Morris Plains School District
Curriculum Document
Unit Title: The Real Number System
Established Goals (CCS)
6.NS.1
6.NS.2
6.NS.3
6.NS.4
6.NS.5
6.NS.6
6.NS.7
6.NS.8
Enduring Understandings
 Being able to determine when to use estimation and when an exact
answer is needed
 Appropriate times to use mental math, paper/pencils and calculators
 How common factors and multiples are used in real world applications
 Understanding the meaning of multiplication and division as it applies
to fractions – that multiplication does not mean that products get
greater or that division means that quotients get smaller.
 Be able to use algorithms to add, subtract, multiply and divide rational
numbers.
 To recognize opposite signs (negative/positive) as indicating locations
on opposite sides of zero and can tell not only magnitude but location
 To understand that absolute value of a rational number can be used
to find magnitude of a number as in distance and other real world
situations.
Essential Questions
 What models or diagrams might be helpful in understanding the
situation and the relationships among quantities?
 What models or diagrams might help decide which operation is useful
in solving a problem?
 How do you determine what method is best for estimating and what is
a reasonable estimate for an answer?
Essential Knowledge
Students will …
 How to use strategies to quickly estimate sums, differences, products,
and quotients.
 How to use benchmarks of 0,1/2, 1, 1-1/2, and 2 to make sense of
how large a sum is
 How to develop strategies for adding, subtracting, multiplying and
dividing fractions and decimals.
 Understand when addition, subtraction, multiplication and division is
the appropriate operation
 Know the relationship between two numbers and their product to
generalize the conditions under which the product is greater than both
factors, between both factors or less than both factors.
Essential Skills
Students will be able to…
 Use benchmarks to estimate by checking the reasonableness of results
of operations with fractions.
 Construct and analyze strategies to model sums, differences, products,
and quotients including the use of areas fraction strips and number
lines.
 Use estimates and exact solutions to make mathematics decisions
 Use knowledge of fractions and equivalence of fractions to develop
algorithms for adding, subtracting, multiplying and dividing fractions.
 Support with reason when addition, subtraction, multiplication or
division is appropriate operations to solve a problem by investigating
real world scenarios.
1
Grade 6
Morris Plains School District
Curriculum Document










Know what tip, tax, discounts means
Know how to set up models to represent situations … ex: showing that
½*½=¼
Understand how to use context to help reason about the problem.
Understand the rectangular coordinate system and how to plot points
on that system
The meaning of absolute value.
Write, interpret and explain statements of order for rational numbers in
real world contexts
How to distinguish comparisons of absolute value from statements
about order.
Know the difference between prime and composite numbers
To know whether a number is prime or composite, even or odd, square
or non-square based on its factor pairs.
Know how to use greatest common factor and least common multiple
in real world situations












Write fact families to show the inverse relationship between addition,
and subtraction; and between multiplication and division.
Illustrate the understanding of fractions by performing the appropriate
operation on fractions.
Use comprehension of positive and negative numbers by describing
integers and rational numbers as quantities having opposite directions
or values.
Use application of integers and rational numbers, by using positive and
negative numbers to represent quantities in real-world contexts.
Use comprehension of integers and rational numbers by plotting points
on the Cartesian Coordinate System
Use synthesis of benchmarking and other strategies by having students
place rational numbers in ascending or descending order.
Use comprehension of absolute value by describing a positive or
negative number as a magnitude for a positive or negative quantity in
a real world situation.
Apply absolute value by determining the distance between two
vertical or horizontal coordinate points.
Use synthesis to relate factor pairs to area of rectangles by visually
arranging all the possible combinations of factor pairs that make up
the area on construction paper.
Develop strategies for find factors and multiples and least common
multiples and greatest common factors
Use the knowledge of factors and multiples to solve problems and to
explain some numerical facts of real world situations.
Formulate a variety of strategies for solving problems – building models,
making lists and tables, drawing diagrams, and solving simpler
problems.
Assessments
Performance Task:
TASK # 1
Greg buys 2/5 of a square pan of brownies that have only 7/10 of the pan left
PART A: Draw a picture of how the brownie pan might look before and after Greg buys his brownies.
PART B: what fraction of the whole pan does Greg buy
PART C: What fractional part is left in the pan after Greg buys his share?
2
Grade 6
Morris Plains School District
Curriculum Document
TASK # 2
Julia and Jordyn are making beaded necklaces. They have several beads in various colors and widths. As they design patterns to use, they want to
figure out how long the final necklace will be. Julia and Jordyn have the following beads widths to work with.
PART A: Explain how you would estimate how wide the beads would be if you used 4 Trade Neck beads
and two Large Rosebud beads in your necklace.
PART B: If Julia used 30 Trade Neck beads, 6 medium Rosebud beads and one large Rosebud bead, how l
long will her necklace be?
PART C: Jordyn would like to make a 16-inch necklace by alternating the medium and large Rosebud
beads. She only has 8 medium Rosebud beads. If she uses 8 medium rosebud beads and 8 large
Rosebud beads, will her necklace be 16 inches long? Use mathematics to verify your answer.
TASK # 3
TASK #4
TASK # 5
Jamel was walking around New York City (see coordinate grid map). He starts at (-3, 3) and walks to (1,3)
PART A: Find two pair of coordinate points so that Jamel would walk in a rectangular pattern
PART B: Find the distance (in neighborhood blocks) that he walked to the coordinate point south or north of his starting location
PART C: Find the distance (in neighborhood blocks) that he walked East of his starting position
PART D: If each block was 80.25 meters in length… How many meters did he walk traveling in his rectangular position
3
Grade 6
Morris Plains School District
Curriculum Document
TASK # 6
On Saturdays, the New Jersey Transit bus # 66 makes roundtrips between MaryEllen’s home and the Movie Theater, and the NJ Transit Bus # 23 makes
roundtrips between the Theater and the mall. Next Saturday, MaryEllen wants to take the bus from her home to the mall. A # 66 bus leaves MaryEllen’s
street every 15 minutes, beginning at 7:30AM. It takes the bus 30 minutes to travel between her street and the theater. A # 23 bus leaves the theater
every 12 minutes, beginning at 7:30AM.
PART A: If MaryEllen gets on the # 66 bus at 9:30AM, how long will she have to wait at the theater for a # 23 bus? Justify your answer using math
PART B: If MaryEllen gets on the # 23 bus at the theater and arrives at the mall at 11:48 AM, how long will she have to wait for the # 66 bus? Use
mathematics to justify your answer.
PART C: At what times between 9AM and noon are the # 66 and # 23 busses at the mall at the same time? Use math to justify your answer.
Other Evidence:
 Unit Test
 Investigation quizzes
 Partner Quizzes
 Classwork investigations
 Checked Homework
 Teacher observation
 Exit Tickets
 Notebook checks
 Word Wall Vocabulary
Learning Activities
 Teacher made investigations for estimating and evaluating sums, differences, products and quotients
 Operation Bingo
 Factor Game
 Product Game
 Textbook and workbook assignments
 Journal Writing Topics:
1. Describe at least two strategies for estimating fraction sums. Give an example for each strategy. Explain how the strategy was useful
2. How do you decide whether an overestimate or an underestimate is most helpful? Give examples to explain your thinking.
3. Suppose you are helping a student who has not studied fractions before, What is the most important thing you can say about adding or
subtracting fractions
4. Describe at least two things that you have to think about when you add or subtract mixed numbers. Choose things that you do not need to
think about when you add or subtract fractions.
5. Use an example to show how addition and subtraction of fractions are related in fact families
6. Describe and illustrate your algorithm for multiplying fractions. Explain how you use your algorithm when you multiply fractions by fractions,
fractions by mixed numbers, and fractions by whole numbers.
7. Illustrate why when you multiply a fraction less than 1 by another fraction, your product is always less than either factor.
8. Explain and illustrate what “OF” means when you find a fraction of another number. What operation is implied by the word “OF”
9. Explain your algorithm for dividing two fractions. Demonstrate your algorithm with an exam for each situation. A whole number divided by a
fraction, a fraction divided by a whole number, a fraction divided by a fraction, and a mixed number divided by a fraction.
10.Explain why the following example can be solved using division. “A local coffee house donates 2 and 2/3 pounds of gourmet coffee beans to
4
Grade 6
Morris Plains School District
Curriculum Document
be sold at a local fundraiser. The people running the fundraiser decided to package and sell the coffee beans in ½ pound packages. How
many ½ pound packages can they make
11.How is the quotient of 20 divided by 1/5 related to the quotient 20 divided by 3/5?
5
Grade 6
Morris Plains School District
Curriculum Document
Unit Title: The Real Number System
Established Goals (CCS)
6.NS.1
6.NS.2
6.NS.3
6.NS.4
6.NS.5
6.NS.6
6.NS.7
6.NS.8
Enduring Understandings
 Being able to determine when to use estimation and when an exact
answer is needed
 Appropriate times to use mental math, paper/pencils and calculators
 How common factors and multiples are used in real world applications
 Understanding the meaning of multiplication and division as it applies
to fractions – that multiplication does not mean that products get
greater or that division means that quotients get smaller.
 Be able to use algorithms to add, subtract, multiply and divide rational
numbers.
 To recognize opposite signs (negative/positive) as indicating locations
on opposite sides of zero and can tell not only magnitude but location
 To understand that absolute value of a rational number can be used
to find magnitude of a number as in distance and other real world
situations.
Essential Questions
 What models or diagrams might be helpful in understanding the
situation and the relationships among quantities?
 What models or diagrams might help decide which operation is useful
in solving a problem?
 How do you determine what method is best for estimating and what is
a reasonable estimate for an answer?
Essential Knowledge
Students will …
 How to use strategies to quickly estimate sums, differences, products,
and quotients.
 How to use benchmarks of 0,1/2, 1, 1-1/2, and 2 to make sense of
how large a sum is
 How to develop strategies for adding, subtracting, multiplying and
dividing fractions and decimals.
 Understand when addition, subtraction, multiplication and division is
the appropriate operation
 Know the relationship between two numbers and their product to
generalize the conditions under which the product is greater than both
factors, between both factors or less than both factors.
Essential Skills
Students will be able to…
 Use benchmarks to estimate by checking the reasonableness of results
of operations with fractions.
 Construct and analyze strategies to model sums, differences, products,
and quotients including the use of areas fraction strips and number
lines.
 Use estimates and exact solutions to make mathematics decisions
 Use knowledge of fractions and equivalence of fractions to develop
algorithms for adding, subtracting, multiplying and dividing fractions.
 Support with reason when addition, subtraction, multiplication or
division is appropriate operations to solve a problem by investigating
real world scenarios.
6
Grade 6
Morris Plains School District
Curriculum Document










Know what tip, tax, discounts means
Know how to set up models to represent situations … ex: showing that
½*½=¼
Understand how to use context to help reason about the problem.
Understand the rectangular coordinate system and how to plot points
on that system
The meaning of absolute value.
Write, interpret and explain statements of order for rational numbers in
real world contexts
How to distinguish comparisons of absolute value from statements
about order.
Know the difference between prime and composite numbers
To know whether a number is prime or composite, even or odd, square
or non-square based on its factor pairs.
Know how to use greatest common factor and least common multiple
in real world situations












Write fact families to show the inverse relationship between addition,
and subtraction; and between multiplication and division.
Illustrate the understanding of fractions by performing the appropriate
operation on fractions.
Use comprehension of positive and negative numbers by describing
integers and rational numbers as quantities having opposite directions
or values.
Use application of integers and rational numbers, by using positive and
negative numbers to represent quantities in real-world contexts.
Use comprehension of integers and rational numbers by plotting points
on the Cartesian Coordinate System
Use synthesis of benchmarking and other strategies by having students
place rational numbers in ascending or descending order.
Use comprehension of absolute value by describing a positive or
negative number as a magnitude for a positive or negative quantity in
a real world situation.
Apply absolute value by determining the distance between two
vertical or horizontal coordinate points.
Use synthesis to relate factor pairs to area of rectangles by visually
arranging all the possible combinations of factor pairs that make up
the area on construction paper.
Develop strategies for find factors and multiples and least common
multiples and greatest common factors
Use the knowledge of factors and multiples to solve problems and to
explain some numerical facts of real world situations.
Formulate a variety of strategies for solving problems – building models,
making lists and tables, drawing diagrams, and solving simpler
problems.
Assessments
Performance Task:
TASK # 1
Greg buys 2/5 of a square pan of brownies that have only 7/10 of the pan left
PART A: Draw a picture of how the brownie pan might look before and after Greg buys his brownies.
PART B: what fraction of the whole pan does Greg buy
PART C: What fractional part is left in the pan after Greg buys his share?
7
Grade 6
Morris Plains School District
Curriculum Document
TASK # 2
Julia and Jordyn are making beaded necklaces. They have several beads in various colors and widths. As they design patterns to use, they want to
figure out how long the final necklace will be. Julia and Jordyn have the following beads widths to work with.
PART A: Explain how you would estimate how wide the beads would be if you used 4 Trade Neck beads
and two Large Rosebud beads in your necklace.
PART B: If Julia used 30 Trade Neck beads, 6 medium Rosebud beads and one large Rosebud bead, how l
long will her necklace be?
PART C: Jordyn would like to make a 16-inch necklace by alternating the medium and large Rosebud
beads. She only has 8 medium Rosebud beads. If she uses 8 medium rosebud beads and 8 large
Rosebud beads, will her necklace be 16 inches long? Use mathematics to verify your answer.
TASK # 3
TASK #4
TASK # 5
Jamel was walking around New York City (see coordinate grid map). He starts at (-3, 3) and walks to (1,3)
PART A: Find two pair of coordinate points so that Jamel would walk in a rectangular pattern
PART B: Find the distance (in neighborhood blocks) that he walked to the coordinate point south or north of his starting location
PART C: Find the distance (in neighborhood blocks) that he walked East of his starting position
PART D: If each block was 80.25 meters in length… How many meters did he walk traveling in his rectangular position
8
Grade 6
Morris Plains School District
Curriculum Document
TASK # 6
On Saturdays, the New Jersey Transit bus # 66 makes roundtrips between MaryEllen’s home and the Movie Theater, and the NJ Transit Bus # 23 makes
roundtrips between the Theater and the mall. Next Saturday, MaryEllen wants to take the bus from her home to the mall. A # 66 bus leaves MaryEllen’s
street every 15 minutes, beginning at 7:30AM. It takes the bus 30 minutes to travel between her street and the theater. A # 23 bus leaves the theater
every 12 minutes, beginning at 7:30AM.
PART A: If MaryEllen gets on the # 66 bus at 9:30AM, how long will she have to wait at the theater for a # 23 bus? Justify your answer using math
PART B: If MaryEllen gets on the # 23 bus at the theater and arrives at the mall at 11:48 AM, how long will she have to wait for the # 66 bus? Use
mathematics to justify your answer.
PART C: At what times between 9AM and noon are the # 66 and # 23 busses at the mall at the same time? Use math to justify your answer.
Other Evidence:
 Unit Test
 Investigation quizzes
 Partner Quizzes
 Classwork investigations
 Checked Homework
 Teacher observation
 Exit Tickets
 Notebook checks
 Word Wall Vocabulary
Learning Activities
 Teacher made investigations for estimating and evaluating sums, differences, products and quotients
 Operation Bingo
 Factor Game
 Product Game
 Textbook and workbook assignments
 Journal Writing Topics:
1. Describe at least two strategies for estimating fraction sums. Give an example for each strategy. Explain how the strategy was useful
2. How do you decide whether an overestimate or an underestimate is most helpful? Give examples to explain your thinking.
3. Suppose you are helping a student who has not studied fractions before, What is the most important thing you can say about adding or
subtracting fractions
4. Describe at least two things that you have to think about when you add or subtract mixed numbers. Choose things that you do not need to
think about when you add or subtract fractions.
5. Use an example to show how addition and subtraction of fractions are related in fact families
6. Describe and illustrate your algorithm for multiplying fractions. Explain how you use your algorithm when you multiply fractions by fractions,
fractions by mixed numbers, and fractions by whole numbers.
7. Illustrate why when you multiply a fraction less than 1 by another fraction, your product is always less than either factor.
8. Explain and illustrate what “OF” means when you find a fraction of another number. What operation is implied by the word “OF”
9. Explain your algorithm for dividing two fractions. Demonstrate your algorithm with an exam for each situation. A whole number divided by a
fraction, a fraction divided by a whole number, a fraction divided by a fraction, and a mixed number divided by a fraction.
10.Explain why the following example can be solved using division. “A local coffee house donates 2 and 2/3 pounds of gourmet coffee beans to
9
Grade 6
Morris Plains School District
Curriculum Document
be sold at a local fundraiser. The people running the fundraiser decided to package and sell the coffee beans in ½ pound packages. How
many ½ pound packages can they make
11.How is the quotient of 20 divided by 1/5 related to the quotient 20 divided by 3/5?
Unit Title: Ratios and Proportional Thinking
Established Goals (CCS)
6.RP.1
6.RP.2
6.RP.3
Enduring Understandings
 That there are more than one way to represent numbers and that
sometimes one form is a better way to represent data than the other.
 There is sometimes more than one way to solve a problem and a
variety of strategies that can be used to solve problems.
 Use mathematical reasoning and models to manipulate practical
applications and solve problems.
 Through investigating the three representation forms of numbers
(percents, decimals and fractions,) students will realize how these
forms are used in the real world each and every day.
 Fractions, decimals and percents can be used interchangeably.
 Benchmarking (decimals, and fractions) opens the door for students to
compare fractional quantities and make useful estimations about the
size of amounts in a wide array of real-world situations
Essential Questions
 Why is it important to identify fractions (thirds, sixths, eighths, tenths) as
representations of equal parts of a whole or of a set?
 What do the parts of a fraction tell about its’ numerator and
denominator?
 If you have 2 fractions, What are some ways that you can tell which is
greater or has more value?
 When is estimation of fractions and decimal products and quotients
useful? •
How does estimation help us understand real world
problems? Or, how can they be use in real life?
 What strategies can be used to compare or order a set of fractions,
decimal and/or percents?
 What does it mean to have more than a whole?
 How can equivalent fractions be used to help solve real life problems?
Essential Knowledge
Students will know…
 That a proper fraction is rational number between 0 and 1.
 How to plot a rational number correctly on a number line.
 Model situations involving fractions, decimals, and percents.
 How to compare and order fractions and decimals.
 Strategies for comparing fractions, percents and decimals including
ratio tables, double number lines, benchmarks and number lines
 Move flexibly among fractions, decimal and percent representations.
Essential Skills
Students will be able to:
 Define what a proper fraction is by its numerator and denominator.
 Create a number line and Plot/label rational numbers correctly on a
number by benchmarking between two whole numbers.
 Create mathematical models (drawings, pictures, etc…) to model
situations involving fractions, decimals and/or percents.
 Mentally compare fractions and decimals by benchmarking the
rational number (e.g. 5/9 or 4/8)
 Convert between forms fractions, decimals and percents by using
benchmarking, or mathematical operations.
 Utilize mathematical models, such as fraction strips to describe realworld situations.
 Synthesize the knowledge gained by developing the fraction strips to
1
1
, 1 , 1 or 2 can help estimate the size
2
2

How Benchmarking to, 0,

of a number or sum.
How to develop and use benchmarks that relate different forms of
10
Grade 6
Morris Plains School District
Curriculum Document
rational numbers (i.e. 50% is the same as



1
2
or 0.5


How to use context, physical models, drawings, patterns or estimation
to help reason about situations involving rational numbers.
What it means for a fraction to be greater than a whole
Whether fractions are equivalent and strategies to find fractions that
are equivalent.






name, estimate and compare given fractions.
Compare and order rational numbers.
Formulate procedures for finding equivalent fractions and be able to
explain why the fractions are equivalent.
Represent fractions with denominators of 10 and powers of 10 as
decimal numbers.
Represent decimal numbers by using a 10 x 10 grid area model.
Explain that a decimal representation of a fraction shows the same
proportion but is based on a power of 10 as a denominator
Apply the division method to change fractions to decimals
Model fractions by using the hundredths grid.
Analyze strategies for finding percents where a set of data has more or
fewer than 100 items.
Assessments
Performance Tasks:
TASK # 1
Below is a drawing that shows part of a centimeter ruler and a paper clip (the drawing has been enlarged). The small marks indicate millimeters and
the larger marks indicate centimeters.
Part A: what fraction of a centimeter is a millimeter?
Part B: Show a mark on the ruler at 2.4 cm
Part C: How many millimeters is 2.4 cm
Part D: Show a mark on the ruler at 32 mm
Part E: How many centimeters is 32 mm.
Part F: According to the ruler, how long is the paper clip… record answers in both centimeters and Millimeters.
Part G: Which would be greater in length… a paper clip or a used pencil that is only 2.01 cm long? Explain.
TASK # 2 (feel free to change the number of slices or people to increase the difficulty of the problem)
After a soccer game you are invited to go out for pizza with several friends. When you get there, your friends are sitting in two groups. You can join
either group. If you join the first group, there will be a total for four people in the group sharing six small pizzas (there are 6 slices of pizza in each small
pie). If you join the second group there will be total of 6 people in the group sharing 8 small pizzas. If pizza will be shared equally in each group, and
11
Grade 6
Morris Plains School District
Curriculum Document
you are very hungry ,
Part A: which group would you join? Explain your answer by using math to demonstrate why you chose the group.
Part B: If you ate all the pieces that you were allowed, How many small pizzas would you have eaten?
Part C: What fraction of all the pizzas did you eat? Show your work using math to verify your answer.
TASK # 3
Jason’s mother owns a pizzeria and has a cutting form that can cut a pizza into 12 slices and another form that can cut a pizza into 8 slices.
PART A: If a family bought three small slices and three large slices, what fraction of the pizza did they buy? (you might want to draw a picture to help
you.)
PART B: How much more pizza (as a fraction) would they need to buy to purchase a whole pizza?
PART C: How many different ways can you combine the small slices and large slices to make a whole pizza? Write each of your responses as number
sentences… SAMPLE: 2/8 + 9/12 = 1
TASK #4
Michael decided to make French toast for himself and his other four family members. He finds a recipe that calls for:
8 slices of bread, 4 eggs , 1 cup of milk , 1 teaspoon of cinnamon
PART A:
If he makes a single recipe and shares the food equally with his family, how much French toast will each person receive?
PART B: How much egg will each person have in their French toast?
PART C:
Other Evidence:
 Unit Test
 Investigation Quizzes given after each investigation
 Partner quizzes
 Checked homework
 Projects
Learning Activities
 Using the 8.5 inch side of an 11x 8.5 piece of paper, cut strips of paper that are 8.5 inches long… Have students fold the strips into halves, thirds,
fourths, fifths, sixths, eighths, ninths, tenths, and twelfths… to be used for comparing fractions.
 Investigation activities of fractions, decimals and percents ( using textbooks and teacher made materials)
 Teacher made review
 Journal Writing :
o Two different classes reached 3/5 of their fundraising goals. Did the two classes raise the same amount of money? Explain.
o What do the numerator and denominators of a fraction tell you?
o If a class goes over its goal, what can you say about the fraction of their goal they have reached?
o Describe your strategy for finding a fraction equivalent to a given fraction.
o Describe strategies you have found for deciding whether a fraction is between 0 and ½ or between ½ and 1. Explain how you can
decide which of two fractions is greater.
o Describe how to write a mixed number as a fraction.
o Describe how to write a fraction greater than 1 as a mixed number.
o What does percent mean?
12
Grade 6
Morris Plains School District
Curriculum Document
Describe how to change a percent to a decimal and to a fraction.
Describe how to change a fraction to a percent.
Describe how you can change a decimal to a percent.
Why are percents useful in making comparisons?
Explain how to find what percent one number is of another number. For example: what percent of 200 is 75. Draw a percent bar to
help explain your thinking.
Homework assigned by worksheets and/or textbook.
o
o
o
o
o

13
Grade 6
Morris Plains School District
Curriculum Document
Unit Title: Expressions and Equations
Established Goals (CCS)
6.EE.1
6.EE.2
6.EE.3
6.EE.4
6.EE.5
6.EE.6
6.EE.7
6.EE.8
6.EE.9
Enduring Understandings
 When writing algebraic sentences/equations from verbal statements
that subtraction and division is not commutative ( y -3 is not the same
as 3 –y)
 That parentheses are important when evaluating expressions, i.e. -3^2
is not the (-3)^2
 That the properties of operations can be used to simplify
mathematical thinking.
 Being able to write an equation or inequality can help solve real world
problems and realize that equations are not just random numbers and
letters.
Essential Questions
 What does it mean to say that two expressions are equivalent?
 What is the difference between an equation and an inequality?
 How can one simplify an algebraic expression?
Essential Knowledge
Students will …
 Know how to write and evaluate expressions with exponents.
 Use appropriate vocabulary when discussing parts of an equation or
inequality, i.e. term, sum, quotient, factor, product, coefficient)
 Use the distributive property to generate equivalent expressions
 Check equations for equivalency.
 Know the algorithm for solving one-step equations and inequalities.
 Know how to use variables to represent two quantities in real world
problems
 Know how to write, and plot on a number line a solution to an
equation and inequality
Essential Skills
Students will be able to…
 Apply and extend previous understandings of arithmetic to algebraic
expressions by writing and evaluating numerical expressions involving
whole number exponents
 Write expressions in which letters stand for numbers by being able to
translate verbal statements to algebraic
expressions/equations/inequalities and then back to verbal sentences.
 Apply the standard order of operations by using the substitution
property to evaluate expressions.
 Apply the properties of operations by mathematically manipulating
expressions to solve linear equations.
 Illustrate applications of the distributive and commutative properties.
 Investigate patterns by using algebraic symbolism to explain data in a
table.
14
Grade 6
Morris Plains School District
Curriculum Document
Assessments
Performance Task
TASK # 1
The students at Borough School want to fundraise for a class trip. They decide to get together on a Saturday and Sunday and have their annual car
wash. The profit “P” from a car wash depends on the number of cars “C” that drive by the corner where the car wash is operated. Based on the past
years the suggested equation model for making a profit is P = 0.001C(C – 5).
PART A: What profit can be expected if 100 cars drive by?
PART B: What profit can be expected if 1000 cars drive by?
PART C: Based on the data collected in Parts A and B, Explain how you could figure out the problem without evaluating the expression.
TASK # 2
In science class you built model rockets and are now launching them today. The height “h” in meters of a model rocket “t” seconds after it is launched
is approximated by the formula h = t ( 50 – 3t)
PART A: How high is the rocket 5 seconds after being launched? 10 seconds?
PART B: Based on your answers in PART A, did the rocket’s height continue to increase after the first 5 seconds? Justify your answer using mathematics.
PART C: What is the height of the rocket after 17 seconds? What can you conclude about the launch of the rocket from your answer? Explain.
TASK #3
Steve mowed lawns over the summer below is a chart that shows the amount earned after a certain number of lawns mowed in a day.
Number of
Money Earned
lawns
mowed
1
$7.50
2
$15.00
3
$22.50
4
M
PART A: How much did Steve earn after the fourth mowed lawn?
PART B: How much would Steve earn if he mowed 8 lawns?
PART C: Explain in words how to find the amount earned for any given number of lawns.
PART D: Write an equation in terms of the money earned M = ___________________
Other Evidence:
 Unit Test
 Investigation quizzes
 Partner Quizzes
 Classwork investigations
 Checked Homework
 Teacher observation
 Exit Tickets
 Notebook checks
 Word Wall Vocabulary
15
Grade 6
Morris Plains School District
Curriculum Document
Learning Activities
 Teacher made investigations for inequalities and equations
 Textbook and workbook assignments
 Algebra Tile activities
 Converting from tables to graphs
 Journal Writing Topics:
(1) Explain how the distributive and commutative properties can be used to write equivalent expressions.
(2) Explain how the distributive and commutative properties can be used to show that two or more expressions are the same.
(3) Describe a situation in which it is helpful to add expressions to form a new expression
(4) Describe a situation in which it is helpful to substitute an equivalent expression for a quantity in an equation.
(5) Describe general strategies for solving one-step linear equations or inequalities.
(6) Describe how and why you could use symbolic statements to show relationships or generalizations and how can you show that your
generalization is correct?
(7) Write an example of a situation that you would have to write an equation. In that equation describe what the independent and dependent
variables are. How do you know which is which?
(8) How do you make a table of values from an equation? How do you make a graph from that table?
(9) How do you make an equation from a table of data?
16
Grade 6
Morris Plains School District
Curriculum Document
Unit Title: Geometry
Established Goals (CCS)
6.G.1
6.G.2
6.G.3
6.G.4
Enduring Understandings
 Students will understand that the area of all polygons can be
composed into rectangles or decomposed into triangles and other
traditional polygons.
 That area is number of square units needed to cover a 2-dimensional
shape
 That perimeter is interpreted as the number of LINEAR units needed to
surround a 2-dimensional shape.
 Students will understand why three dimensional figures are measured
in cubic units, while two-dimensional figures are measured in square
units and one dimensional measurement is measured in units.
 Algebra and geometry are integrated and should not be seen as
separate subjects… that geometry is the pictorial representation of
algebra.
 Faces of three dimensional figures are made up of two dimensional
polygons.
 In order to draw a three dimensional figure on a two dimensional
plane, you much manipulate the figure to trick your senses… i.e. using
parallelogram to make a rectangular prism. Students should be able
to see that although when drawn it looks like the faces are
parallelograms (not rectangular) that all faces are indeed rectangles
with right angles.
Essential Questions:
 How do simple polygons work together to make more complex shapes?
 How do you know whether area or perimeter is involved?
 What are you finding when you find area and when you find perimeter?
 How can you find area and perimeter of irregular shapes
 How do you find area of regular polygons
 What does it mean for a figure to be “regular?”
 What shapes make up a rectangular prism? Cylinder? rectangular
pyramid?
 What do the nets look like for each of the following 3-dimensional
shapes?… rectangular prism/cube, cylinder, rectangular pyramid
Essential Knowledge
Students will know…
 How to use and relate area to cover a figure
 How to use perimeter and related perimeter to surrounding a figure
 What it means to measure area and perimeter
 Develop strategies for finding areas and perimeters of rectangular and
non-rectangular shapes.
 How the area of a triangle and the area of a parallelogram are
related to the area of a rectangle
 How to develop formulas and procedures, stated in words and/or
Essential Skills
Students will be able to:
 Synthesize area and perimeter by formulating techniques for exactly
figuring out and estimating areas and perimeters of geometric and
non-geometric figures
 Comprehend how the perimeters of rectangles can vary considerably
by given situations where the areas are held constant.
 Analyze maximum and minimum perimeter by exploring problems
involving rectangles of a fixed area.
 Analyze maximum and minimum area by exploring problems involving
17
Grade 6
Morris Plains School District
Curriculum Document





symbols, for finding the area and perimeters of rectangles,
parallelograms, triangles and circles.
How to recognize situations in which measuring perimeter or area will
help answer real-world/practical questions.
How to draw nets for cylinders, rectangular prisms/cubes, rectangular
pyramids, cones.
How to draw polygons in the coordinate plane given coordinates for
the vertices.
How to find the lengths of the sides (that are vertical or horizontal) of a
polygon drawn in a coordinate plane
How to calculate/find the volume of a rectangular prism with whole
number and fractional lengths by using algorithm and packing unit
cubes












rectangles of a fixed perimeter.
Analyze the relationship between rectangles and parallelograms by
using unit squares to justify equivalent areas of figures given the same
base and height.
Apply techniques for finding areas and perimeters of rectangles and
parallelograms by investigating problems using the polygons in
practical situations.
Use the relationships between rectangles and parallelograms and
between parallelograms and triangles to develop techniques for
finding the area and perimeter of triangles.
Apply techniques for finding areas and perimeters of rectangles,
parallelograms and triangles by giving a variety of problem situations.
Investigate area of triangles by having students complete the
rectangle and count the number of unit squares it takes to cover the
surface of the figure.
Evaluate area of triangles by having students demonstrate visually on
centimeter grid paper that the area of a triangle is half that of the
area of a rectangle.
Use synthesis to develop strategies for finding areas and perimeters of
non-rectangular shapes
Use synthesis to construct a polygon on a rectangular coordinate grid
by given coordinates and asking the student to find the remaining
coordinates to complete the figure.
Analyze volume of a rectangular figure by packing unit cubes and
verifying that the volume is the same as multiplying the edge lengths of
the prism.
Analyze three dimensional figures by examining the nets of a specific
three dimensional figure and then using the nets to build the three
dimensional figure.
Analyze three dimensional figures by having the students construct the
net of the given polyhedron
Apply the algorithms for area and perimeter by having the students
explain how to find the area and perimeter of given figures.
Assessments
Performance Tasks:
TASK # 1
Because the winters are very windy and snowy for Sarah Fieldler, her mom decides to build a small snow shelter for her children to wait in before the
school bus arrives in the morning. Mrs. Fieldler has only enough wood to build a shelter whose floor has a total perimeter of 20 feet.
a. Make a table of all the whole number possibilities for the length and width of the shelter.
b. What dimensions should Mrs. Fieldler choose to have the greatest floor area in her shelter?
c. What dimensions should Mrs. Fieldler choose to have the least floor area in her shelter?
18
Grade 6
Morris Plains School District
Curriculum Document
d. Township building codes require 3 square feet for each child in a snow shelter. Which shelter from part a will fit the most children? How many
children is this?
TASK # 2
Jenna was using cardboard to make mats for her photos. The photos were 3 inches by 4 inches. The mats were different sizes and different shapes.
a. How much cardboard (in square inches) will be showing in the rectangular mat?
b. How much cardboard (in square inches) will be showing in the non-rectangular mat?
c. If she decided to put a narrow frame around each mat, how many inches of frame material would she need to surround each of the mats?
TASK # 3
Jason is planning to redecorate his bedroom. He measured the room and made this rough sketch.
a. Jason is planning to buy paint for the walls and ceiling. Will he need to find the perimeter or area to figure out how much paint to buy? What unit of
measure should he use?
b. To determine how much new carpet to buy, will Jason need to find the perimeter or area? What unit of measure should he use?
c. Jason also needs baseboard for around the bottom of the walls. Will he need to find the perimeter or area to figure out how much baseboard to
buy? What unit of measure should he use?
d. How much carpeting does Jason need? Show how you found your answer.
e. How much baseboard does Jason need? Show how you found your answer.
f. If a gallon of paint covers 350 square feet, how much paint does Jason need for the walls and ceiling?
TASK # 4
Lara is helping her family build a recreation room in their basement. The room will be 28 feet by 20 feet. They have already put up the walls.
19
Grade 6
Morris Plains School District
Curriculum Document
a.
b.
c.
d.
e.
The family wants to tile the floor. Lara decides to buy 1-foot-square tiles. How many tiles will she need? Show your work.
The tiles Lara has chosen cost $.75 each. How much will the tile floor cost? Show how you found your answer.
Lara needs to buy baseboard to put along the wall. How much baseboard does she need? Show how you found your answer.
The baseboard comes in 10-foot and 16-foot lengths. How many boards of each length should Lara buy? Show how you found your answer.
When you encounter problems like this in the real world, you will often have to consider several factors. Questions (e)-(g) look at conditions that
Lara might think are important.
Suppose these are the prices of the baseboard.
How many boards of each length should Lara buy if she wants to spend the least amount of money? Explain your answer.
f. When two sections of baseboard meet, they create a seam.
If Lara wants as few seams as possible, how many baseboards of each length should she buy?
g. If you were Lara, how many baseboards of each length would you buy?
TASK # 5
Susan is helping her father measure the living room floor because they want to buy new carpeting. The floor is in the shape of a rectangle with a width
of 10 feet and a length of 14 feet.
a. Draw a sketch that shows the shape of the floor and label the length and width.
b. If the carpeting costs $1.75 per square foot, how much will it cost to buy the exact amount of carpeting needed to carpet the living room?
Explain your reasoning.
c. Baseboard needs to be installed along the base of the walls to hold the carpeting in place. Baseboard costs $2.35 per foot. There is one 6-foot
wide entry into the living room that does not need baseboard. Find the exact amount of baseboard needed and the exact cost. Explain your
reasoning.
Other Evidence:
 Unit Test
20
Grade 6
Morris Plains School District
Curriculum Document








Investigation quizzes
Partner Quizzes
Classwork investigations
Checked Homework
Teacher observation
Exit Tickets
Notebook checks
Word Wall Vocabulary
Learning Activities

Teacher made investigations, including using centimeter grid paper and cooperative learning

Textbook/worksheets

Word Wall Vocabulary
21
Grade 6
Morris Plains School District
Curriculum Document
Unit Title: Statistics and Probability
Established Goals (CCS)
6.SP.1
6.SP.2
6.SP.3
6.SP.4
6.SP.5
Enduring Understandings
 Recognize that statistical questions have to contain variability in the
data related to the question and is accountable for it in the answer.
 Understand that a set of data collected to answer a statistical
question has a distribution that is described by its center, spread, and
overall shape.
 Understand that the measure of central tendency (mean, median and
mode) are all averages for a numerical data set and summarizes the
values of that set with a single number.
 Recognize which measure of central tendency is best used for the
given data
 Data can be summarized and be able to be described in many
different ways, i.e. graphs and tables
Essential Questions:
 What makes an effective statistical question?
 What does the measure of central tendency tell us about our data?
 How can you use mean, median, mode and/or range to describe a
data distribution
 How can I use graphs and statistics to describe a data distribution or to
compare two data distributions in order to answer my original
question?
 What is a sample?
 What is a population?
 Can I use my results to make predictions or generalizations about my
population
Essential Knowledge
Students will …
 Compare sample distributions using measures of center (mean,
median and mode), measures of variability (range, minimum,
maximum data values), and displays that group data (histograms, boxand-whisker plots)
 Know the process of statistical investigation to pose questions, to
identify ways data are collected and to determine strategies for
analyzing data in order to answer the posed questions.
 Recognize that variability occurs whenever data are collected and
can describe that variability in the distribution of a given data set.
 Know whether to use mean, median or mode to describe a distribution
 Know how to use a variety of representations, including tables,
histograms, bar graphs, box and whisker plots and line plots to display
distributions.
Essential Skills
Students will be able to:
 Use Synthesis in statistics, by creating a statistical question in which
students can collect and analyze data.
 Use Analysis of central tendency by examining which measure would
best describe a given data distribution.
 Use Analysis to summarize data distributions by examining a set of data
and being able to report the number of observations, describe the nature
of the attribute under investigation, describe the measure of central
tendency and relate the choice of measure of center and variability to
the shape of the data distribution and the context in which the data was
gathered.
Assessments
22
Grade 6
Morris Plains School District
Curriculum Document
Performance Tasks:
TASK # 1
A group of middle school students wondered:
What’s the typical number of hours of sleep middle school students get in a week/weekend?
Just how many movies and/or videos do middle school students watch in a week/weekend?
This check-up uses data collected from 330 middle school students to be used to answer these questions. The data are:
Hours of Sleep – typical number of hours of sleep each student had per night during a week
Movies and Videos – the number of movies and videos each student watched a week/weekend
For each student, we also know:
Grade – sixth, seventh, or eighth
Gender – boy or girl
PART A: Describe how you think these data were collected.
PART B: Here is a graph that shows the numbers of movies and videos watched during a week/weekend by each of the 330 students.
a. How would you name the shape of this distribution (bell-shaped, skewed, uniform or flat, clumped with clusters in different locations)?
b. Describe the variability in this distribution.
c. Draw and label a line that shows where you estimate the median would be located. Explain your reasoning.
d. Draw and label a line that shows where you estimate the mean would be located. Explain your reasoning.
PART C: Here is a graph that shows the typical hours of sleep per night during a week each of the 330 students had.
23
Grade 6
Morris Plains School District
Curriculum Document
a.
b.
c.
d.
How would you name the shape of this distribution (bell-shaped, skewed, uniform or flat, clumped with clusters in different locations)?
Describe the variability in this distribution.
Draw and label a line that shows where you estimate the median would be located. Explain your reasoning.
Draw and label a line that shows where you estimate the mean would be located. Explain your reasoning.
TASK # 2
Below are two dot plots that display data about the number of hours boys slept and the number of hours girls slept on a Friday night. Means and
medians are marked on each graph.
a.
b.
c.
d.
Write two comparison statements comparing the number of hours the boys slept to the number of hours the girls slept.
What fraction of boys slept longer than the mean? What percent of boys slept longer than the mean?
What fraction of girls slept longer than the mean? What percent of girls slept longer than the mean?
The number of boys reporting sleep times is not the same as the number of girls reporting sleep times. If you made a frequency bar graph of
each set of data, would you show the frequencies as counts or percents? Explain your thinking.
24
Grade 6
Morris Plains School District
Curriculum Document
e. What is the typical number of hours slept for the boys on Friday night? Which statement seems to be a sensible answer? Explain your reasoning.
i. Use the mode: The typical number of hours slept on Friday night is 6.5 hours.
ii. Use the median: The typical number of hours slept on Friday night is 8 hours.
iii. None of the above: Write your own statement about what you consider to be the typical number of hours boys slept on Friday night.
f. If you added data from 10 more boys about the number of hours they slept on Friday night, what do you predict would happen to the median?
The mean? The range? Explain your reasoning.
Other Evidence:
 Unit Test
 Investigation quizzes
 Partner Quizzes
 Classwork investigations
 Checked Homework
 Teacher observation
 Exit Tickets
 Notebook checks
 Word Wall Vocabulary
Learning Activities

Teacher made investigations

Project… student develop question to investigate

Textbook/worksheets

Word Wall Vocabulary
25
Grade 6