Fifth Grade Math

Numbers and Operations

 

Algebra

 

Geometry

 

Measurement

 

Data Analysis

 

Number and Operation

Content Standard 1.0 The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

Fifth Grade Benchmarks

Performance Indicators State:

As documented through state assessment –

at Level 1, the student is able to

5.1.spi.1. read and write numbers from millions to thousandths;

5.1.spi.2. connect symbolic representations of proper and improper fractions to models of proper and improper fractions;

5.1.spi.3. represent whole numbers and two-place decimals in expanded form.

at Level 2, the student is able to

5.1.spi.4. add, subtract, multiply, and divide whole numbers (multipliers and divisors no more than two-digits).

5.1.spi.5. identify the place value of a given digit from millions to thousandths;

5.1.spi.6. represent, compare, and order whole numbers and decimals to thousandths;

5.1.spi.7. use estimation to select a reasonable solution to a whole number computation;

5.1.spi.8. add, subtract, and multiply decimals;

5.1.spi.9. solve one- or two-step real-world problems involving addition, subtraction, and/or multiplication of whole numbers and decimals;

5.1.spi.10. represent numbers as both improper fractions and mixed numbers;

5.1.spi.11. compare and order fractions using the appropriate symbol (<,>,=);

5.1.spi.12. add and subtract commonly used fractions.

at Level 3, the student is able to

5.1.spi.13. generate equivalent forms of commonly used fractions, decimals, and percents (e.g., 1/10, 1/4, 1/2, 3/4);

5.1.spi.14. multiply a fraction by a multiple of its denominator (denominator less than or equal to 10) (3)

Algebra

Content Standard 2.0 The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and problems using graphs, tables, and equations.

Fifth Grade Benchmarks

Performance Indicators State:

As documented through state assessment –

at Level 1, the student is able to

5.2.spi.1. extend numerical patterns;

5.2.spi.2. extend geometric patterns.

at Level 2, the student is able to

5.2.spi.3. apply basic function rules;

5.2.spi.4. connect open sentences to real-world situations;

5.2.spi.5. solve open sentences involving addition, subtraction, multiplication, and division.

at Level 3, the student is able to

5.2.spi.6. generalize numerical patterns using a variable;

5.2.spi.7. select an equation that represents a given mathematical relationship;

5.2.spi.8. extend rate charts to solve real-world problems.

Geometry

Content Standard 3.0 The student will develop an understanding of geometric concepts and relationships as the basis for geometric modeling and reasoning to solve problems involving one-, two-, and three-dimensional figures.

Fifth Grade Benchmarks

Performance Indicators State:

As documented through state assessment –

at Level 1, the student is able to

5.3.spi.1. identify lines, line segments, rays, and angles;

5.3.spi.2. identify lines of symmetry in two-dimensional geometric figures.

at Level 2, the student is able to

5.3.spi.3. identify two- or three-dimensional shapes given defining attributes;

5.3.spi.4. use spatial reasoning to predict the result of sliding, flipping, or turning a two-dimensional shape;

5.3.spi.5. locate and specify a point in Quadrant I of a coordinate system.

at Level 3, the student is able to

5.3.spi.6. classify geometric figures using properties;

5.3.spi.7. 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

Content Standard 4.0 The student will become familiar with the units and processes of measurement in order to use a variety of tools, techniques, and formulas to determine and to estimate measurements in mathematical and real-world problems.

Fifth Grade Benchmarks

Performance Indicators State:

As documented through state assessment –

at Level 1, the student is able to

5.4.spi.1. read temperature using Fahrenheit and Celsius scales;

5.4.spi.2. use a ruler to measure to the nearest centimeter and 1/4 inch;

5.4.spi.3. use estimation to determine if a length or volume measurement is reasonable;

5.4.spi.4. solve real-world problems involving addition and subtraction of measurements.

at Level 2, the student is able to

5.4.spi.5. select appropriate standard units to measure length, perimeter, area, capacity, volume, weight, time, temperature, and angles;

5.4.spi.6. connect simple units of measurement within the same system of measurement;

5.4.spi.7. use strategies to estimate perimeter and area of rectangles;

5.4.spi.8. solve real-world problems involving elapsed time.

at Level 3, the student is able to

5.4.spi.9. apply formulas to find the area of parallelograms and triangles;

5.4.spi.10. solve real-world problems involving perimeter and area of rectangles.

Data Analysis & Probability

Content Standard 5.0 The student will understand and apply basic statistical and probability concepts in order to organize and analyze data and to make predictions and conjectures.

Fifth Grade Benchmarks

Performance Indicators State:

As documented through state assessment –

at Level 1, the student is able to

5.5.spi.1. represent data using bar graphs and pictographs;

5.5.spi.2. interpret data displayed in bar graphs and pictographs.

at Level 2, the student is able to

5.5.spi.3. determine the median of a data set;

5.5.spi.4. determine the mode of a data set;

5.5.spi.5. determine the most likely, least likely, or equally likely outcomes in simple experiments;

5.5.spi.6. represent the likelihood of an event using a fractional number from zero to one.

at Level 3, the student is able to

5.5.spi.7. determine the mean of a data set;

5.5.spi.8. make predictions based on data.