enVision Mathematics Topic 3
6th Grade; October – November (4 weeks); 2nd Quarter
Embedded Files
Topic Title(s):
Numeric and Algebraic Expressions
Prepared Graduates:
MP3. Construct viable arguments and critique the reasoning of others.
MP6. Attend to precision.
MP7. Look for and make use of structure.
MP8. Look for and express regularity in repeated reasoning.
Standard(s):
1. Number and Quantity
2. Algebra and Functions
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
6.NS.B. The Number System: Compute fluently with multi-digit numbers and find common factors and multiples.
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). (CCSS: 6.NS.B.4)
6.EE.A. Expressions & Equations: Apply and extend previous understandings of arithmetic to algebraic expressions.
Write and evaluate numerical expressions involving whole-number exponents. (CCSS: 6.EE.A.1)
Write, read, and evaluate expressions in which letters stand for numbers. (CCSS: 6.EE.A.2)
Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. (CCSS: 6.EE.A.2.a)
Identify 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. For example, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. (CCSS: 6.EE.A.2.b)
Evaluate 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). For example, use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2. (CCSS: 6.EE.A.2.c)
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. (CCSS: 6.EE.A.3)
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. (CCSS: 6.EE.A.4)
Recognize the structures of factors and multiples when identifying the greatest common factor and least common multiple of two whole numbers. Use the greatest common factor to rewrite an expression using the distributive property. (MP7)
Recognize that expressions can be written in multiple forms and describe cause-and-effect relationships and patterns. (Entrepreneurial Skills: Critical Thinking/Problem Solving and Inquiry/Analysis)
Communicate a justification of why expressions are equivalent using arguments about properties of operations and whole numbers. (MP3)
See the structure of an expression like x + 2 as a sum but also as a single factor in the product 3(x + 2). (MP7)
Recognize equivalence in variable expressions with repeated addition (such as y + y + y = 3y) and repeated multiplication (such as y × y × y = y3) and use arithmetic operations to justify the equivalence. (MP8)
Inquiry Questions
How does rewriting the sum of two whole numbers using the distributive property yield new understanding and insights on the sum?
How are algebraic expressions similar to and different from numerical expressions?
What does it mean for two variable expressions to be equivalent?
How might the application of the order of operations differ when using grouping symbols, such as parentheses, for numerical expressions as compared to algebraic expressions?
Coherence Connections
This expectation (6.NS.B) is in addition to the major work of the grade.
This expectation (6.EE.A) represents major work of the grade.
In previous grades, students understand and apply properties of operations, relationships between inverse arithmetic operations, and write and interpret numerical expressions.
In Grade 6, this expectation connects with applying and extending previous understandings of arithmetic to algebraic expressions.
In Grade 6, this expectation connects to fluency with multi-digit numbers, finding common factors and multiples, and one-variable equations and inequalities.
In future grades, students work with radicals and integer exponents and interpret the structure of more complex algebraic expressions.
Academic Vocabulary & Language Expectations:
Base, evaluate, exponent, power, composite number, factor tree, greatest common factor (GCF), least common multiple (LCM), prime factorization, prime number, numerical expression, algebraic expression, coefficient, term, variable, substitution, equivalent expressions, like terms, simplify
Assessments:
Instructional Resources & Notes:
enVision Mathematics Topic 3
Let's Investigate! Tasks
Let's Investigate! Dance Numbers (TE) (relates to Lesson 3-2)
Let's Investigate! Equali-tile (TE) (relates to Lesson 3-6)
5th-to-6th Grade Warm-Ups for Activating Prior Knowledge (Geoff Krall)
Tier 1 Intervention & Supports (i-Ready Tools for Instruction):
Tier 1 Intervention: Find the Greatest Common Factor, Evaluate Expressions Containing Exponents, Evaluate Variable Expressions, Use Order of Operations, Write Equivalent Expressions
Coherence Map/Concept Progressions: 6.NS.B.4, 6.EE.A.1, 6.EE.A.2.a, 6.EE.A.2.c, 6.EE.A.3
enVision Mathematics 6-8 & Number Worlds Connections (for SVVSD Special Education teachers only)
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