Mathematics Curriculum Standards |
| Department of Catholic Schools Diocese of Oakland Math Standards K-8 August 2010 |
Those closest to the level of implementation are best suited to develop curriculum. Through the process teachers increase their content and pedagogical knowledge and reflect on their teaching. |
- Susan Loucks Horsley |
…when teachers are given the opportunity to study and design powerful lessons based on standards, more students experience success. |
- Stephanie Hirsh |
Over the course of the 2009-2010 school year, over 600 diocesan elementary
administrators and teachers gathered to learn and work together towards developing
a rational, coherent curriculum that was understood and valued by all, clearly articulated rigorous, relevant, challenging, and doable (J curve) standards and
concepts, was articulated grade level to grade level, course to course, grew in
complexity over time, and aligned standards, concepts, assessment and instruction.
This work was lead by our Vertical Team members who assisted us in reviewing our
standards vertically, working to ensure that there were no gaps or unnecessary These Mathematics Curriculum Standards were developed through a careful analysis of both the California State Standards and NCTM Standards. The opening remarks at each grade level provide a ‘Focus for Instruction’ based on the newly released (2010) Common Core Standards and a ‘By the end of…’ grade level comment from the California Standards. With the knowledge gained from these documents, and the expertise of our classroom teachers, we have adopted these newly defined standards as of August 2010. We know that all educational materials need to be ‘living documents’, so continuous review and updating will occur to ensure that we have a rich and rigorous curriculum that promotes academic excellence for all of the students entrusted to our care within the Diocese of Oakland. |
Vertical Team Members |
| K-2 Julie Clement, Holy Rosary Karen Kreider, St. Francis of Assisi LaTanya Buckley- Williams, St. Anthony Margie Chu, Our Lady of Guadalupe Kimberly Mikus, St. Martin de Porres Jennifer Fischer, Our Lady of Grace Lucia Prince, Queen of All Saints Ann Marie Drabin, Holy Spirit Katie Klinger, Christ the King Sharon Menicou, St. Joseph- Fremont Marea Palmer-Loh, Corpus Christi Paulette Santa Maria, Holy Rosary |
| 3-5 Pam Hovanic, St. Raymond Lenore Walsh, Assumption Merrilee Silviera, St. Agnes Juleana Carmona-Shaw, St. Edwards Courtney Gomez, St. Joachim Jessica Murray, Corpus Christi Alison McFerrin, Assumption Darlene Wherlie, Queen of All Saints Jesse Smith, St. John- San Lorenzo Joseph Petersen, St. Elizabeth Donna Petri, St. Jerome Suzanne Board, St. Patrick Kelly Mendoza, St. Joseph- Fremont |
| 6-8 Karen Francis, St. Patrick Myriam Godfrey, St. Martin de Porres Rachel Gonsalves, St. John- San Lorenzo Sharon Calhoun, St. Michael Dana Bayer, St. Joachim Maria Ward, St. Isidore Mele Sablan, St. Elizabeth Lisa DeLapo, St. Joseph- Fremont Barbara Lacy, Our Lady of Grace Shyra Dawson, Assumption Gina Flint, Holy Rosary Joyce Holden, St. Theresa Cara Varon, St. Isidore Julie Castro, St. Edward Natalie Deininger, St. Perpetua Carlos Trujillo, St. Philip Neri Bruce Amundson, Bishop O’Dowd High School Robyn Canga, De La Salle High School |
GRADE SEVEN |
In Grade Seven, instructional time is focused on four critical areas: (1) Developing
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NUMBERS AND OPERATIONS |
| Arithmetic operations with rational and irrational numbers and how they relate to one another are the foundation for all systematic problem solving. |
1.1 Show proficiency with the four arithmetic operations with whole numbers, integers, fractions, decimals, ratios, proportions, and absolute value. 1.2 Understand and demonstrate the relationship between fractions, decimals, and percents. 1.3 Solve problems using fractions, decimals, and percents. 1.4 Differentiate between and apply the commutative, associative, identity, and distributive properties to simplify variable expressions. 1.5 Convert numbers to scientific notation with positive and negative exponents. 1.6 Estimate roots to the nearest whole number. 1.7 Calculate percent change and simple interest. |
MEASUREMENT & GEOMETRY |
| Spatial patterns in the physical world can be represented by a fairly small collection of fundamental geometrical shapes and relationships. |
| 1.1 Compare capacities, mass, linear measure, time, and temperature between metric and customary systems. 1.2 Derive and calculate the area and perimeter of parallelograms and trapezoids. 1.3 Derive and calculate the surface area of right solids. (rectangular prism) 1.4 Derive and calculate the volume of prisms and cylinders. 1.5 Model surface area and volume with nets. 1.6 Interpret drawings and models made to scale and apply knowledge to real life problems. 1.7 Predict and apply linear dimensional analysis. ( Squared, cubed, and exponential values) 1.8 Estimate and formulate the area of irregular two-dimensional figures. 1.9 Visualize and graph two-dimensional figures on a coordinate plane. 1.10 Use properties of special angles to solve geometry problems. |
REASONING & PROOF |
| A well constructed argument uses stated assumptions, definitions, and previously established results. |
| 1.1 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed. 1.2 Verify the reasonableness of calculated results using estimation. 1.3 Apply strategies and results from simpler problems to more complex problems. 1.4 Use real number properties to justify the process of solving algebraic equations. 1.5 Model different problem solving strategies. |
ALGEBRA & FUNCTIONS |
| Quantities can be represented as symbols and manipulated with real number properties to describe and find new values or relationships. |
| 1.1 Construct and solve 1-step equations. 1.2 Construct and solve 2-step equations with integers. 1.3 Combine like terms using the distributive property. 1.4 Evaluate expressions with multiple variables. 1.5 Graph inequalities of one variable on a number line and verify by selecting a point from the solution set. 1.6 Translate word problems into a simple algebraic inequality. 1.7 Evaluate expressions with multiple variables by implementing order of operations. 1.8 Apply properties of exponents to multiply and divide monomials. 1.9 Solve a simple proportion using equivalent fractions and the cross products property. |
STATISTICS & PROBABILITY |
| Data can be organized and analyzed to make predictions and draw conclusions. |
| 1.1 Select appropriate data display. 1.2 Create a circle graph using Excel that represents parts of whole based on the type of data used. 1.3 Create a display of bias-free data. 1.4 Apply measures of central tendency to other subject areas. 1.5 Formulate probabilities as ratios, decimals and percents. 1.6 Test and identify that if P is the probability of an event occurring, then -P is the probability of an event not occurring. 1.7 Distinguish between independent and dependent events. 1.8 Make predictions of experimental probability based on theoretical expectations. (i.e. Scientific method) |
GRADE EIGHT |
| In Grade Eight, instructional time is focused on three critical areas: (1) Formulating and reasoning about expressions and equations, including modeling and association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) Grasping the concept of a function and using functions to describe quantitative relationships; (3) Analyzing two and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem. |
NUMBERS & OPERATIONS |
| Arithmetic operations with rational and irrational numbers and how they relate to one another are the foundation for all systematic problem solving. |
| 1.1 Demonstrate a mastery of inverse relationships between exponents and roots including simplification of quotients and products. 1.2 Construct and apply a proportion to solve problems. 1.3 Apply percents to problems involving discounts, markups, commissions, profit, simple and compound interest. 1.4 Apply algebraic equations to solve real world problems using integers, fractions and decimals. 1.5 Add, subtract, multiply and divide scientific notation. |
MEASUREMENT & GEOMETRY |
| Spatial patterns in the physical world can be represented by a fairly small collection of fundamental geometrical shapes and relationships. |
| 1.1 Compare units expressed as rates (speed, density) and products. (person-days, work). 1.2 Apply the concepts of surface area and volume to solve real world problems. 1.3 Determine how a change of linear scale affects both area and volume. 1.4 Describe & compare how two or more objects are related in space (i.e., skew, perpendicular and parallel lines and planes). 1.5 Formulate a method and construct models of the area of more complex or irregular two and three-dimensional figures by breaking the figures down into common figures. 1.6 Apply formulas to calculate surface area and volume of pyramids, cones, and spheres. |
REASONING & PROOF |
| A well constructed argument uses stated assumptions, definitions, and previously established results. |
| 1.1 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed. 1.2 Verify the reasonableness of calculated results using estimation. 1.3 Apply strategies and results from simpler problems to more complex problems. 1.4 Use real number properties to justify the process of solving algebraic equations. 1.5 Model different problem solving strategies. 1.6 Understand the concept of intersection, union, and set theory. |
ALGEBRA & FUNCTIONS |
| Quantities can be represented as symbols and manipulated with real number properties to describe and find new values or relationships. |
| 1.1 Formulate and solve multistep equations using rational numbers in order to solve real world problems. 1.2 Solve and graph single variable inequalities. 1.3 Solve and graph linear functions with two variables. 1.4 Understand the slope is the ratio of rise to run. Identify slope and the y intercept graphically and from a linear equation. 1.5 Relate distances of two points in a figure on a coordinate plane using the Pythagorean Theorem. 1.6 Find the midpoint of a line segment. 1.7 Model and evaluate variable expressions involving roots and the three properties of exponents. 1.8 Apply the four basic operations to simplify multi-variable monomial expressions. 1.9 Write an algebraic equation to represent a variety of patterns from tables and graphs. 1.10 Transform formulas for a given variable. |
STATISTICS & PROBABILITY |
| Data can be organized and analyzed to make predictions and conclusions. |
| 1.1 Graph two variables to represent data in multiple forms such as scatter plots, plots, bar graphs and be able to describe linear relationships. 1.2 Identify and analyze the minimum, lower quartile, upper quartile, and maximum of a data set with a box and whisker plot. 1.3 Analyze the correspondence between data sets and their graphical representations including trends and correlations. 1.4 Use observations about differences between two or more samples to make conjectures about populations from which the samples were taken. 1.5 Apply concepts of probability to real world situations. |