Grade 6 Math

NECAP Standards
Cycle of Review and Revision
K-8 Curriculum Alignment
YHS Syllabi
Curriculum Brochures
Curriculum Maps
YHS Program of Studies
Maine Learning Results 

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Barbara Maling
Director of Curriculum and Instruction

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207- 363-3403

Grade Six Math
Scope and Sequence

Students will follow the Connected Mathematics Project Program:
  • Develop a variety of strategies to solve mathematical problems.
  • Bits and Pieces Units II and III- addition, subtraction, multiplication, division of fractions; percents to compute taxes, tips and discounts; equivalent fractions; order of operations, decimals.
  • Shapes & Designs-Geometry in our world.
  • Covering and Surrounding Unit- use real world data to solve area and perimeter problems; circumference and use of Pi.
  • How Likely Is It Unit- use graphs and tally to represent data, probability, use coordinate graphs to locate and label points.
  • Data About Us– statistics, exploring, computing and graphing data.

YORK SCHOOL DEPARTMENT
CURRICULUM ALIGNMENT
SUBJECT AREA: MATHEMATICS GRADE: 6

Content Standards

Performance Indicators

Instructional Practice

Assessment Tools

Reporting Tools

A. NUMBER:  Students use numbers in everyday and mathematical contexts to quantify or describe phenomena, develop concepts of operations with different types of numbers, use the structure and properties of numbers with operations to solve problems, and perform mathematical computations.  Students develop number sense related to magnitude, estimation, and the effects of mathematical operations on different types of numbers.  It is expected that students use numbers flexibly, using forms of numbers that best match a situation. Students compute efficiently and accurately.  Estimation should always be used when computing with numbers or solving problems.
WHOLE NUMBER


 


 


 


 


A.1. Students use factors and multiples.


a. Identify prime numbers and composite numbers and use their properties to solve problems.


Find the factors of numbers up to 30. (Prime Time - 1.1)
Find multiples of numbers 1-9. (Prime Time - 1.3)
Develop an understanding of square numbers. (Prime Time - 2.1)
Find the prime factorization of a number using factor trees. (Prime Time - 4.2)
Identify multiples and common factors in real life problems. (Prime Time - 3.2, 3.2, 3.3, & 3.4)
  • classroom tests
  • classroom quizzes
  • projects
  • common assessments
  • performances/displays/presentations
  • teacher checklists
  • teacher rubrics
  • large scale assessments: NWEA, MEA
  • report cards
  • progress reports
  • student/parent conferences
  • teacher websites
  • email communication
  • power school
  • community performances/displays 
 


b. Use the property that every integer greater than one is a prime number or can be written as a unique product of prime numbers.


Find the factors of number up to 30. (Prime Time - 1.1)
Find the multiple of numbers 1-9. (Prime Time - 1.3)
Find the prime factorization using factor trees. (Prime Time - 4.2)
Find Common Multiples and Common Factors in real life problems. (Prime Time - 3.2, 3.2, 3.3, & 3.4)
  • classroom tests
  • classroom quizzes
  • projects
  • common assessments
  • performances/displays/presentations
  • teacher checklists
  • teacher rubrics
  • large scale assessments: NWEA, MEA
  • report cards
  • progress reports
  • student/parent conferences
  • teacher websites
  • email communication
  • power school
  • community performances/displays 
 


c. Interpret and use exponential notation as repeated multiplication.


Write prime factorization using exponents. (Prime Time - 4.2)


  • classroom tests
  • classroom quizzes
  • projects
  • common assessments
  • performances/displays/presentations
  • teacher checklists
  • teacher rubrics
  • large scale assessments: NWEA, MEA
  • report cards
  • progress reports
  • student/parent conferences
  • teacher websites
  • email communication
  • power school
  • community performances/displays 
 


d. Find the least common multiple and greatest common factor of two numbers.


Use Venn diagrams to find Greatest Common Factor and Least Common Multiple. (Prime Time 2.3)
Find Common Multiples and Common Factors in real life problems. (Prime Time - 3.2, 3.2, 3.3, & 3.rk.

  • classroom tests
  • classroom quizzes
  • projects
  • common assessments
  • performances/displays/presentations
  • teacher checklists
  • teacher rubrics
  • large scale assessments: NWEA, MEA
  • report cards
  • progress reports
  • student/parent conferences
  • teacher websites
  • email communication
  • power school
  • community performances/displays 
RATIONAL NUMBER


 


 


 


 


A.2Students express fractions greater than 0 as decimals and compare positive numbers that are written as fractions and decimals and place them on the number line.


 


Represent situations with fractions, percents, and decimals. (Bits I - 1.1)
Change decimals to fractions and then write number sentences to solve. (Bits III - 1.3)
Compare fractions to benchmark fractions by placing them in correct intervals and using inequalities. (Bits I - 2.3)
Find fractions that lie between a given pair of fractions. (Bits I - 2.4)
Find numbers between two decimal numbers. (Bits I - 3.2)
Determine decimal benchmarks. (Bits I - 3.3)
Order decimals from least to greatest. (Bits I - 3.5)
Convert terminating and repeating decimals to fractions. (Bits I - 4.3)
Convert ratios to percents. (Bits I - 4.3)
Convert between improper fractions and mixed numbers. (Bits I - 2.5)
Identify equivalent fractions. (Bits I - 2.2)
Use fractions and decimals to solve real life problems. (Bits I - 3.1 & 3.4)

  • classroom tests
  • classroom quizzes
  • projects
  • common assessments
  • performances/displays/presentations
  • teacher checklists
  • teacher rubrics
  • large scale assessments: NWEA, MEA

  • report cards
  • progress reports
  • student/parent conferences
  • teacher websites
  • email communication
  • power school
  • community performances/displays 

A.3. Students add, subtract, multiply, and divide numbers expressed as fractions and as decimals including mixed numbers.


 


Write and solve number sentences for adding, subtracting, multiplying and dividing decimals. (Bits III - 1.2, & 3.1)
Add, subtract, multiply and divide fractions. (Bits II - 2.2, 2.4, 3.4, 4.1, 4.2, 4.3, & 4.4)
Solve percent problems. (Bits III - 4.1 & 5.2)

  • classroom tests
  • classroom quizzes
  • projects
  • common assessments
  • performances/displays/presentations
  • teacher checklists
  • teacher rubrics
  • large scale assessments: NWEA, MEA
  • report cards
  • progress reports
  • student/parent conferences
  • teacher websites
  • email communication
  • power school
  • community performances/displays 
A.4. Students understand how to express relative quantities as percentages and as decimals and fractions.


a. Use ratios to describe relationships between quantities.


Represent situations with fractions, percents, and decimals. (Bits I - 1.1)
Compare fractions to benchmark fractions by placing them in correct intervals and using inequalities. (Bits I - 2.3)
Find fractions that lie between a given pair of fractions. (Bits I - 2.4)
Identify equivalent fractions. (Bits I - 2.2)
Use fractions and decimals to solve real life problems. (Bits I - 3.1 & 3.4)
  • classroom tests
  • classroom quizzes
  • projects
  • common assessments
  • performances/displays/presentations
  • teacher checklists
  • teacher rubrics
  • large scale assessments: NWEA, MEA
  • report cards
  • progress reports
  • student/parent conferences
  • teacher websites
  • email communication
  • power school
  • community performances/displays 

 


b. Use decimals, fractions, and percentages to express relative quantities.


Represent situations with fractions, percents, and decimals. (Bits I - 1.1)
Change decimals to fractions and then write number sentences to solve. (Bits III - 1.3)
Convert terminating and repeating decimals to fractions. (Bits I - 4.3)
Convert ratios to percents. (Bits I - 4.3)
Convert between improper fractions and mixed numbers. (Bits I - 2.5)
  • classroom tests
  • classroom quizzes
  • projects
  • common assessments
  • performances/displays/presentations
  • teacher checklists
  • teacher rubrics
  • large scale assessments: NWEA, MEA
  • report cards
  • progress reports
  • student/parent conferences
  • teacher websites
  • email communication
  • power school
  • community performances/displays 
 


c. Interpret relative quantities expressed as decimals, fractions and percentages.


Change decimals to fractions and then write number sentences to solve. (Bits III - 1.3)
Identify equivalent fractions. (Bits I - 2.2)
Use fractions and decimals to solve real life problems. (Bits I - 3.1 & 3.4)


  • classroom tests
  • classroom quizzes
  • projects
  • common assessments
  • performances/displays/presentations
  • teacher checklists
  • teacher rubrics
  • large scale assessments: NWEA, MEA
  • report cards
  • progress reports
  • student/parent conferences
  • teacher websites
  • email communication
  • power school
  • community performances/displays 
A.5. Students multiply and divide decimals with up to 3-decimal places by tens, hundreds, and thousands.


 


Solve number sentences for multiplying and dividing decimals. (Bits III - 2.3, 2.4, 3.2, & 3.3)
  • classroom tests
  • classroom quizzes
  • projects
  • common assessments
  • performances/displays/presentations
  • teacher checklists
  • teacher rubrics
  • large scale assessments: NWEA, MEA
  • report cards
  • progress reports
  • student/parent conferences
  • teacher websites
  • email communication
  • power school
  • community performances/displays 
REAL NUMBERS


 


 


 


 


No performance indicator. Although no performance indicators are state, students are expected to have instructional experiences in which they use rational numbers including rational approximations   for pi or square roots.


 


 


 


 


B. DATA: Students make measurements and collect, display, evaluate, analyze and compute with data to describe or model phenomena and to make decisions based on data. Students compute statistics to summarize data sets and use concepts of probability to make predictions and describe the uncertainty inherent in data collection and measurement. It is expected that when working with measurements students:

  • understand that most measurements are approximations and that taking repeated  measurements reveals this variability;
  •  understand that a number without a unit is not a measurement, and that an appropriate unit must always be attached to a number to provide a measurement;
  •  understand that the precision and accuracy of a measurement depends on selecting the appropriate tools and units; and use estimation comparing measures to benchmarks appropriate to the type of measure and units.
MEASUREMENT AND APPROXIMATION


 


 


 


 


B.1. Students convert within measurement systems.


a. Solve problems where different units are used within the metric and traditional systems of measurement.


 


 


 


DATA ANALYSIS


 


 


 


 


B.2. Students read, and interpret pie charts.


 


 


 


 


B.3. Students find and compare the mean, median, mode and range for sets of data.


 


Compute the mean, median, mode, and range of data given and collected. (Data about us) Identify which statistical measure is the most appropriate to describe a data distribution. (Data about us)

  • classroom tests
  • classroom quizzes
  • projects
  • common assessments
  • performances/displays/presentations
  • teacher checklists
  • teacher rubrics
  • large scale assessments: NWEA, MEA
  • report cards
  • progress reports
  • student/parent conferences
  • teacher websites
  • email communication
  • power school
  • community performances/displays 
PROBABILITY


 


 


 


 


No performance indicator. Although no performance indicators are stated, students are expected to have experiences with probability in grade six, but it is not expected that the knowledge will be secure.


 


 Develop strategies for finding both experimental and theoretical probabilities. (How Likely is it?)
Find probabilities including values of zero and one and explain what they mean. (How Likely is it?) 

  • classroom tests
  • classroom quizzes
  • projects
  • common assessments
  • performances/displays/presentations
  • teacher checklists
  • teacher rubrics
  • large scale assessments: NWEA, MEA
  • report cards
  • progress reports
  • student/parent conferences
  • teacher websites
  • email communication
  • power school
  • community performances/displays 
C. GEOMETRY: Students use measurement and observation to describe objects based on their sizes and shapes; model or construct two-dimensional and three-dimensional objects; solve problems involving geometric properties; compute areas and volumes based on object properties and dimensions; and perform transformations on geometric figures. When making or calculating measures, students use estimation to check the reasonableness of results.
GEOMETRIC FIGURES


 


 


 


 


C.1. Students represent solid figures in two dimensions.


a. Represent cubes, prisms, and square-based or triangular-based pyramids using nets.


 


 


 


 


b. Recognize and classify solids presented in picture views.


 


 


 


 


c. Sketch three-dimensional figures.


 


 


 


GEOMETRIC MEASUREMENT


 


 


 


 


C.2. Students find the perimeters and areas of geometric figures.


a. Triangles

 


Find the area and perimeter of triangles and rectangles. (Covering - 1.3 & 3.1)
Analyze how the area of a triangle and the area of a parallelogram are related to the area of a rectangle.  (Covering & Surrounding)
Develop formulas and procedures, stated in words or symbols, for finding areas and perimeters of rectangles, parallelograms, triangles, and circles.  (Covering & Surrounding)
  • classroom tests
  • classroom quizzes
  • projects
  • common assessments
  • performances/displays/presentations
  • teacher checklists
  • teacher rubrics
  • large scale assessments: NWEA, MEA
  • report cards
  • progress reports
  • student/parent conferences
  • teacher websites
  • email communication
  • power school
  • community performances/displays 
 


b. Quadrilaterals


Find the area and perimeter of triangles and rectangles. (Covering - 1.3 & 3.1)
Design floor plans with given areas and perimeters. (Covering - 1.1)
Analyze how the area of a triangle and the area of a parallelogram are related to the area of a rectangle.  (Covering & Surrounding)
Develop formulas and procedures, stated in words or symbols, for finding areas and perimeters of rectangles, parallelograms, triangles, and circles.  (Covering & Surrounding)
  • classroom tests
  • classroom quizzes
  • projects
  • common assessments
  • performances/displays/presentations
  • teacher checklists
  • teacher rubrics
  • large scale assessments: NWEA, MEA
  • report cards
  • progress reports
  • student/parent conferences
  • teacher websites
  • email communication
  • power school
  • community performances/displays  
 


c. Circles


Determine the diameter and circumference of multiple circles to determine a relationship.  (Covering 5.3)
Develop formulas and procedures, stated in words or symbols, for finding areas and perimeters of rectangles, parallelograms, triangles, and circles.  (Covering & Surrounding)
  • classroom tests
  • classroom quizzes
  • projects
  • common assessments
  • performances/displays/presentations
  • teacher checklists
  • teacher rubrics
  • large scale assessments: NWEA, MEA
  • report cards
  • progress reports
  • student/parent conferences
  • teacher websites
  • email communication
  • power school
  • community performances/displays 
C.3. Students find the volume and surface areas of right prisms with bases that are triangles and quadrilaterals.


 


 


 


 


TRANSFORMATIONS


 


 


 


 


C.4. Students understand and use reflections, rotations, and translations to define and identify congruent plane figures.


a. Apply the understanding that if a plane figure can be laid on top of another plane figure by rotations, translations or reflections then the figures are congruent.


Investigate reflection and rotation symmetries of a shape.  (Shapes & Designs)

  • classroom tests
  • classroom quizzes
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  • common assessments
  • performances/displays/presentations
  • teacher checklists
  • teacher rubrics
  • large scale assessments: NWEA, MEA
  • report cards
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  • student/parent conferences
  • teacher websites
  • email communication
  • power school
  • community performances/displays 
C.5. Students understand how to use proportional relationships to make indirect linear measurements and use scale drawings to make linear measurements.


 


 


 


 


D.  ALGEBRA: Students use symbols to represent or model quantities, patterns and relationships and use symbolic manipulation to evaluate expressions and solve equations.  Students solve problems using symbols, tables, graphs and verbal rules choosing the most effective representation and converting among representations.
SYMBOLS AND EXPRESSIONS  


 


 


 


 


D.1. Students create and evaluate expressions.


a. Create and evaluate expressions using whole numbers.


 


 


 


 


b. Create and evaluate expressions using positive fractions including decimals.


Solve problems using operations on fractions.  (Bits II)


  • classroom tests
  • classroom quizzes
  • projects
  • common assessments
  • performances/displays/presentations
  • teacher checklists
  • teacher rubrics
  • large scale assessments: NWEA, MEA
  • report cards
  • progress reports
  • student/parent conferences
  • teacher websites
  • email communication
  • power school
  • community performances/displays 
EQUATIONS AND INEQUALITIES


 


 


 


 


D.2. Students recognize and solve problems involving linear equations and recognize examples and non-examples of linear equations.


a. Solve equations of the form ax +/- b = c where a, b, and c are whole numbers.


Solve for unknowns by using fact families. (Bits III - 3.3)


  • classroom tests
  • classroom quizzes
  • projects
  • common assessments
  • performances/displays/presentations
  • teacher checklists
  • teacher rubrics
  • large scale assessments: NWEA, MEA
  • report cards
  • progress reports
  • student/parent conferences
  • teacher websites
  • email communication
  • power school
  • community performances/displays 
 


b. Recognize from a table whether a relationship has a constant rate of change.


 


 


 


FUNCTIONS AND RELATIONS


 


 


 


 


D.3. Students use tables, formulas, diagrams, and graphs to analyze relationships between quantities.


a. Use tables, formulas and graphs to analyze constant difference (additive) relationships.


Graph the relationships between length and perimeter for a fixed area as well as length vs. area for a fixed perimeter. (Covering - 2.1 & 2.3)
Determine rules for finding area and perimeter of rectangles, parallelograms, and triangles. (Covering - 1.3 & 4.2)
Determine the diameter and circumference of multiple circles to determine a relationship.  (Covering 5.3
  • classroom tests
  • classroom quizzes
  • projects
  • common assessments
  • performances/displays/presentations
  • teacher checklists
  • teacher rubrics
  • large scale assessments: NWEA, MEA
  • report cards
  • progress reports
  • student/parent conferences
  • teacher websites
  • email communication
  • power school
  • community performances/displays 
 


b. Use tables, formulas and graphs to analyze constant ratio (multiplicative) relationships.


Graph the relationships between length and perimeter for a fixed area as well as length vs. area for a fixed perimeter. (Covering - 2.1 & 2.3)
Determine rules for finding area and perimeter of rectangles, parallelograms, and triangles. (Covering - 1.3 & 4.2)
Determine the diameter and circumference of multiple circles to determine a relationship.  (Covering 5.3
  • classroom tests
  • classroom quizzes
  • projects
  • common assessments
  • performances/displays/presentations
  • teacher checklists
  • teacher rubrics
  • large scale assessments: NWEA, MEA
  • report cards
  • progress reports
  • student/parent conferences
  • teacher websites
  • email communication
  • power school
  • community performances/displays 

469 U.S. Route 1 York, Maine | Phone: 207-363-3403 | Fax: 207-363-5602 | Contact Us 

Vision
As the tides of the ocean and the strength of the mountain shape our community, the York Schools' commitment to educational excellence and individual achievement shapes the future of each student. 
Mission
The mission of York Schools is to educate, inspire and challenge all learners to be ethical citizens who will make a difference in a changing and complex world.