# Montana State Standards for Mathematics: Grade 5

MT.1. Number Sense and Operation: A student, applying reasoning and problem solving, will use number sense and operations to represent numbers in multiple ways, understand relationships among numbers and number systems, make reasonable estimates, and compute fluently within a variety of relevant cultural contexts, including those of Montana American Indians.

1.1 Rational Number Relationships: Recognize, model, and compare different forms of integers and rational numbers including percents, fractions, decimals, and numbers using exponents and scientific notation.

1.2 Estimation and Reasonableness: Select and apply appropriate estimation strategies to judge the reasonableness of solutions to problems including those computed on a calculator. Demonstrate correct use of order of operations.

1.3 Number Theory: Use number theory concepts such as prime factorization, greatest common factor, and least common multiple in problem situations.

1.4 Rational Number Operations: Compute fluently and solve multi-step problems using integers, fractions, decimals, and numbers in exponential form.

1.5 Metric and Standard Measurement: Use metric and standard units of measurement in relevant scientific and cultural situations, including those of Montana American Indians, compare and convert within systems, and use appropriate technology.

1.6 Proportional Reasoning: Understand and apply proportional relationships to model real world situations and to solve problems involving rates, ratios, proportions, percents, and direct variation.

MT.2. Data Analysis: A student, applying reasoning and problem solving, will use data representation and analysis, simulations, probability, statistics, and statistical methods to evaluate information and make informed decisions within a variety of relevant cultural contexts, including those of Montana American Indians.

2.1 Representing and Comparing Data: Collect data from a variety of contexts (e.g., science, history, and culture, including Montana American Indians). Organize and represent data in box plots, scatter plots, histograms, and circle graphs using technology when appropriate.

2.2 Evaluating Data and Making Conjectures: Interpret, analyze, and evaluate data using mean, median, range, and quartiles to identify trends and make decisions and predictions about data within scientific and cultural contexts, including those of Montana American Indians.

2.3 Finding Probability and Predicting: Create sample spaces and simulations from events found in different cultures, including those of Montana American Indians, determine experimental and theoretical probabilities, and use probability to make predictions.

MT.3. Geometric Reasoning: A student, applying reasoning and problem solving, will understand geometric properties, spatial relationships, and transformation of shapes, and will use spatial reasoning and geometric models to analyze mathematical situations within a variety of relevant cultural contexts, including those of Montana American Indians.

3.1 Properties of Solids and Figures: Define, classify and compare properties of solids and plane figures, including lines and angles.

3.2 Congruence and Similarity: Use spatial reasoning to determine congruence, similarity, and symmetry of objects in mathematics, art, science, and culture, including Montana American Indians.

3.3 Transformations including Dilations: Define, identify, and execute transformations including translations, rotations, reflections, and dilations with appropriate technology.

3.4 Angles, Surface Area, and Volume: Measure and compute angles, perimeter, area, surface area, and volume including the use of formulas and choosing appropriate units.

3.5 Justifying Relationships: Develop informal arguments to verify geometric relationships and solve problems such as an informal justification of the Pythagorean Theorem in a variety of contexts.

MT.4. Algebraic and Functional Reasoning: A student, applying reasoning and problem solving, will use algebraic concepts and procedures to understand processes involving number, operation, and variables and will use procedures and function concepts to model the quantitative and functional relationships that describe change within a variety of relevant cultural contexts, including those of Montana American Indians.

4.1 Representing and Generalizing Patterns: Create and use tables, graphs or diagrams, symbolic expressions, and verbal descriptions to represent, analyze, and generalize a variety of patterns involving numbers and operations.

4.2 Linear Functions: Identify linear and non-linear functional relationships and contrast their properties using tables, graphs, or equations with appropriate technology.

4.3 Multi-step equations and inequalities: Use number properties and inverse operations to solve multi-step equations and inequalities involving a single variable.

4.4 Equivalent Algebraic Expressions: Recognize, simplify, and generate equivalent forms of algebraic expressions, justifying each step with properties of operations.

4.5 Linear Modeling: Identify and compute rate of change/slope and intercepts from equations, graphs, and tables; model and solve contextual problems involving linear proportions or direct variation using cultural contexts, including those of Montana American Indians.

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