6th grade
number system
STANDARDS
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ESSENTIAL QUESTIONS
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CC.6.NS.1 Apply and extend previous understandings of multiplication and division to divide fractions by fractions. 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?
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What strategies can be used to compute quotients of fractions? What strategies can you use to solve division word problems containing fractions? Why can you use the reciprocal of the divisor and multiply to solve a fraction division problem?
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CC.6.NS.2 Compute fluently with multi-digit numbers and find common factors and multiples. Fluently divide multi-digit numbers using the standard algorithm.
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What is division? What are the benefits of using a standard algorithm to divide numbers?
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CC.6.NS.3 Compute fluently with multi-digit numbers and find common factors and multiples. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
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Why do we need decimals? What are the benefits of using a standard algorithm to add, subtract, multiply, or divide decimals?
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CC.6.NS.4 Compute fluently with multi-digit numbers and find common factors and multiples. 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).
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What is the difference between a factor and a multiple.
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CC.6.NS.5 Apply and extend previous understandings of numbers to the system of rational numbers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, debits/credits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
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What is the difference between a positive and negative number and how is this used to represent real life situations? When placing positive and negative numbers on a number line, how does its placement relative to zero help explain the meaning of the situation represented?
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CC.6.NS.6 Apply and extend previous understandings of numbers to the system of rational numbers. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
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CC.6.NS.6a Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.
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What are some mathematical ways to represent the opposite of being positive or the opposite of being negative? Does a vertical number line also display opposites as the same distance from zero?
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CC.6.NS.6b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
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How can you identify on a coordinate plane the direction of the point on the grid based on the ordered pair? How is the system of graphing locations similar to being given directions from the web or G.P.S.? What is unique about the relationship between two ordered pairs that differ only in their signs?
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CC.6.NS.6c 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.
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What is a coordinate plane? What does knowing which quadrant a point is located in tell you about the coordinates for that point?
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CC.6.NS.7 Apply and extend previous understandings of numbers to the system of rational numbers. Understand ordering and absolute value of rational numbers.
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CC.6.NS.7a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.
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What does the position of a number on a number line have to do with its value? How do you determine the relationship of two numbers by comparing them on a number line?
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CC.6.NS.7b Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3°C > –7°C to express the fact that –3°C is warmer than –7°C.
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What is the meaning of an inequality statement? What would happen to an inequality statement if the numbers were listed in a different order?
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CC.6.NS.7c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.
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How does the opposite of a number differ from its absolute value? How does the distance of a number from zero differ from the distance of the opposite of that same number? Why is it important to relate absolute value to real world situations?
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CC.6.NS.7d Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.
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Why is the absolute value of a number never negative? How does this impact ordering numbers written in absolute value?
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CC.6.NS.8 Apply and extend previous understandings of numbers to the system of rational numbers. 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.
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How do you plot points in all 4 quadrants? How can plotting points on a coordinate plane be used to determine specific locations in real life? How would you find the distance between two vertical points on a coordinate plane? How would you find the distance between two horizontal points on the coordinate plane?
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