1. ALGEBRA WORKSHOP SESSION 3 Tricia Profic, Erie 1 BOCES

2. NYS Assessments  Roundtable discussion:  Comments about the assessments  Concepts that were assessed  Topics for workshops next school year

3. State Updates  Module 1for grades 6-12 became available today  Ken Wagner’s Memo regarding High School Math Assessments  Algebra Clarifications and sample questions

4. Major 5 th grade Topics  Operations with Fractions  Operations with decimals  Order of operations  Place value, expanded notation  Metric conversions  Line plots with fractional data  Volume of rectangular prisms  Properties of quadrilaterals  Graphing in the first quadrant

5. Major 6 th grade Topics  Ratios and Rates  Division of Fractions  Introduction to rational numbers (order, absolute values, plotting points in the coordinate plane)  Writing expressions and equations  Measures of center and variability  Area, surface area, and volume (fractional side lengths)

6. Major 7 th grade Topics  Ratios and proportional relationships, multi-step and percent problems  Operations with rational numbers  Write and solve equations/inequalities with rational coefficients  Area and circumference of circles  Volume and surface area of three-dimensional rectangular figures  Compare data distributions and generate data through random distributions  Probability

7. Major 8 th grade Topics  Operations with scientific notation and exponents  Linear equations and systems of equations  Functions  Transformations  Volume of cones, cylinders, and spheres  Pythagorean Theorem  Bivariate statistics, scatter plots, line of best fit  Two-way frequency tables

8. Major Algebra Topics  Linear equations, inequalities, systems of equations  Bivariate statistics, line of best fit, correlation coefficients, residuals, two-way frequency tables  Linear, quadratic, exponential functions  Arithmetic and geometric sequences  Operations with polynomials  Solve quadratic equations (factoring, complete the square, quadratic equation) and exponential equations (rewriting bases)

9. Implications of Accelerating  If students are accelerated, they will miss:  Transformations  Scientific notation and exponent operations  Pythagorean Theorem  Introduction to systems of equations, functions, graphing lines, slope, bivariate statistics, higher level equation solving  Volume formulas for cones, cylinders, and spheres

10. Probability and Statistics  We love it or we hate it….  Probability and Statistics has significantly changed at each grade level  The difficulty level has increased  Focus on modeling situations through probability and statistics

11. Grade 6  Construction of box-and-whisker plots, dot plots, and histograms  Compare and contrast measures of center (mean and median) and variability (mean absolute deviation and interquartile range)  Describe and summarize numerical data sets

12. Grade 6 Sample Question  Take a moment to complete the sample task, “Puppy Weights”

13. Grade 7  Compare two data distributions  Begin random sampling to generate data sets and discuss the importance in drawing accurate inferences  Apply probabilities to model situations  6 th grade statistics are post-assessment standards and could be assessed in 7 th grade

14. Grade 7 Sample Question  Complete the sample task, “College Athletes”

15. Grade 8  Bivariate Statistics  Construct scatter plots and line of best fit  Two-way frequency tables  Interpret the linear model in the context of the data and express the model as a linear relationship

16. Grade 8 Sample Question  As a group complete the sample task, “Hand Span and Height”

17. Algebra  Modeling with data in terms of a situation  Draw inferences about statistical data  Analyze the fit of a function by plotting and analyzing residuals  Correlation vs. causation  Describe associations among bivariate data through calculations of correlation coefficient

18. Algebra Sample Question  Please complete the sample task, “Haircut Costs”

19. Six Shifts in Mathematics  Teacher evaluators are expected by NYSED to observe how the six shifts in mathematics are being implemented in the classroom  FOCUS  COHERENCE  FLUENCY  DEEP UNDERSTANDING  APPLICATION  DUAL INTENSITY

20. Sample Lesson Review  Each grade level has been given a sample lesson developed by the Mathematics Assessment Project  Use the Lesson Review worksheet to evaluate the lesson at your grade level