Marnell A. Cooper Chair, Baltimore City Board of School Commissioners Gregory E. Thornton, Ed.D. CEO, Baltimore City Public Schools Mathematics Overview 1 Learning Journey Community meeting November 17, 2015

Agenda 2 Overview of Standards in Mathematics Scope and Sequence in Mathematics Questions

Shifts for Students Demanded by the Common Core 3

Overview of Math Domains 3

Math Instructional Model 5

Kindergarten Overview 6

Year at a Glance Grades Number Fractions Geometry Measurement Number and Geometry Measurement Grades 1-5 Year at a Glance

Focus – Elementary Example 8 Second Grade Number Skills Before Common Core Second Grade Number Skills After Common Core 1.Use concrete materials to compose and decompose quantities up to List multiple representations for a number 3.Develop a sense of the size of a number in relation to other numbers 4.Use the numbers of 10, 50, and 100 as anchors in relationship to other numbers 5.Read, write, and represent whole numbers using models, symbols, and words through Express whole numbers up to 999 using expanded form 7.Identify the place value of a digit in whole numbers up to Compare and order whole numbers up to 999 using words and relational symbols ( >, <, =) 9.Estimate quantities up to 100 using a reference point such as 10 and the terminology "about" 10.Count forward by 2s, 5s, and 10s starting with numbers other than one 11.Count backward by 2s, 5s, and 10s from a multiple of that number 12.Use ordinal numbers to indicate position up to thirty-first 1.Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: can be thought of as a bundle of ten tens — called a "hundred." 3.The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). 4.Count within 1000; skip-count by 5s, 10s, and 100s. 5.Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. 6.Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

Year at a Glance Grades 6-8 9

Middle School Example 10 MSA

Middle School Example 11 PARCC

Year at a Glance High School 12

Year at a Glance High School Cont. 13

Standard at a Glance moving towards Calculus 14 TYPICAL GRADE

Focus – High School Example 15 Algebra/Data Analysis Before Common Core High School Statistics and Probability After Common Core 1. The student will design and/or conduct an investigation that uses statistical methods to analyze data and communicate results. 1. The student will design investigations stating how data will be collected and justify the method. 2. Types of investigations may include: simple random sampling, representative sampling, and probability simulations. 3. Probability simulations may include the use of spinners, number cubes, or random number generators. 4. In simple random sampling each member of the population is equally likely to be chosen and the members of the sample are chosen independently of each other. Sample size will be given for these investigations. 2. The student will use the measures of central tendency and/or variability to make informed conclusions. 1. Measures of central tendency include mean, median, and mode. 2. Measures of variability include range, interquartile range, and quartiles. 3. Data may be displayed in a variety of representations, which may include: frequency tables, box and whisker plots, and other displays. 3. The student will calculate theoretical probability or use simulations or statistical inferences from data to estimate the probability of an event. 1. This indicator does not include finding probabilities of dependent events. 4. The student will make informed decisions and predictions based upon the results of simulations and data from research. 5. The student will interpret data and/or make predictions by finding and using a line of best fit and by using a given curve of best fit. 1. Items should include a definition of the data and what it represents. 2. Data will be given when a line of best fit is required. 3. Equation or graph will be given when a curve of best fit is required. 6. The student will communicate the use and misuse of statistics. 1. Summarize, represent, and interpret data on a single count or measurement variable 2. Represent data with plots on the real number line (dot plots, histograms, and box plots). 3. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 4. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). 5. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

Comments or Questions? 16

Board of School Commissioners Marnell Cooper, Chair Tina Hike-Hubbard, Vice ‑ Chair Lisa Akchin Cheryl Casciani Linda Chinnia Martha James ‑ Hassan Peter Kannam Jonathan Townes, Student Commissioner A.J. Bellido de Luna, Board Executive Officer Senior Management Team Gregory Thornton, Chief Executive Officer Naomi Gubernick, Chief of Staff Linda Chen, Chief Academic Officer Theresa Jones, Chief Achievement and Accountability Officer Donald Kennedy, Sr., Chief Financial Officer Karl Perry, Sr., Chief School Supports Officer Keith Scroggins, Chief Operations Officer Deborah Sullivan, Interim Chief Human Capital Officer Kenneth Thompson, Chief Technology Officer Tammy Turner, Chief Legal Officer 17