Okaloosa County School District
Curriculum Guide for Math
OKALOOSA COUNTY SCHOOL DISTRICT
MATH CURRICULUM GUIDE
CONTENTS
Mission Statement 3
Suggestions for Implementing Curriculum Guides 3
Florida Department of Education ≠ Office of Math and Science Essential Websites 4
OCSD Curriculum and Pacing Guide ∞ Overview 4
Cognitive Complexity/Depth of Knowledge Rating for Mathematics 5
4th Grade General Content Limits 7
Quarterly Benchmarks 8
Grade-level Curriculum Guide 13
Quarter 1 13
Quarter 2 20
Quarter 3 25
Quarter 4 33
Go Math! Online Math Concept Readers 35
Literature Connection Chart 37
Mission Statement
Develop the highest quality math instruction to maximize student achievement through alignment of grade-level benchmarks to appropriate instructional practices, materials, resources, and pacing.
Suggestions for Implementing Curriculum Guides
The role of the teacher is to:
ü Teach students the Next Generation Standards as dictated by state law for their grade-level.
ü Provide learning-rich classroom activities that teach the benchmarks in depth.
ü Enhance the curriculum by using resources and instructional technology.
ü Differentiate instruction by varying methods of instruction and frequently offering relevant lab activities.
ü Regularly administer assessment to include higher-level questions, and performance task assessment.
In addition, teachers should:
ü Collaborate with other grade-level teachers to maximize school resources and teacher expertise.
ü Consult with other grade-levels to define absolute skill goals for each grade-level.
ü Document questions and suggestions for improvement of the curriculum Guide.
ü Integrate science into math and reading curriculum.
ü Consider applying for a grant to support project-based learning for their school.
ü Visit the Okaloosa Math Central Website at: http://www.okaloosa.k12.fl.us/math
Days allotted to each benchmark are approximate and have been suggested based on the level of the complexity of the benchmark. To insure benchmarks are taught to mastery and completed by the conclusion of the school year, it is recommended that teachers not veer significantly from the suggested pacing.
Florida Department of Education ≠ Office of Math and Science Essential Websites
Next Generation Sunshine State Standards:
http://www.fldoestem.org/uploads/1/docs/2007_FL_Mathematics_Standards_9_13_07.pdf
Searchable Next Generation Sunshine State Standards Database:
http://www.floridastandards.org/index.aspx
Printable Downloads of Next Generation Sunshine State Standards with or without remarks:
http://www.floridastandards.org/downloads.aspx
OCSD Curriculum and Pacing Guide ∞ Overview
This document provides a math curriculum and pacing guide. It is designed to help teachers to efficiently pace the delivery of quality instruction for each nine-week period.
Purpose:
This guide was created by a team of grade-level teachers to correlate to the Next Generation Standards with the goal of providing teachers ready access to resources for teaching those new standards and a pace for accomplishing benchmark mastery.
Description:
The OCSD Math Curriculum Guide specifies the math content to be covered within each nine-week instructional period. Their guide identifies Next Generation Standards (NGS) Benchmarks. Furthermore, it allows teachers to input information specific to their students or school needs.
Ø Top Block – Big Idea and Essential Questions
Identifies the Big Idea and the components of the Big Idea
Lists the Essential Questions addressed in the section’s Benchmarks.
Ø Column One – Benchmark/Text Alignment
Lists the specific Benchmark by number and states the Benchmark.
Cites the Harcourt Textbook chapters that correlate to the Benchmark.
Ø Column Two – FCAT Info
Serves as a placeholder for future FCAT information; to include content limits, assessment status, and crosswalk correlation.
Ø Column Three – Additional Resources/Activities
Suggests instructional activities, including media (DVD/Video/CD), websites, and student involvement tasks.
Ø Column Four – Literacy Connection/Vocabulary/Reading
Lists vocabulary terms, and books or stories connected to the Benchmark goals.
Ø Column Five – Open: Specific to Teacher/Grade/Subject/School
Serves as a placeholder for teachers to add information that is specific to their school’s or student’s needs.
NOTE:
Addendums to this curriculum guide, as well as additional information/forms will be posted at http://www.okaloosaschools.com/OkaloosaSchools/SchoolDistrict/CurriculumInstruction/CurriculumGuides/tabid/378/Default.aspx.
Cognitive Complexity/Depth of Knowledge Rating for Mathematics
Florida’s revised mathematics standards emphasize teaching and learning the most important K-12 mathematics concepts in depth at each grade level. After adoption of the new math standards, the Florida Center for Research in Science, Technology, Engineering and Mathematics (FCR-STEM) at Florida State University convened a group of Florida math teachers, district math supervisors, and math education faculty to rate the cognitive demand of each benchmark. Meeting in teams for each body of knowledge, they reviewed and discussed each benchmark, then reached consensus on level of cognitive complexity using a classification system adapted from the “depth of knowledge” system developed by Dr. Norman Webb at the University of Wisconsin.
Cognitive complexity refers to the cognitive demand of tasks associated with the benchmark. The depth of knowledge levels (Webb, 1999) reflect the relative complexity of thinking that a given benchmark demands of students — what it requires the student to recall, understand, analyze, and do. Florida’s depth of knowledge rating system focuses on expectations of students at three levels:
Low Complexity
This category relies heavily on the recall and recognition of previously learned concepts and principles. Items typically specify what the student is to do, which is often to carry out some procedure that can be performed mechanically. It is not left to the student to come up with a low complexity original method or solution. Skills required to respond to low complexity items include
· solving a one-step problem;
· computing a sum, difference, product, or quotient;
· evaluating a variable expression, given specific values for the variables;
· recognizing or constructing an equivalent representation;
· recalling or recognizing a fact, term, or property;
· retrieving information from a graph, table, or figure;
· identifying appropriate units or tools for common measurements; or
· performing a single-unit conversion.
Moderate Complexity
Items in the moderate complexity category involve more flexible thinking and choice among alternatives than low complexity items. They require a response that goes beyond the habitual, is not specified, and ordinarily has more than a single step. The student is expected to decide what to do—using informal methods of reasoning and problem-solving strategies—and to bring together skill and knowledge from various domains. Skills required to respond to moderate complexity items include
· solving a problem requiring multiple operations;
· solving a problem involving spatial visualization and/or reasoning;
· selecting and/or using different representations, depending on situation and purpose;
· retrieving information from a graph, table, or figure and using it to solve a problem;
· determining a reasonable estimate;
· extending an algebraic or geometric pattern;
· providing a justification for steps in a solution process;
· comparing figures or statements;
· representing a situation mathematically in more than one way; or
· formulating a routine problem, given data and conditions.
High Complexity
High complexity items make heavy demands on student thinking. Students must engage in more abstract reasoning, planning, analysis, judgment, and creative thought. The high-complexity item requires that the student think in an abstract and sophisticated way. Skills required to respond correctly to high complexity items include
· performing a procedure having multiple steps and multiple decision points;
· solving a non-routine problem (as determined by grade-level appropriateness);
· solving a problem in more than one way;
· describing how different representations can be used for different purposes;
· generalizing an algebraic or geometric pattern;
· explaining and justifying a solution to a problem;
· describing, comparing, and contrasting solution methods;
· providing a mathematical justification;
· analyzing similarities and differences between procedures and concepts;
· formulating an original problem, given a situation;
· formulating a mathematical model for a complex situation; or
· analyzing or producing a deductive argument.
4th Grade General Content Limits
The content limits described below are applicable to all items developed for Grade 4; however, the content limits defined in the individual benchmark specifications can supersede these general content limits.
REV 052011 Fourth Grade Math Page 9
Okaloosa County School District
Curriculum Guide for Math
Whole numbers
• Items should not require the use of more than two operations.
• Place values should range from ones through hundred millions.
Addition
Items should not exceed three 7-digit addends or two 8-digit addends.
Subtraction
Subtrahends, minuends, and differences should not exceed eight digits.
Multiplication
Factors used may include up to two 3-digit numbers, or, when a four-digit factor is used, the other factor may not exceed two digits.
Division
• Divisors should not exceed one digit, unless it is a related division fact of 0 X 0 through 12 X 12.
• Dividends should not exceed three digits.
• Quotients may include remainders expressed only as whole numbers.
• Items will not require the use of long division.
Decimals
Place values could range from tenths through thousandths with no more than five total digits.
Addition, Subtraction, Multiplication, and Division
Not assessed at Grade 4.
Fractions
Items may have denominators of 1–10, 12, or 1000, or denominators that are derived from basic multiplication facts through 12 X 12 may also be used (e.g., 24 has the two factors 6 and 4; 72 has the factors 8 and 9).
Addition, Subtraction, Multiplication, and Division
Not assessed at Grade 4.
Percent
• Percents must be equivalent only to halves, fourths, tenths, or hundredths.
• Items dealing with percents will not involve computation using the percent
Measurement
• Items will not assess weight/mass, time, temperature, perimeter, and/or capacity in isolation.
• Items may use customary and/or metric units.
• See Geometry and Measurement benchmarks for specifics.
Gridded-Response Items
• Answers may not exceed five digits.
• Answers may not include fractions.
• See grid types for appropriate answer formats.
REV 052011 Fourth Grade Math Page 9
Okaloosa County School District
Curriculum Guide for Math
REV 052011 Fourth Grade Math Page 9
Okaloosa County School District
Curriculum Guide for Math
Quarterly Benchmarks
Each quarter shows when a concept or skill is introduced. It is understood that these skills and concepts will be ongoing throughout the year.
Quarter 1 - Big Idea 1Quarter 1 (begin here) / Quarter 1 continued
First 2 days
of school / Multiplication Facts Review
Introduction to Big Idea 1 / Chapter 3
Lessons
3.1-3.10
Mid-Chapter Checkpoint;
Chapter Review/Test;
Remediation
15 days / · MA.4.A.1.1--Moderate
Use and describe various models for multiplication in problem-solving situations and demonstrate recall of basic multiplication and related division facts with ease. Identify multiples.
· MA.4.A.4.1--High
Generate algebraic rules and use all four operations to describe patterns, including nonnumeric growing or repeating patterns
· MA.4.A.4.2--High
Describe mathematics relationships using expressions, equations, and visual representations.
· MA.4.A.4.3--High
Recognize and write algebraic expressions for functions with two operations.
Chapter 1
Lessons
1.1-1.6
Mid-Chapter Checkpoint;
Chapter Review/Test;
Remediation
15 days / · MA.4.A.6.1--Moderate
Use and represent numbers through millions in various contexts, including estimation of relative sizes, including ordering numbers.
· MA.4.A.6.6--High
Estimate and describe reasonableness of estimates; determine the appropriateness of an estimate versus an exact answer. Include rounding, length.
Chapter 2
Lessons
2.1.-2.9
Mid-Chapter Checkpoint;
Chapter Review/Test;
Remediation
15 days / · MA.4.A.1.1--Moderate
Use and describe various models for multiplication in problem-solving situations and demonstrate recall of basic multiplication and related division facts with ease. Identify multiples.
· MA.4.A.4.2--High
Describe mathematics relationships using expressions, equations, and visual representations.
· MA.4.A.6.2--Moderate
Use models to represent division as: the inverse of multiplication; as partitioning; as successive subtraction.
· MA.4.A.6.4--Moderate
Determine factors and multiples for specified whole numbers / Things to remember when reviewing the math curriculum/pacing guide:
· This pacing guide is meant to serve as a guide to assist in planning.
· It is set up with the intention that each lesson will take one day; however, some lessons may be combined to fit within your time constraints.
· This guide allows a full day for the Mid-Chapter Checkpoint—however it may not take the whole class period. Use this extra time to remediate or move ahead to the next lesson.
· It is important to review multiplication facts as an ongoing practice.
Quarter 2 - Big Ideas 1 & 2
Quarter 2 (begin here) / Quarter 2 continued
Chapter 4
Lessons
4.1-4.11
Mid-Chapter Checkpoint;
Chapter Review/Test;
Remediation
10 days / · MA.4.A.1.1--Moderate
Use and describe various models for multiplication in problem-solving situations and demonstrate recall of basic multiplication and related division facts with ease. Identify multiples.
· MA.4.A.1.2--High
Multiply multi-digit whole numbers through four digits fluently, demonstrating understanding of the standard algorithm, and checking for reasonableness of results, including solving real-world problems.
· MA.4.A.4.2--High
Describe mathematics relationships using expressions, equations, and visual representations.
· MA.4.A.6.4--Moderate
Determine factors and multiples for specified whole numbers.
· MA.4.A.6.6--High
Estimate and describe reasonableness of estimates; determine the appropriateness of an estimate versus an exact answer. Include rounding, length. / Chapter 6
Lessons
6.1-6.6
Mid-Chapter Checkpoint;
Chapter Review/Test;
Remediation
6 days / · MA.4.A.1.1--Moderate
Use and describe various models for multiplication in problem-solving situations and demonstrate recall of basic multiplication and related division facts with ease. Identify multiples.
· MA.4.A.1.2--High
Multiply multi-digit whole numbers through four digits fluently, demonstrating understanding of the standard algorithm, and checking for reasonableness of results, including solving real-world problems.
· MA.4.A.4.2--High
Describe mathematics relationships using expressions, equations, and visual representations.
· MA.4.A.6.2--Moderate
Use models to represent division as: the inverse of multiplication; as partitioning; as successive subtraction.
· MA.4.A.6.4--Moderate
Determine factors and multiples for specified whole numbers.
Chapter 5
Lessons
5.1-5.11
Mid-Chapter Checkpoint;
Chapter Review/Test;
Remediation
10 days / · MA.4.A.1.1--Moderate
Use and describe various models for multiplication in problem-solving situations and demonstrate recall of basic multiplication and related division facts with ease. Identify multiples.
· MA.4.A.1.2--High
Multiply multi-digit whole numbers through four digits fluently, demonstrating understanding of the standard algorithm, and checking for reasonableness of results, including solving real-world problems.
· MA.4.A.4.2--High
Describe mathematics relationships using expressions, equations, and visual representations.
· MA.4.A.6.6—High
Estimate and describe reasonableness of estimates; determine the appropriateness of an estimate versus an exact answer. Include rounding, length. / Chapter 7