concept of ratio as part-to-part and part-to-whole, and the concept of percent as part-to-whole.
  • Use various forms of "one" to demonstrate the equivalence of fractions; 
    (e.g., 18/24 = 9/12 X 2/2 = 3/4 X 6/6)
  • Identify and generate equivalent forms of fractions, decimals and percents.
  • Round decimals to a given place value and round fractions (including mixed numbers) to the nearest half.
  • Recognize and identify perfect squares and their roots.
Meaning of Operations
  • Represent and compare numbers less than 0 by extending the number line and using familiar applications (e.g., temperature, owing money).
  • Use commutative, associative, distributive, identity and inverse properties to simplify and perform computations.
  • Identify and use relationships between operations to solve problems.
  • Use order of operations, including use of parentheses, to simplify numerical expressions.
  • Justify why fractions need common denominators to be added or subtracts.
  • Explain how place value is related to addition and subtraction of decimals (e.g., 0.2 + 0.14), the two tenths is added to the one tenth because they are both tenths.
Computation and Estimation
  • Use physical models, points of reference, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals.
  • Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies.

Measurement 

Measurement Units
  • Identify and select appropriate units to measure angles, i.e., degrees.
  • Identify paths between points on a grid or coordinate place and compare the lengths of the paths, e.g., shortest path, paths of equal length.
  • Demonstrate and describe the differences between covering the faces (surface area) and filling the interior (volume) of three- dimensional objects.
  • Demonstrate understanding the differences among linear units, square units and cubic units.
Use Measurement Techniques & Tools
  • Make conversions within the same measurement system while performing computations.
  • Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms.
  • Use benchmark angles (e.g., 45 degrees, 90 degrees, 120 degrees) to estimate the measure of angles, and use a tool to measure and draw angles.

 

Geometry and Spatial Sense 

 

Characteristics & Properties
  • Draw circles, and identify and determine relationships among the radius, diameter, center and circumference, e.g., radius is half the diameter, the ratio of the circumference of a circle to its diameter is an approximation of  p.
  • Use standard language to describe line, segment, ray, angle, skew, parallel and perpendicular.
  • Label vertex, rays, interior and exterior for an angle.
  • Describe and use properties of congruent figures to solve problems.
  • Use physical models to determine the sum of the interior angles of triangles and quadrilaterals.
Spatial Relationships Extend understanding of coordinate system to include points whose x or y values may be negative numbers.
Transformations & Symmetry
  • Understand that the measure of an angle is determined by the degree of rotation of an angle side rather the the length of either side.
  • Predict what three-dimensional object will result from folding a two-dimensional net, then confirm the prediction by folding the net. 

Patterns, Functions and Algebra 

Use Patterns, Relations & Functions
  • Justify a general rule for a pattern or a function by using physical materials, visual representations, words, tables or graphs.
  • Use calculators or computers to develop patterns, and generalize them using tables and graphs.
Use Algebraic Representations
  • Use variable as unknown quantities in general rules when describing patterns and other relationships.
  • Create and interpret the meaning of equations and inequalities representing problem situations.
  • Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions. 
Analyze Change Describe how the quantitative change in a variable affects the value of a related variable, e.g., describe how the rate of growth varies over time, based upon data in a table or graph.

Data Analysis and Probability 

Data Collection
  • Read, construct and interpret frequency tables, circle graphs and line graphs.
  • Select and use a graph that is appropriate for the type of data to be displayed; e.g., numerical vs. categorical data, discrete vs. continuous data.
  • Represent and interpret data using tables, bar graphs, line plots and line graphs.
  • Read and interpret increasingly complex displays of data, such as double bar graphs.
  • Determine appropriate data to be collected to answer questions posed by students or teacher, collect and display data, and clearly communicate finding.
Statistical Methods
  • Modify initial conclusions, propose and justify new interpretations and predictions as additional data are collected.
  • Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data.
Probability
  • List and explain all possible outcomes in a given situation.
  • Identify the probability of events within a simple experiment, such as three chances out of eight.
  • Use 0, 1 and ratios between 0 and 1 to represent the probability of outcomes for an event, and associate the ratio with the likelihood of the outcome.
  • Compare what should happen (theoretical/ expected results) with what did happen (experimental/actual results) in a simple experiment. 
  • Make predictions based on experimental and theoretical probabilities.