1. ESD M ATH C URRICULUM Presentation by the District Math Committee December 2, 2010

2. C OMMITTEE M EMBERS Epping Elementary School Sandy Landis Deanna Mayne Epping Middle School Nancy Lehoux Kara Reynolds Epping High School Kerry McDermott Jacqui Pender District Office Lyn Healy

3. L AYERS OF C URRICULUM Each content area will have: a stated philosophy stated goals a diagram outlining the important concepts in their discipline a section on metacognition – “As a mathematicitian this is how I think.” a sequence from PK-12

4. L AYERS OF C URRICULUM Each grade level will have: a chart of key concepts vocabulary defined “I can” statements so that students know what they should be able to do!

5. PHILOSOPHY FOR MATHEMATICSDraft The Epping School District believes that mathematics can and must be learned by all students. We strive to offer a learning environment that fosters habits of deliberation, orderliness, analytical thinking, logical reasoning, problem-solving, perseverance and an appreciation for the precision of mathematics. We show students the real life applications of mathematics so that they will graduate with the mathematical knowledge and skills to be college and career ready.

6. GOALS FOR MATHEMATICS All students will develop number sense and computational fluency basic understanding of key concepts in geometry, algebra, probability, and data analysis while appreciating the interrelationships of all areas of mathematics. strong problem solving and reasoning abilities. ability to use appropriate technology to solve mathematical problems. ability to communicate their understanding of mathematics effectively. ability to apply mathematics to the 21 st century interdisciplinary themes.

7. Mathematical Processes: Representing and Communicating Mathematical Thinking Problem Solving Connections outside of mathematics Reasoning and Proof Modeling Mathematical Processes: Representing and Communicating Mathematical Thinking Problem Solving Connections outside of mathematics Reasoning and Proof Modeling Data Analysis, Probability and Statistics Data Organization Data Analysis Probability Data Analysis, Probability and Statistics Data Organization Data Analysis Probability Geometry and Measurement Geometric Figures Applications Relationships Measurement and Application Geometry and Measurement Geometric Figures Applications Relationships Measurement and Application Number and Quantity Number Sense Computational Fluency Estimation Number and Quantity Number Sense Computational Fluency Estimation Algebra and Functions Patterns Relationships Applications Algebra and Functions Patterns Relationships Applications

8. Number and Quantity Number Sense Understand numbers and various ways of representing them. Understand relationships among numbers and number systems Computational Fluency Solve problems using the relationships among operations and knowledge about the base ten system Estimation Use estimation skills to solve problems and check reasonableness of solutions Number and Quantity Number Sense Understand numbers and various ways of representing them. Understand relationships among numbers and number systems Computational Fluency Solve problems using the relationships among operations and knowledge about the base ten system Estimation Use estimation skills to solve problems and check reasonableness of solutions

9. Algebra and Functions Patterns Recognize, generate and analyze patterns Relationships Express relationships verbally, symbolically, graphically or as a table of values Analyze change in various contexts Applications Use algebraic representations to solve problems, make predictions, draw conclusions, with and without technology Algebra and Functions Patterns Recognize, generate and analyze patterns Relationships Express relationships verbally, symbolically, graphically or as a table of values Analyze change in various contexts Applications Use algebraic representations to solve problems, make predictions, draw conclusions, with and without technology

10. Geometry and Measurement Geometric Figures Analyze characteristics and properties of two and three dimensional shapes Applications Reason and solve problems with shapes and their attributes Relationships Develop mathematical arguments about geometric relationships Measurement and Application Understand measurable attributes of objects Geometry and Measurement Geometric Figures Analyze characteristics and properties of two and three dimensional shapes Applications Reason and solve problems with shapes and their attributes Relationships Develop mathematical arguments about geometric relationships Measurement and Application Understand measurable attributes of objects

11. Data Analysis Probability and Statistics Data Organization Collect, organize and display data using appropriate statistical and graphical methods Data Analysis Formulate questions and analyze data sets to form hypotheses and make predictions Probability Understand and apply basic concepts of probability Use probability to make decisions Data Analysis Probability and Statistics Data Organization Collect, organize and display data using appropriate statistical and graphical methods Data Analysis Formulate questions and analyze data sets to form hypotheses and make predictions Probability Understand and apply basic concepts of probability Use probability to make decisions

12. Mathematical Processes: Representing and Communicating Mathematical Thinking Problem Solving Connections outside of mathematics Reasoning and Proof Modeling/Representing Mathematical Processes: Representing and Communicating Mathematical Thinking Problem Solving Connections outside of mathematics Reasoning and Proof Modeling/Representing

13. H OW D O M ATHEMATICIANS T HINK ? P ROBLEM S OLVING What do I see or visualize when I look at this problem? What information do I have? What information do I need? How do I get that information? What strategy do I use to solve the problem? What strategies do others use? What strategy would be best? What do I do when I get stuck? What common mistakes do people make when working with this type of problem? What is the misunderstanding that causes the mistake?

14. H OW D O M ATHEMATICIANS T HINK ? C ONNECTIONS Have I seen this before? How does that connection help? Where do I recognize and apply mathematics in my life?

15. H OW D O M ATHEMATICIANS T HINK ? R EASONING AND P ROOF Does my answer or solution make sense? How do I prove it? Is there a pattern or rule? What is it? Does it always work?

16. H OW D O M ATHEMATICIANS T HINK ? R EPRESENTATION How do I best show my thinking?

17. LEARNER STRATEGIES Draw a diagram Make a table or t-chart Look for patterns Solve a simple similar problem Write and solve an equation Make connections to prior knowledge Use literacy skills of determining importance, questioning, making inferences, making predictions Conduct experiments Conjecture (generalizing or educational guessing) and check guesses Estimate

18. G RADES K-5 T OPIC S EQUENCE K12345 Number – Counting and Cardinality Number Names Counting to tell the number of objects Comparing and ordering numbers Number- Operations and the Problems They Solve Composing and decomposing numbers; addition and subtraction Addition and subtraction Describing situations and solving problems with addition and subtraction Addition and subtraction Describing situations and solving problems with addition and subtraction Multiplication and division Describing situations and solving problems with multiplication and division Multiplication and division Problem solving with the four operations Number – Base Ten Two digit numbers Composing and decomposing ten Numbers up to 100 Adding and subtracting in base ten Numbers up to 1,000 Adding and subtracting in base ten Numbers up to 10,000 Adding and subtracting in base ten Multiplying and dividing in base ten Numbers up to 100,000 Multiplying and dividing in base ten Whole numbers in base ten Decimal concepts Operations on decimals Number -- Fractions Fractions as representations of numbers Fractional quantities Operations on fractions Decimal concepts Fraction equivalence Operations on fractions Measurement and Data Direct measurement Representing and interpreting data Length measurement Time measurement Representing and interpreting data Length measurement Time and money Representing and interpreting data The number line and units of measure Perimeter and area Representing and interpreting data The number lines and units of measure Perimeter and area Angle measurement Representing and interpreting data Units of measure Volume Representing and interpreting data Geometry Shapes, their attributes, and spatial reasoning Properties of 2-dimensional shapes Structuring rectangular shapes Lines and angles Line symmetry Coordinates Plane figures

19. G RADES 6-8 T OPIC S EQUENCE

20. S AMPLE S EQUENCE : N UMBER O PERATIONS K – composing and decomposing numbers; addition and subtraction 1 – addition and subtraction 2 – addition and subtraction 3 – multiplication and division 4 – multiplication and division 5- using operations on decimals

21. S AMPLE G RADE L EVEL I NFORMATION : G RADE S IX – R ATIOS AND P ROPORTIONAL R ELATIONSHIPS Key Concepts: Ratio Concept Ratio Reasoning Vocabulary: Ratio Rate Equivalent ratios Tape diagram Double number line diagram Equation Table Coordinate plane Measurement units (e.g. inches, centimeters)

22. G RADE S IX R ATIOS AND P ROPORTIONAL R ELATIONSHIPS I Can… Describe a ratio using ratio language Describe a rate that is associated with a ratio Solve real-world ratio/rate math problems that involve: Making tables Plotting pairs on coordinate planes Converting between different units Converting between percent and rate

23. N EXT S TEPS FOR THE COMMITTEE AND FOR OUR TEACHERS High School Teachers are discussing their options as CCSS provide two different pathways to learning mathematics. Middle School Teachers are working to develop key concepts, vocabulary and I can statements which lead to unit design. Teachers in PreK- 2 will be looking at CCSS to plan their trajectories (units).