Mathematics

Geometry – Students will:

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Geometry – Students will:

Understand congruence and similarity using physical models, transparencies, or geometry software.

Verify experimentally the properties of rotations, reflections, and translations:

Lines are taken to lines, and line segments are taken to line segments of the same length.

Geometry and Measurement

Geometric Properties: Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.

Justify which objects in a collection match a given geometric description.

Geometry: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.

Demonstrate and apply geometric concepts involving points, lines, planes and space.

Identify and describe how geometric figures are used in practical settings (e.g., construction, art, advertising).

Algebra and Analytical Methods: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results.

Use algebraic concepts and procedures to represent and solve problems.

Apply properties of powers, perfect squares and square roots.

Data Analysis, Probability, and Discrete Mathematics

Data Analysis (Statistics): Understand and apply data collection, organization, and representation to analyze and sort data.

Formulate and answer questions by interpreting and analyzing displays of data, including double bar graphs, single line graphs, or circle graphs

Number and Operations in Base Ten - Students will:

Use place value understanding and properties of operations to perform multi-digit arithmetic.

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Number and Operations in Base Ten - Students will:

Use place value understanding and properties of operations to perform multi-digit arithmetic.

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Measurement and Data

Represent and interpret data.

Explain the classification of data from real-world problems shown in graphical representations including the use of terms mean and median with a given set of data. (L)

Worksheet Pie Chart PercentsGrade 5

Data Analysis, Probability, and Discrete Mathematics

Data Analysis (Statistics): Understand and apply data collection, organization, and representation to analyze and sort data.

Formulate and answer questions by interpreting and analyzing displays of data, including double bar graphs, single line graphs, or circle graphs

Data Analysis, Probability, and Discrete Mathematics

Data Analysis (Statistics): Understand and apply data collection, organization, and representation to analyze and sort data.

Formulate and answer questions by interpreting and analyzing displays of data, including double bar graphs, single line graphs, or circle graphs

Number and Operations in Base Ten - Students will:

Use place value understanding and properties of operations to perform multi-digit arithmetic.

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Number and Operations in Base Ten - Students will:

Use place value understanding and properties of operations to perform multi-digit arithmetic.

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Number and Operations in Base Ten - Students will:

Perform operations with multi-digit whole numbers and with decimals to hundredths.

Fluently multiply multi-digit whole numbers using the standard algorithm.

Measurement and Data – Students will:

Represent and interpret data.

Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs.

Data Analysis, Probability, and Discrete Mathematics

Data Analysis, Probability, and Discrete Mathematics

Worksheet Student PictographGrade 4

Measurement and Data

Convert like measurement units within a given measurement system and solve problems involving time.

Identify, estimate measure, and convert equivalent measures within systems English length (inches, feet, yards, miles) weight (ounces, pounds, tons) volume (fluid ounces, cups, pints, quarts, gallons) temperature (Fahrenheit) Metric length (millimeters, centimeters, meters, kilometers) volume (milliliters, liters), temperature (Celsius), (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems using appropriate tools.

Data Analysis, Probability, and Discrete Mathematics

Worksheet Pie Chart BudgetGrade 4

Counting and Cardinality - Students will:

Compare numbers.

Compare two numbers between 1 and 10 presented as written numerals.