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6.1
Students develop number sense and use numbers and number relationships in problem-solving situations and communicate the reasoning used in solving these problems.
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6.1.1
Demonstrate meanings for integers, rational numbers, percents, exponents, square roots and pi using physical materials and technology in problem-solving situations.
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6.1.1.a
Locate commonly used positive rational numbers including terminating decimals through hundredths, fractions (halves, thirds, fourths, eighths, and tenths), mixed numbers, and percents on a number line.
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6.1.1.b
Using physical materials or pictures to demonstrate the meaning and equivalence of fractions, decimals and/or percents (for example, write the fractions, decimal, and percent value for the shaded portion of a partially shaded circle).
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6.1.2
Read and write and order integers, rational numbers and common irrational numbers such as square root of 2, square root of 5 and x.
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6.1.2.a
Read, write, order and compare common fractions, decimals, and percents in a variety of forms.
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6.1.3
Apply number theory concepts (for example, primes, factors, multiples) to represent numbers in various ways.
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6.1.3.a
Identify and use the concepts of factor, multiple, prime, composite, and square numbers.
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6.1.3.b
Describe numbers by characteristics (divisibility, even, odd, prime, composite, square).
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6.1.4
Use the relationships among fractions, decimals, and percents, including the concepts of ratio and proportion, in problem-solving situations.
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6.1.4.a
Demonstrate equivalence relationships among fractions, decimals and percents in problem-solving situations (for example, two students out of eight is the same as 25%)
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6.1.5
Develop, test, and explain conjectures about properties of integers and rational numbers.
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6.1.5.a
Develop, test, and explain conjectures about properties of numbers (associative, commutative, identity, distributive multiplicative property of zero on whole and rational numbers.)
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6.1.6
Use number sense to estimate and justify the reasonableness of solutions to problems involving inteters, rational numbers, and common irrational numbers such as square root of 2, square root of 5 and pi.
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6.1.6.a
Use number sense to estimate, determine, and justify the reasonableness of solutions involving whole numbers, decimals, and common fractions (only sums and differences for fractions and decimals). For example: Is 1/2 + 1/3 closer to 0, 1/2 or 1?
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6.2
Students use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in solving these problems.
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6.2.1
Represent, describe, and analyze patterns and relationships using tables, graphs, verbal rules, and standard algebraic notation.
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6.2.1.a
Represent, describe, and analyze geometric and numeric patterns using tables, words, symbols, concrete objects, or pictures.
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6.2.1.b
Use a variable to represent an unknown (letter, box, symbol).
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6.2.2
Describe patterns using variables, expressions, equations, and inequalities in problem-solving situations.
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6.2.2.a
Solve problems by representing and analyzing patterns using tables, words, concrete objects, or pictures.
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6.2.3
Analyze functional relationships to explain how a change in one quantity results in a change in another (for example, how the area of a circle changes as the radius increases, or how a person's height changes over time).
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6.2.3.a
Predict and describe how a change in one quantity results in a change in another quantity in a linear relationship (for example, A creature gains 3 oz. a day, how much will it have gained over 10 days?)
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6.2.4
Distinguish between linear and nonlinear functions through informal investigations.
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6.2.4.a
Explain whether data presented in a chart or graph is changing at a constant rate.
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6.2.5
Solve simple linear equations in problem-solving situations using a variety of methods (informal, formal, and graphical) and a variety of tools (physical materials, calculators, and computers).
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6.2.5.a
Solve problems using tables, concrete objects, or pictures involving linear relationships with whole numbers.
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6.3
Students use data collection and analysis, statistics, and probability in problem-solving situations and communicate the reasoning used in solving these problems.
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6.3.1
Read and construct displays of data using appropriate techniques (for example, line graphs, circle graphs, scatter plots, box plots, stem-and-leaf plots) and appropriate technology.
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6.3.1.a
Organize and construct a line graph, bar graph, and frequency table from a given set of data.
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6.3.1.b
Read, interpret and draw conclusions from a line graph, bar graph, circle graph and frequency table.
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6.3.2
Display and use measures of central tendency, such as mean, median and mode and measures of variability, such as range and quartiles.
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6.3.2.a
Find and use measures of central tendency including mean, median, and mode.
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6.3.2.b
Find and use the range from a given set of data (for example, find the range from 2 to 12. Note: the range is 10).
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6.3.3
Evaluate arguments that are based on statistical claims.
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6.3.4
Formulate hypotheses, drawing conclusions, and making convincing arguments based on data analysis.
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6.3.4.a
Analyze data and draw conclusions to predict outcomes based on data displays such as line graphs, bar graphs, or frequency tables.
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6.3.5
Determine probabilities through experiments or simulations.
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6.3.6
Make predictions and compare results using both experimental and theoretical probability drawn from real-world problems.
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6.3.6.a
Using a chance device, such as a number cube or spinner, design a fair game and an unfair game, and explain why they are fair and unfair respectively.
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6.3.6.b
Make predictions based on data obtained from simple probability experiments.
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6.3.6.c
Describe an event as likely or unlikely and explain the degree of likelihood using words such as certain, very likely, not likely, or impossible.
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6.3.7
Use counting strategies to determine all the possible outcomes from an experiment (for example, the number of ways students can line up to have their picture taken).
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6.3.7.a
Determine the number of possible outcomes for simple events using a variety of methods such as: organized lists or tree diagrams.
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6.4
Students use geometric concepts, properties, and relationships in problem-solving situations and communicate the reasoning used in solving these problems.
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6.4.1
Construct two-and three-dimensional models using a variety of materials and tools.
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6.4.2
Describe, analyze and reason informally about the properties (for example, parallelism, perpendicularity, congruence) of two- and three-dimensional figures.
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6.4.2.a
Identify, compare, and analyze the attributes of two-and three-dimensional shapes and develop vocabulary to describe the attributes (for example, acute, obtuse, right angle, parallel lines, perpendicular lines, intersecting lines, and line segments).
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6.4.2.b
Make and test conjectures about geometric relationships and develop logical arguments to justify conclusions.
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6.4.3
Apply the concept of ratio, proportion and similarity in problem-solving situations
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6.4.4
Solve problems using coordinate geometry.
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6.4.4.a
Plot points on a coordinate graph in quadrant 1
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6.4.4.b
Draw a graph (in quadrant 1) from a given scenario or table.
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6.4.5
Solving problems involving perimeter and area in two dimensions, and involving surface area and volume in three dimensions.
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6.4.5.a
Solve problems involving the perimeter of polygons.
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6.4.5.b
Solve problems involving area of polygons (square, rectangle, parallelogram, rhombus, triangle)
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6.4.6
Transforming geometric figures using reflections, translations, and rotations to explore congruence.
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6.4.6.a
Identify congruent shapes using reflections, rotations, and translations.
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6.4.6.b
Show lines of symmetry on a two-dimensional figure.
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6.5
Students use a variety of tools and techniques to measure, apply the results in problem-solving situations, and communicate the reasoning used in solving these problems.
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6.5.1
Estimate, use and describe measures of distance, perimeter, area, volume, capacity, weight, mass, and angle comparison.
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6.5.1.a
Determine the appropriate unit of measure, metric and US customary, when estimating distance, capacity, and weight.
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6.5.1.b
Estimate and use standard and/or metric units for length, weight and temperature.
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6.5.1.c
Estimate the area of a polygon.
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6.5.2
Estimate, make, and use direct and indirect measurements to describe and make comparisons.
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6.5.2.a
Estimate, make and use direct and indirect measurements to describe and make comparisons.
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6.5.3
Read and interpret various scales including those based on number lines, graphs, and maps.
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6.5.3.a
Read and interpret scales on numberer lines, graphs, and maps.
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6.5.3.b
Select the appropriate scale for a given problem (for example, using the appropriate scale when setting up a graph or determining the order of numbers on a number line).
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6.5.4
Develop and use formulas and procedures to solve problems involving measurement.
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6.5.4.a
Use formulas and/or procedures to solve problems involving the perimeter of a polygon.
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6.5.4.b
Use formulas and/or procedures to solve problems involving the area of squares, rectangles, parallelograms, rhombus, and triangles.
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6.5.5
Describe how a change in an object's linear dimensions affects its perimeter, area, and volume.
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6.5.5.a
Demonstrate how changing one of the dimensions of a rectangle or triangle affects its perimeter and area using concrete materials or graph paper.
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6.5.6
Select and use appropriate units and tools to measure to the degree of accuracy required in a particular problemsolving situation.
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6.6
Students link concepts and procedures as they develop and use computational techniques, including estimation, mental arithmetic, paper-and-pencil, calculators, and computers, in problem-solving situations and communicate the reasoning used in solving these problems.
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6.6.1
Use models to explain how ratios, proportions, and percents can be used to solve real-world problems.
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6.6.1.a
Use concrete materials or pictures to determine commonly used percentages (for example, 25%, 50%) in problem-solving situations.
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6.6.2
Construct, use and explain procedures to compute and estimate with whole numbers, fractions, decimals, and integers.
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6.6.2.a
Demonstrate conceptual meaning of addition and subtraction of fractions and decimals, in problem solving situations.
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6.6.2.b
Use and explain strategies to add/subtract decimals and fractions in problem-solving situations (common fractions with like and unlike denominators, mixed numbers, and decimals to thousandth.)
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6.6.2.c
Find equivalent representations by decomposing and composing whole numbers (for example, 48 x 12 = (48 x 10) + (48 x 2)).
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6.6.2.d
Demonstrate proficiency with the four basic operations using whole numbers.
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6.6.3
Develop, apply and explain a variety of different estimation strategies in problem-solving situations, and explain why an estimate may be acceptable in place of an exact answer.
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6.6.3.a
Develop, apply and explain a variety of different estimation strategies in problem-solving situations and explain why an estimate may be acceptable in place of an exact answer.
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6.6.4
Select and use appropriate methods for computing with commonly used fractions and decimals, percents, and integers in problem-solving situations from among mental arithmetic, estimation, paper-and-pencil, calculator, and computer methods, and determining whether the results are reasonable.
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6.6.4.a
Apply appropriate computation methods to solve problems involving whole numbers, common fractions, and decimals (use only addition and subtraction of fractions and decimals).
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6.6.4.b
In a problem-solving situation, determine whether the results are reasonable and justify those results with accurate computation.
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