Holyoke Public Schools: Grade 6 Curriculum Map
Unit Two: Arithmetic Operations Including Dividing by a Fraction (~25 days)
Standards
6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual
fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model
to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In
general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup
servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
Supporting Standards
 6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.
 6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
 6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole
numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor
as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
Critical Concepts
Arithmetic Operations
 Review Addition and Subtraction of Whole Numbers
 Review of Multiplication by 1, 2, and 3 Digit Numbers
 Review of Division by 1 or 2 Digit Numbers
Fractions
 Multiplying Fractions by a Whole Number
 Multiplying Two Fractions
 Multiplying Fractions by a Mixed Number
 Multiplying Mixed Numbers by Mixed Numbers
 Dividing Fractions by a Whole Number
 Dividing Two Fractions
 Dividing Fractions by a Mixed Number
 Dividing Mixed Numbers by Mixed Numbers
Decimals
 Adding Decimals
 Subtracting Decimals
 Multiplying Decimals
*These instructional maps were created and developed using information from Engage NY, Shelby County Schools, Saugus Public Schools,
Somerville Public Schools, and www.mdk12.org.
Holyoke Public Schools: Grade 6 Curriculum Map
 Dividing Decimals
Factors v. Multiples
 Differentiate Between Factors and Multiples
 Solve Word Problems
Student Objectives:
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Add multi-digit numbers
Subtract multi-digit numbers
Multiply multi-digit numbers
Divide multi-digit numbers
Multiply fractions
Multiply a fraction by a whole number
Multiply two fractions
Multiply a fraction by a mixed number
Divide fractions
Divide a fraction by a whole number
Divide two fractions
Divide two mixed numbers
Compute quotients of fractions.
Construct visual fraction models to represent quotients and explain the relationship between multiplication and division of fractions.
Solve real-world problems involving quotients of fractions and interpret the solutions in the context given.
Fluently add, subtract, multiply and divide multi-digit decimals and whole numbers using standard algorithms
Compute with fractions to determine quotients.
Divide with fractions to solve word problems.
Use visual models of the procedure/process used to determine quotients.
Analyze multiplication and division of fractions to discover the relationship between these two operations and their effect on
fractions.
Identify and differentiate between common factors and common multiples.
Find the Greatest Common Factor
Find the Least Common Multiple
Solve word problems involving GCF and LCM
See GoMath Resources for student practice (Chapter.Lesson)
*These instructional maps were created and developed using information from Engage NY, Shelby County Schools, Saugus Public Schools,
Somerville Public Schools, and www.mdk12.org.
Holyoke Public Schools: Grade 6 Curriculum Map
IT’S IMPERATIVE TO EXPOSE STUDENTS TO OTHER RESOURCES TO ENSURE MASTERY
Essential Questions:
How do you divide fractions?
How do you divide multi-digit numbers?
How do you add, subtract, multiply and divide decimals?
How does division of fractions relate to multiplication of fractions?
How is division of fractions used in the real world?
How do mathematical operations relate to each other?
How does one know which mathematical operation (+, -, x, ÷) to use?
Vocabulary
Whole Numbers, Fractions, Decimals, Add, Subtract, Multiply, Divide, Quotient, Factors, Multiples
Misconceptions
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Incorrectly use model for division of fractions.
Need to explore the measurement concept and the partition concept of division of fractions.
Need more practice with the standard algorithm so they will be fluent when working on addition, subtraction, multiplication
and division of decimals.
Need to know the differences between factors and multiples.
Need to differentiate between common factors and common multiples.
Lack complete conceptual understanding of the distributive property.
Resources
Go Math
Engage NY
https://www.engageny.org/resource/grade-6-mathematics
*These instructional maps were created and developed using information from Engage NY, Shelby County Schools, Saugus Public Schools,
Somerville Public Schools, and www.mdk12.org.
Holyoke Public Schools: Grade 6 Curriculum Map
Unpacked Standards
http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/6th.pdf
Model Lessons by Standard
http://www.mdk12.org/instruction/curriculum/mathematics/index.html
*These instructional maps were created and developed using information from Engage NY, Shelby County Schools, Saugus Public Schools,
Somerville Public Schools, and www.mdk12.org.