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Embed code for: 6th ADV Unit C 14-15 MAFS (V1 5-24-14) (1)
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Math Florida Standards
Highlighted Standards for Mathematical Practice
Students will apply and extend previous understandings of arithmetic to algebraic expressions.
In 5th grade students learned to:
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.
Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms.
In 4th grade students learned to:
Represent problems using equations with a letter standing for an unknown quantity
MAFS.K.12.MP.7.1 Look for and make use of structure
MAFS.K12.MP.8.1 Look for and express regularity in repeated reasoning
MAFS.K12.MP.6.1 Attend to Precision
MAFS.K12.MP.1.1 Make sense of problems and persevere in solving them
MH FL Math
HMH GO MATH
Inquiry Lab: Structure of Expressions, Write Expressions, The Distributive Property, Equivalent Expressions
Problem Solving Investigation: Act it Out
College & Career Readiness: Water Slide Engineer
Real-World Link Video: 6.4, 6.6
Lesson Video: 6.2
“Power Up” Performance Task: Cross Country Tryouts
Real-World Videos: Viral Video (Module 9), Carpenters (Module 10)
Animated Math: 9.2, 10.3
Tasks: Unit 4 Performance Tasks: Freelance Computer Programmer, Pictures
The system includes tasks or problems that teachers can implement with their students, and rubrics that help the teacher interpret students' responses. Teachers using MFAS ask students to perform mathematical tasks, explain their reasoning, and justify their solutions. Rubrics for interpreting and evaluating student responses are included so that teachers can differentiate instruction based on students' strategies instead of relying solely on correct or incorrect answers. The objective is to understand student thinking so that teaching can be adapted to improve student achievement of mathematical goals related to the standards. Like all formative assessment, MFAS is a process rather than a test. Research suggests that well-designed and implemented formative assessment is an effective strategy for enhancing student learning.
Rectangle Perimeter 3
The Djinni’s Offer
Watch out for Parentheses
Unit Scale (Multidimensional) (MDS)
The multidimensional, unit scale is a curricular organizer for PLCs to use to begin unpacking the unit. The MDS should not be used directly with students and is not for measurement purposes. This is not a scoring rubric. Since the MDS provides a preliminary unpacking of each focus standard, it should prompt PLCs to further explore question #1, “What do we expect all students to learn?” Notice that all standards are placed at a 3.0 on the scale, regardless of their complexity. A 4.0 extends beyond 3.0 content and helps students to acquire deeper understanding/thinking at a higher taxonomy level than represented in the standard (3.0). It is important to note that a level 4.0 is not a goal for the academically advanced, but rather a goal for ALL students to work toward. A 2.0 on the scale represents a “lightly” unpacked explanation of what is needed, procedural and declarative knowledge i.e. key vocabulary, to move students towards proficiency of the standards.
In addition to displaying a 3.0 performance, the student must demonstrate in-depth inferences and applications that go beyond what was taught within these standards. Examples:
Design multiple real-world situations that represent the same algebraic or numeric expression
Generate multiple equivalent expressions and justify their equivalence by proving the validity of the properties utilized
The Student will:
Write and evaluate numerical expressions involving whole-number exponents. (MAFS.6.EE.1.1)
Write, read, and evaluate expressions in which letters stand for numbers. (MAFS.6.EE.1.2)
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. (MAFS.6.EE.1.2a)
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. (MAFS.6.EE.1.2b)
Evaluate expressions at specific values of their variables. Include expressions 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 = 6 s² to find the volume and surface area of a cube with sides of length s = 1/2. *Note: Examples of using formulas to find volume and surface area will be introduced during Unit E (MAFS.6.EE.1.2c)
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. (MAFS.6.EE.1.3)
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. (MAFS.6.EE.1.4)
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). (MAFS.6.NS.2.4)
The student will recognize or recall specific vocabulary, such as:
sum, term, product, factor, product, quotient, coefficient, exponent, expression, variable, Distributive Property, Associative Property, Commutative Property, Identity Property, Equivalent Expressions, like terms
The student will perform basic processes, such as:
Evaluate whole-number exponents within an expression
Know key vocabulary and substitute values for variables in expressions. Recognize the unknown quantity in a given situation. With help, follow the order of operations to evaluate the expression
With help, partial success at 2.0 content but not at score 3.0 content
Unpacking the Standard: What do we want students to Know, Understand and Do (KUD):
The purpose of creating a Know, Understand, and Do Map (KUD) is to further the unwrapping of a standard beyond what the MDS provides and assist PLCs in answering question #1, “What do we expect all students to learn?” It is important for PLCs to study the focus standards in the unit to ensure that all members have a mutual understanding of what student learning will look and sound like when the standards are achieved. Additionally, collectively unwrapping the standard will help with the creation of the uni-dimensional scale (for use with students). When creating a KUD, it is important to consider the standard under study within a K-12 progression and identify the prerequisite skills that are essential for mastery.
Domain: Expressions and Equations
Cluster: Title Students will apply and extend previous understandings of arithmetic to algebraic expressions. (Major Cluster)
Standard: (MAFS.6.EE.1.1) Write and evaluate numerical expressions involving whole-number exponents.
“Essential understandings,” or generalizations, represent ideas that are transferable to other contexts.
Expressions are used to model real-life problems and represent quantitative relationships
Order of operations must always be followed to properly evaluate an expression
Exponents represent repeated multiplication
Declarative knowledge: Facts, vocab., information
Procedural knowledge: Skills, strategies and processes that are transferrable to other contexts.
Power, squared, cubed
Explain the order of operations
Explain what an exponent is and how to evaluate it with repeated multiplication
Write a numerical expression involving whole-number exponents
Evaluate a numerical expression involving whole-number exponents using the order of operations
Prerequisite skills: What prior knowledge (foundational skills) do students need to have mastered to be successful with this standard?
Use parentheses, brackets, or braces in numerical expressions
I can explain what an exponent is and how to evaluate it with repeated multiplication
I can write a numerical expression involving whole-number exponents
I can evaluate a numerical expression involving whole-number exponents using the order of operations
Moving Beyond: MAFS.7.EE.1.3 Solve multi-step real life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
Uni-Dimensional, Lesson Scale:
The uni-dimensional, lesson scale unwraps the cognitive complexity of a focus standard for the unit, using student friendly language. The purpose is to articulate distinct levels of knowledge and skills relative to a specific topic and provide a roadmap for designing instruction that reflects a progression of learning. The sample performance scale shown below is just one example for PLCs to use as a springboard when creating their own scales for student-owned progress monitoring. The lesson scale should prompt teams to further explore question #2, “How will we know if and when they’ve learned it?” for each of the focus standards in the unit and make connections to Design Question 1, “Communicating Learning Goals and Feedback” (Domain 1: Classroom Strategies and Behaviors). Keep in mind that a 3.0 on the scale indicates proficiency and includes the actual standard. A level 4.0 extends the learning to a higher cognitive level. Like the multidimensional scale, the goal is for all students to strive for that higher cognitive level, not just the academically advanced. A level 2.0 outlines the basic declarative and procedural knowledge that is necessary to build towards the standard.
Write a situation that could be modeled with a numerical expression involving whole-number exponents and evaluate the numerical expression.
Write a real world situation that models the following numerical expression:
I can do everything at a 3.0, and I can demonstrate partial success at score 4.0.
There is a $200 entrance fee for each band plus a $25 entrance fee for each drill team. The competition has a total of 32 bands and 25 drill teams. Write and evaluate an expression for the total amount of money collected from entrance fees.
I can do everything at a 2.0, and I can demonstrate partial success at score 3.0.
What would you do first to evaluate the following expression?
5 + (34 – 4)
I need prompting and/or support to complete 2.0 tasks.
Sample High Cognitive Demand Tasks:
These task/guiding questions are intended to serve as a starting point, not an exhaustive list, for the PLC and are not intended to be prescriptive. Tasks/guiding questions simply demonstrate one way to help students learn the skills described in the standards. Teachers can select from among them, modify them to meet their students’ needs, or use them as an inspiration for making their own. They are designed to generate evidence of student understanding and give teachers ideas for developing their own activities/tasks and common formative assessments. These guiding questions should prompt the PLC to begin to explore question #3, “How will we design learning experiences for our students?” and make connections to Marzano’s Design Question 2, “Helping Students Interact with New Knowledge”, Design Question 3, “Helping Students Practice and Deepen New Knowledge”, and Design Question 4, “Helping Students Generate and Test Hypotheses” (Domain 1: Classroom Strategies and Behaviors).
MAFS Mathematical Content Standard(s)
Design Question 1; Element 1
MAFS.6.EE.1.1 Write and evaluate numerical expressions involving whole-number exponents.
Standards for Mathematical Practice(s)
MAFS.K12.MP.4.1 Model with Mathematics
Questions to develop mathematical thinking, possible misconceptions/misunderstandings, how to differentiate/scaffold instruction, anticipate student problem solving strategies
This task is designed as an introductory lesson since students learned powers in previous grades. A visual model or table would be a great way to organize information for a discussion once the task is complete. Look for the different ways students represent the numerical expression. An anticipated error would be simplifying the expression:
*These tasks can either be teacher created or modified from a resource to promote higher order thinking skills. Please cite the source for any tasks.
On Monday, five students make up a rumor. On each of the next two days, every student that knows the rumor tells five other students. On Thursday, the two guidance counselors and three administrators found out. Write a power to represent the number of students that know the rumor at the end of the day on Thursday. Then find the number of students.
6th Grade Advanced Mathematics Unit C: Expressions and Number Properties
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015 and procedural knowledge that is necessary to build towards the standard.
I can do everything at a 3.0, and I