Delaware State Standards for Mathematics: Grade 8

DE.1(5-8) Numeric Reasoning: Students will develop Numeric Reasoning and an understanding of Number and Operations by solving problems in which there is a need to represent and model real numbers verbally, physically, and symbolically; to explain the relationship between numbers; to determine the relative magnitude of real numbers; to use operations with understanding; and to select appropriate methods of calculations from among mental math, paper-and-pencil, calculators, or computers.

1(5-8).1. Enduring Understandings: Numbers can be represented in multiple ways. The same operations can be applied in problem situations that seem quite different from one another. Being able to compute fluently means making smart choices about which tools to use and when to use them. Knowing the reasonableness of an answer comes from using good number sense and estimation strategies.

1(5-8).1.1. Essential Questions: What makes an estimate reasonable? What makes an answer exact? What makes a strategy both effective and efficient? What makes a solution optimal?

1(8).1.1.1. Number sense:

1(8).1.1.2. Operations:

DE.2(5-8) Algebraic Reasoning: Students will develop Algebraic Reasoning and an understanding of Patterns and Functions by solving problems in which there is a need to recognize and extend a variety of patterns; to progress from the concrete to the abstract using physical models, equations, and graphs; to describe, represent, and analyze relationships among variable quantities; and to analyze, represent, model, and describe real-world functional relationships.

2(5-8).1. Enduring Understandings: Change is fundamental to understanding functions. Numbers or objects that repeat in predictable ways can be described or generalized. An operation can be ''undone'' by its inverse. Rules of arithmetic and algebra can be used together with notions of equivalence to transform equations and inequalities so solutions can be found.

2(5-8).1.1. Essential Questions: How can change be described mathematically? How are patterns of change related to the behavior of functions? How do mathematical models/representations shape our understanding of mathematics?

2(8).1.1.1. Patterns and change:

2(8).1.1.2. Representations:

2(8).1.1.3. Symbols:

DE.3(5-8) Geometric Reasoning: Students will develop Geometric Reasoning and an understanding of Geometry and Measurement by solving problems in which there is a need to recognize, construct, transform, analyze properties of, and discover relationships among geometric figures; and to measure to a required degree of accuracy by selecting appropriate tools and units.

3(5-8).1. Enduring Understandings: Two- and three-dimensional objects can be described, classified, and analyzed by their attributes. An object in a plane or in space can be oriented in an infinite number of ways while maintaining its size or shape. An object's location on a plane or in space can be described quantitatively. Linear measure, area, and volume are fundamentally different but may be related to one another in ways that permit calculation of one given the other.

3(5-8).1.1. Essential Questions: How are measurement and counting related? How does what we measure affect how we measure? How can space be defined through numbers/measurement? Why do we compare contrast and classify objects? How do decomposing and recomposing shapes help us build our understand of mathematics? How can transformations be described mathematically?

3(8).1.1.1. Classification:

3(8).1.1.2. Location and transformation:

3(8).1.1.3. Measurement:

DE.4(5-8) Quantitative Reasoning: Students will develop Quantitative Reasoning and an understanding of Data Analysis and Probability by solving problems in which there is a need to collect, appropriately represent, and interpret data; to make inferences or predictions and to present convincing arguments; and to model mathematical situations to determine the probability.

4(5-8).1. Enduring Understandings: The question to be answered determines the data to be collected and how best to collect it. Basic statistical techniques can be used to analyze data in the workplace. The probability of an event can be used to predict the probability of future events.

4(5-8).1.1. Essential Questions: What is average? What makes a data representation useful? How does my sample affect confidence in my predication? What is fair?

4(8).1.1.1. Collect:

4(8).1.1.2. Represent:

4(8).1.1.3. Analyze:

4(8).1.1.4. Probability:

DE.5(K-12) Process Standards - Problem Solving: Students will develop their Problem Solving ability by engaging in developmentally appropriate problem-solving opportunities in which there is a need to use various approaches to investigate and understand mathematical concepts; to formulate their own problems; to find solutions to problems from everyday situations; to develop and apply strategies to solve a wide variety of problems; and to integrate mathematical reasoning, communication and connections. All students in grades K-12 will be able to:

5(K-12).1. Enduring Understandings: Mathematics can be used to solve problems outside of the mathematics classroom. Mathematics is built on reason and always makes sense. Reasoning allows us to make conjectures and to prove conjectures. Classifying helps us build networks of mathematical ideas. Precise language helps us express mathematical ideas and receive them.

5(K-12).1.1. Essential Questions: Is your plan working? Do you need to reconsider what you are doing? How are solving and proving different? How are showing and explaining different? How do you know when you have proven something? What does it take to verify a conjecture? How do you develop a convincing argument? How do you make sense of different strategies? How do you determine their strengths and weaknesses? How do you determine similarities and differences? Why do we classify? Why do we classify numbers? Why do we classify geometric objects? Why do we classify functions?

5(K-12).1.1.1. Build new mathematical knowledge

5(K-12).1.1.2. Solve problems that arise in mathematics and in other contexts

5(K-12).1.1.3. Apply and adapt a variety of appropriate strategies to solve problems

5(K-12).1.1.4. Monitor and reflect on the process of mathematical problem solving

DE.6(K-12) Process Standards - Reasoning and Proof: Students will develop their Reasoning and Proof ability by solving problems in which there is a need to investigate significant mathematical ideas in all content areas; to justify their thinking; to reinforce and extend their logical reasoning abilities; to reflect on and clarify their own thinking; to ask questions to extend their thinking; and to construct their own learning. All students in grades K-12 will be able to:

6(K-12).1. Enduring Understandings: Mathematics can be used to solve problems outside of the mathematics classroom. Mathematics is built on reason and always makes sense. Reasoning allows us to make conjectures and to prove conjectures. Classifying helps us build networks of mathematical ideas. Precise language helps us express mathematical ideas and receive them.

6(K-12).1.1. Essential Questions: Is your plan working? Do you need to reconsider what you are doing? How are solving and proving different? How are showing and explaining different? How do you know when you have proven something? What does it take to verify a conjecture? How do you develop a convincing argument? How do you make sense of different strategies? How do you determine their strengths and weaknesses? How do you determine similarities and differences? Why do we classify? Why do we classify numbers? Why do we classify geometric objects? Why do we classify functions?

6(K-12).1.1.1. Understand that reasoning and proof are fundamental aspects of mathematics

6(K-12).1.1.2. Make and investigate mathematical conjectures

6(K-12).1.1.3. Develop and evaluate mathematical arguments and proofs

6(K-12).1.1.4. Select and use various types of reasoning and methods of proof

DE.7(K-12) Process Standards - Communication: Students will develop their mathematical Communication ability by solving problems in which there is a need to obtain information from the real world through reading, listening and observing; to translate this information into mathematical language and symbols; to process this information mathematically; and to present results in written, oral, and visual formats. All students in grades K-12 will be able to:

7(K-12).1. Enduring Understandings: Mathematics can be used to solve problems outside of the mathematics classroom. Mathematics is built on reason and always makes sense. Reasoning allows us to make conjectures and to prove conjectures. Classifying helps us build networks of mathematical ideas. Precise language helps us express mathematical ideas and receive them.

7(K-12).1.1. Essential Questions: Is your plan working? Do you need to reconsider what you are doing? How are solving and proving different? How are showing and explaining different? How do you know when you have proven something? What does it take to verify a conjecture? How do you develop a convincing argument? How do you make sense of different strategies? How do you determine their strengths and weaknesses? How do you determine similarities and differences? Why do we classify? Why do we classify numbers? Why do we classify geometric objects? Why do we classify functions?

7(K-12).1.1.1. Organize and consolidate their mathematical thinking through communication

7(K-12).1.1.2. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others

7(K-12).1.1.3. Analyze and evaluate the mathematical thinking and strategies of others

7(K-12).1.1.4. Use the language of mathematics to express mathematical ideas precisely

DE.8(K-12) Process Standards - Connections: Students will develop mathematical Connections by solving problems in which there is a need to view mathematics as an integrated whole and to integrate mathematics with other disciplines, while allowing the flexibility to approach problems, from within and outside mathematics, in a variety of ways. All students in grades K-12 will be able to:

8(K-12).1. Enduring Understandings: Mathematics can be used to solve problems outside of the mathematics classroom. Mathematics is built on reason and always makes sense. Reasoning allows us to make conjectures and to prove conjectures. Classifying helps us build networks of mathematical ideas. Precise language helps us express mathematical ideas and receive them.

8(K-12).1.1. Essential Questions: Is your plan working? Do you need to reconsider what you are doing? How are solving and proving different? How are showing and explaining different? How do you know when you have proven something? What does it take to verify a conjecture? How do you develop a convincing argument? How do you make sense of different strategies? How do you determine their strengths and weaknesses? How do you determine similarities and differences? Why do we classify? Why do we classify numbers? Why do we classify geometric objects? Why do we classify functions?

8(K-12).1.1.1. Recognize and use connections among mathematical ideas

8(K-12).1.1.2. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole

8(K-12).1.1.3. Recognize and apply mathematics in contexts outside of mathematics