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

The Process 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 StandardsWhat is standards-based curriculum and

instruction? Glenn Commission Report: “Before It’s Too

Late”Emphasizes the importance of “high-quality”

teaching TIMSS Data

U.S. curriculum lacks focus and coherence

TIMSS Video Study

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Australia Czech Republic Hong Kong Japan Netherlands United States

Using ProceduresMaking Connections

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20 19

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Australia Czech Republic Hong Kong Japan Netherlands United States

Using ProceduresMaking Connections

FIGURE 1 Types of Math Problems Presented

FIGURE 2 How Teachers Implemented

Making Connections Math Problems

So…. 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?

Knowledge Networks

Big Ideas

Key Components

Key Components

Building Blocks

Building Blocks

Building Blocks

Building Blocks

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 MeasureUnderstand 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

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

Read interpret, and construct

charts, tables, line plots, pictographs and bar graphs.

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 Transformatio

ns on the Coordinate

PlaneIdentify Examples of Geometric and Numeric Patterns

Identify and draw lines of

symmetryRepresent, 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

Grade 6

Problem Solving, Reasoning, Communication, Connections, and

Representations should be integrated throughout the web.

Understand and Apply Concepts of Probability

Experimental Probability

Theoretical Probability

Understand data-based probability distributions from the results of a

simulation.

Compute and interpret the

expected value of random variables in simple cases.

Construct sample spaces and probability

distributions in simple cases.

Distinguish between and

compute probability and

odds.

Solve problems involving

conditional probability and independent

events.

Draw and justify conclusions regarding the validity of a probability or statistical

argument.

Use area models to calculate probabilities

High School Grades 9-12

Use experimental and theoretical probability distributions to make judgments about the likelihood of uncertain

situations.

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Knowledge Webs from Framework2.7.11 Grade 11

PA StandardsPA Assessment Anchor

9-12 Understand and Apply Concepts of Probability

A. Compare odds and probability.E.3 Understand and/or apply basic

concepts of probability or outcomes

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

A. Apply probability and statistics to perform an experiment involving a sample and generalize its results to the entire population.

E.2 Select and/or use appropriate statistical methods to analyze data

E.3 Understand and/or apply basic concepts of probability or outcomes

A. Draw and justify a conclusion regarding the validity of a probability or statistical argument.

E.4 Develop and/or evaluate inferences and predictions or draw conclusions based on data or data displays

9-12 Understand and Apply Concepts of Probability

A. Use experimental and theoretical probability distributions to make judgments about the likelihood of various outcomes in uncertain situations.

A. Solve problems involving independent simple and compound events.

E.3 Understand and/or apply basic concepts of probability or outcomes

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

Standards-Based Classrooms 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 Adapt/adopt

As a Professional Development tool Use to start discussions within and across grade

levels Use activities and assessments in professional

development