All Mathematical Expressions Are Evaluated Using the Order of Operations

MS 104

Unit 1 Plan

Unit Name:
Factors and Multiples / Grade: 6 / Month(s): September / Duration: 22 days
Essential Questions:
HOW is it helpful to write numbers in different ways?
The following questions will be asked at different times throughout the unit to build on the essential question above:
-How does writing numbers using factors and multiples help you solve real-world problems?
-How is using exponents helpful?
-How can the distributive property help you to rewrite expressions? / Big Ideas/Enduring Understandings:

• Finding the least common multiple allows you to determine when two cyclical events will occur simultaneously
• Finding the greatest common factor helps us arrange two or more sets of objects into the largest groups using all of the elements in each set.
• All mathematical expressions are evaluated using the order of operations
• Algebraic properties can be used to show equivalent expressions that illustrate different ways of solving problems.

Common Core Learning Standards:
6.NS.4Find 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.Investigations 2, 3, and 4 Note:The development of the Distributive Property with variables is continued inVariables and Patterns.
6.EE.1Write and evaluate numerical expressions involving whole-number exponents.Investigations 3 and 4
6.EE.2aWrite expressions that record operations with numbers and with letters standing for numbers.Investigations 1, 2, 3, and 4Note:The development in this Unit is primarily with numerical expressions and is further developed with expressions containing variables inVariables and Patterns.
6.EE.2bIdentify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.Investigations 1, 2, and 4Note:The wordstermandcoefficientare developed inVariables and Patterns.
6.EE.2cEvaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).Investigation 4Note:Expressions with variables are further developed inVariables and PatternsandCovering and Surrounding.
6.EE.3Apply the properties of operations to generate equivalent expressions.Investigations 1, 3, and 4Note:The development in this Unit is primarily with numerical expressions and is further developed with expressions containing variables inVariables and Patterns.
6.EE.4Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).Investigations 1, 3, and 4Note:The development in this Unit is primarily with numerical expressions and is generalized to expressions containing variables inVariables and Patterns.
Student Objectives:How will the students show evidence of meeting the standards?
6.NS.4
Classify numbers as prime, composite, even, odd, or square
Recognize that factors of a number occur in pairs
Recognize situations that call for common factors and situations that call for common multiples
Recognize situations that call for the greatest common factor and situations that call for the least common multiple
Develop strategies for finding factors and multiples
Develop strategies for finding the least common multiple and the greatest common factor
Relate the prime factorization of two numbers to the least common multiple and greatest common factor of two numbers.
Solve problems involving factors and multiples
6.EE.1
Recognize and use the fact that every whole number can be written in exactly one way as a product of prime numbers
Use exponential notation to write repeated factors
6.EE.2b/6.EE.2c/6.EE.3/6.EE.4
Relate the area of a rectangle to the Distributive Property
Recognize that the Distributive Property relates the multiplicative and additive structures of whole numbers
Use the properties of operations of numbers, including the Distributive Property, and the Order of Operations convention to write equivalent numerical expressions
Solve problems involving the Order of Operations and Distributive Property
Activities
Investigation 1 – Building on Factors and Multiples
In the Factor Game students in a friendly distinguishing between numbers with many factors and numbers with few factors. Students are then guided through an analysis of game strategies and introduced to the definitions of prime and composite numbers.
In the Product Game, students find products of factors. Factor pairs are introduced when students find the whole-number dimensions of all rectangles that can be made withnunit squares. This problem also reinforces basic multiplication facts.
Investigation 2 – Common Multiples and Factors
Students explore real-life situations that involve finding common factors and common multiples. The concepts of least common multiple and greatest common factor occur naturally within the context of the problems..
Investigation 3 – Factorization – Searching for Factor Strings
Students use the prime factorization to find the least common multiple and greatest common factor of two numbers. Exponents are introduced as an efficient way to write repeated factors in the factorization of a number.
Investigation 4 – Linking Multiplication and Addition: The Distributive Property
In this Investigation students use rectangular area models to discover the distributive property. Students also work with equivalent numerical expressions in which they are introduced to the order of operations. Students end this investigation by deciding which operations are needed to solve problems.
Assessments:
Quizzes
Prime Time Check Up 1
Prime Time Check Up 2
Unit Assessment(Teacher Created)
Key Terms/Vocabulary:
common Factor / Common Multiple / Composite number / Conjecture / Counterexample
Distributive Property / Divisor / Equivalent Expressions / Even Number / Expanded Form
Exponent / Factor / Factor Pair / Factored Form / Factorization
Greatest Common Factor / Least Common Multiple / Multiple / Odd Number / Order of Operations
Prime Factorization / Prime Number / Proper Factors / Relatively Prime Numbers / Square Numbers
Resources:
CMP3: Prime Time
DASH teacher’s guide