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 SIX |
In Grade Six, instructional time is focused on four critical areas: (1) Connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) Completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) Writing, interpreting, and using expressions and equations; and (4) Developing understanding of statistical thinking.
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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 Express a value in equivalent forms using fractions, decimals, and percents. 1.2 Show mastery of the four basic arithmetic operations with whole numbers and integers, fractions and decimals. 1.3 Analyze the reasonableness of a result using estimation. 1.4 Order and compare signed integers on a number line, as well as decimals, fractions, and mixed numbers. 1.5 Determine the Least Common Multiple and the Greatest Common Factor of whole numbers using prime factorization with exponents and use them to solve problems with fractions. 1.6 Interpret and use ratios and proportions in different contexts. 1.7 Express rates and ratios in terms of division. 1.8 Interpret powers of 10 with exponents and apply to scientific notation. 1.9 Apply order of operations to simplify expressions with addition, subtraction, multiplication and division. 1.10 Explain/model proportions and equivalent fractions. 1.11 Demonstrate understanding of the relationship between standard and scientific notation. 1.12 Demonstrate understanding of the inverse relationship between exponents and roots. |
ALGEBRA & FUNCTIONS |
| Quantities can be represented as symbols and manipulated with real number properties to describe and find new values or relationships. |
| 1.1 Write and solve one-step linear equations with one variable (verbal model to an equation). 1.2 Generate one-step linear equations with one variable from a real world scenario. (word problem) 1.3 Solve problems using Order of Operations and the commutative, associative, identity, and distributive properties. 1.4 Understand rate and begin to solve problems involving rate, average, speed, distance and time. 1.5 Evaluate variable expressions describing geometric quantities such as perimeter, area, surface area, and circumference. 1.6 Create algebraic equations based on basic geometric relationships (ex. side lengths of figure using perimeter or area formula). 1.7 Evaluate a linear function and graph the resulting ordered pair of integers on a coordinate plane. (Make a table of values) 1.8 Recognize the relationship between the domain and range as a function of the other. |
MEASUREMENT & GEOMETRY |
| Spatial patterns in the physical world can be represented by a fairly small collection of fundamental geometrical shapes and relationships. |
| 1.1 Model and describe polygons. 1.2 Decompose all polygons into triangles. 1.3 Understand the concept of “π “as the ratio of its circumference to its diameter and its use in the formulas for circumference and area. 1.4 Apply the properties of complementary and supplementary angles and the sum of the measures of the angles of a triangle to solve problems. 1.5 Model and calculate surface area of rectangular prisms. 1.6 Model the concept of perimeter and understand that perimeter is the sum of the lengths of sides. 1.7 Compare capacities, mass, linear measure, time, and temperature in both metric and customary systems. 1.8 Create a circle graph to represent parts of a whole manually. |
STATISTICS & PROBABILITY |
| Data can be organized and analyzed to make predictions and draw conclusions. |
| 1.1 Identify appropriate use of circle, bar, and graph lines. 1.2 Identify and graph independent and dependent variables. 1.3 Select appropriate scale and intervals and understand relationship between x and y coordinates. 1.4 Analyze and apply concepts of range, mean, median, and mode of data sets. 1.5 Understand how outliers affect measures of central tendency. 1.6 Justify and evaluate the characteristics and limitations of a data sample. 1.7 Identify different ways of selecting a sample and the possible influence of bias. 1.8 Evaluate the validity of claims based on statistical data. 1.9 Recognize types of bias and evaluate the usefulness of the data. 1.10 Represent probability and odds as ratios, proportions, decimals and percents. 1.11 Verify the reasonableness of the probability. 1.12 Calculate theoretical and measure experimental probabilities. 1.13 Justify that a probability is the ratio of favorable outcomes to all possible outcomes. |
REASONING & PROOF |
| A well constructed argument uses stated assumptions, definitions, and previously established results. |
| 1.1 Continuously develop and integrate previously learned skills to solve more complex problems. 1.2 Distinguish relevant from irrelevant information. 1.3 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed. 1.4 Verify the reasonableness of calculated results using estimation. 1.5 Apply strategies and results from simpler problems to more complex problems. 1.6 Justify the simplification of numeral expressions with real number properties. 1.7 Observe and use simple number patterns to recognize algebraic rules. 1.8 Develop generalizations and apply them to other circumstances. |