Standard

Instruction and Assessment

STANDARD 1. The student understands and applies the concepts and procedures of mathematics

1.1 NUMBER SENSE

* Applies the four computational processes with whole numbers in solving multi-step problems
* Develops conceptual understanding of computational processes with fractions and decimals
* Uses addition, subtraction, and multiplication of fractions and decimals in solving problems
* Experiences introductory activities with ratio, proportion, and percent and their application in real-world contexts
* Explores primes, composites, greatest common factor/divisor, least common multiple, and prime factorization, and applies these understandings in solving real-world problems
* Understands concepts related to negative integers
* Explores number patterns involving odd and even numbers, multiples, and divisibility
* Uses estimation to assess reasonableness of answers

1.2 MEASUREMENT

* Understands concepts of dimension, area, and volume
* Explores and creates methods to find perimeters, areas, and volumes of common geometric shapes
* Explores the use of standard measuring tools, including protractor and compass
* Understands the concept of rate when using scale models, maps, etc.
* Uses familiarity with both metric and customary units to convert among units within a system using tables of measures

1.3 GEOMETRIC SENSE

* Identifies and constructs lines, angles, perpendiculars, polygons, and circles
* Understands construction of polyhedra (prisms, pyramids, cylinders, cones)
* Classifies angles by their measure
* Classifies angles, triangles, and quadrilaterals
* Explores transformations (slides, flips and turns)
* Graphs ordered pairs on the full coordinate plane

1.4 PROBABILITY AND STATISTICS

* Finds probability of independent events
* Counts outcomes using tree diagrams
* Conducts experiments to determine experimental probabilities and uses results to make predictions
* Uses line plots, bar graphs, pictographs, line graphs, and circle graphs to organize and display data
* Finds the range, mean, median, and mode for a set of data and uses these measures to interpret the data
* Interprets information given in tables and graphs

1.5 ALGEBRAIC SENSE

* Explores functional relationships in number patterns and determines rules for data
* Applies order of operation rules in simplifying numerical expressions to solve problems
* Writes expressions with variables to define real-world relationships
* Expresses relationships among numbers using =, >, <
* Solves simple equations using addition, subtraction, multiplication and division

Instructional Support Materials

* Connected Mathematics

Instructional Strategies

1.1
* Mental Math
* Practice solving multi-step problems
* Interpret everyday situations involving fractions, decimals, percents
* Break difficult computation problems into manageable parts
* Compare and order fractions, decimals, and percents using a variety of models
* Use models and real-world examples to make clear the concept of positive and negative integers

1.2
* Decide when precise measurement is required and when estimates are sufficient
* Practice measuring items around the classroom/school using a variety of measuring tools (some with U.S. measurements and some with metric)

1.3
* Create geometric art while exploring such concepts as rotational and mirror symmetry and slides, flips, and turns
* Practice graphing on the full coordinate plane using games such as Hurkle and graphing pictures
* Use literacy strategies such as taxonomy, defining format, and list/group/label to become familiar with the vocabulary

1.4
* Explore different ways of recording the outcomes of theoretical probability
* Interpret tables and graphs drawn from numerous sources (e.g., newspapers, textbooks, magazines)
* Create graphs of data that are appropriately and clearly labeled

1.5
* Build designs that change in a regular way and/or grow according to number patterns
* Explore the order of operation rules
* Practice writing and solving simple equations based on real-world situations

Assessment

Standard 2. The student understands the meaning of what is read

2.1 Investigates situations

2.2 Formulates questions and defines the problem

2.3 Constructs solutions

* Searches systematically for patterns in simple situations
* Develops, uses and explains a variety of strategies and approaches
* Identifies what information is necessary to solve a given problem
* Defines question to be answered in a given problem
* Organizes relevant available information to develop solutions
* Selects and uses appropriate mathematical tools to develop solutions

Instructional Support Materials

* Connected Mathematics

Instructional Strategies

* Introduce students to strategies such as, make a picture, guess and check, look for a pattern, make an organized list, make a table, solve a simpler problem, and work backwards
* Share and explain alternate solutions in class
* Analyze problems sentence by sentence using a strategy like progressive disclosure

Assessment

Standard 3. The student uses mathematical reasoning

3.1 Analyzes information

3.2 Predicts results and makes inferences

3.3 Draws conclusions and verifies results

* Interprets, compares, and contrasts information from a variety of sources
* Validates thinking and mathematical ideas using models, known facts, and patterns
* Makes conjectures and inferences based on analysis of new problem situations
* Tests conjectures and inferences and explains why they are true or false
* Uses inductive reasoning to support arguments and justify results in problem situations

Instructional Support Materials

* Connected Mathematics

Instructional Strategies

* Raise key questions like:?What information are we still not confident about?? What relationships do our data fail to reveal?? What questions did we fail to ask?? What information did we never monitor?
* Reason from what they know
* Construct a model of thinking from evidence
* Make/test conjectures
* Explain/justify answers
* Make generalizations
* Draw conclusions

Assessment

Standard 4. The student communicates knowledge and understanding in both everyday and mathematical language

4.1 Gathers information

4.2 Organizes and interprets information

4.3 Represents and shares information

* Develops a plan for collecting information
* Uses reading, listening, and observation skills to access and extract mathematical information from multiple sources such as pictures, diagrams, and physical models
* Organizes and clarifies mathematical information by reflecting, verbalizing, discussing, and/or writing
* Clearly and effectively expresses or presents ideas and situations using both everyday and mathematical languages such as models, tables, charts, graphs, written reflection, or algebraic notation
* Expresses mathematical ideas with clarity using both everyday and mathematical language appropriate to the audience

Instructional Support Materials

* Connected Mathematics

Instructional Strategies

* Math journals
* Talk about solutions and transferring the verbalizing into writing
* Revise and refining mathematical writing
* Build an atmosphere of trust and mutual respect to promote student learning of mathematics

Assessment

Standard 5. The student understands how mathematical ideas connect within mathematics, to other subject areas, and to real-life situations

5.1 Relates concepts and procedures within mathematics

5.2 Relates mathematical concepts and procedures to other disciplines

5.3 Relates mathematical concepts and procedures to real-life situations

* Connects conceptual and procedural understanding among different mathematical content areas
* Relates and uses different mathematical models and representations for the same situation
* Identifies mathematical patterns and ideas in other disciplines
* Uses mathematical thinking and modeling in other disciplines
* Recognizes the extensive use of mathematics outside the classroom (e.g., in banking and sports statistics)
* Investigates the use of mathematics within several occupational career areas of interest

Instructional Support Materials

* Connected Mathematics

Instructional Strategies

* Integrate everyday uses of mathematics into the classroom learning process
* Develop connections within mathematical ideas and the potential uses of those connections

Assessment