ppt 8
Post on 30-Jun-2015
1.575 Views
Preview:
TRANSCRIPT
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
61
77
84
41
57
69
15 1613
54
24
17
0
10
20
30
40
50
60
70
80
90
100
Australia Czech Republic Hong Kong Japan Netherlands United States
Using ProceduresMaking Connections
31
1618
20 19
59
8
52
4648
37
00
10
20
30
40
50
60
70
80
90
100
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.
94
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
top related