Content Area: Math
Unit Title: Algebraic Expressions Unit: 5
Target Course/Grade Level: Sixth Grade Timeline: 3 Weeks
Unit Summary: Students will evaluate numerical and algebraic expressions using order of operations. Students then write algebraic expressions to represent real-world situations. Students will apply Commutative, Associative, Identity, and Distributive Properties to solve problems and to show that two expressions are equivalent.
Primary interdisciplinary connections: Language Arts and Technology
9.1 21st-Centuries Life & Career Skills
Standard 9.1 All students will demonstrate the creative, critical thinking, collaboration, and problem-solving skills needed to function successfully as both global citizens and workers in diverse ethnic and organizational cultures.
Strand: A. Critical Thinking and Problem Solving
B. Creativity and Innovation
C. Collaboration, Teamwork and Leadership
Content Statement:
9.1.8: A The ability to recognize a problem and apply critical thinking skills and problem
solving skills to solve the problem is a lifelong skill that develops over time.
9.1.8: B Gathering and Evaluating knowledge and information from a variety of sources,
including global perspective, fosters creativity and innovative thinking.
9.1.8: C Collaboration and team work enable individuals or groups to achieve common goals
with greater efficiency.
Leadership abilities develop over time through participation in group and or teams that
that are engaged in challenging or competitive activities.
.
21st Century themes and skills: Critical Thinking and Problem Solving, Collaboration, Teamwork and
Leadership, Creativity and Innovation
Mathematical Practices:
6.MP.1 Make sense of problems and persevere in solving them.
6.MP.2 Reason abstractly and quantitatively.
6.MP.3 Construct viable arguments and critique the reasoning of others.
6.MP.4 Model with mathematics.
6.MP.6 Attend to precision.
6.MP.7 Look for and make use of structure.
Learning Targets
Domain: Expressions and Equations
Cluster: Apply and extend previous understandings of arithmetic to algebraic expressions
Standard # / Standards
6.EE.1 / Write and evaluate numerical expressions involving whole-number exponents
6.EE.2 / Write, read, and evaluate expressions in which letter stand numbers.
6.EE.2a / Write expressions that record operations with numbers and with letters standing for numbers.
6.EE.2b / Indentify parts of an expression using mathematical terms (sum, product, factor, quotient, coefficient) view one of more parts of an expression as a single entity.
6.EE.2c / 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.
6.EE.3 / Apply the properties of operations to generate equivalent expressions.
6.EE.4 / Identify when two expressions are equivalent.
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 multiple of a sum of two whole numbers with no common factor.
6.NS.6 / Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative coordinates.
Unit Essential Questions
- What are mathematical expressions and how are they used to solve problems?
- Why is it important to have a set of rules, such as order of operations, for simplifying or evaluating expressions?
- How do properties and number patterns assist in simplifying expressions?
- Mathematical expressions and equations correspond to given situations.
- Variables represent numbers whose exact values are not yet specified.
- Expressions in different forms can be equivalent and be rewritten to represent a quantity in a different way.
- Solutions to equations are the quantity of the variable.
Unit Learning Targets
Students will ...
- Find the value of expressions using the order of operations.
- Evaluate algebraic expressions.
- Use models to write expressions.
- Write verbal phrases as simple algebraic expressions
- Solve problems by acting them out.
- Use the Commutative, Associative, and Identity Properties to simplify expressions.
- Model the Distributive Property.
- Use the Distributive Property to compute multiplication problems mentally and to rewrite algebraic expressions.
Evidence of Learning
Summative Assessment
- Write and evaluate numerical expressions.
- Write and evaluate algebraic expressions.
- Apply the Commutative, Associative, and Distributive Properties to simplify expressions.
- Use expressions and formulas to solve problems.
Equipment needed: Smart Board, white boards, calculators, Elmo, dry eraser boards, markers and erasers.
Teacher Instructional Resources: TBD
Study Island
Khan Academy Videos
Formative Assessments
- Skill sheets
- Quizzes/Tests
- Student workbook
- Homework
- Math games
- Study Island
Integration of Technology:
- Smart Board to play online games, utilize online resources, generate models with Smart Software.
- Kahn Academy Videos
- Elmo – for demonstration
- Study Island
Technology Resources:
– Interactive 2.0 instructional and practice site. Students can view instructional videos and complete practice modules for additional practice/remediation.
- Web-based instruction, practice, assessment and reporting built from NJ standards.
- IXL 6th grade online interactive activities for the students to complete
- AAA math 6th grade – online interactive activities and problems for the student to complete.
– Grade level material for practice, lessons, games, etc.
Opportunities for Differentiation:
Decelerate: Have a students use an index card to explain each property being represented in their own words.
Accelerated: Applying simplifying algebraic expressions and evaluating expressions with integers. Assign each student a number, such as 12, 36, or 72. Have each student use the commutative, associative and identity properties of multiplication to write expressions that are equivalent to their number.
Teacher Notes:
Distributive Property is very important concept/process in simplifying algebraic expressions