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Aim-for-A Tutoring Curriculums
NYSE Standards


  • Problem solving
  • Reasoning and Proof
  • Communication
  • Connections
  • Representation
Problem solving
6.PS.1 Explore, examine, and make observations about a social problem or mathematical situation
6.PS.2 Understand that some ways of representing a problem are more helpful than others
6.PS.3 Interpret information correctly, identify the problem, and generate possible solutions
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
6.PS.6 Translate from a picture/diagram to a numeric expression
6.PS.7 Represent problem solving situations in oral, written, concrete, pictorial, and graphical forms
6.PS.8 Select an appropriate representation of a problem
6.PS.9 Use trial and error to solve problems
6.PS.10 Use process of elimination to solve problems
6.PS.11 Make pictures/diagrams of problems
6.PS.12 Use physical objects to model problems
6.PS.13 Work in collaboration with others to solve problems
6.PS.14 Make organized lists to solve numerical problems
6.PS.15 Make charts to solve numerical problems
6.PS.16 Analyze problems by identifying relationships
6.PS.17 Analyze problems by identifying relevant versus irrelevant information
6.PS.18 Analyze problems by observing patterns
6.PS.19 State a problem in their own words
6.PS.20 Determine what information is needed to solve a problem
6.PS.21 Discuss with peers to understand a problem situation
6.PS.22 Discuss the efficiency of different representations of a problem
6.PS.23 Verify results of a problem
6.PS.24 Recognize invalid approaches
6.PS.25 Determine whether a solution is reasonable in the context of the original problem
Reasoning and Proof
6.RP.1 Use representations to support mathematical ideas
6.RP.2 Determine whether a mathematical statement is true or false and explain why
6.RP.3 Investigate the use of knowledgeable guessing by generalizing mathematical ideas
6.RP.4 Make conjectures from a variety of representations
6.RP.5 Justify general claims or conjectures, using manipulatives, models, and expressions
6.RP.6 Develop and explain an argument using oral, written, concrete, pictorial, and/or graphical forms
6.RP.7 Discuss, listen, and make comments that support or reject claims made by other students
6.RP.8 Support an argument by trying many cases
6.CM.1 Understand and explain how to organize their thought process
6.CM.2 Verbally explain their rationale for strategy selection
6.CM.3 Provide reasoning both in written and verbal form
6.CM.4 Organize and accurately label work
6.CM.5 Share organized mathematical ideas through the manipulation of objects, drawings, pictures, charts, graphs, tables, diagrams, models, symbols, and expressions in written and verbal form
6.CM.6 Answer clarifying questions from others
6.CM.7 Listen for understanding of mathematical solutions shared by other students
6.CM.8 Consider strategies used and solutions found in relation to their own work
6.CM.9 Increase their use of mathematical vocabulary and language when communicating with others
6.CM.10 Describe objects, relationships, solutions and rationale using appropriate vocabulary
6.CM.11 Decode and comprehend mathematical visuals and symbols to construct meaning
6.CN.1 Recognize, understand, and make connections in their everyday experiences to mathematical ideas
6.CN.2 Compare and contrast mathematical ideas
6.CN.3 Connect and apply mathematical information to solve problems
6.CN.4 Understand multiple representations and how they are related
6.CN.5 Model situations with objects and representations and be able to make observations
6.CN.6 Recognize the presence of mathematics in their daily lives
6.CN.7 Apply mathematics to solve problems that develop outside of mathematics
6.CN.8 Recognize and apply mathematics to other disciplines
6.R.1 Use verbal and written language, physical models, drawing charts, graphs, tables, symbols, and equations as representations
6.R.2 Share mental images of mathematical ideas and understandings
6.R.3 Recognize and use external mathematical representations
6.R.4 Use standard and nonstandard representations with accuracy and detail
6.R.5 Understand similarities and differences in representations
6.R.6 Connect mathematical representations with problem solving
6.R.7 Construct effective representations to solve problems
6.R.8 Use mathematics to show and understand physical phenomena (e.g., estimate and represent the number of apples in a tree)
6.R.9 Use mathematics to show and understand social phenomena (e.g., determine the number of buses required for a field trip)
6.R.10 Use mathematics to show and understand mathematical phenomena (e.g., use a multiplication grid to solve odd and even number problems)
The Process Strands highlight ways of acquiring and using content knowledge. Though the Process Strands are not individually covered, students are required to problem solve, reason, and apply their knowledge throughout.


Number Sense and Operations Strand

Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.
Number Systems
6.N.1 - Read and write whole numbers to trillions
6.N.2 - Define and identify the commutative and associative properties of addition and multiplication
6.N.3 - Define and identify the distributive property of multiplication over addition
6.N.4 - Define and identify the identity and inverse properties of addition and multiplication
6.N.5 - Define and identify the zero property of multiplication
6.N.6 - Understand the concept of ratio
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.11 - Read, write, and identify percents of a whole (0% to 100%)
6.N.12 - Solve percent problems involving percent, rate, and base
6.N.13 - Define absolute value and determine the absolute value of rational numbers (including positive and negative)
6.N.14 - Locate rational numbers on a number line (including positive and negative)
6.N.15 - Order rational numbers (including positive and negative)
Students will understand meanings of operations and procedures, and how they relate to one another.
6.N.16 - Add and subtract fractions with unlike denominators
6.N.17 - Add, subtract, multiply, and divide fractions with unlike denominators.
6.N.18 - Multiply and divide mixed numbers with unlike denominators
6.N.19 - Identify the multiplicative inverse (reciprocal) of a number
6.N.20 - Represent fractions as terminating or repeating decimals
6.N.21 - Find multiple representations of rational numbers (fractions, decimals, and percents 0 to 100)
6.N.22 - Evaluate numerical expressions using order of operations (may include exponents of two and three)
6.N.23 - Represent repeated multiplication in exponential form
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 Exponents
Students will compute accurately and make reasonable estimates.
6.N.26 - Estimate a percent of quantity (0% to 100%)
6.N.27 - Justify the reasonableness of answers using estimation (including rounding)

Algebra Strand

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
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)
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.)

Geometry Strand

Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric 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
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 Strand

Students will determine what can be measured and how, using appropriate methods and formulas.
Units of Measurement
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)
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)
Tools and Methods
6.M.6 - Determine the tool and technique to measure with an appropriate level of precision: capacity
Students will develop strategies for estimating measurements.
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

Statistics and Probability Strand

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
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)
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
Students will make predictions that are based upon data analysis.
Predictions from Data
6.S.8 - Justify predictions made from data
Students will understand and apply concepts of 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
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