Download - Math Common Core State Standards
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Common Core State Standards
What’s Next???Michelle L. Williams
East Feliciana Parish Schools
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Include only items that measure content common to the current grade-level expectations (GLEs) and the Common Core State Standards (CCSS)
Content coverage will narrow to more closely match the CCSS focus areas.
Level of test difficulty will be comparable to current tests.
“Cut scores” will remain the same. New CCSS content will not be added until
2014-2015
Transition to CCSS2012-2013
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Math tests will include only items that measure content common to the current grade-level expectations (GLEs) and the CCSS.
Grades 3, 5, 6, and 7 iLEAP : To better align with CCSS, the math tests will no longer include the Iowa Test of Basic Skills (ITBS).
Grades 4 and 8 LEAP: The math tests will be grade-level specific, rather than grade-span assessments.
Content coverage will narrow to more closely match the CCSS focus areas.
Transition Assessments
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Grade Ratio/Proportion/
Algebra
Number System
Measurement/Data/Geometry
6 40% 40% 20%
7 60% 25% 15%
8 60% 15% 25%
Focus Areas for Middle School Mathematics
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Content Area
Expressions and
Equations
Linear Relationshi
ps
Functions
Number System,
Measurement, and Data
Algebra 20% 25% 35% 20%
Geometry
Proportion/ Algebra
Measurement /Data
Geometry 60% 25% 15%
Focus Areas for MathematicsEOC
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Grade Level
English Language
Arts Mathematics
ScienceSocial
Studies
6th 2 2 1 1
7th 2 2 1 1
8th 2 2 1 1
New MathAccountability 2012-2013
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High School Accountability
25%
25%25%
25%
ACT Average EOCGraduation Index Cohort Graduation
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2012-2013CCSS
Concerns
Teach from the CCSS
1. Grades 6-12 2. Class of 13’ & 14’ will not be
effected by full implementation
3. Teachers will have 2 years to prepare for full implementation
• Gaps in student learning•Rigor•Student background knowledge•Materials•Activities•Curriculum Maps
What Will I TEACH?
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Vertical alignment of curriculum is planning curriculum across the grade levels, from Kindergarten through high school, building upon instruction based upon standards.
Correct vertical curriculum alignment improves student performance by decreasing the amount of instructional time consumed with re-teaching concepts
CCSS Vertical Alignment
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K-5
• A strong foundation K-5, students are provided hands on learning in geometry, algebra and probability and statistics. Students who have completed 7th grade and mastered the content and skills through the 7th grade will be well-prepared for algebra in grade 8.
6-8
• The middle school standards are robust and provide a coherent and rich preparation for high school mathematics.
9-12
• Students practice applying mathematical ways of thinking to real world issues and challenges; they prepare students to think and reason mathematically. • Set a rigorous definition of college and career readiness by helping students develop a depth of understanding and ability to apply mathematics to novel situations
The Mathematics Plan
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Conceptual Understandi
ng
Procedural Skill
Common Core Focus
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6.EE.9- Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
7.EE.4-Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
8.F.4-Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions)
Algebra “Looking at Lines”
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Essential Question: What can we learn about the circumference of a circle as a function of its diameter?
Objective: The learner will recognize that the table, graph and rule assign a value to pi and that pi and that the slope equals pi
Materials: rulers, cans or containers, paper, and markers
Prerequisite skills: proportional reasoning, function concept
Functions in Circles
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Use functions to model relationships between quantities.
8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values
What Standard Does it Address?
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1. Work in groups of 42. Each person is assigned a responsibility3. Materials are located on one table, once
you’re finished return all materials
Responsibilities- Time Manager, Reader, Materials Manager, Presenter/Writer
Managagement of Activities
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Make sense of the problems and persevere in solving them.
Reason abstractly and quantitatively. Construct viable arguments and critique the
reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated
reasoning.
What Mathematical Practices Were Used?
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John Van de Walle, “It is both a qualitative and quantitative process”.
What is Proportional Reasoning?
QualitativeProcess
relationships
analysis is based on
observations
QuantitiveProcess
evaluate
assigns value
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Proportional Reasoning
6th Grade Conceptual
8th Grade
Make Connections
7th GradeAnalyze
Algebra I Describe
Relationships
Geometry Prove Theorems
Similarity
Proportional Reasoning Strand?
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Preoperational- occurs between ages of 2-6 years. Students use symbolic thinking
Concrete Operational-occurs between ages of 7-12 years. Students’ thought processes become organized and integrated with one another. Logical processes become more developed and are able to handle more complex problems.
Formal Operational -begins at 12 years and lasts into adulthood. Students develop the ability to think about abstract concepts.
How Does Our Thinking Develop?
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● Group the rectangles into three groups of four rectangles and an odd one out.
● Discuss reasons for groupings. ● Measure and record the sides of each
rectangle, calculate ratios for short to long sides for each one.
● Draw a graph plotting length against width.
Look Alike Rectangles
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G-CO.12Make Geometric Constructions Make formal geometric constructions with a variety of
tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Geometry
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6.G.4-Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
7.G.6-Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Surface Area
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Essential Question: How can you measure how much cardboard it takes to make a net for a box?
Objective: The learner will develop a definition for surface area
Materials: rulers, blackline master, comic strip (AIMS), scissors, tape
Prerequisite skills: area and counting centimeter grids to calculate area
Net Work
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Make sense of the problems and persevere in solving them.
Reason abstractly and quantitatively. Construct viable arguments and critique the
reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated
reasoning.
What Mathematical Practices Were Used?