Measurement and Geometry
1.0 Students understand the concept of time and units to measure it; they understand that objects have properties, such as length, weight, and capacity, and that comparisons may be made by referring to those properties:

1.1 Compare the length, weight, and capacity of objects by making direct comparisons with reference objects (e.g., note which object is shorter, longer, taller, lighter, heavier, or holds more).

Statistics, Data Analysis, and Probability
1.0 Students collect information about objects and events in their environment:

1.1 Pose information questions; collect data; and record the results using objects, pictures, and picture graphs.

Measurement and Geometry
1.0 Students use direct comparison and nonstandard units to describe the measurements of objects:

1.1 Compare the length, weight, and volume of two or more objects by using direct comparison or a nonstandard unit.

Statistics, Data Analysis, and Probability
1.0 Students organize, represent, and compare data by category on simple graphs and charts:

1.1 Sort objects and data by common attributes and describe the categories.
1.2 Represent and compare data (e.g., largest, smallest, most often, least often) by using pictures, bar graphs, tally charts, and picture graphs.

Mathematical Reasoning
1.0 Students make decisions about how to set up a problem:

1.1 Determine the approach, materials, and strategies to be used.
1.2 Use tools, such as manipulatives or sketches, to model problems.

2.0 Students solve problems and justify their reasoning:

2.1 Explain the reasoning used and justify the procedures selected.
2.2 Make precise calculations and check the validity of the results from the context of the problem.

Number Sense
6.0 Students use estimation strategies in computation and problem solving that involve numbers that use the ones, tens, hundreds, and thousands places:

6.1 Recognize when an estimate is reasonable in measurements (e.g., closest inch).

Algebra and Functions
1.0 Students model, represent, and interpret number relationships to create and solve problems involving addition and subtraction:

1.1 Use the commutative and associative rules to simplify mental calculations and to check results.
1.2 Relate problem situations to number sentences involving addition and subtraction.
1.3 Solve addition and subtraction problems by using data from simple charts, picture graphs, and number sentences.

Measurement and Geometry
1.0 Students understand that measurement is accomplished by identifying a unit of measure, iterating (repeating) that unit, and comparing it to the item to be measured:

1.1 Measure the length of objects by iterating (repeating) a nonstandard or standard unit.
1.2 Use different units to measure the same object and predict whether the measure will be greater or smaller when a different unit is used.
1.3 Measure the length of an object to the nearest inch and/ or centimeter.

Statistics, Data Analysis, and Probability
1.0 Students collect numerical data and record, organize, display, and interpret the data on bar graphs and other representations:

1.1 Record numerical data in systematic ways, keeping track of what has been counted.
1.2 Represent the same data set in more than one way (e.g., bar graphs and charts with tallies).
1.3 Identify features of data sets (range and mode).
1.4 Ask and answer simple questions related to data representations.

Mathematical Reasoning
1.0 Students make decisions about how to set up a problem:

1.1 Determine the approach, materials, and strategies to be used.
1.2 Use tools, such as manipulatives or sketches, to model problems.

2.0 Students solve problems and justify their reasoning:

2.1 Defend the reasoning used and justify the procedures selected.
2.2 Make precise calculations and check the validity of the results in the context of the problem.

Measurement and Geometry
1.0 Students choose and use appropriate units and measurement tools to quantify the properties of objects:

1.4 Carry out simple unit conversions within a system of measurement (e.g., centimeters and meters, hours and minutes).

Statistics, Data Analysis, and Probability
1.0 Students conduct simple probability experiments by determining the number of possible outcomes and make simple predictions:

1.3 Summarize and display the results of probability experiments in a clear and organized way (e.g., use a bar graph or a line plot).

Mathematical Reasoning
1.0 Students make decisions about how to approach problems:

1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
1.2 Determine when and how to break a problem into simpler parts.

2.0 Students use strategies, skills, and concepts in finding solutions:

2.1 Use estimation to verify the reasonableness of calculated results.
2.2 Apply strategies and results from simpler problems to more complex problems.
2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
2.4 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
2.6 Make precise calculations and check the validity of the results from the context of the problem.

Statistics, Data Analysis, and Probability
1.0 Students organize, represent, and interpret numerical and categorical data and clearly communicate their findings:

1.1 Formulate survey questions; systematically collect and represent data on a number line; and coordinate graphs, tables, and charts.
1.2 Identify the mode(s) for sets of categorical data and the mode(s), median, and any apparent outliers for numerical data sets.
1.3 Interpret one-and two-variable data graphs to answer questions about a situation.

Mathematical Reasoning
1.0 Students make decisions about how to approach problems:

1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
1.2 Determine when and how to break a problem into simpler parts.

2.0 Students use strategies, skills, and concepts in finding solutions:

2.1 Use estimation to verify the reasonableness of calculated results.
2.2 Apply strategies and results from simpler problems to more complex problems.
2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
2.4 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
2.6 Make precise calculations and check the validity of the results from the context of the problem.

3.0 Students move beyond a particular problem by generalizing to other situations:

3.1 Evaluate the reasonableness of the solution in the context of the original situation.
3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.
3.3 Develop generalizations of the results obtained and apply them in other circumstances.

Algebra and Functions
1.0 Students use variables in simple expressions, compute the value of the expression for specific values of the variable, and plot and interpret the results:

1.1 Use information taken from a graph or equation to answer questions about a problem situation.

Statistics, Data Analysis, and Probability
1.0 Students display, analyze, compare, and interpret different data sets, including data sets of different sizes:

1.1 Know the concepts of mean, median, and mode; compute and compare simple examples to show that they may differ.

Mathematical Reasoning
1.0 Students make decisions about how to approach problems:

1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
1.2 Determine when and how to break a problem into simpler parts.

2.0 Students use strategies, skills, and concepts in finding solutions:

2.1 Use estimation to verify the reasonableness of calculated results.
2.2 Apply strategies and results from simpler problems to more complex problems.
2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
2.4 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
2.6 Make precise calculations and check the validity of the results from the context of the problem.

3.0 Students move beyond a particular problem by generalizing to other situations:

3.1 Evaluate the reasonableness of the solution in the context of the original situation.
3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.
3.3 Develop generalizations of the results obtained and apply them in other circumstances.

Algebra and Functions
2.0 Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions:

2.1 Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches).

Mathematical Reasoning
1.0 Students make decisions about how to approach problems:

1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.
1.3 Determine when and how to break a problem into simpler parts.

2.0 Students use strategies, skills, and concepts in finding solutions:

2.1 Use estimation to verify the reasonableness of calculated results.
2.2 Apply strategies and results from simpler problems to more complex problems.
2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.
2.4 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
2.5 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
2.6 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
2.7 Make precise calculations and check the validity of the results from the context of the problem.

3.0 Students move beyond a particular problem by generalizing to other situations:

3.1 Evaluate the reasonableness of the solution in the context of the original situation.
3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.
3.3 Develop generalizations of the results obtained and the strategies used and apply them in new problem situations.

Measurement

PK - 2nd: Understand measurable attributes of objects and the units, systems, and processes of measurement and select an appropriate unit and tool for the attribute being measured.
Apply appropriate techniques, tools, and formulas to determine measurements
use repetition of a single unit to measure something larger than the unit, for instance, measuring the length of a room with a single meterstick;
use tools to measure
3rd - 5th: Understand measurable attributes of objects and the units, systems, and processes of measurement understand the need for measuring with standard units and become familiar with standard units in the customary and metric systems
Apply appropriate techniques, tools, and formulas to determine measurements
select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles;
select and use benchmarks to estimate measurements
6th - 8th: Understand measurable attributes of objects and the units, systems, and processes of measurement
understand both metric and customary systems of measurement;
understand relationships among units and convert from one unit to another within the same system;
Apply appropriate techniques, tools, and formulas to determine measurements
use common benchmarks to select appropriate methods for estimating measurements;
select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision

Data Analysis

PreK - 2nd: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer
pose questions and gather data about themselves and their surroundings;
sort and classify objects according to their attributes and organize data about the objects; represent data using concrete objects, pictures, and graphs.
Select and use appropriate statistical methods to analyze data
describe parts of the data and the set of data as a whole to determine what the data show.
3rd - 5th: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer
design investigations to address a question and consider how data-collection methods affect the nature of the data set;
collect data using observations, surveys, and experiments;
represent data using tables and graphs such as line plots, bar graphs, and line graphs
6th - 8th: Select and use appropriate statistical methods to analyze data find, use, and interpret measures of center and spread, including mean and interquartile range;
discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots.