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Rationale For Second Grade Instructional Guide
Organizational Highlights All power standards are being assessed. Second grade has twenty power standards. There was an attempt made to reduce the number of standards being assessed by only focusing on assessing the power standards. However, in discussions with teachers and coaches, it was felt that some standards needed to be benchmarked over several quarters. In addition, it was felt that there were nonpower standards that also needed to be assessed because they are on the Blueprint for the California Standards Assessment. Also, there was a concern that certain standards needed to be assessed more than one time. For these reasons, the number of assessed standards is high for each quarter in the second grade. Recommended lessons from Harcourt Math, Second Grade are listed for each of the content standards The mathematics program in second grade includes the use of manipulatives. All students should have access to concrete objects and/or manipulatives during mathematics. Manipulatives enables the students to create models which facilitate their understanding of the mathematics being taught. Throughout Harcourt Math the publisher includes manipulatives when introducing a lesson. Use of the teaching suggestions labeled “Getting Started Options” as well as the Intervention and Extension Resources, is strongly recommended. Lessons listed in Additional Resources by Marilyn Burns and from LUCI also provide activities using manipulatives. It is recommended that the use of manipulatives extend beyond the introduction of a lesson. The teacher resource pages of the teacher edition provide a number of activities that involve the use of manipulatives. However, manipulatives should not be used in isolation. It is important that a link be created between the manipulative and the paper and pencil representations. The Problem of the Day should be included as part of the daily routine when teaching mathematics. The Instructional Guide lists the recommended Lesson Resource pages and accompanying lessons for each of the content standards. Harcourt Math also provides various resources such as literature connections, strategies for English Language Learners, the Family Involvement Activities, Activities and Games for Home and School, and Intervention Strategies and Activities.
Quarter One This quarter begins with a focus on Graphing and Interpreting Data. The writers of the 2nd grade instructional guide felt that
the beginning of school is a time when data about the class is collected and can be integrated with mathematics instruction. Addition and Subtraction strategies reinforce learnings from the 1st grade and emphasize the inverse relationship between the two operations. Teachers need to continue to emphasize these understandings to encourage more flexible methods of thinking about and solving problems. Time is taught over the first two quarters to provide more time for mastery. Telling time emphasizes counting by fives which will support learning the five times table. Number Sense, Place Value, and Patterns are spread over the first three quarters to enable a focus on a portion of these key standards that spiral in difficulty from quarter to quarter.
Quarter Two This quarter introduces the content standards relating to money. The focus in only on coins which provides students an
opportunity to reinforce addition facts when adding a five or a ten or when adding ten to a two-digit number. The Quarter continues with a review of the inverse relationship of addition and subtraction that was taught in the First Quarter before beginning addition and subtraction of two-digit numbers with and without regrouping. Geometry is added with a focus on attributes of plane and solid figures. While concepts of symmetry and congruency are introduced, students will have another opportunity to work on these concepts in Quarter Four. Place Value is continued from Quarter One and is extended through 500. Time is reinforced and assessed in this quarter. Attention needs to be paid to time equivalencies. Patterns are again revisited to reinforce previous learning and provide time for mastery.
Quarter Three This Quarter begins with instruction in the content standards of measurement. In teaching measurement, there should be an
emphasis on estimation before actual measurement. Lesson planning should include experiences with measuring real world objects. It should first begin with non standard measurement before the introduction of standard measurement to provide opportunities for students to understand why standards units are needed. Understanding how to measure the length of objects and lines will be expanded in 3rd grade as students learn about perimeter. Instruction continues in place value building on concepts learned in Quarters 1 and 2 and extends to 1000. Fractions begin and focus on parts of a whole and parts of a group as well as fractions equal to one. Addition and subtraction with and without regrouping builds on the learning from Quarter 2 and extends to using three-digit numbers. Money continues with a review of coins and expands to include bills. At this time, the decimal notation for coins and bills are also introduced as students add and subtract problems with decimal notation. Multiplication and division begin in this Quarter and extend to Quarter Four. These concepts build on the addition and subtraction concepts taught in the first three Quarters. The emphasis is on learning the concepts of multiplication and division and memorizing the facts of 2, 5, and 10. By learning these facts in the second grade prepares students for learning additional multiplication facts in the third grade.
Quarter Four This Quarter continues developing measurement concepts with an emphasis on mass, capacity and temperature and extends
linear measurement to perimeter. These topics are not 2nd grade standards but are key standards in 3rd grade. The remainder of this quarter is spent Reviewing 2nd Grade Number Sense Standards. These standards prepare students for the first Quarter of the third grade. Student data should be used to determine differentiated concepts for review. Additional resources such as Marilyn Burns’ material and LUCI investigations can provide a rich experience for students to grasp a deeper understanding of mathematical concepts.
LOS ANGELES UNIFIED SCHOOL DISTRICT Second Grade
Mathematics Instructional Guide: Quarter One
DATA ANALYSIS NUMBER SENSE PLACE VALUE PATTERNS TIME Standards: 100 * NS 1.1 Count, read, and write numbers to 1000 and identify place value for each digit. 100 * NS 1.2 Use words, models, and expanded forms (e.g., 45 = 4 tens + 5) to represent numbers (to 1,000). 100 * NS 1.3 Order/ compare whole numbers to 1000 by using the symbols . * NS 2.1 Understand and use the inverse relationship between addition and subtraction (e.g., an opposite number sentence for 8 + 6 = 14 is 14 – 6 = 8) to solve problems and check solutions. NS 6.0 Students use estimation strategies in computation and problem solving that involve numbers that use the ones, tens, hundreds, and thousands places. AF 1.0 Students model, represent, and interpret number relationships to create and solve problems involving addition and subtraction. * AF 1.1 Use the commutative and associative rules to simplify mental calculations and to check results. AF 1.2 Relate problem situations to number sentences involving addition and subtraction. * AF 1.3 Solve addition and subtraction problems by using data from simple charts, picture graphs, and number sentences. MG 1.4 Tell time to nearest quarter hour and know relationships of time (e.g., minutes in an hour, days in a month, weeks in a year). MG 1.5 Determine the duration of intervals of time in hours (e.g., 11:00 a.m. to 4:00 p.m.) * SDAP 1.0 Students collect numerical data and record, organize, display, and interpret the data on bar graphs and other representations. SDAP 1.1 Record numerical data in systematic ways, keeping track of what has been counted. SDAP 1.2 Represent the same data set in more than one way (e.g. bar graphs and charts with tallies). * SDAP 1.3 Identify features of data sets (range and mode). * SDAP 1.4 Ask and answer simple questions related to data representations. * SDAP 2.0 Students demonstrate an understanding of patterns and how patterns grow and describe them in general ways. SDAP 2.1 Recognize, describe, and extend patterns and determine a next term in linear patterns (e.g., 4, 8, 12…; the number of ears on one horse, two horses, three horses, four horses). SDAP 2.2 Solve problems involving simple number patterns. MR 1.0-3.0 Embedded
Key: Power Standard * Assessed Standard Strikethrough: Topic not taught or assessed this quarter ** Dates to be determined at school site
LAUSD Mathematics Program Instructional Guide, Grade 2
Quarter One, 2003-2004
LOS ANGELES UNIFIED SCHOOL DISTRICT Second Grade
Mathematics Instructional Guide: Quarter One
DATA ANALYSIS NUMBER SENSE PLACE VALUE PATTERNS TIME
Dates ** Standard # Concepts Harcourt Additional Resources AF 1.3
SDAP 1.0 SDAP 1.1 SDAP 1.2 SDAP 1.3 SDAP 1.4 MR 1.0 MR 2