LOGAN-ROGERSVILLE R-VIII MATHEMATICS CURRICULUM

4^th Grade

Course Rational

The fourth grade math course at Logan-Rogersville strives to provide students with life skills that prepare them to be life-long learners and to succeed in the real world of the 21^st century. The fourth grade math course helps to prepare students to achieve as employees, family members, and citizens.

Course Description

Math skills are needed in every area of study and for life. With that in mind, the fourth grade math course focuses on problem solving; communication; reasoning; connections; number sense; geometric and spatial sense; data analysis, probability, and statistics; patterns and relationships; mathematical systems and number theory; and discrete mathematics.

Competencies

1. Students will use problem-solving approaches to investigate and understand mathematical content.

Students will use problem-solving strategies to construct meaning from mathematical tasks.
Students will recognize and define theoretical and actual problems encountered in everyday life, mathematical situations, and various disciplines.
Students will develop and apply strategies to predict, prevent, and solve a wide variety of problems.
Students will verify, interpret, and evaluate whether a solution addresses the original problem.
Students will select and apply appropriate mathematical tools and technology to solve problems
Students will relate physical materials, pictures, and diagrams to mathematical ideas.
Students will organize information into useful forms, such as verbal symbolic, or graphic.
Students will reflect on and clarify thinking about mathematical ideas and situations.
Students will communicate the relationship between everyday language, mathematical language, and symbols.
Students will demonstrate the ability to select and apply appropriate strategies, such as representing, discussing, reading, writing, listening and using technology in mathematics.
Students will draw logical conclusions about mathematics.
Students will use models, know facts, properties, and relationships to explain their thinking.
Students will justify answers and solution processes in an organized and convincing way.
Students will use patterns and relationships to analyze mathematical situations.
Students will relate concepts to student-generated procedures.
Students will relate various representations of concepts or procedures to one another using a variety of methods, forms, and technologies.
Students will recognize relationships among different topics in mathematics.
Students will use Mathematics in other curriculum areas and in daily living.
Students will use technology to manipulate data.
Students will make and use standard and nonstandard measurements in problems and everyday situations.
Students will manipulate fractions, mixed numbers, and decimals and apply them to problem situations.
Students will investigate and predict the results of combining, subdividing, and changing shapes.
Students will investigate concepts of lines, angles, similarity, and congruence, and symmetry
Students will investigate length, capacity, weight, mass, area, volume, area, volume, time, and temperature.
Students will construct, read, and interpret displays of data through verbal, nonverbal, symbolic, and graphic forms.
Students will interpret concepts of chance.
Students will investigate the use of variables and open sentences in expressing relationships.
Students will identify the need for whole numbers, integers and rational numbers, including fractions and decimals by looking for patterns and relationships to solve problems.
Students will develop and use number operations and order relations for decimals (money).
Students will develop and use number theory concept, including factors and multiples in problem solving.
Students will model, develop, and explain basic facts and algorithms with reasonable proficiency.

Grade and/or class: Fourth Grade

Date of Last Revision: 2002-2003

Writer: Jonnye Queen

Strand I. Problem Solving

By the end of grade 4, all students should know and be able to do

NOTE: Each item in the DO column is designed to address several elements of the “KNOW”

KNOW:

1.A variety of problem-solving strategies (such as making a list, drawing a picture, looking for a pattern, acting out the problem,)

2. Computational strategies with whole numbers (addition, subtraction, multiplication, and division).

3. When to use concrete objects, calculators, computers, charts, graphs, etc. to organize and solve problems.

4. Mathematical problem-solving strategies can apply to all disciplines and real-world problems.

Missouri Frameworks	District Skill Competency		Activities	Assessment		Content Standards	Performance Standards
I.a.	1. Students will use problem-solving approaches to investigate and understand mathematical content.		Students will work individually and with others to use problem-solving approaches to investigate and understand mathematical content (Saxon lessons 11,45, 130).	Students will work individually to use problem-solving approaches to investigate and understand mathematical content (Saxon assessment 2, 9,26).			3.2, 3.3
I.b.	2. Students will use problem-solving strategies to construct meaning from mathematical tasks.		Students will use problem-solving strategies to construct meaning from mathematical tasks (Saxon lesson 9).	Grade 4 state asses. Use problem-solving strategies to construct meaning from mathematical tasks (Saxon assessment 2).			3.2, 3.3
I.c..	3. Students will recognize and define theoretical and actual problems encountered in everyday life, mathematical situations, and various disciplines.	Students will recognize and define theoretical and actual problems encountered in everyday life, mathematical situations, and various disciplines (Saxon lessons 21,39, 80)			Individually, students will recognize and define theoretical and actual problems encountered in everyday life, mathematical situations, and various disciplines (Saxon assessments 4, 8, 16)		3.2, 3.3
I. d.	4. Students will develop and apply strategies to predict, prevent, and solve a wide variety of problems.	Students will develop and apply strategies to predict, prevent, and solve a wide a variety of problems (Saxon lessons 4,22,106).			Individually, students will develop and apply strategies to predict, prevent, and solve a wide a variety of problems (Saxon assessment 1, 4,21).		3.2, 3.3
I. e.	5. Students will verify, interpret, and evaluate whether a solution addresses the original problem.	Students will verify, interpret, and evaluate whether a solution addresses the original problem (Saxon lessons 22,43,69).			. Individually, students will verify, interpret, and evaluate whether a solution addresses the original problem (Saxon assessments 4,8,13)		3.2, 3.3

Missouri Frameworks

District Skill Competency

Activities

Assessment

Content

Standards

Performance Standards

I. f.

6. Students will select and apply appropriate mathematical tools and technology to solve problems.

Students will select and apply appropriate mathematical tools and technology to solve problems (Saxon lessons 15,32,53).

State assessment will address use of some manipulatives—pattern blocks, money, and ruler.

Individually, students will select and apply appropriate mathematical tools and technology to solve problems (Saxon assessments 3,6,10).

1.4

Strand II. Communication

By the end of grade 4, all students should know and be able to do

KNOW:

1. The language of mathematics may be used in reading, writing, listening, and speaking.

2. Mathematical ideas may be represented by visual models.

3. Mathematical symbols represent real-world situations.

4. Information may be organized in a variety of ways.

DO:

Missouri Frameworks	District Skill Competency		Activities		Assessment	Content Standards	Performance Standards
II. a.		7. Students will relate physical materials, pictures, and diagrams to mathematical ideas.	Students will relate physical materials, pictures, and diagrams to mathematical ideas (Saxon lessons 10,59,69).	Individually, students will relate physical materials, pictures, and diagrams to mathematical ideas (Saxon assessments 2, 12,14).				1.8
II. b.		8. Students will organize information into useful forms, such as verbal symbolic, or graphic.	Students will organize information into useful forms, such as verbal, symbolic, or graphic (Saxon lessons 18, 25, 63).	Individually, students will organize information into useful forms, such as verbal, symbolic, or graphic (Saxon assessments 3, 5, 12).				1.8
II. c		9. Students will reflect on and clarify thinking about mathematical ideas and situations.	Students will reflect on and clarify thinking about mathematical ideas and situations (Saxon lessons 20, 50, 106).	Individually, students will reflect on and clarify thinking about mathematical ideas and situations (Saxon assessments 4, 10, 21).				1.5, 3.4
II. d.		10. Students will communicate the relationship between everyday language, mathematical language, and symbols.	Students will communicate the relationship between everyday language, mathematical language and symbols (Saxon lessons 25, 63, 94).	Individually, students will communicate the relationship between everyday language, mathematical language and symbols (Saxon assessments 5, 12, 18).				1.5
II. e.		11. Students will demonstrate the ability to select and apply appropriate strategies, such as representing, discussing, reading, writing, listening and using technology in mathematics.	Students will demonstrate the ability to select and apply appropriate strategies, such as representing, discussing, reading, writing, listening, and using technology in mathematics (Saxon lessons 12, 87, 130).	Individually, students will demonstrate the ability to select and apply appropriate strategies, such as representing, discussing, reading, writing, listening, and using technology in mathematics (Saxon assessments 2, 17, 26).				1.8, 4.1

Strand III. Reasoning

By the end of grade 4, all students should know and be able to

KNOW:

1. Objects/numbers may be used in more than one way to determine or construct relationships between and among them.

2. Results must be verified.

3. Data may be organized in a variety of forms to look for patterns.

4. Geometric and number properties.

DO:

Missouri Frameworks	District Skill Competency	Activities	Assessment	Content Standards	Performance Standards
III. a.	12. Students will draw logical conclusions about mathematics.	Students will draw logical conclusions about mathematics (Saxon lessons 61, 67, 100).	Individually, students will draw logical conclusions about mathematics (Saxon assessments 12, 13, 20).		1.6
III. b.	13. Students will use models, know facts, properties, and relationships to explain their thinking.	Students will use models, know facts, properties, and relationships to explain their thinking (Saxon lessons 21, 76, 116).	Individually, students will use models, know facts, properties, and relationships to explain their thinking (Saxon assessments 4, 15, 23).		1.8, 4.1
III. c.	14. Students will justify answers and solution processes in an organized and convincing way.	Students will justify answers and solution processes in an organized and convincing way (Saxon lessons 26, 73, 118).	Individually, students will justify answers and solution processes in an organized and convincing way (Saxon assessments 5, 14, 23).		4.1
III. d. .	15. Students will use patterns and relationships to analyze mathematical situations.	Students will use patterns and relationships to analyze mathematical situations (Saxon lessons 67, 106, 133).	Grade 4 state assessment Individually, students will use patterns and relationships to analyze mathematical situations (Saxon assessments 13, 21, 26).		1.6

Strand IV Connections

By the end of grade 4, all students should know and be able to do

KNOW:

1. Problems may be looked at in more than one way.

2. Mathematics is used in other subject areas.

3. Mathematics is used in the real world.

DO:

Missouri Frameworks	District Skill Competency	Activities	Assessment	Content Standards	Performance Standards
IV. a.	16. Students will relate concepts to student-generated procedures.	Students will relate concepts to student-generated procedures (Saxon lessons 10, 39, 80).	Individually, students will relate concepts to student-generated procedures (Saxon assessments 1, 7, 16).		3.3
IV. b	17. Students will relate various representations of concepts or procedures to one another using a variety of methods, forms, and technologies.	Students will relate various representations of concepts or procedures to one another using a variety of methods, forms, and technologies (Saxon lessons 12, 44, 77).	Individually, students will relate various representations of concepts or procedures to one another using a variety of methods and forms (Saxon assessments 2, 8, 14).		1.6
IV. c	18. Students will recognize relationships among different topics in mathematics.	Students will recognize relationships among different topics in mathematics (Saxon lessons 23, 34).	Individually, students will recognize relationships among different topics in mathematics (Saxon assessments 4, 6).		1.6
IV. d.	19. Students will use Mathematics in other curriculum areas and in daily living.	Students will use Mathematics in other curriculum areas and in daily living (science lessons—metrics, measurement, graphs, social studies lessons—tables, charts, graphs).	Use Mathematics in other curriculum areas and in daily living (science assessment Unit A, Ch. 2, social studies assessment Ch. 7).		3.2, 3.3

Strand V. Number Sense ( Show-Me Standards, Math 1)

By the end of grade 4, all students should know and be able to do

KNOW:

1. Counting and grouping strategies.

2. Mental computation and estimation strategies.

3. Place value.

4. Basic computation facts of addition, subtraction, multiplication and division with whole numbers.

5. Addition and subtraction of fractions with like denominators.

6. U.S. customary and metric units of measure.

7. The appropriate use of calculators.

Assessment

All assessed at local level.

DO:

Missouri Frameworks	District Skill Competency	Activities	Assessment	Content Standards	Performance Standards
V. b.	20. Students will use technology to manipulate data.	In small groups, students will use a calculator to manipulate data by finding the average of a set of data (Saxon lesson 94), balancing a checkbook (95), finding the square root of a number (122), and figuring sales tax (135).	Individually, students will use a calculator to manipulate data by finding the square root of a number (Saxon assessment 26), and figuring sales tax (27).	M1	1.4
V. h.	21. Students will make and use standard and nonstandard measurements in problems and everyday situations.	Students will estimate length and distance using standard and nonstandard measurements (Saxon lesson 18), measure length using customary units (27), measure length using metric units (14), and draw line segments making using customary and metric units (15).	Individually, students will make and use measurements of given figures using customary and metric units and draw line segments according to given measurements in both customary and metric units (Saxon assessment 3, 5).	M1	3.2, 3.3
V. i	22. Students will manipulate fractions, mixed numbers, and decimals and apply them to problem situations.	Students will manipulate a fraction to show a part of a whole (Saxon lesson 17), represent and write mixed numbers (82), write tenths using common and decimal fractions (119) and add and subtract fractions (103).	Individually, students will manipulate fractions and mixed numbers (Saxon assessment 17) and decimals ().	M1	1.6, 3.2

Strand VI. Geometric and Spatial Sense (Show-Me Standards, Math 2)

By the end of grade 4, all students should know and be able to

KNOW:

1. Standard and nonstandard units of measure.

2. Descriptions of two- and three-dimensional figures.

3. Geometric shapes are found in the real world.

4. Objects can be located by relative position.

5. The process of measurement.

DO:

Missouri Frameworks	District Skill Competency	Activities	Assessment	Content Standards	Performance Standards
VI. b	23. Students will investigate and predict the results of combining, subdividing, and changing shapes.	Students will investigate and predict the results of combining, subdividing, and changing shapes (Saxon lesson 86, 90	Individually, students will predict the results of combining, subdividing, and changing shapes (Saxon assessment 18)	M2	1.6
VI. f.	24. Students will investigate concepts of lines, angles, similarity, and congruence, and symmetry.	Students will investigate the concept of lines of symmetry through drawing (Saxon lesson 45), the concepts of congruency and similarity through identification (70), the concept of angles through identification (109).	Individually, students will investigate the concepts of lines (Saxon assessment 9), angles (22), similarity, congruence (14), and symmetry (10) through identification.	M2	1.6, 1.4
VI. g.	25. Students will investigate length, capacity, weight, mass, area, volume, area, volume, time, and temperature.	Students will investigate length (Saxon lesson 14), capacity (84), weight and mass (137), area (30), volume (130), time (42) and temperature (77) through identification and calculation.	Individually, students will investigate length (Saxon assessment 3), area (12), volume (27), time (8) and temperature (16) through identification and calculation.	M2	1.6, 1.4

Strand VII. Data Analysis, Probability, and Statistics (Show-Me Standards, Math 3)

By the end of 4, all students should know and be able to do

KNOW:

1. Strategies to collect data.

2. Strategies to organize data.

3. Different ways of displaying data.

4. The appropriate display of data.

5. The appropriate use of technology,

DO:

Missouri Frameworks

District Skill Competency

Activities

Assessment

Content

Standards

Performance Standards

VII. b.

26. Students will construct, read, and interpret displays of data through verbal, nonverbal, symbolic, and graphic forms.

Students will construct, read, and interpret displays of data through verbal, nonverbal, symbolic (pictographs), and graphic (combination charts, bar graphs) forms (Saxon lessons 2, 3, 57)

Individually, students will construct, read, and interpret displays of data through nonverbal, symbolic (pictographs), and graphic forms (combination charts, bar graphs) (Saxon assessments 1, 2, 11)

1.2, 1.8

VII. d.

27. Students will interpret concepts of chance.

Students will interpret the concepts of chance through identification of the probability of an event (Saxon lesson 110)

Individually, students will interpret the concepts of chance through identification of the probability of an event (Saxon assessment 23)