6th Grade MATH
COURSE OUTLINE
Course Description: Mathematics plays an essential role both within the school and society. It promotes powerful universal language, analytical reasoning, and problem solving skills that contribute to the development of logical, abstract, and critical thinking. (IBMYP Mathematics Content Guide, 2008). Sixth Grade Mathematics uses the enVision2.0 program by Pearson Publishing that integrates inquiry, technology and cooperative learning, and it is driven by the New York State Standards. enVision2.0 develops mathematical proficiency through various elements to support all learners. Students are given opportunities to be inquirers, thinkers, open minded, and caring. Sixth Grade focuses on number sense and preparing students for higher level mathematics.
NYS Standards:
Ratios and Proportional Relationships
*Understand ratio concepts and use ratio reasoning to solve problems.
The Number System
*Apply and extend previous understandings of multiplication and division to divide fractions by fractions
*Multiply and divide multi-digit numbers and find common factors and multiples.
*Apply and extend previous understanding of numbers to the system of rational numbers.
Expressions and Equations
*Apply and extend previous understandings of arithmetic to algebraic expressions.
*Reason about and solve one-variable equations and inequalities.
*Represent and analyze quantitative relationships between dependent and independent variables.
Geometry
*Solve real-world and mathematical problems involving area, surface area, and volume.
Statistics and Probability
*Develop understanding of statistical variability.
*Summarize and describe distribution.
Mathematical Practices
*Make sense of problems and persevere in solving them.
*Reason abstractly and quantitatively.
*Construct viable arguments and critique the reasoning of others.
*Model with mathematics.
*Use appropriate tools strategically.
*Attend to precision.
*Look for and make use of structure.
*Look for and express regularity in repeated reasoning.
Middle School Math Objectives
Knowledge and Understanding
Knowledge and Understanding
Knowledge and understanding are fundamental to studying mathematics and form the base from which to explore concepts and develop problem-solving skills. Through knowledge and understanding students develop mathematical reasoning to make deductions and solve problems. Students will gain knowledge through number sense including the study of decimals, fractions, and integers. Expressions and equations will provide an application for these skills.
Investigating Patterns
Investigating patterns allows students to experience the excitement and satisfaction of mathematical discovery. Mathematical inquiry encourages students to become risk-takers, inquirers, and critical thinkers.
Through the use of mathematical investigations, students are given the opportunity to apply mathematical knowledge and problem-solving techniques to investigate a problem, generate and/or analyze information, find relationships and patterns, describe these mathematically as general rules and justify or prove them.
Students will work with rates and geometry with a heavy emphasis on two and three dimensional figures.
Communication in Mathematics
Mathematics provides a powerful and universal language. Students are expected to use mathematical language appropriately when communicating mathematical ideas, reasoning, and findings – both orally and in writing.
In every lesson, students are expected to communicate mathematically as well as use appropriate vocabulary.
Reflection in Mathematics
Students are encouraged to share their thinking with teachers and peers and to examine different problem-solving strategies. Critical reflection in mathematics helps students gain insight into their strengths and weaknesses as learners and to appreciate the value of errors as powerful motivators to enhance learning and understanding. Students are asked to reflect on the focus question for each lesson.
Text and Resources:
enVisionmath 2.0 - Pearson
The following additional resources will be used:
* NYS Common Core Mathematics Curriculum
* EngageNY material for curriculum enhancement
* Other “real-world” problems found on PearsonRealize.com
* Illuminations.nctm.org
Methodologies: An inquiry and project based learning environment that involves multimedia allowing all students to develop a global perspective is the focus of the mathematics curriculum. Real life situations are used for the context of mathematics tasks where appropriate. Local and/or global issues are used to promote inquiry into the role of mathematics in society and the environment. A variety of teaching strategies are used to challenge all students.
Course Units:
Unit 1: Ratios and Proportional Relationships
Unit 2: The Number System
Unit 3: Expressions and Equations
Unit 4: Geometry
Unit 5: Statistics and Probability
Assessment Criteria:
Knowledge and Understanding
The student will demonstrate:
*Consistent knowledge and understanding of the concept
*Consistent use of basic strategies/models and skills to solve simple problems in both familiar and unfamiliar situations, including those in real-life contexts.
*The ability to apply rules to solve real-world problems
Patterns and Understanding
The student will:
*Apply inquiry and mathematical problem solving techniques
*Construct simple patterns
*Be able to describe patterns in words and/or diagrams with guidance from the teacher
*Be able to arrive at a result or set of results by making the patterns and making predictions
Communication in Math
The student will:
*Use appropriate mathematical language in familiar and unfamiliar situations
*Create different forms of mathematical representation
*Clearly communicate a mathematical line of reasoning in solving simple problems using different forms of representation
Reflection
The student will:
*Justify the reasonableness of the results in the context of a problem
*Consider and reflect on the importance of her findings
*Demonstrate and explain an appreciation between types of error and degrees of error
*Consider and use alternative methods to solve simple problems
Assessment Student work will be assessed in math in order to support, engage, and provide feedback on the learning process. A broad range of assessment strategies and tasks will allow students multiple opportunities to demonstrate their knowledge, skills, and attitudes in math, and to ensure students are learning the objectives.
Assessment is used in order to provide foundation and support for student learning. We aim to understand what students comprehend and can do throughout different stages of the learning process. In this vein, both the process and product of learning are evaluated. Formative assessments include observations made by the teacher during class activities, group activities, written reflections, assignments, and practice opportunities for utilizing what students know in the subject area.
Summative assessment is accomplished through projects executed at the end of a unit and through various quizzes and tests that take place during each unit’s course. Math tests are designed to parallel course content and provide tangible feedback. These tests should be signed and returned.
Homework
Homework will be collected and/or checked daily to ensure student completion. All homework for the trimester will count toward the subject grade for the report card. Missing homework detracts from the final grade.
√+ Well done, no errors all work shown, neat
√ Completed satisfactorily, contains some errors, all work shown
√- Homework attempted but has many errors, or work is not shown and it lacks neatness
0 Homework not submitted
Report Cards:
Students' math grades are based upon the following criteria:
Class participation – includes preparedness, lateness/absence, willingness to try
Homework
Tests and quizzes
Projects
Problem solving activities
Notebooks and journal reflections