Unit

Overarching Question

Essential Questions

Big Ideas

Full Objectives

Unit 0:
Growth Mindset

How does mindset affect learning mathematics? 

 Math is about learning, not performing.
 Math is about making sense.
 Math is filled with conjectures, creativity, and uncertainty.
 Mistakes are beautiful things.

 Develop a deep and flexible conceptual understanding
 Develop accurate and appropriate procedural fluency
 Develop strategies for problem solving
 Develop mathematical reasoning
 Develop a productive mathematical disposition
 Develop the ability to make conjectures, model, and generalize
 Develop the ability to communicate mathematically

Unit 1:
Rational Numbers
Timing
56 weeks
Objectives
6.N.1.1
6.N.1.2
6.N.1.3
6.N.1.4
6.N.2.1
6.N.2.2
6.N.2.3
6.N.2.4
6.N.2.5
6.N.2.6
6.N.4.1
6.N.4.2
6.N.4.3
6.N.4.4

How do we work with rational numbers in realworld situations?


How can number relationships help with problem solving?

What is the relationship between fractions, decimals, and percents?

How does comparing numbers describe their relationship?

How can operations with rational numbers help solve real world problems?

How can we use a variety of models to understand rational numbers?

 Factors and multiples can be used to find relationships between numbers.
 Equivalencies exist among fractions, decimals, and percents.
 Positive rational numbers in different forms can be compared and ordered.
 Fractions, decimals, and mixed numbers can be multiplied and divided.
 Integers can be added and subtracted.

6.N.1.1 Use manipulatives and models (e.g., number lines) to determine positive and negative numbers and their contexts, identify opposites, and explain the meaning of 0 (zero) in a variety of situations.
6.N.1.2 Compare and order positive rational numbers, represented in various forms, or integers using the symbols "<", ">", and "=".
6.N.1.3 Explain that a percent represents parts “out of 100” and ratios “to 100.”
6.N.1.4 Determine equivalencies among fractions, mixed numbers, decimals, and percents.
6.N.2.1 Estimate solutions for integer addition and subtraction of problems in order to assess the reasonableness of results.
6.N.2.2 Illustrate addition and subtraction of integers using a variety of representations.
6.N.2.3 Add and subtract integers in a variety of situations; use efficient and generalizable procedures including but not limited to standard algorithms.
6.N.2.4 Identify and represent patterns with wholenumber exponents and perfect squares. Evaluate powers with wholenumber bases and exponents.
6.N.2.5 Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents.
6.N.2.6 Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of twodigit numbers with a common factor using the distributive property.
6.N.4.1 Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers, and use the estimates to assess the reasonableness of results in the context of the problem.
6.N.4.2 Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships. 6.N.4.3 Multiply and divide fractions and decimals using efficient and generalizable procedures.
6.N.4.4 Use mathematical modeling to solve and interpret problems including money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.

Unit 2:
Expressions, Equations, and Inequalities
Timing
45 weeks
Objectives
6.A.1.1
6.A.1.2
6.A.1.3
6.A.2.1
6.A.3.1
6.A.3.2
6.N.2.3 *
6.N.4.3 *
6.N.4.4 *

How do expressions, equations, and inequalities help to solve realworld problems?


How can patterns in realworld scenarios be explored using mathematics?

How can properties help to simplify realworld problems?

How can the order of operations be used to find solutions in realworld problems?

How can equations be used to find solutions to realworld problems?


Mathematical relationships can be expressed using different representations.

Order of operations is used to evaluate and compare expressions.

The commutative, associative, and distributive properties are used to find equivalent expressions.

Equations can be used to find an unknown value.

6.A.1.1 Plot integer and rationalvalued (limited to halves and fourths) orderedpairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs.
6.A.1.2 Represent relationships between two varying positive quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.
6.A.1.3 Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.
6.A.2.1 Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to model and solve mathematical problems.
6.A.3.1 Model mathematical situations using expressions, equations and inequalities involving variables and rational numbers.
6.A.3.2 Use number sense and properties of operations and equality to model and solve mathematical problems involving equations in the form x + p = q and px = q, where p and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.
6.N.2.3 Add and subtract integers in a variety of situations; use efficient and generalizable procedures including but not limited to standard algorithms.
6.N.4.3 Multiply and divide fractions and decimals using efficient and generalizable procedures.
6.N.4.4 Use mathematical modeling to solve and interpret problems including money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.

Unit 3:
Ratios
Timing
34 weeks
Objectives
6.N.3.1
6.N.3.2
6.N.3.3
6.N.1.3 *
6.N.1.4 *
6.N.2.5 *
6.N.2.6 *
6.A.1.2 *
6.A.3.1 *
6.A.3.2 *
6.GM.4.1
6.GM.4.2

How can ratios be applied in realworld situations?


How can we compare quantities?

How do we use the relationship between ratio and rates to solve problems?

How and when are percents useful in realworld scenarios?


Ratios are used to compare quantities.

Unit rates compare quantities with different units where the second quantity in the comparison is 1.

A percent represents a ratio out of a 100.

6.N.3.1 Identify and use ratios to compare and relate quantities in multiple ways. Recognize that multiplicative comparison and additive comparison are different.
6.N.3.2 Determine the unit rate for ratios.
6.N.3.3 Apply the relationship between ratios, equivalent fractions, unit rates, and percents to solve problems in various contexts.
6.N.1.3 Explain that a percent represents parts “out of 100” and ratios “to 100.”
6.N.1.4 Determine equivalencies among fractions, mixed numbers, decimals, and percents.
6.N.2.5 Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents.
6.N.2.6 Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of twodigit numbers with a common factor using the distributive property.
6.A.1.2 Represent relationships between two varying positive quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations. 6.A.3.1 Model mathematical situations using expressions, equations and inequalities involving variables and rational numbers.
6.A.3.2 Use number sense and properties of operations and equality to model and solve mathematical problems involving equations in the form x + p = q and px = q, where p and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.
6.GM.4.1 Estimate weights and capacities using benchmarks in customary and metric measurement systems with appropriate units.
6.GM.4.2 Solve problems that require the conversion of lengths within the same measurement systems using appropriate units.

Unit 4:
Angle Relationships
Timing
12 weeks
Objectives
6.GM.3.1
6.GM.3.2
6.A.3.1 *
6.A.3.2 *

How can angle relationships be used to answer questions in everyday life?


How can we use angle relationships to help solve for missing measures of angles?

What methods can be used to find missing measures of triangles?

 Vertical, complementary, and supplementary angles are formed by intersecting lines.
 The sum of the measure of interior angles of triangles is 180 ̊.

6.GM.3.1 Solve problems using the relationships between the angles (vertical, complementary, and supplementary) formed by intersecting lines.
6.GM.3.2 Develop and use the fact that the sum of the interior angles of a triangle is 180 ̊ to determine missing angle measures in a triangle.
6.A.3.1 Model mathematical situations using expressions, equations and inequalities involving variables and rational numbers.
6.A.3.2 Use number sense and properties of operations and equality to model and solve mathematical problems involving equations in the form x + p = q and px = q, where p and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.

Unit 5:
Transformations
Timing
23 weeks
Objectives
6.GM.1.1
6.GM.1.2
6.GM.1.3
6.A.1.1 *
6.A.1.2 *

How can transformations be applied to realworld situations?


How do transformations affect twodimensional figures?

How can transformations be used to show twodimensional figures are congruent?

How can transformations be used to find lines of symmetry?

 Translations, reflections, and rotations can be used to transform a twodimensional figure.
 Translations, reflections, and rotations preserve congruency and reflections can be used to find lines of symmetry for a twodimensional figure.

6.GM.1.1 Predict, describe, and apply translations (slides), reflections (flips), and rotations (turns) to a twodimensional figure.
6.GM.1.2 Recognize that translations, reflections, and rotations preserve congruence and use them to show that two figures are congruent.
6.GM.1.3 Identify and describe the line(s) of symmetry in twodimensional shapes.
6.A.1.1 Plot integer and rationalvalued (limited to halves and fourths) orderedpairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs.
6.A.1.2 Represent relationships between two varying positive quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.

Unit 6:
Area
Timing
34 weeks
Objectives
6.GM.2.1
6.GM.2.2
6.GM.2.3
6.A.3.1 *
6.A.3.2 *

Why is finding area important?


How can we use rectangles to help to find the area of other quadrilaterals?

How can finding the area of other shapes help to find the area of a triangle?

How can we find area without a formula for that shape?

 The area of a square and a parallelogram is related to the area of a rectangle.
 The area of a triangle is half the area of a rectangle or parallelogram.
 The area of composite figures can be found by decomposing the polygon into rectangles and triangles.

6.GM.2.1 Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithms and finding unknown measures.
6.GM.2.2 Develop and use formulas to determine the area of triangles and find unknown measures.
6.GM.2.3 Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes.
6.A.3.1 Model mathematical situations using expressions, equations and inequalities involving variables and rational numbers.
6.A.3.2 Use number sense and properties of operations and equality to model and solve mathematical problems involving equations in the form x + p = q and px = q, where p and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.

Unit 7:
Data Analysis
Timing
12 weeks
Objectives
6.D.1.1
6.D.1.2
6.N.3.3 *
6.N.4.4 *

How can data analysis be used in realworld scenarios?


How can we analyze data?

What information about a data set is gained from analyzing a visual representation for the data?

 Mean, median, and mode are measures of central tendency that provide information about the center of a data set.
 Box and whisker plots are used to represent the distribution of a data set.

6.D.1.1 Interpret the mean, median, and mode for a set of data.
6.D.1.2 Explain and justify which measure of center (mean, median, or mode) would provide the most descriptive information for a given set of data
6.N.3.3 Apply the relationship between ratios, equivalent fractions, unit rates, and percents to solve problems in various contexts.
6.N.4.4 Use mathematical modeling to solve and interpret problems including money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.

Unit 8:
Probability
Timing
12 weeks
Objectives
6.D.2.1
6.D.2.2
6.D.2.3
6.N.1.4 *
6.N.2.6 *

Why do we need to understand probability?


How can we recognize and compare patterns in probability?

How can the likelihood of an event be represented?

 Probability can be used to predict the likelihood of events.
 Visual representations can be used to show and compare sample space.

6.D.2.1 Represent possible outcomes using a probability continuum from impossible to certain.
6.D.2.2 Determine the sample space for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by the use of tree diagrams, tables or pictorial representations.
6.D.2.3 Demonstrate simple experiments in which the probabilities are known and compare the resulting relative frequencies with the known probabilities, recognizing that there may be differences between the two results.
6.N.1.4 Determine equivalencies among fractions, mixed numbers, decimals, and percents.
6.N.2.6 Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of twodigit numbers with a common factor using the distributive property.

Culminating Unit
Timing
12 weeks

How can patterns in realworld scenarios be explored using mathematics? 



Distance Learning Resources/ Supplemental Activities 
How can students develop and show evidence of understanding? 


Multiple objectives are covered in this material. These math tasks are designed to enhance current curriculum and support distance learning. 
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