Our Lady of Grace Curriculum Map

Grade: 6

Subject(s): Operations with Whole Numbers and Decimals

Time Frame: Quarter 1

Essential Question(s):

• How can you extend the use of place value to decimal operations?
• How can you use what you know about repeated subtraction, equal sharing, and forming equal groups to solve division problems?
• How can estimating be helpful?
• How does division undo multiplication?

IN Standards

Prior Learning

Content and Skills

Key Vocabulary

Assessments

Resources

Brainstorms

Extensions

STEM Integration

✓+ (Critical)

• 6.C.1 Divide multi-digit whole numbers fluently using a standard algorithmic approach.
• 6.C.2 Compute with positive fractions and positive decimals fluently using a standard algorithmic approach.
• 6.C.3 Solve real-world problems with positive fractions and decimals by using one or two operations.

✓ (Important)

• 6.NS.7 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 from 1 to 100, with a common factor as a multiple of a sum of two whole numbers with no common factor.

✓- (Additional)

• 6.NS.6 Identify and explain prime and composite numbers.

• Multiplication and division facts up to 10
• Find factor pairs for a whole number in the range 1-100
• Compare two decimals to the hundredths
• Multi-digit whole number multiplication using models and the standard algorithm
• Find whole number quotients and remainders with up to 4-digit dividends and 2-digit divisors

1. Identify if a number is prime or composite and explain why
2. Find the GCF of two whole numbers  ≤ 100
3. Find the LCM of two whole numbers  ≤ 12
4. Add and subtract positive decimals
5. Multiply positive decimals
6. Divide multi-digit whole numbers (decimal remainders)
7. Divide positive decimals
8. 1-2 step problem solving with decimal operations

1. Prime number
2. Composite number
3. Factors
4. Multiples
5. Greatest common factor
6. Least common multiple
7. Prime factorization
8. Quotient
9. Dividend
10. Divisor

Checks for Understanding

• ConnectEd guided practice problems
• Mid-chapter checks
• Multi-digit whole number division quiz

Summative

• Decimal operations test

-Indiana Glencoe Math Course 1 and ConnectEd:

• Chapter 1 lesson 1
•  Chapter 3 

-Khan Academy

-IXL

-www.multiplication.com timed tests

Adding/Subtracting/Multiplying decimals jeopardy

Inquiry Lab- multiply powers of 10

Grade: 6

Subject(s): Fraction Understanding and Application

Time Frame: Quarter 1

Essential Question(s):

• How can estimating be helpful?
• A fraction is part of a whole. What is a fraction of a fraction?
• How is dividing a fraction the same and different than dividing a whole number?

IN Standards

Prior Learning

Content and Skills

Key Vocabulary

Assessments

Resources

Brainstorms

Extensions

STEM Integration

✓+ (Critical)

• 6.NS.5 Know commonly used fractions (halves, thirds, fourths, fifths, eighths, tenths) and their decimal and percent equivalents.  Convert between any two representations (fractions, decimals, percents ) of positive rational numbers without the use of a calculator.
• 6.C.2 Compute with positive fractions and positive decimals fluently using a standard algorithmic approach.
• 6.C.3 Solve real-world problems with positive fractions and decimals by using one or two operations.

✓ (Important)

• None

✓- (Additional)

• 6.C.4 Compute quotients of positive fractions and solve real-world problems involving division of fractions by fractions.  Use a visual fraction model and/or equation to represent these calculations.

• Place value
• Add and subtract fractions and mixed numbers
• Use LCM to make common denominators
• Use GCF to simplify fractions
• Convert between mixed numbers and improper fractions
• Whole number operations with borrowing

1. Convert between fractions, decimals, and percents
2. Know commonly used fractions and their conversions
3. Add and subtract fractions and mixed numbers with or without common denominators
4. Multiply fractions and mixed numbers
5. Divide fractions and mixed numbers
6. Solve real world problems using fraction and mixed number operations

1. Compatible numbers
2. Estimate
3. Quotient
4. Model
5. Proper and improper fractions
6. Mixed numbers
7. Simplify
8. Reciprocal
9. Inverse
10. Percent

Checks for Understanding

• ConnectEd guided practice problems
• Conversion Quiz
• Mid-chapter checks

Summative

• Fraction understanding test

-Indiana Glencoe Math Course 1 and ConnectEd:

• Chapter 2 Fractions, Decimals, and Percents 
•  Chapter 4 Multiply and Divide Fractions

-Khan Academy

-IXL

-Conversion foldable

-”Keep change flip” song

Grade: 6

Subject(s): Ratios and Proportional Reasoning

Time Frame: Quarter 2

Essential Question(s):

• How are comparisons helpful for making plans, predictions, and decisions?
• How do you use equivalent ratios in the real world?
• What math models can you use to make comparisons? When is each type of model helpful?

IN Standards

Prior Learning

Content and Skills

Key Vocabulary

Assessments

Resources

Brainstorms

Extensions

STEM Integration

✓+ (Critical)

• 6.NS.10 Use reasoning involving rates and ratios to model real-world and other mathematical problems (e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations).

✓ (Important)

• 6.NS.8 Interpret, model, and use ratios to show  the relative sizes of two quantities.  Describe how a ratio shows the relationship between two quantities.  Use the following notations: a/b, a to b, a:b.
• 6.NS.9 Understand the concept of a unit rate and use terms related to rate in the context of a ratio relationship.
• 6.AF.9 Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane.

✓- (Additional)

• None

• Fraction understanding and applications (unit 2)
• Divide and multiply whole numbers
• Understand numerator and denominator as comparison of parts
• Coordinate plane, tables, variables

1. Write ratios in 3 forms (a:b, a/b, a to b)
2. Write and model ratios as part to whole, whole to part, part to part
3. Find equivalent ratios using a table, equivalent fractions, number line, etc. and plot as an ordered pair
4. Apply equivalent ratios to create unit rates (as a ratio to one)

1. Ratio
2. Rate
3. Unit rate
4. Equivalent ratios
5. Factors
6. Model
7. Table
8. Ordered pair
9. Coordinate plane

Checks for Understanding

• ConnectEd guided practice problems
• Mid-chapter checks

Summative

• Ratios and rates test

-Indiana Glencoe Math Course 1 and ConnectEd:

• Chapter 1 Ratios and Rates (lessons 2-7)

-Khan Academy

-IXL

Grade: 6

Subject(s): Integers and Absolute Value

Time Frame: Quarter 2

Essential Question(s):

• What does it mean to have less than nothing (zero)?
• How are integers and absolute value used in real world situations?
• How do you know when to use positive and negative numbers?

IN Standards

Prior Learning

Content and Skills

Key Vocabulary

Assessments

Resources

Brainstorms

Extensions

STEM Integration

✓+ (Critical)

• 6.NS.3 Compare and order rational numbers and plot them on a number line.  Write, interpret, and explain statements of order for rational numbers in real-world contexts.

✓ (Important)

• 6.NS.1 Understand that positive and negative numbers are used to describe quantities having opposite directions or values.  Use positive and negative numbers to represent and compare quantities in real-world contexts, explaining the meaning of 0 in each situation.
• 6.NS.4 Understand that the absolute value of a number is the distance from zero on a number line.  Find the absolute value of real numbers and know that the distance between two numbers on the number line is the absolute value of their difference.  Interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.
• 6.AF.7 Understand that signs of numbers in ordered pairs indicate the quadrant containing the point; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  Graph points with rational number coordinates on a coordinate plane.
• 6.AF.8 Solve real-world and other mathematical problems by graphing points with rational number coordinates on a coordinate plane.  Include the use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

✓- (Additional)

• 6.NS.2 Understand the integer number system.  Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line.

• Whole numbers and the number line
• Coordinate plane, origin,  and 4 quadrants
• Plot whole number ordered pairs on the coordinate plane
• Explain the x-axis and y-axis
• Explain an ordered pair’s distance from each axis

1. Understand positive and negative numbers as opposites
2. Use positive and negative numbers to represent real world situations and contexts
3. Understand the integer number system
4. Know each integer has an opposite with the opposite sign, they are the same distance from 0 on the number line
5. Know that 0 is neither negative or positive and its own opposite
6. Compare rational numbers and plot them on the number line
7. Find and show absolute value using correct symbol
8. Understand absolute value is the distance of a number from 0 on the number line, and it is always positive
9. Opposites have the same absolute value
10. Graph points with rational numbers on the coordinate plane
11. Understand the signs of numbers within ordered pairs indicate their quadrant on the coordinate plane
12. Understand reflections across each axis
13. Solve real world problems by graphing ordered pairs with rational numbers on the coordinate plane

1. Opposite
2. Integers
3. Absolute value
4. Distance
5. Positive numbers
6. Negative numbers
7. Rational numbers
8. Opposite signs
9. Coordinate
10. Coordinate plane
11. Axes
12. Reflection

Checks for Understanding

• ConnectEd guided practice problems
• Mid-chapter checks

Summative

• Integers and absolute value test

-Indiana Glencoe Math Course 1 and ConnectEd:

• Chapter 5 Integers and the Coordinate Plane

-Khan Academy

-IXL

• Construct real world number line models
• Virtual manipulatives
• Graphing Battleship

Grade: 6

Subject(s): Expressions, Equations, and Inequalities

Time Frame: Quarter 3

Essential Question(s):

• What are mathematical properties and why are they useful?
• How can you represent equal and unequal relationships?
• When do you need a variable? Two variables?
• How are symbols such as less than, greater than, and equal to useful?

IN Standards

Prior Learning

Content and Skills

Key Vocabulary

Assessments

Resources

Brainstorms

Extensions

STEM Integration

✓+ (Critical)

• 6.C.6 Apply the order of operations and properties of operations to evaluate numerical expressions with nonnegative rational numbers, including those using grouping symbols, such as parentheses, and involving whole number exponents.
• 6.AF.1 Evaluate expressions for specific values of their variables, including expressions with whole-number exponents and those that arise from formulas used in real-world problems.
• 6.AF.5 Solve equations of the form x + p = q, x - p = q, px = q, x/p = q fluently for cases in which p, q and x are all nonnegative rational numbers.  Represent real world problems using equations of these forms and solve such problems.

✓ (Important)

• 6.C.5 Evaluate positive rational numbers with whole number exponents
• 6.AF.3 Define and use multiple variables when writing expressions to represent real-world and other mathematical problems, and evaluate them for given values.
• 6.AF.2 Apply the properties of operations  to create equivalent linear expressions and to justify whether two linear expressions are equivalent when the two expressions name the same number regardless of which value is substituted into them.
• 6.AF.6 Write an inequality of the form x> c, x> or equal to  c, x < c, or x < or equal to c, where c is a rational number, to represent a constraint or condition in a real-world or other mathematical problem.  Recognize inequalities have infinitely many solutions and represent solutions on a number line diagram

✓- (Additional)

• 6.AF.4 Understand that solving an equation or inequality is the process of answering the following question:  Which values from a specified set, if any, make the equation or inequality true?  Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

• Distributive property
• Evaluate expressions with parentheses
• Show that order and grouping will not affect sums and products
• Determine an unknown whole number in a multiplication or division problem
• Create and extend multiplication patterns within 1000
• Define variables in real world situations

1. Apply the Order of Operations to evaluate multi-step expressions (including grouping symbols)
2. Analyze and explain each step of the order of operations, determine errors
3. Evaluate positive exponents
4. Write expressions, equations, and inequalities  to represent real world situations and define variables
5. Apply the distributive property
6. Justify equivalent and non-equivalent expressions
7. Understand that solving an equation/inequality is a process of “what value makes the equation/inequality true?”
8. Justify the independent and dependent variables in real world situations
9. Graph inequalities on a number line
10. Translate between equations, tables, and graphs

1. Exponent
2. Base
3. Inverse operations
4. Distributive property
5. Variable
6. Equation
7. Inequality
8. Infinitely many solutions

Checks for Understanding

• ConnectEd guided practice problems
• Mid-chapter checks
• Expressions quiz
• Equations quiz

Summative

• Expressions, equations, and inequalities test

-Indiana Glencoe Math Course 1 and ConnectEd:

• Chapter 6 Expressions
• Chapter 7 Equations
• Chapter 8 Functions and Inequalities

-Khan Academy

-IXL

-Algebra tiles

• Order of operations puzzle challenge (rearrange expression parts on board to make the correct solution)
• Virtual manipulatives

Grade: 6

Subject(s): Geometry and Measurement

Time Frame: Quarter 3/4

Essential Question(s):

• How can you rearrange shapes to make other shapes?
• How do you use nets to represent three-dimensional figures?
• How do you find the surface area of a prism? Pyramid?
• How does the net of a shape relate to its surface area?
• How can you use a formula to find area, surface area, or volume?

IN Standards

Prior Learning

Content and Skills

Key Vocabulary

Assessments

Resources

Brainstorms

Extensions

STEM Integration

✓+ (Critical)

• None

✓ (Important)

• 6.GM.1 Convert between measurement systems (English to metric and metric to English) given conversion factors, and use these conversions in solving real-world problems.
• 6.GM.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 to solve real-world and other mathematical problems.
• 6.GM.2 Know that the sum of the interior angles of any triangle is 180 degrees and that the sum of the interior angles of any quadrilateral is 360 degrees.  Use this information to solve real-world and mathematical problems.
• 6.GM.4 Know that the sum of the interior angles of any triangle is 180 degrees and that the sum of the interior angles of any quadrilateral is 360 degrees.  Use this information to solve real-world and mathematical problems.
• 6.GM.5 Find the volume of a right rectangular prism with fractional edge lengths using unit cubes of the appropriate unit fraction edge lengths  and show that the volume is the same as would be found by multiplying the edge lengths of the prism.  Apply the formulas V=lwh and V=Bh to find volumes of right rectangular prisms with fractional edge lengths to solve real-world and other mathematical problems.

✓- (Additional)

• 6.GM.6 Construct right rectangular prisms from nets and use the nets to compute the surface area of prisms; apply this technique to solve real-world and other mathematical problems.

• Estimate and measure mass
• Convert within the same measurement system, solve real world problems with conversion
• Find area and perimeter of rectangles
• Solve for area and perimeter  of triangles, parallelograms, and trapezoids
• Solve for volume of a rectangular prism with whole number side lengths

1. Convert between measurement systems given a conversion factor
2. Draw polygons on the coordinate plane
3. Apply the sum of the interior angles of triangles (180) and quadrilaterals (360) to solve problems
4. Create a plan to solve for the area of complex shapes by composing or decomposing simpler shapes
5. Construct prisms and pyramids using nets
6. Use nets to calculate surface area
7. Find volume of right rectangular prisms
8. Use formulas to find volume of prisms with fractional side lengths
9. Solve real world problems with area, surface area, and volume
10. Label answers to real world problems with reasonable units, convert when necessary

1. Complex shape
2. Composing and decomposing
3. Surface area
4. Variable
5. Volume
6. Prism
7. Pyramid
8. English measurement
9. Metric measurement
10. Polygon
11. Quadrilateral

Checks for Understanding

• ConnectEd guided practice problems
• Mid-chapter checks
• Area of composite shapes quiz

Summative

• Area, volume, and surface area test

-Indiana Glencoe Math Course 1 and ConnectEd:

• Chapter 9 Area
• Chapter 10 Volume and Surface Area

-Khan Academy

-IXL

-3D shape models

• Virtual manipulatives
• “Build a park” project
• Compare volume and surface area of real world shapes by creating nets (boxes, etc.)

Grade: 6

Subject(s): Data, Statistics and Probability

Time Frame: Quarter 4

Essential Question(s):

• When would you use each kind of data display?
• What can you do with data to make it more useful?
• Why are measures of center useful in describing data?

IN Standards

Prior Learning

Content and Skills

Key Vocabulary

Assessments

Resources

Brainstorms

Extensions

STEM Integration

✓+ (Critical)

• 6.DS.3 Formulate statistical questions; collect and organize the data; display and interpret the data with graphical representations.

✓ (Important)

• 6.DS.2 Select, create, and interpret graphical representations of numerical data, including line plots, histograms, and boxplots.
• 6.DS.4 Summarize numerical data sets in relation to their context in multiple ways, such as: report the number of observations; describe the nature of the attribute under investigation, including how it was measured and its units of measurement; determine quantitative measures of center and spread, as well as describe any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered; and relate the choice of measures of center and spread to the shape of the data distribution and the context in which the data were gathered.

✓- (Additional)

• 6.DS.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for the variability in the answers.  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.

• Represent data with picture graphs, bar graphs, and frequency tables
• Measure using a ruler to the nearest ¼ inch
• Formulate a question that can be addressed with data
• Understand and use mean, median, mode and range
• Interpret data in circle graphs

1. Recognize and formulate statistical questions
2. Understand how to answer statistical questions using data
3. Select and analyze graphical representations including box plots, histograms, and line plots
4. Display and interpret data
5. Determine and analyze measures of center
6. Describe overall patterns in data including distribution, spread, variability, reliability, etc.

1. Variability (relationship to variable)
2. Statistical question
3. Histogram
4. Distribution
5. Spread
6. Center
7. Graphical representations
8. Numerical data
9. Box plots
10. Measure of central tendency
11. Interquartile range
12. Upper quartile
13. Lower quartile

Checks for Understanding

• ConnectEd guided practice problems
• Mid-chapter checks
• Measures of center quiz

Summative

• Data collection, display, and analysis test

-Indiana Glencoe Math Course 1 and ConnectEd:

• Chapter 11 Statistical Measures
• Chapter 12 Statistical Displays

-Khan Academy

-IXL

https://www.census.gov/programs-surveys/sis/activities/math.Grades_6-8.html

• Data collection and analysis project - create a study, collect data, display, and analyze
• Human box plot activity