K-12 Regional Mathematics Curriculum Framework Math & Science Collaborative Allegheny Intermediate Unit
Curriculum Frameworks Are Resources To:
Assist districts in developing curriculum consistent with the PA Standards for Mathematics and PA Assessment Anchors
Indicate what students should know and be able to do at each grade level
Provide high quality learning experiences for students so that they may develop deep conceptual understanding of the essential learnings
Curriculum Frameworks Are Not:
Required by law
Detailed lesson plans
Items for which students must be tested
Directives for uniform programs and textbook adoption
Curriculum formats that all districts must follow
Team members identified ‘big ideas’ at each grade level
Discussed essential learnings across grade levels
Eliminated unnecessary repetition while assuring there were no gaps
Confirmed that PA and NCTM Standards are addressed
Provided a chart with alignment of Big Ideas to PA Standards and Assessment Anchors
Background and Rationale
Implement PA and NCTM Standards
What is standards-based curriculum and instruction?
Glenn Commission Report: “Before It’s Too Late”
Emphasizes the importance of “high-quality” teaching
U.S. curriculum lacks focus and coherence
FIGURE 1 Types of Math Problems Presented FIGURE 2 How Teachers Implemented Making Connections Math Problems TIMSS Video Study
How can we identify and organize a few big ideas at each grade level?
What might the curriculum look like as it’s organized around big ideas in mathematics?
These ideas represent the essential learning at this grade level. All learning is correlated with the Pennsylvania Mathematics standards. Problem solving, reasoning, communications, connections, and representations are integrated throughout the curriculum. Teachers should encourage students to demonstrate and deepen their understanding of numbers and operations by solving interesting, contextualized problems and by discussing the representations and strategies they use . Understand the Base 10 Number System Understand the Relationship between Addition and Subtraction Analyze Data Understand Multiplication and Division Classify Figures Select and Use Appropriate Units and Systems to Measure Understand Patterns, Relations, and Functions Third Grade
Understand Multiplication and Division within 100 Understand multiplication as repeated addition, combining equal groups, using arrays, area models, linear models, Cartesian models. Represent multiplication and division problems using many different models. Use different strategies to solve multiplication and division facts and problems, including multi-step problems and determine reasonableness of answers. Know multiplication and division facts to 10. Apply multiplication and division to non-routine problems Find missing factors. Problem solving, reasoning, connections, communication and representations should be integrated throughout the web. Understand division as repeated subtraction, finding equal shares. Understand the relation between multiplication and division. Grade 3
Read interpret, and construct charts, tables, line plots, pictographs and bar graphs. Analyze Data Form and justify an opinion on whether a given statement is reasonable based on analyzed data. Gather, organize, analyze and display data using tables, charts, pictures, graphs, etc. Predict the likely number of times a condition will occur based on analyzed data. Problem solving, reasoning, connections, communication and representations should be integrated throughout the web. List or graph the possible results of an experiment, (e.g. design a fair or unfair game). Grade 3
Grade 6 Investigate and Understand the Processes of Measurement Understand the Meaning and Effects of Arithmetic Operations with Decimals, Fractions and Percents Recognize and Create Examples of Geometric and Numeric Patterns Construct and Interpret Data Displays in order to Make Inferences, Predictions and Arguments Understand Number Theory with respect to Factors and Multiples
Grade 6 Recognize and Create Examples of Geometric and Numeric Patterns Demonstrate Transformations on the Coordinate Plane Identify Examples of Geometric and Numeric Patterns Identify and draw lines of symmetry Represent, analyze, and generalize patterns with tables, graphs, words, and/or rules Problem Solving, Reasoning, Communication, Connections, and Representations should be integrated throughout the web. Determine and describe sizes, positions, and orientations of shapes, after rotations, dilations, reflections, and translations Relate and compare these different forms of representations for a relationship Use some transformations to create tesselations Identify and construct similar figures that model proportional relationships
E.3 Understand and/or apply basic concepts of probability or outcomes
Solve problems involving independent simple and compound events.
Use experimental and theoretical probability distributions to make judgments about the likelihood of various outcomes in uncertain situations.
9-12 Understand and Apply Concepts of Probability E.4 Develop and/or evaluate inferences and predictions or draw conclusions based on data or data displays
Draw and justify a conclusion regarding the validity of a probability or statistical argument.
E.2 Select and/or use appropriate statistical methods to analyze data E.3 Understand and/or apply basic concepts of probability or outcomes
Apply probability and statistics to perform an experiment involving a sample and generalize its results to the entire population.
9-12 Select and Use Appropriate Statistical Methods to Analyze Data 9-12 Develop and Evaluate Inferences and Predictions Based Upon Data Analysis 9-12 Understand and Apply Concepts of Probability E.3 Understand and/or apply basic concepts of probability or outcomes
Compare odds and probability.
9-12 Understand and Apply Concepts of Probability PA Assessment Anchor 2.7.11 Grade 11 PA Standards Knowledge Webs from Framework
Reasons to Use Framework
To avoid feeling overwhelmed with so much content
To move from concrete to graphic to abstract at all levels
To shift from a focus on teaching procedures to engaging students in problem solving
To lead students to a deep conceptual understanding of the essential learnings
Curriculum that includes:
Content linked to standards
Instructional practices that foster problem solving, communication, reasoning and connections through multiple representations
Authentic assessments that enable students to show what they know and can do in mathematics
Using the Framework
As an aid in writing District-level curriculum
As a Professional Development tool
Use to start discussions within and across grade levels
Use activities and assessments in professional development