§111.22. Mathematics, Grade 6.

(1) Within a well-balancedmathematics curriculum, the primary focal points at Grade 6 are using ratios todescribe direct proportional relationships involving number, geometry,measurement, probability, and adding and subtracting decimals and fractions.

(2) Throughout mathematics inGrades 6-8, students build a foundation of basic understandings in number,operation, and quantitative reasoning; patterns, relationships, and algebraicthinking; geometry and spatial reasoning; measurement; and probability andstatistics. Students use concepts, algorithms, and properties of rationalnumbers to explore mathematical relationships and to describe increasinglycomplex situations. Students use algebraic thinking to describe how a change inone quantity in a relationship results in a change in the other; and theyconnect verbal, numeric, graphic, and symbolic representations ofrelationships. Students use geometric properties and relationships, as well asspatial reasoning, to model and analyze situations and solve problems. Studentscommunicate information about geometric figures or situations by quantifyingattributes, generalize procedures from measurement experiences, and use theprocedures to solve problems. Students use appropriate statistics,representations of data, reasoning, and concepts of probability to drawconclusions, evaluate arguments, and make recommendations.

(3) Problem solving in meaningfulcontexts, language and communication, connections within and outside mathematics,and formal and informal reasoning underlie all content areas in mathematics.Throughout mathematics in Grades 6-8, students use these processes togetherwith graphing technology and other mathematical tools such as manipulativematerials to develop conceptual understanding and solve problems as they domathematics.

§111.23. Mathematics, Grade 7.

(1) Within a well-balancedmathematics curriculum, the primary focal points at Grade 7 are using directproportional relationships in number, geometry, measurement, and probability;applying addition, subtraction, multiplication, and division of decimals,fractions, and integers; and using statistical measures to describe data.

(2) Throughout mathematics inGrades 6-8, students build a foundation of basic understandings in number,operation, and quantitative reasoning; patterns, relationships, and algebraicthinking; geometry and spatial reasoning; measurement; and probability andstatistics. Students use concepts, algorithms, and properties of rationalnumbers to explore mathematical relationships and to describe increasinglycomplex situations. Students use algebraic thinking to describe how a change inone quantity in a relationship results in a change in the other; and theyconnect verbal, numeric, graphic, and symbolic representations ofrelationships. Students use geometric properties and relationships, as well asspatial reasoning, to model and analyze situations and solve problems. Studentscommunicate information about geometric figures or situations by quantifyingattributes, generalize procedures from measurement experiences, and use theprocedures to solve problems. Students use appropriate statistics,representations of data, reasoning, and concepts of probability to draw conclusions,evaluate arguments, and make recommendations.

(3) Problem solving in meaningfulcontexts, language and communication, connections within and outsidemathematics, and formal and informal reasoning underlie all content areas inmathematics. Throughout mathematics in Grades 6-8, students use these processestogether with graphing technology and other mathematical tools such asmanipulative materials to develop conceptual understanding and solve problemsas they do mathematics.

§111.24. Mathematics, Grade 8.

(1) Within a well-balancedmathematics curriculum, the primary focal points at Grade 8 are using basicprinciples of algebra to analyze and represent both proportional andnon-proportional linear relationships and using probability to describe dataand make predictions.

(2) Throughout mathematics inGrades 6-8, students build a foundation of basic understandings in number,operation, and quantitative reasoning; patterns, relationships, and algebraicthinking; geometry and spatial reasoning; measurement; and probability andstatistics. Students use concepts, algorithms, and properties of rationalnumbers to explore mathematical relationships and to describe increasinglycomplex situations. Students use algebraic thinking to describe how a change inone quantity in a relationship results in a change in the other; and theyconnect verbal, numeric, graphic, and symbolic representations ofrelationships. Students use geometric properties and relationships, as well asspatial reasoning, to model and analyze situations and solve problems. Studentscommunicate information about geometric figures or situations by quantifyingattributes, generalize procedures from measurement experiences, and use theprocedures to solve problems. Students use appropriate statistics,representations of data, reasoning, and concepts of probability to drawconclusions, evaluate arguments, and make recommendations.

(3) Problem solving in meaningfulcontexts, language and communication, connections within and outside mathematics,and formal and informal reasoning underlie all content areas in mathematics.Throughout mathematics in Grades 6-8, students use these processes togetherwith graphing technology and other mathematical tools such as manipulativematerials to develop conceptual understanding and solve problems as they domathematics.