MST Standard 3 Math:
Grade 6
|
Through the integrated study of number sense and operations, algebra, geometry, measurement,
and statistics and probability, students will:
- understand the concepts of and become proficient with the skills of mathematics;
- communicate and reason mathematically;
- become problem solvers by using appropriate tools and strategies;
|
Algebra
Students will represent and analyze algebraically a wide variety of problem solving situations.
Variables and Expressions
|
| |
6.A.1 |
Translate two-step verbal expressions into algebraic expressions
|
|
| |
|
|
|
Algebra
Students will perform algebraic procedures accurately.
Equations and Inequalities
|
| |
6.A.3 |
Translate two-step verbal sentences into algebraic equations
|
|
| |
6.A.4 |
Solve and explain two-step equations involving whole numbers using inverse operations
|
|
| |
6.A.5 |
Solve simple proportions within context
|
|
| |
6.A.6 |
Evaluate formulas for given input values (circumference, area, volume, distance, temperature, interest, etc.)
|
|
| |
|
|
|
Algebra
Students will perform algebraic procedures accurately.
Variables and Expressions
|
| |
6.A.2 |
Use substitution to evaluate algebraic expressions (may include exponents of one, two and three)
|
|
| |
|
|
|
Communication
Students will organize and consolidate their mathematical thinking through communication.
|
| |
6.CM.3 |
Organize and accurately label work
|
|
| |
6.CM.2 |
Explain a rationale for strategy selection
|
|
| |
6.CM.1 |
Provide an organized thought process that is correct, complete, coherent, and clear
|
|
| |
|
|
|
Communication
Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
|
| |
6.CM.5 |
Answer clarifying questions from others
|
|
| |
6.CM.4 |
Share organized mathematical ideas through the manipulation of objects, numerical tables, drawings, pictures, charts, graphs, tables, diagrams, models, and symbols in written and verbal form
|
|
| |
|
|
|
Communication
Students will analyze and evaluate the mathematical thinking and strategies of others.
|
| |
6.CM.8 |
Consider strategies used and solutions found by others in relation to their own work
|
|
| |
6.CM.7 |
Raise questions that elicit, extend, or challenge others' thinking
|
|
| |
6.CM.6 |
Understand mathematical solutions shared by other students
|
|
| |
|
|
|
Communication
Students will use the language of mathematics to express mathematical ideas precisely.
|
| |
6.CM.11 |
Decode and comprehend mathematical visuals and symbols to construct meaning
|
|
| |
6.CM.10 |
Use appropriate vocabulary when describing objects, relationships, mathematical solutions, and rationale
|
|
| |
6.CM.9 |
Increase their use of mathematical vocabulary and language when communicating with others
|
|
| |
|
|
|
Connections
Students will recognize and use connections among mathematical ideas.
|
| |
6.CN.2 |
Explore and explain the relationship between mathematical ideas
|
|
| |
6.CN.3 |
Connect and apply mathematical information to solve problems
|
|
| |
6.CN.1 |
Understand and make connections and conjectures in their everyday experiences to mathematical ideas
|
|
| |
|
|
|
Connections
Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
|
| |
6.CN.4 |
Understand multiple representations and how they are related
|
|
| |
6.CN.5 |
Model situations with objects and representations and be able to draw conclusions
|
|
| |
|
|
|
Connections
Students will recognize and apply mathematics in contexts outside of mathematics.
|
| |
6.CN.9 |
Recognize and apply mathematics to other disciplines and areas of interest
|
|
| |
6.CN.7 |
Apply mathematics to problem situations that develop outside of mathematics
|
|
| |
6.CN.6 |
Recognize and provide examples of the presence of mathematics in their daily lives
|
|
| |
6.CN.8 |
Investigate the presence of mathematics in careers and areas of interest
|
|
| |
|
|
|
Geometry
Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.
Shapes
|
| |
6.G.1 |
Calculate the length of corresponding sides of similar triangles, using proportional reasoning
|
|
| |
6.G.2 |
Determine the area of triangles and quadrilaterals (squares, rectangles, rhombi, and trapezoids) and develop formulas
|
|
| |
6.G.3 |
Use a variety of strategies to find the area of regular and irregular polygons
|
|
| |
6.G.4 |
Determine the volume of rectangular prisms by counting cubes and develop the formula
|
|
| |
6.G.5 |
Identify radius, diameter, chords and central angles of a circle
|
|
| |
6.G.6 |
Understand the relationship between the diameter and radius of a circle
|
|
| |
6.G.7 |
Determine the area and circumference of a circle, using the appropriate formula
|
|
| |
6.G.8 |
Calculate the area of a sector of a circle, given the measure of a central angle and the radius of the circle
|
|
| |
6.G.9 |
Understand the relationship between the circumference and the diameter of a circle
|
|
| |
|
|
|
Geometry
Students will apply coordinate geometry to analyze problem solving situations.
Coordinate Geometry
|
| |
6.G.10 |
Identify and plot points in all four quadrants
|
|
| |
6.G.11 |
Calculate the area of basic polygons drawn on a coordinate plane (rectangles and shapes composed of rectangles having sides with integer lengths)
|
|
| |
|
|
|
Measurement
Students will determine what can be measured and how, using appropriate methods and formulas.
Units of Measurement
|
| |
6.M.3 |
Identify equivalent customary units of capacity (cups to pints, pints to quarts, and quarts to gallons)
|
|
| |
6.M.4 |
Identify metric units of capacity (liter and milliliter)
|
|
| |
6.M.5 |
Identify equivalent metric units of capacity (milliliter to liter and liter to milliliter)
|
|
| |
6.M.1 |
Measure capacity and calculate volume of a rectangular prism
|
|
| |
6.M.2 |
Identify customary units of capacity (cups, pints, quarts, and gallons)
|
|
| |
|
|
|
Measurement
Students will determine what can be measured and how, using appropriate methods and formulas.
Tools and Methods
|
| |
6.M.6 |
Determine the tool and technique to measure with an appropriate level of precision: capacity
|
|
| |
|
|
|
Measurement
Students will develop strategies for estimating measurements.
Estimation
|
| |
6.M.7 |
Estimate volume, area, and circumference (see figures identified in geometry strand)
|
|
| |
6.M.8 |
Justify the reasonableness of estimates
|
|
| |
6.M.9 |
Determine personal references for capacity
|
|
| |
|
|
|
Number Sense and Operations
Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.
Number Systems
|
| |
6.N.15 |
Order rational numbers (including positive and negative)
|
|
| |
6.N.14 |
Locate rational numbers on a number line (including positive and negative)
|
|
| |
6.N.13 |
Define absolute value and determine the absolute value of rational numbers (including positive and negative)
|
|
| |
6.N.12 |
Solve percent problems involving percent, rate, and base
|
|
| |
6.N.6 |
Understand the concept of rate
|
|
| |
6.N.7 |
Express equivalent ratios as a proportion
|
|
| |
6.N.8 |
Distinguish the difference between rate and ratio
|
|
| |
6.N.9 |
Solve proportions using equivalent fractions
|
|
| |
6.N.10 |
Verify the proportionality using the product of the means equals the product of the extremes
|
|
| |
6.N.5 |
Define and identify the zero property of multiplication
|
|
| |
6.N.4 |
Define and identify the identity and inverse properties of addition and multiplication
|
|
| |
6.N.3 |
Define and identify the distributive property of multiplication over addition
|
|
| |
6.N.2 |
Define and identify the commutative and associative properties of addition and multiplication
|
|
| |
6.N.1 |
Read and write whole numbers to trillions
|
|
| |
6.N.11 |
Read, write, and identify percents of a whole (0% to 100%)
|
|
| |
|
|
|
Number Sense and Operations
Students will understand meanings of operations and procedures, and how they relate to one another.
Operations
|
| |
6.N.24 |
Represent exponential form as repeated multiplication
|
|
| |
6.N.25 |
Evaluate expressions having exponents where the power is an exponent of one, two, or three
|
|
| |
6.N.23 |
Represent repeated multiplication in exponential form
|
|
| |
6.N.22 |
Evaluate numerical expressions using order of operations (may include exponents of two and three)
|
|
| |
6.N.21 |
Find multiple representations of rational numbers (fractions, decimals, and percents 0 to 100)
|
|
| |
6.N.20 |
Represent fractions as terminating or repeating decimals
|
|
| |
6.N.19 |
Identify the multiplicative inverse (reciprocal) of a number
|
|
| |
6.N.18 |
Add, subtract, multiply, and divide mixed numbers with unlike denominators
|
|
| |
6.N.17 |
Multiply and divide fractions with unlike denominators
|
|
| |
6.N.16 |
Add and subtract fractions with unlike denominators
|
|
| |
|
|
|
Number Sense and Operations
Students will compute accurately and make reasonable estimates.
Estimation
|
| |
6.N.27 |
Justify the reasonableness of answers using estimation (including rounding)
|
|
| |
6.N.26 |
Estimate a percent of quantity (0% to 100%)
|
|
| |
|
|
|
Problem Solving
Students will build new mathematical knowledge through problem solving.
|
| |
6.PS.2 |
Understand that some ways of representing a problem are more efficient than others
|
|
| |
6.PS.3 |
Interpret information correctly, identify the problem, and generate possible strategies and solutions
|
|
| |
6.PS.1 |
Know the difference between relevant and irrelevant information when solving problems
|
|
| |
|
|
|
Problem Solving
Students will solve problems that arise in mathematics and in other contexts.
|
| |
6.PS.8 |
Select an appropriate representation of a problem
|
|
| |
6.PS.9 |
Understand the basic language of logic in mathematical situations (and, or, and not)
|
|
| |
6.PS.6 |
Translate from a picture/diagram to a numeric expression
|
|
| |
6.PS.7 |
Represent problem situations verbally, numerically, algebraically, and/or graphically
|
|
| |
6.PS.4 |
Act out or model with manipulatives activities involving mathematical content from literature
|
|
| |
6.PS.5 |
Formulate problems and solutions from everyday situations
|
|
| |
|
|
|
Problem Solving
Students will apply and adapt a variety of appropriate strategies to solve problems.
|
| |
6.PS.14 |
Analyze problems by observing patterns
|
|
| |
6.PS.15 |
Make organized lists or charts to solve numerical problems
|
|
| |
6.PS.13 |
Model problems with pictures/diagrams or physical objects
|
|
| |
6.PS.11 |
Translate from a picture/diagram to a number or symbolic expression
|
|
| |
6.PS.12 |
Use trial and error and the process of elimination to solve problems
|
|
| |
6.PS.10 |
Work in collaboration with others to solve problems
|
|
| |
|
|
|
Problem Solving
Students will monitor and reflect on the process of mathematical problem solving.
|
| |
6.PS.23 |
Verify results of a problem
|
|
| |
6.PS.22 |
Discuss whether a solution is reasonable in the context of the original problem
|
|
| |
6.PS.16 |
Discuss with peers to understand a problem situation
|
|
| |
6.PS.17 |
Determine what information is needed to solve problem
|
|
| |
6.PS.18 |
Determine the efficiency of different representations of a problem
|
|
| |
6.PS.21 |
Explain the methods and reasoning behind the problem solving strategies used
|
|
| |
6.PS.19 |
Differentiate between valid and invalid approaches
|
|
| |
6.PS.20 |
Understand valid counterexamples
|
|
| |
|
|
|
Reasoning and Proof
Students will recognize reasoning and proof as fundamental aspects of mathematics.
|
| |
6.RP.2 |
Understand that mathematical statements can be supported, using models, facts, and relationships to explain their thinking
|
|
| |
6.RP.1 |
Recognize that mathematical ideas can be supported using a variety of strategies
|
|
| |
|
|
|
Reasoning and Proof
Students will make and investigate mathematical conjectures.
|
| |
6.RP.4 |
Make and evaluate conjectures, using a variety of strategies
|
|
| |
6.RP.3 |
Investigate conjectures, using arguments and appropriate mathematical terms
|
|
| |
|
|
|
Reasoning and Proof
Students will develop and evaluate mathematical arguments and proofs.
|
| |
6.RP.7 |
Verify claims other students make, using examples and counterexamples when appropriate
|
|
| |
6.RP.6 |
Develop and explain an argument verbally, numerically, algebraically, and/or graphically
|
|
| |
6.RP.5 |
Justify general claims or conjectures, using manipulatives, models, expressions, and mathematical relationships
|
|
| |
|
|
|
Reasoning and Proof
Students will select and use various types of reasoning and methods of proof.
|
| |
6.RP.9 |
Devise ways to verify results
|
|
| |
6.RP.8 |
Support an argument through examples/counterexamples and special cases
|
|
| |
|
|
|
Representation
Students will create and use representations to organize, record, and communicate mathematical ideas.
|
| |
6.R.1 |
Use physical objects, drawings, charts, tables, graphs, symbols, equations, or objects created using technology as representations
|
|
| |
6.R.2 |
Explain, describe, and defend mathematical ideas using representations
|
|
| |
6.R.3 |
Read, interpret, and extend external models
|
|
| |
6.R.4 |
Use standard and nonstandard representations with accuracy and detail
|
|
| |
|
|
|
Representation
Students will select, apply, and translate among mathematical representations to solve problems.
|
| |
6.R.5 |
Use representations to explore problem situations
|
|
| |
6.R.6 |
Investigate relationships between different representations and their impact on a given problem
|
|
| |
|
|
|
Representation
Students will use representations to model and interpret physical, social, and mathematical phenomena.
|
| |
6.R.8 |
Use mathematics to show and understand social phenomena (e.g., construct tables to organize data showing book sales)
|
|
| |
6.R.9 |
Use mathematics to show and understand mathematical phenomena (e.g., Find the missing value: (3 + 4) + 5 = 3 + (4 + ___ )
|
|
| |
6.R.7 |
Use mathematics to show and understand physical phenomena (e.g., determine the perimeter of a bulletin board)
|
|
| |
|
|
|
Statistics and Probability
Students will collect, organize, display, and analyze data.
Collection of Data
|
| |
6.S.1 |
Develop the concept of sampling when collecting data from a population and decide the best method to collect data for a particular question
|
|
| |
|
|
|
Statistics and Probability
Students will collect, organize, display, and analyze data.
Organization and Display of Data
|
| |
6.S.2 |
Record data in a frequency table
|
|
| |
6.S.3 |
Construct Venn diagrams to sort data
|
|
| |
6.S.4 |
Determine and justify the most appropriate graph to display a given set of data (pictograph, bar graph, line graph, histogram, or circle graph)
|
|
| |
|
|
|
Statistics and Probability
Students will collect, organize, display, and analyze data.
Analysis of Data
|
| |
6.S.5 |
Determine the mean, mode and median for a given set of data
|
|
| |
6.S.6 |
Determine the range for a given set of data
|
|
| |
6.S.7 |
Read and interpret graphs
|
|
| |
|
|
|
Statistics and Probability
Students will make predictions that are based upon data analysis.
Predictions from Data
|
| |
6.S.8 |
Justify predictions made from data
|
|
| |
|
|
|
Statistics and Probability
Students will understand and apply concepts of probability.
Probability
|
| |
6.S.9 |
List possible outcomes for compound events
|
|
| |
6.S.10 |
Determine the probability of dependent events
|
|
| |
6.S.11 |
Determine the number of possible outcomes for a compound event by using the fundamental counting principle and use this to determine the probabilities of events when the outcomes have equal probability
|
|
| |
|
|
|
