In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.
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
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Problems
Fractions
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3 - Interpret (Quotients of fractions)
2 - Compute (Quotients of fractions)
3 - Solve (Word problems)
3 - Use (Visual fraction models)
3 - Use (Equations)
2 - Represent (Problem)
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3 - I can interpret quotients of fractions.
2 - I can compute quotients of fractions.
3 - I can solve word problems involving division of fractions.
3 - I can use visual fraction models.
3 - I can use equations.
2 - I can represent a word problem by using visual fraction models and equations.
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A. Real world problems can be solved by dividing fractions by fractions, by using visual fraction models and by using equations to represent the problem.
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A.1 How does one interpret quotients of fractions?
A.2 How does one compute quotients of fractions.
A.3 How does one solve word problems involving division of fractions?
A.4 What is a visual fraction model?
A.5 How does one write an equation to represent a word problem involving fractions?
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Compute fluently with multi-digit numbers and find common factors and multiples.
Fluently divide multi-digit numbers using the standard algorithm.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Numbers
Algorithm
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2 - Divide (Multiple digit numbers)
3 - Use (Standard algorithm)
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2 - I can divide multiple digit numbers.
3 - I can use the standard algorithm to divide.
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A. A standard algorithm can be used to divide multi-digit numbers.
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A.1 What is the standard algorithm for division?
A.2 How does one use the standard algorithm to divide multiple digit numbers?
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Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Decimals
Algorithm
Operations
|
2 - Add (Multiple digit decimals)
2 - Subtract (Multiple digit decimals)
2 - Multiply (Multiple digit decimals)
2 - Divide (Multiple digit decimals)
3 - Use (Standard algorithm)
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2 - I can add multiple digit decimals.
2 - I can subtract multiple digit decimals.
2 - I can multiply multiple digit decimals.
2 - I can divide multiple digit decimals.
3 - I can use the standard algorithm for each operation.
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A. One can add, subtract, multiply and divide multiple digit decimals.
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A.1 What is the standard algorithm for each operation.
A.2 How does one use the standard algorithm to add multiple digit decimals?
A.3 How does one use the standard algorithm to subtract multiple digit decimals?
A.4 How does one use the standard algorithm to multiply multiple digit decimals?
A.5 How does one use the standard algorithm to divide multiple digit decimals?
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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).
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Factor
Multiple
Property
Sum
Numbers
|
2 - Find (Greatest common factor)
2 - Find (Least common multiple)
3 - Use (Distributive property)
2 - Express (Sum as factors)
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2 - I can find the greatest common factor or two whole numbers less than or equal to 100.
2 - I can find the least common multiple of two whole numbers less than or equal to 12.
3 - I can use the distributive property.
2 - I can express the sum of two whole numbers under 101 with a common factor as a multiple of a sum of two whole numbers with no common factor.
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A. One can find the greatest common factor and the least common multiple of two whole numbers.
B. One can use the distributive property to express the sum of two whole numbers as a multiple of a sum of two whole numbers with no common factor.
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A.1 What is a factor?
A.2 How does one find the greatest common factor?
A.3 What is a multiple?
A.4 How does one find the least common multiple?
B.1 What is the distributive property?
B.2 How does one use the distributive property to express the sum of two whole numbers with a common factor?
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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, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Rational Numbers
Opposite quantities e.g.
Contexts
|
2 - Understand (Opposite quantities)
3 - Use (Positive and negative numbers)
2 - Represent (Quantities)
2 - Explain (Meaning of zero)
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2 - I understand that positive and negative numbers are used to describe opposite quantities.
3 - I can use positive and negative numbers to represent quantities in real world context.
2 - I can represent quantities by using positive and negative numbers.
2 - I can explain the meaning of zero when representing real world contexts.
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A. Positive numbers, negative numbers and zero can be used to represent quantities in real world contexts.
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A.1 What are some real world contexts for the use of positive numbers?
A.2 What are some real world contexts for the use of negative numbers?
A.3 What is the meaning of zero when representing real world contexts?
A.4 How does one use positive numbers, negative numbers and zero to represent quantities in real life context?
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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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Number line
Negative coordinates
Opposites [a]
Signed numbers [b]
Opposite coordinates [b]
Number lines [c]
Coordinate plane [c]
|
2 - Understand (Rational numbers)
2 - Extend (Number line diagrams)
2 - Extend (Coordinate axis)
2 - Represent (Points)
2 - Recognize (Opposites locations [a])
2 - Recognize (Opposite values [a])
2 - Recognize (Opposite of zero [a])
2 - Understand (Location of signed coordinates [b])
2 - Recognize (Location of opposite coordinates on axes [b])
3 - Reflect (Coordinates over axes [b])
2 - Find (Integers on a number line [c])
2 - Find (Rational numbers on a number line [c])
3 - Position (Integers on a number line [c])
3 - Position (Rational numbers on a number line [c])
2 - Find (Pairs of integers on a coordinate plane [c])
2 - Find (Pairs of rational numbers on a coordinate plane [c])
3 - Position (Pairs of integers on a coordinate plane [c])
3 - Position (Pairs of rational numbers on a coordinate plane [c])
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2 - I understand that rational numbers are a points on the number line.
2 - I can extend number line diagrams to include negative numbers.
2 - I can extend the coordinate axes to include negative numbers.
2 - I can represent negative number coordinates on the number line and in the plane.
2 - I can recognize that opposite numbers are located on opposite sides of zero on a number line. [a]
2 - I can recognize that the opposite of an opposite is the number itself. [a]
2 - I can recognize that the opposite of zero is zero. [a]
2 - I can understand that signed coordinates indicate locations in the coordinate plane. [b]
2 - I can recognize that the location of opposite coordinates are reflections about the axes. [b]
3 - I can reflect coordinates over one or both axes. [b]
2 - I can find integers on a number line. [c]
2 - I can find rational numbers on a number line. [c]
3 - I can position integers on a number line. [c]
3 - I can position rational numbers on a number line. [c]
2 - I can find pairs of integers on a coordinate plane. [c]
2 - I can find pairs of rational numbers on a coordinate plane. [c]
3 - I can position pairs of integers on a coordinate plane. [c]
3 - I can position pairs of rational numbers on a coordinate plane. [c]
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A. Positive and negative rational numbers can be represented on a number line.
B. One understands how to locate opposites on a number line.
C. Coordinates that differ only by signs are located in different quadrants and are related by reflections across one or both axis
D. One understands how to represent rational numbers and rational coordinates on the number line and in the coordinate plane.
|
A.1 What is a rational number
A.2 How does one find the location of a rational number on a number line?
A.3 How does one extend the number line to include negative numbers?
A.4 How does one extend both coordinate’s axes in a coordinate plane to represent negative numbers?
B.1 What does the term opposite mean?
B.2 Where does one locate the opposite of a number on the number line?
B.3 What is the opposite of an opposite?
B.4 What is the opposite of zero?
C.1 How does one find the location of signed coordinates in the coordinate plane?
C.2 What is a reflection?
C.3 How does one reflect across an axis or both axes?
C.4 What is the relationship when you graph opposite coordinates on the coordinate plane?
D.1 How does one position integers on a number line?
D.2 How does one position rational numbers on a number line?
D.3 How does one position pairs of integers on a coordinate plane?
D.4 How does one position pairs of rational numbers -on a coordinate plane?
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Understand ordering and absolute value of rational numbers.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Rational numbers
Statements [a]
Statements [b]
Absolute value [c]
Magnitude [c]
Comparisons [d]
|
2 - Understand (Ordering rational numbers)
2 - Understand (Absolute value)
2 - Interpret (Statements of inequality [a])
2 - Interpret (Locations on a number line [a])
1 - Write (Statements of order [b])
2 - Interpret (Statements of order [b])
4 - Explain (Statements of order [b])
2 - Understand (Absolute value [c])
2 - Interpret (Absolute value [c])
2 - Distinguish (Comparisons [d])
|
2 - I understand how to put rational numbers in order.
2 - I understand how to find the absolute value of rational numbers.
2 - I can interpret statements of inequality as statements about positions on a number line. [a]
2 - I can interpret statements about positions of two numbers on a number line as statements about inequality. [a]
1 - I can write statements of order for rational numbers in real world contexts. [b]
2 - I can interpret statements of order for rational numbers in real world contexts. [b]
4 - I can explain statements of order for rational numbers in real world contexts. [b]
2 - I understand the absolute value or a rational number is its distance from zero on the number line. [c]
2 - I can interpret the absolute value as magnitude for positive or negative quantities in real world situations. [c]
2 - I can distinguish comparisons of absolute value from statements about order. [d]
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A. Rational numbers have order and an absolute value.
B. The relative position of two numbers on a number line can be determined by interpreting a statement of inequality.
C. Real world inequalities can be interpreted and explained.
D. The magnitude of a quantity is equal to its absolute value, its distance from zero.
E. The absolute value of two numbers can be compared to determine order.
|
A.1 What are the different ways that rational numbers can be ordered?
A.2 How does one order rational numbers?
A.3 How does one change rational numbers to different forms for comparison?
A.4 What does absolute value mean?
A.5 How does one find the absolute value of a rational number?
B.1 How does one interpret statements of inequality as statements about the relative position of two numbers on a number line?
B.2 How does one interpret statements about the relative position of two points on a number line as statements of inequality?
B.3 What are the inequality symbols?
C.1 How does one write statements of order for rational numbers in real world contexts?
C.2 How does one interpret statements of order for rational numbers in real world contexts?
C.3 How does one explain statements of order for rational numbers in real world contexts?
D.1 What is the magnitude of a positive or negative quantity?
D.2 How does one interpret the absolute value as a magnitude for positive or negative quantity in real world situations?
E.1 How does one distinguish comparisons of absolute value from statements about order?
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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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Problems
Distance between points
Value
|
3 - Solve (Real world problems)
3 - Solve (Mathematical problems)
3 - Graph (Points)
3 - Use (Coordinates)
3 - Use (Absolute value)
2 - Find (Distance)
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3 - I can solve real world mathematical problems by graphing on the coordinate plane.
3 - I can solve mathematical problems by graphing on a coordinate plane.
3 - I can use the coordinates of two points to find the distance between the points if their first or second coordinate is the same.
3 - I can use absolute value to find the distance between two points if their first or second coordinate is the same.
2 - I can find the distance between two points if their first or second coordinate is the same.
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A. One can use graphing in the coordinate plane to solve real world and mathematical problems.
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A.1 How does one solve real world problems by graphing on a coordinate plane?
A.2 How does one solve mathematical problems by graphing on a coordinate plane?
A.3 How does one find the distance between two points with the same first or second coordinate?
A.4 What does absolute value mean?
A.5 What is a coordinate plane?
A.6 What are quadrants?
A.7 How does one graph points on the coordinate plane?
A.7 Why must the first or second coordinates be the same to find the distance using these methods?
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