Unit 2: National, State, and Local Mathematics Standards

Excellence in mathematics education requires high expectations and strong support for all students 1. Equity 2. Curriculum 3. Teaching 4. Learning 5. Assessment 6. Technology

1. Equity

-Apply and adapt a variety of appropriate strategies to solve problems -Monitor and reflect on the process of mathematical problem solving -Solve problems that arise in mathematics and in other contexts 1. Problem Solving 2. Reasoning and Proof 3. Communication 4. Connections 5. Representation

1. Problem Solving Look for words such as monitor and reflect

During a lesson on area and perimeter, a teacher encourages students to explore multiple ways to solve a problem. How does this lesson address the Problem-Solving standards for school mathematic? 1. Students will monitor and reflect on the process of mathematics 2. Students will use models and interpret physical, social, and mathematical phenomena 3. Students will provide reasoning and proof for a math problem. 4. Students will analyze and evaluate the mathematical thinking and strategies of others while using precise math language

1. Students will monitor and reflect on the process of mathematics monitor and reflect are words that are connected with problem solving

-Analyze and evaluate the mathematical thinking and strategies of others -Use the language of mathematics to express mathematical ideas precisely 1. Problem Solving 2. Reasoning and Proof 3. Communication 4. Connections 5. Representation

3. Communication Such as think pair share or math talks

Which stakeholder is directly in charge of choosing mathematical standards? 1. Parent-teacher organizations 2. Teacher organizations 3. State departments of education 4. Federal department of education

3. State departments of education The state department of education in each state determines which standards will be taught in their schools. While the federal government may suggest standards, and even financially incentivize adopting those standards, the decision of which standard is implemented lies with each individual state.

According to the Teaching Principle defined by NCTM, effective mathematics teaching requires __________. 1. instructional and financial support 2. understanding what students know and need to learn 3. educated mathematics teachers who possess certification in their subject 4. knowing the important ideas to teach

2. understanding what students know and need to learn

-2+3=1 A teacher is planning a lesson on adding and subtracting positive and negative integers. The teacher will use red and black chips as a manipulative and allow students to develop patterns for understanding the addition and subtraction problems. The following NCTM standard is associated with the lesson: "Represent the idea of a variable as an unknown quantity using a letter or a symbol." How do you rate the activity and alignment to the standard? 1. The activity is effective at showing students how to add and subtract integers but the standard is not aligned. 2. The activity is not effective at showing students how to add and subtract integers and the standard is not aligned. 3. The activity is not effective at showing students how to add and subtract integers but the standard is aligned. 4. The activity is effective at showing students how to add and subtract integers and the standard is aligned.

1. The activity is effective at showing students how to add and subtract integers but the standard is not aligned. While this lesson does a very good job of teaching students to represent integers both numerically and with a manipulative, it does not address the use of variables. Since the standard relates to variables, not integers, the lesson is not aligned.

A _____________ is more than a collection of activities: it must be coherent, focused on important mathematics, and well-articulated across the grades 1. Equity 2. Curriculum 3. Teaching 4. Learning 5. Assessment 6. Technology

2. Curriculum

-Recognize this as a fundamental aspect of mathematics -Make and investigate mathematical conjectures -Develop and evaluate mathematical arguments 1. Problem Solving 2. Reasoning and Proof 3. Communication 4. Connections 5. Representation

2. Reasoning and Proof Look for words such as evaluate or investigation

A lesson is being designed to address the Communication standard from Principles and Standards for School Mathematics (PSSM). The lesson requires that students write out directions for using fraction bars to model several addition problems. How does this lesson meet the Communication standard? 1. Students recognize and use connections among mathematical ideas. 2. Students use the language of mathematics to express ideas precisely. 3. Students create and use their own measurement units to measure an object. 4. Students model physical phenomenon with algebraic equations and appropriate technology.

2. Students use the language of mathematics to express ideas precisely.

A teacher wants students to write out how to use positive and negative chips to model operations with integers. How does this lesson address the representation process standard? 1. Students will use precise math language to express their reasoning. 2. Students will model an abstract concept using manipulatives. 3. Students will use the manipulative to show the teacher how to add and subtract integers. 4. It allows students to connect previously learned math to newly learned math content.

2. Students will model an abstract concept using manipulatives. The textbook readings will provide additional information about the Principles and Standards for School Mathematics. When students work through various math problems, it is important that you encourage them to use multiple representations to model math concepts. Translating between multiple representations of a math concept builds conceptual understanding.

A teacher is planning a lesson on adding and subtracting negative and positive integers. The teacher will use two-colored counters as a manipulative and allow students to practice solving addition and subtraction equations using two colored counters. The following NCTM standard is associated with the lesson: Represent the idea of a variable as an unknown quantity using a letter or a symbol. How do you rate the activity and alignment to the standard? 1. The activity is effective at showing students how to add integers and the standard is aligned. 2. The activity is effective at showing students how to add integers, but the standard is not aligned 3. The activity is not effective at showing students how to add integers but the standard is aligned. 4. The activity is not effective at showing students how to add integers and the standard is not aligned.

2. The activity is effective at showing students how to add integers, but the standard is not aligned

According to the teaching principles defined by NCTM, what does effective mathematics teaching require? 1. Knowing the important main ideas to teach 2. Understanding what students know and need to learn 3. Having instructional and financial support 4. Having educated mathematics teachers who possess certification in their subject

2. Understanding what students know and need to learn

A teacher encourages students to use two-colored counters when performing operations with integers. How does this activity address the Representation standards for school mathematics? 1. This activity allows students to connect previously learned math content to newly learned math content 2. Students will analyze and evaluate the work of others 3. Students will model an abstract concept using manipulatives 4. Students will use precise math language to express their reasoning

3. Students will model an abstract concept using manipulatives model

Effective mathematics _____________ requires understanding what students know and need to learn and then challenging and supporting them to learn it well 1. Equity 2. Curriculum 3. Teaching 4. Learning 5. Assessment 6. Technology

3. Teaching

-Understand how mathematical ideas build on one another to produce a coherent whole -Recognize and apply mathematics in contexts outside of mathematics 1. Problem Solving 2. Reasoning and Proof 3. Communication 4. Connections 5. Representation

4. Connections Look for words such as interconnect

Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge. 1. Equity 2. Curriculum 3. Teaching 4. Learning 5. Assessment 6. Technology

4. Learning

A teacher wants students to write out in narrative form the process of using two-colored counters when performing operations with integers. How does this lesson address the Communication standards for school mathematics? 1. This activity allows students to connect previously learned math content to newly learned math content 2. Students will use the manipulative to demonstrate how to add and subtract integers 3. Students will model an abstract concept using manipulatives 4. Students will use precise math language to express their reasoning

4. Students will use precise math language to express their reasoning math language

A teacher is planning a lesson on finding the area of rectangles. The teacher allows students to use a geoboard to create rectangles and assist in finding the area of those rectangles. The following standard is associated with the lesson: Measure and estimate liquid volumes and masses of objects. How should the teacher rate the activity and alignment to the standard? How should a teacher rate the activity and alignment to the standard? 1. The activity is not effective at showing students how to find area of rectangles, and the standard is not aligned. 2. The activity is not effective at showing students how to find area of rectangles, but the standard is aligned. 3. The activity is effective at showing students how to find area of rectangles, and the standard is aligned. 4. The activity is effective at showing students how to find area of rectangles; however, the standard is not aligned.

4. The activity is effective at showing students how to find area of rectangles; however, the standard is not aligned. While this lesson does a very good job of teaching students to find the area of a rectangle, it does not address liquid or mass. Since the standard relates to volume and mass, not area, the lesson is not aligned.

A teacher writes a fifth-grade lesson plan in which students will use a pan balance to demonstrate equalities in equations. The students will use counters and the pan balance to make the equations balance for ten open-sentence equations (15 + 34 = n + 21). The following standard was included within the plan: NCTM (National Council of Teachers of Mathematics): Principles & Standards for School Mathematics: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. How would an administrator rate the learning activity for its overall quality and alignment with the standard? 1. The activity was ineffective in demonstrating the concept, but the standard aligned with the lesson. 2. The activity was effective in demonstrating the concept of equality in equations, and the standard aligned with the lesson. 3. The activity was ineffective in demonstrating the concept of equality in equations, and the standard did not align. 4. The activity was effective in demonstrating the concept of equality in equations, but the standard did not align with the lesson.

4. The activity was effective in demonstrating the concept of equality in equations, but the standard did not align with the lesson.

______________ should support the learning of important mathematics and furnish useful information to both teachers and students 1. Equity 2. Curriculum 3. Teaching 4. Learning 5. Assessment 6. Technology

5. Assessment Assessment gives both teachers and students info on learning

-Use to model and interpret physical, social, and mathematical phenomena -Select, apply, and translate among mathematical models and graphs to solve problems 1. Problem Solving 2. Reasoning and Proof 3. Communication 4. Connections 5. Representation

5. Representation Things such as a model

________________ is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning 1. Equity 2. Curriculum 3. Teaching 4. Learning 5. Assessment 6. Technology

6. Technology