Mathematics Curriculum Standards and Essential Questions

Grade Six     Grade Seven     Grade Eight


Grade Six

Standards

Essential Questions

Number and Operations

Content Standard 1.0   The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

1.    How is an understanding of positive rational numbers, their representations, and relationships useful in problem solving?

2.    How does understanding numerical operations on positive rationals, and their relationships to each other, provide a basis for understanding more complex mathematical operations?

3.    How does the ability to use multiple methods and tools to compute fluently—and make reasonable estimates—help to simplify mathematical tasks involving fractions and decimals?

Algebra

Content Standard 2.0  The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and and problems using graphs, tables, and equations.

1.    How do models, tables, and graphs help to represent, analyze, and extend numerical and geometrical patterns?

2.    How can algebraic symbols be used to efficiently express mathematical situations?

Geometry

Content Standard 3.0   The student will develop an understanding of geometric concepts and relationships as the basis for geometric modeling and reasoning to solve problems involving one-, two-, and three- dimensional figures.

1.    How can describing, classifying, and comparing properties of different lines, angles, and certain 2- and 3-dimensional shapes be useful for solving geometric problems in our 3-D world?

2.    How can location maps, charts, grids, and spreadsheets be efficiently indicated by using ordered pairs?

3.    How can transformations and symmetry be used to investigate and describe geometric situations?

4.    How can manipulatives and nets increase the ability to visualize, model, and reason about geometric concepts and entities?

Measurement

Content Standard 4.0   The student will become familiar with the units and processes of measurement in order to use a variety of tools, techniques, and formulas to determine and to estimate measurements in mathematical and real-world problems.

1.    How will using the tools and relationships of measures in the metric and customary systems help to estimate or find solutions to real-world problems to a required degree of accuracy?

2.    How will applying appropriate and varied models, ratios, and formulas help to estimate or calculate missing dimensions/distances or measurements of perimeter/circumference, area, and volume?

Data, Analysis, and Probability

Content Standard 5.0   The student will understand and apply basic statistical and probability concepts in order to organize and analyze data and to make predictions and conjectures.

1.    How can the collection, organization, and display of data help to interpret, evaluate inferences, and make predictions about real-life situations and circumstances?

2.    How can the understanding and use of measures of central tendency be useful for interpreting and drawing conclusions about data?

3.    How can devising and carrying out surveys and simulations help to determine the possible outcomes and probability of simple events?

 

 


 

Grade Seven

Standards

Essential Questions

Number and Operations

Content Standard 1.0   The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

1.    How is an understanding of positive and negative rational numbers, their representations, and relationships useful in problem solving?

2.    How does understanding the properties of operations on positive and negative rationals provide a basis for understanding more complex mathematical concepts?

3.    How does the ability to use multiple methods and tools to compute fluently—and make reasonable estimates—help to simplify mathematical tasks involving integers?

Algebra

Content Standard 2.0  The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and and problems using graphs, tables, and equations.

1.    How do models, tables, and graphs help to represent, analyze, and extend numerical and geometrical patterns, and to understand quantitative relationships?

2.    How can simple algebraic equations be written and solved to find unknown values?

3.    How can rate tables be used to identify and predict changes in quantity?

Geometry

Content Standard 3.0   The student will develop an understanding of geometric concepts and relationships as the basis for geometric modeling and reasoning to solve problems involving one-, two-, and three- dimensional figures.

1.    How can comparing, classifying, and determining congruence or similarity of polygons help to solve problems involving 2- and 3-dimensional figures?

2.    How can ordered pairs involving negative numbers be used to indicate locations on a coordinate grid?

3.    How can rotation and reflection be used to investigate congruence and symmetry, and vice versa?

4.    How will scale models and geometric constructions increase the ability to visualize spatial objects, and draw conclusions about them?

Measurement

Content Standard 4.0   The student will become familiar with the units and processes of measurement in order to use a variety of tools, techniques, and formulas to determine and to estimate measurements in mathematical and real-world problems.

1.    How will mastering conversions within the customary and metric systems of measurement guide in choosing the appropriate tool or unit of measurement to solve problems?

2.    How will applying appropriate techniques, tools, and formulas help determine or estimate needed measurements of figures or real things, to the required accuracy?

Data, Analysis, and Probability

Content Standard 5.0   The student will understand and apply basic statistical and probability concepts in order to organize and analyze data and to make predictions and conjectures.

1.    How can various data organizers be used to make predictions and conjectures in real world problems?

2.    How can data be analyzed so that misleading representations and interpretations be recognized and inferences will be reasonable?

3.    How can devising and carrying out experiments and simulations help develop counting theory and an understanding of theoretical probability?

 

 

 

 

 

 

 

 

 

 

 

 

Grade Eight

Standards

Essential Questions

Number and Operations

Content Standard 1.0   The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

1.    How is an understanding of rational numbers, their representations, and relationships useful in problem solving?

2.    How does understanding numerical operations, language, symbols, and their properties, and relationships to each other provide a basis for understanding more complex number theory?

3.    How does the ability to use multiple methods and tools to compute fluently—and make reasonable estimates—help to simplify, analyze, and develop mathematical tasks?

Algebra

Content Standard 2.0  The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and and problems using graphs, tables, and equations.

1.    How do variables and the concepts of relation and function help to represent, analyze, and extend numerical and geometrical patterns, and to understand input/output relationships?

2.    How can algebraic symbols be used to represent and model mathematical situations?

3.    How can tables, graphs, and equations be used to represent verbal descriptions of quantitative relationships, and vice versa?

4.    How can the rate of change be found in various representations of linear data?

Geometry

Content Standard 3.0   The student will develop an understanding of geometric concepts and relationships as the basis for geometric modeling and reasoning to solve problems involving one-, two-, and three- dimensional figures.

1.    How can analyzing the relations of angles and lines in certain 2-dimensional figures provide justification for conclusions about more complex figures?

2.    How can coordinate graphing aid reasoning to help solve real-world spatial problems?

3.    How can a coordinate grid be used to model and describe the results of various transformations?

Measurement

Content Standard 4.0   The student will become familiar with the units and processes of measurement in order to use a variety of tools, techniques, and formulas to determine and to estimate measurements in mathematical and real-world problems.

1.    How does fluency with customary and metric systems of measurement improve accuracy and speed in solving problems?

2.    How will applying appropriate measurement techniques, tools, and formulas help solve geometric problems efficiently?

Data, Analysis, and Probability

Content Standard 5.0   The student will understand and apply basic statistical and probability concepts in order to organize and analyze data and to make predictions and conjectures.

1.    How can the formulation of questions and conjectures be prompted by the analysis of data?

2.    How can data be organized so that inferences and predictions can be developed and evaluated?

3.    How can finding ways to count the possible outcomes of compound events be used to determine their probability?