Grade 6
Outcomes
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Ratios And Proportional Relationships
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Understand Ratio Concepts And Use Ratio Reasoning To Solve Problems.
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6.RP.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, 'The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.' 'For every vote candidate A received, candidate C received nearly three votes.'Examples
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6.RP.3
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.Play Activities 158Examples
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6.RP.3.c
Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.Examples
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6.RP.1
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Understand Ratio Concepts And Use Ratio Reasoning To Solve Problems.
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The Number System
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Apply And Extend Previous Understandings Of Multiplication And Division To Divide Fractions By Fractions.
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6.NS.1
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) / (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) / (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) / (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?Examples
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6.NS.1
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Compute Fluently With Multi-Digit Numbers And Find Common Factors And Multiples.
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6.NS.2
Fluently divide multi-digit numbers using the standard algorithm.Examples
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6.NS.3
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.Play Activities 202Examples
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6.NS.4
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).Examples
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6.NS.2
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Apply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers.
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6.NS.6.c
Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.Examples
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6.NS.7
Understand ordering and absolute value of rational numbers.Examples
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6.NS.8
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.Examples
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6.NS.6.c
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Apply And Extend Previous Understandings Of Multiplication And Division To Divide Fractions By Fractions.
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Expressions And Equations
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Apply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions.
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6.EE.1
Write and evaluate numerical expressions involving whole-number exponents.Examples
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6.EE.2
Write, read, and evaluate expressions in which letters stand for numbers.Examples
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6.EE.2.a
Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation 'Subtract y from 5' as 5 - y.Examples
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6.EE.3
Apply the properties of operations to generate equivalent expressions.Examples
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6.EE.1
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Reason About And Solve One-Variable Equations And Inequalities.
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6.EE.6
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.Examples
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6.EE.7
Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.Examples
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6.EE.6
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Apply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions.
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Geometry
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Solve Real-World And Mathematical Problems Involving Area, Surface Area, And Volume.
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6.G.1
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.Examples
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6.G.3
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.Examples
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6.G.4
Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.Examples
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6.G.1
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Solve Real-World And Mathematical Problems Involving Area, Surface Area, And Volume.
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Statistics And Probability
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Develop Understanding Of Statistical Variability.
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6.SP.2
Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.Examples
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6.SP.2
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Summarize And Describe Distributions.
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6.SP.4
Display numerical data in plots on a number line, including dot plots, histograms, and box plots.Examples
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6.SP.5
Summarize numerical data sets in relation to their context, such as by:Examples
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6.SP.5.a
Reporting the number of observations.Examples
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6.SP.5.c
Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.Examples
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6.SP.4
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Develop Understanding Of Statistical Variability.