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MONTESSORI UPPER ELEMENTARY

MATH CURRICULUM ALIGNMENT

Based on the Maryland Voluntary State Curriculum

Montessori Mathematics

Grades 4 to 6

June 2006

Prince George’s County Public Schools

0

5

10

15

20

25

Week 1

Week 2

Week 3

Boys

Girls

PGIN 7690-3472

BOARD OF EDUCATION

OF

PRINCE GEORGE’S COUNTY, MARYLAND

Beatrice P. Tignor, Ed.D., Chair

Howard W Stone, Jr., Vice Chair

John R. Bailer, Member

Abby L. W. Crowley, Ed.D., Member

Charlene M. Dukes, Ed.D., Member

Robert O. Duncan, Member

Jose R. Morales, Member

Judy G. Mickens- Murray, Member

Dean Sirjue, Member

Leslie Hall, Student Board Member

John E. Deasy, Ph. D., Chief Executive Officer

Shelley Jallow, Chief Academic Officer

Patricia Miller, Director of Curriculum and Instruction

Gladys Whitehead, Ph.D., Coordinating Supervisor, Academic Programs

Pamela Shetley, Ph.D., Director of the FOCUS Office

ACKNOWLEDGEMENTS

We wish to acknowledge the following teachers for their hard work and dedication to the creation of this outstanding document:

John Feeley

Susan Holmes

Laure Fleming

Marion Lebensbaum

Janet Goodspeed

Cynthia Peil

Gwendolyn C. HarrisKimberly Strayhorn

We also wish to thank all of the Curriculum Writing Production Center staff for their assistance.

Table of Contents

Introduction……………………………………………………………………………………………………………………………………………………………5

Montessori Math Materials List…………………………………………………………………………………………………………………………………….6

Voluntary State Curriculum Chart (VSC) ………………………………………………………………………………………………………………………..8

Quarterly Guidelines ……………………………………………………………………………………………………………………………………………….14

Montessori Alignment with VSC………………………………………………………………………………………………………………………………….15

Montessori Great Lessons ………………………………………………………………………………………………………………………………………..93

Montessori Sample Lessons ……………………………………………………………………………………………………………………………………104

Appendix ……………………………………………………………………………………………………………………………………………………………123

History of Math Command Cards

Rounding and Estimating Lessons

Calculator Lessons

Problem Solving Sequence

Problem Solving Activity Cards

Measurement Activity Cards

Money Lessons

Probability Activity Cards

Statistics Activity Cards

Introduction to Mathematics in the Montessori Elementary Classroom

The human mind is naturally mathematical. Mathematics is another language of communications. Mathematical inventions are a reflection of the culture. The child at the second plane of development (6-12 years old) is interested in exploring how and why mathematics was developed and its usefulness to humanity. To assist the child’s inner development, the elementary teacher offers experiences that lead towards mathematical abstraction. First, the Montessori Great Lessons are introduced. Next, concrete experiences are presented, using hands-on materials manipulative practice with individual concepts. Then the teacher gives math nomenclature as the first step leading to abstraction. Repetition through a variety of parallel, interrelated work is given to keep the child's interest. Also, interest is maintained through work on problem solving skills, as the child creates his/her own problems. After extensive work with the sensorial (manipulative) materials, the child naturally moves toward abstraction until only paper and pencil remain.

The child's work follows five steps:

1. The teacher presents "The Story of Numbers,” giving a vision of the whole and inviting children to begin

the adventure of mastering mathematics.

2. Children work individually with math materials, acquiring precision.

3. The teacher presents mathematical vocabulary.

4. Children are encouraged through questioning to begin to make generalizations.

5. Children begin to work on paper (abstract level).

The mathematics program at the 6-12 level is designed to awaken the exploratory imagination of the reasoning mind. The child, from his work in the Montessori preschool, already has as a strong base for understanding math concepts. Correlation between quantity and symbol, base-ten place value to thousands, an introduction to the four operations using whole numbers, and memorization of math facts have been introduced and practiced. The major domains of study in the elementary class are:

1. Algebra, patterns, and functions

2. Geometry

3. Measurement

4. Statistics

5. Probability

6. Number relationships and computation

7. Processes of mathematics

Description of Montessori Math Materials

The 100 Board has 100 tiles numbered from 1-100, designed to be laid out in rows of ten on a 10 x 10 grid.

The Bead Bars are colored bead bars representing different quantities, used to explore patterns of numbers.

The Chain Cabinet holds ten cubes 1-10, the squares of the cubes, the chains of the cubes and the chains of the squares. Colors are the same as for the Bead Bars.

The Strip Boards are used to learn addition and subtraction facts and to lead children to discover numerical patterns. They are printed with a grid of squares, and use strips of wood cut in sizes from 1-9, and 1-18 to represent quantities.

The Multiplication Board is a wooden board with ten holes vertically and ten holes horizontally totaling 100 holes. Red beads are used to create the product.

The Division Board has nine holes vertically and nine holes horizontally totaling 81 holes. Green beads are used to create the quotient. Skittles represent the divisor.

The Finger Charts are series of charts with the basic math facts printed on them. They lead students to discover numerical patterns.

The Golden Bead Material is a three dimensional representation of place value. It uses single beads to represent units, ten beads on a wire to represent tens, 10 ten bars wired together in a square to represent hundreds, and 10 hundred squares stacked and held together in a cube to represent thousands.

The Stamp Game uses color-keyed "stamps" to represent the decimal system. Green stamps represent units and thousands, blue stamps represent tens, and red stamps represent hundreds. Place value is written on each stamp.

The Dot Game uses the same color coding system on a board divided into 5 columns. Each column has 25 rows of 10 small squares. The dot game reinforces the concept of exchanging tens in addition.

The Small and Large Bead Frames are color-coded abacuses.

The Racks and Tubes are used for division. They contain 700 color-coded beads sorted in tubes with ten each. The beads are used to represent the dividend. Color-coded boards with indentation to hold the beads are used to hold the quotient. The divisor is created with color coded skittles.

The Wooden Hierarchical Material is a large three-dimensional representation of place value to one million. It uses the same color coding system.

The Checkerboard is a rectangular board with four horizontal rows, each row containing color-coded nine squares.

The Bank Game is a set of cards to 9,000,000 in the hierarchical colors.

The Golden Bead Frame is an abacus is made of golden beads.

The Peg Board is a board with thirty holes vertically and thirty holes horizontally. Colored pegs use the same color coding system- green for units, blue for tens, red for 100. Color-coded skittles are also used with the pegboard.

The Fraction Insets, Divided Square Material, and Equivalency Insets are used in the study of fraction equivalence and operations on fractions.

The Decimal Material is laid out in columns to represent place values less than one unit.

The Constructive Triangle Boxes are a set of boxes holding various triangles color-coded to encourage exploration of geometric forms created by combining triangles.

The Geometry Cabinet has six drawers containing wooden figures to represent plane-closed figures.

The Geometry Sticks consist of sticks of several sizes and colors that can be fixed to a cork board to aid in the study of geometric figures such as lines and angles.

The Geometric Solids consist of nine different wooden forms painted blue.

The Yellow Area Material uses flat yellow quadrilaterals to encourage exploration of the concept of area.

The Volume Material is a series of containers and cubes used to explore volume.

The Binomial, Trinomial and Arithmetic Cubes contain colored cubes and prisms used in the preschool to refine the visual sense and discrimination of form. In the elementary a series of exercises leads students to discovery of the algebraic formulas.

The Numerical Decanomial helps in the memorization of multiplication tables, and is a preparation for squares, cubes and square and cube roots .

VSC and Montessori Upper Elementary

Math Curriculum Alignment

Table of Contents

Grade 4

Grade 5

Grade 6

VSC

1.0

Algebra, Patterns, and Functions

VSC

1.0


VSC

1.0


1.A.1.a

Page 15

1.A.1.a

Page 15

1.A.1.a

Page 15

1.A.1.b

15

1.A.1.b

15

1.A.1.b

15

1.A.1.c

16

1.A.1.c

16

1.A.1.c

16

1.A.1.d

16

1.A.1.d

16

1.A.1.d

16

1.A.2.a

17

1.A.2.b

17

1.A.2.c

18

1.B.1.a

18

1.B.1.a

18

1.B.1.a

18

1.B.1.b

18

1.B.1.b

18

1.B.1.b

18

1.B.1.c

19

1.B.1.c

19

1.B.1.d

19

1.B.2.a

19

1.B.2.a

19

1.B.2.a

19

1.B.2.b

21

1.B.2.b

21

1.B.2.b

21

1.B.2.c

21

1.B.2.d

21

1.B.2.e

22

1.C.1.a

23

1.C.1.a

23

1.C.1.a

23

1.C.1.b

24

1.C.1.b

24

1.C.1.b

24

1.C.1.c

26

1.C.2.a

25

1.C.2.b

25

Grade 4

Grade 5

Grade 6

VSC

2.0

Geometry

VSC

2.0

Geometry

VSC

2.0

Geometry

2.A.1.a

26

2.A.1.a

26

2.A.1.a

26

2.A.1.b

26

2.A.1.b

26

2.A.1.b

26

2.A.1.c

27

2.A.1.c

27

2.A.1.c

27

2.A.2.a

28

2.A.2.a

28

2.A.2.b

28

2.A.2.b

28

2.A.2.c

28

2.A.2.d

29

2.B.1.a

29

2.B.1.a

29

2.B.1.b

30

2.B.1.b

30

2.B.2.a

31

2.B.2.a

31

2.C.1.a

2.C.1.a

32

2.C.1.a

32

2.C.1.b

33

2.C.1.c

33

2.D.1.a

34

2.D.1.a

34

2.D.1.a

34

2.E.1.a

35

2.E.1.a

35

2.E.1.a

35

Grade 4

Grade 5

Grade 6

VSC

3.0

Measurement

VSC

3.0

Measurement

VSC

3.0

Measurement

3.A.1.a

36

3.A.1.a

36

3.A.1.b

37

3.A.1.b

37

3.A.1.c

37

3.B.1.a

38

3.B.1.a

38

3.B.1.a

38

3.B.2

39

3.B.2.a

39

3.B.2

39

3.C.1.a

40

3.C.1.a

40

3.C.1.a

40

3.C.1.b

41

3.C.1.b

41

3.C.1.b

41

3.C.1.c

41

3.C.1.c

41

3.C.1.c

41

3.C.1.d

42

3.C.1.d

42

3.C.1.e

42

3.C.2.a

42

3.C.2.a

42

3.C.2.b

43

3.C.2.b

43

3.C.2.c

44

Grade 4

Grade 5

Grade 6

VSC

4.0

Statistics

VSC

4.0

Statistics

VSC

4.0

Statistics

4.A.1.a

45

4.A.1.a

45

4.A.1.a

45

4.A.1.b

45

4.A.1.b

45

4.A.1.b

45

4.A.1.c

46

4.A.1.c

46

4.A.1.d

46

4.A.1.e

47

4.A.1.f

48

4.B.1.a

48

4.B.1.a

48

4.B.1.a

48

4.B.1.b

49

4.B.1.b

49

4.B.1.b

49

4.B.1.c

50

4.B.1.c

50

4.B.1.d

50

4.B.1.e

51

4.B.2.a

52

4.B.2.a

52

4.B.2.a

52

4.B.2.b

52

4.B.2.b

52

Grade 4

Grade 5

Grade 6

VSC

5.0

Probability

VSC

5.0

Probability

VSC

5.0

Probability

5.A.1.a

53

5.B.1.a

54

5.B.1.a

54

5.B.1.a

54

5.B.1.b

54

5.B.1.c

55

5.C.1.a

56

5.C.2

56

5.C.3

56

5.C.4

56

Grade 4

Grade 5

Grade 6

VSC

6.0

Number Relationships and Computation

VSC

6.0


VSC

6.0


6.A.1.a

58

6.A.1.a

58

6.A.1.a

58

6.A.1.b

59

6.A.1.b

59

6.A.1.b

59

6.A.1.c

60

6.A.1.c

60

6.A.1.c

60

6.A.1.d

61

6.A.1.d

61

6.A.1.d

61

6.A.1.e

61

6.A.1.e

61

6.A.2.a

62

6.A.2.b

62

6.A.2.c

63

6.A.2.d

63

6.A.2.e

64

6.A.2.f

64

6.A.2.g

65

6.A.2.h

66

6.A.3.a

67

6.A.3.b

67

6.B.1.a

68

6.B.1.a

68

6.B.1.a

68

6.B.1.b

69

6.B.1.b

69

6.B.1.c

69

6.B.1.c

69

6.B.1.d

70

6.C.1.a

71

6.C.1.a

71

6.C.1.a

71

6.C.1.b

72

6.C.1.b

72

6.C.1.b

72

6.C.1.c

73

6.C.1.c

73

6.C.1.c

73

6.C.1.d

74

6.C.1.d

74

6.C.1.d

74

6.C.1.e

75

6.C.1.e

75

6.C.1.e

75

6.C.1.f

76

6.C.1.f

76

6.C.1.f

76

6.C.1.g

77

6.C.1.g

77

6.C.1.h

78

6.C.2.a

79

6.C.2.a

79

6.C.2.a

79

6.C.2.b

79

6.C.2.b

79

6.C.2.c

80

6.C.3.a

80

6.C.3.b

82

Grade 4

Grade 5

Grade 6

VSC

7.0

Processes of Mathematics

VSC

7.0


VSC

7.0


7.A.1.a

82

7.A.1.a

82

7.A.1.a

82

7.A.1.b

82

7.A.1.b

82

7.A.1.b

82

7.A.1.c

82

7.A.1.c

82

7.A.1.c

82

7.A.1.d

83

7.A.1.d

83

7.A.1.d

83

7.A.1.e

83

7.A.1.e

83

7.A.1.e

83

7.A.1.f

83

7.A.1.f

83

7.A.1.f

83

7.A.1.g

84

7.A.1.g

84

7.A.1.g

84

7.A.1.h

84

7.A.1.h

84

7.A.1.h

84

7.B.1.a

85

7.B.1.a

85

7.B.1.a

85

7.B.1.b

85

7.B.1.b

85

7.B.1.b

85

7.B.1.c

85

7.B.1.c

85

7.B.1.c

85

7.B.1.d

86

7.B.1.d

86

7.B.1.d

86

7.C.1.a

87

7.C.1.a

87

7.C.1.a

87

7.C.1.b

87

7.C.1.b

87

7.C.1.b

87

7.C.1.c

87

7.C.1.c

87

7.C.1.c

87

7.C.1.d

88

7.C.1.d

88

7.C.1.d

88

7.C.1.e

89

7.C.1.e

89

7.C.1.e

89

7.C.1.f

89

7.C.1.f

89

7.C.1.f

89

7.C.1.g

89

7.C.1.g

89

7.C.1.g

89

7.C.1.h

89

7.C.1.h

89

7.C.1.h

89

7.D.1.a

90

7.D.1.a

90

7.D.1.a

90

7.D.1.b

90

7.D.1.b

90

7.D.1.b

90

7.D.1.c

91

7.D.1.c

91

7.D.1.c

91

7.D.1.d

92

7.D.1.d

92

7.D.1.d

92

Montessori Upper Elementary Mathematics

Quarterly Overview for 4th, 5th, and 6th Grade Students

First Quarter

Second Quarter

Third Quarter

Fourth Quarter

Statistics (All Indicators)

Algebra:

1.) Patterns and Functions

2.) Expressions / Order of Operations

3.) Coordinate Grids

Number Concepts:

1.) Whole Number Place Value

2.) Whole Number Operations

3.) Integers and Exponents (6th Grade)

4.) Divisibility

5.) Factors and Multiples

Processes: All Indicators

Algebra:

Equations and Inequalities

Geometry:

1.) Nomenclature (lines, angles, and polygons)

2.) Congruence and Similarity

3.) Transformations

4.) Analyzing Quadrilaterals, Triangles, and Circles

Measurement:

1.) Length (Standard and Metric)

2.) Degrees of an Angle

Numbers:

1.) Analyze Fractions

2.) Equivalent Forms

3.) Fraction Operations (+,-,x)


Probability (All Indicators)

Measurement:

1.) Weight and Capacity (Standard and Metric)

2.) Applications of Formulas (Area, Perimeter, Volume)

3.) Composite Figures

4.) Time

Number Concepts:

1.) Decimal Place Value

2.) Decimal Operations

3.) Equivalent Forms

4.) Money

5.) Percent


Accelerated Curriculum with Extended Assessment Limits:

Number Concepts:

1.) Whole Number Operations

2.) Fraction Operations

3.) Decimal Operations

4.) Integers Operations

5.) Ratios and Scale Models

Geometry:

1.) Analyze Circles

Measurement:

1.) Use Measurement Tools

2.) Apply Measurement Formulas (Surface Area, Volume)


Montessori Math and the Maryland Voluntary State Curriculum

This sequence has been kept as closely aligned to the Montessori math curriculum as possible, but adjustments have been made based on the indicators tested quarterly in Prince George’s County Public Schools. If teachers systematically incorporate these indicators into their presentations and discussions, students will be comfortable with quarterly benchmark tests and the Maryland School Assessment (MSA). The Montessori Math Lessons are designed to be presented individually or in small groups. Each presentation isolates one learning objective. Where students begin in the sequence, and how quickly they progress, depends on the developmental needs of each individual student. The teacher observes and responds to each individual child’s learning needs. Grade level expectations are intended to be used only as an aid to planning. Teachers will use their Montessori curriculum albums as their primary guides, and each student will progress at his or her own unique and appropriate pace.

Montessori Upper Elementary Math Curriculum Alignment

VSC-Mathematics-Standard 1.0 Knowledge of Algebra, Patterns, and Functions: Students will algebraically represent, model, analyze, or solve mathematical or real-world problems involving patterns or functional relationships.

Grade 4

Grade 5

Grade 6

Topic 1.A. Patterns and Functions



1.A.1. Identify, describe,

extend, and create numeric patterns and functions

Quarter

1

1.A.1. Identify, describe,

extend, and create numeric patterns and functions

Quarter

1

1.A.1 Identify, describe, extend, and create numeric patterns and functions

Quarter

1

a. Represent and analyze numeric patterns using skip counting

Assessment limit: Use patterns of 3, 4, 6, 7, 8, or 9 starting with any whole number (0 – 100)

Montessori Lessons:

Short and Long Bead Chains, Bead Bars, Flash Cards, Multiplication Charts

Albanesi Cards:

9.A -K

10.A –G

POW (06-07): Week 1

SFAW 2-9; TE 1

DIS: M-35; p. 69-70, 127

SFAW 2-10 / 2-11; TE 1

DIS: M-15; p. 29-30, 107

DIS: J-18; p. 35-36, 100

MSA Finish Line:

Pages 8-11

a. Interpret and write a rule for a one-operation (+, -, x, ÷ with no remainders) function table

Assessment limit: Use whole numbers or decimals with no more than 2 decimal places (0 – 1000)

Montessori Materials:

Command Cards

SFAW: 2-14; TE 1

DIS: J-8; p. 15-16, 90

MSA Finish Line:

Pages 8-11

a. Identify and describe sequences represented by a physical model or in a function table

Montessori Lessons:

Short and Long Bead Chains, Bead Bars; Student Created Models

Glencoe: 7-6, 7-6a

b. Create a one-operation

(+ or -) function table to solve a real world problem

Montessori Lessons:

Word Problem Cards

b. Create a one-operation

(x, ÷ with no remainders) function table to solve a real world problem

Montessori Lessons:

Word Problem Cards

SFAW: 3-15; TE 1

b. Interpret and write a rule for one-operation (+, -, x, ÷ ) function table

Assessment limit: Use whole numbers or decimals with no more than two decimal places (0 – 10,000)

Montessori Lessons:

Word Problem Cards

GLencoe: 9-6a, 9-6

Grade 4

Grade 5

Grade 6

c. Complete a function table using a one operation (+, -, ×, ÷ with no remainders) rule

Assessment Limit: Use operational symbols (+, -, x) and whole numbers (0-200)


Command Cards

SFAW 3-13; TE 1

DIS: J-13; p. 25-26, 95

c. Complete a one-operation function table

Assessment limit: Use whole numbers with +, -, x, ÷ (with no remainders) or use decimals with no more than two decimal places with +, - (0 – 200)


Command Cards

POW (06-07): Week 3

SFAW: 2-14; TE 1

DIS: J-8; p. 15-16, 90

c. Complete a function table with a given two-operation rule

Assessment limit: Use the operations of (+, -, x), numbers no more than 10 in the rule, and whole numbers (0 - 50)


Command Cards

MSA Finish Line:

Pages 8-11

d. Describe the relationship that generates a one-operation rule


Command Cards

d. Apply a given two operation rule for a pattern

Assessment limit: Use two operations (+, -, x) and whole numbers (0 – 100)


Command Cards

POW (06-07): Week 4

SFAW: 3-15; TE 1

MSA Finish Line:

Pages 12-15

1.A. 2. Identify, describe, extend, analyze, and create a non-numeric growing or repeating pattern

Quarter

1

a. Generate a rule for the next level of the growing pattern

Assessment limit: Use at least 3 levels but no more than 5 levels


Command Cards; Student Created Models

POW (06-07): Week 2

MSA Finish Line:

Pages 12-15

Grade 4

Grade 5

Grade 6

b. Generate a rule for a repeating pattern

Assessment limit: Use no more than 4 objects in the core of the pattern


Command Cards; Student

Created Models

MSA Finish Line:

Pages 12-15

c. Create a non-numeric growing or repeating pattern


Command Cards; Student Created Models

Grade 4

Grade 5

Grade 6

Topic 1.B. Expressions, Equations, and Inequalities

Topic 1. B. Expressions, Equations, and Inequalities

Topic 1. B. Expressions, Equations, and Inequalities

1.B.1 Write and identify expressions

Quarter

1

1.B.1 Write and identify expressions

Quarter

1

1.B.1 Write and evaluate expressions

Quarter

1

a. Represent numeric quantities using operational symbols (+, -, ×, ÷ with no remainders)

Assessment limit: Use whole numbers (0 – 100)

Montessori Lessons:

Word Problem Cards; Math Vocabulary Card Set; Chart for four basic operations;


SFAW 2-12; TE 1

DIS: J-18; p. 35-36, 100

SFAW 3-13 / 3-14; TE 1

DIS: J-20; p. 39-40, 102

DIS: J-21; p. 41-42, 103

a. Represent unknown quantities with one unknown and one operation (+, -, ×, ÷ with no remainders)

Assessment limit: Use whole numbers (0 – 100) or money ($0 - $100)

Montessori Lessons:

Word Problem Cards; Math Vocabulary Card Set; Chart for four basic operations; Problem Solving Sequence

SFAW: 2-12; TE 1

a. Write an algebraic expression to represent unknown quantities

Assessment limit: Use one unknown and one operation (+, -) with whole numbers, fractions with denominators as factors of 24, or decimals with no more than two decimal places (0-200)

Montessori Lessons:

Word Problem Cards; Math Vocabulary Card Set; Chart for four basic operations; Problem Solving Sequence

Glencoe: 1-1 / 1-6

PGCPS 6th CFPG: Supplemental Lesson 1

b. Determine equivalent expressions



Math Fact Families; Bead Bars

SFAW 2-13; TE 1

DIS: J-19; 37-38, 101

MSA Finish Line:

Pages 16-19

b. Determine the value of algebraic expressions with one unknown and one operation

Assessment limit: Use +, - with whole numbers (0-1000) or ×, ÷ (with no remainders) with whole numbers (0-100) and the number for the unknown is no more than 9



POW (06-07): Week 22

SFAW: 2-13; TE 1

MSA Finish Line:

Pages 16-19

b. Evaluate an algebraic expression

Assessment limit: Use one unknown and one operation (+, -) with whole numbers (0 – 200), fractions with denominators as factors of 24 (0 – 50), or decimals with no more than two decimal places (0 – 50)



Albanesi Cards:

72.A-G

Glencoe: 1-6, 1-7

MSA Finish Line:

Pages12-15


Grade 4

Grade 5

Grade 6

c. Use parenthesis to evaluate a numeric expression

Fourth Quarter

Accelerated Curriculum


Command Cards

POW (06-07) Week 35

SFAW: 3-13 and 3-16; TE 1

DIS: J-23; p. 45-46,105

c. Evaluate numeric expressions using the order of operations

Assessment limit: Use no more than 4 operations

(+, -, x, ÷ with no remainders) with or without 1 set of parentheses or a division bar and whole numbers (0-100)

Montessori Lessons:

Integers

POW (06-07) Week 2

Glencoe: 1-5, 9-1

MSA Finish Line:

Pages 16-19

d. Represent algebraic expressions using physical models, manipulatives, and drawings


Command Cards, Student Created Models

1.B.2. Identify, write, solve, and apply equations and inequalities

Quarter

2


Quarter

2


Quarter

2

Grade 4

Grade 5

Grade 6

a. Represent relationships using relational symbols

(>, <, =) and operational symbols (+, -, ×, ÷) on either side

Assessment limit: Use operational symbols (+, -, ×) and whole numbers (0 – 200)

Montessori Lessons:

Word Problem Cards; Math Vocabulary Card Set / Chart for four basic operations;


POW (06-07): Week 31

SFAW 12-1; TE 4

DIS: J-10; p. 19-20, 92

SFAW 12-2; TE 4

DIS: J-11; p. 21-22, 93

SFAW 12-3; TE 4

DIS: J-12; p. 23-24, 94

a. Represent relationships by using the appropriate relational symbols (>, <, =) and one operational symbol (+, -, ×, ÷ with no remainders) on either side


Montessori Lessons:



SFAW: 3-15; TE 1

Reasoning and

Problem Solving

DIS: J-13; p. 25-26, 95

SFAW: 3-15; TE 1

Extend lesson to

reach limit

SFAW: 12-2; TE 4

(Teacher will need to

include inequalities.)

a. Identify and write equations and inequalities to represent relationships

Assessment limit: Use a variable, the appropriate relational symbols (>, <, =), and one operational symbol (+, -, ×, ÷) on either side and use fractions with denominators as factors of 24 (0 – 50) or decimals with no more than two decimal places (0 – 200)

Montessori Lessons:



Glencoe: 9-1

Grade 4

Grade 5

Grade 6

b. Find the unknown in an equation with one operation

Assessment limit: Use multiplication (×) and whole numbers (0-81)

Montessori Lessons:

Euclids’s Laws/Balancing Equations; Word Problem Cards

SFAW 3-15; TE 1

MSA Finish Line:

Pages 20-23

b. Find the unknown in an equation use one operation (+, -, ×, ÷ with no remainders)


Montessori Lessons:


SFAW: 2-12; TE 1

DIS: J-13; p. 25-26, 95

SFAW: 2-15, TE 1

DIS: J-21; p. 41-42, 1

MSA Finish Line:

Pages 20-23

Fourth Quarter

Accelerated Curriculum:

POW (06-07): Week 36

SFAW: 12-2; TE 4

DIS J-25; pg. 49-50,107

SFAW: 12-3; TE 4

DIS J-26; pg 51-52, 108

(Include decimal examples.)

b. Determine the unknown in a linear equation

Assessment limit: Use one operation (+, -, ×, ÷ with no remainders) and use positive whole number coefficients using decimals with no more than two decimal places (0 – 100)

Montessori Lessons:


Albanesi Cards:

41.A-D

Glencoe: 9-2, 9-2a, 9-3, 9-4, 9-4b

MSA Finish Line:

Pages 20-23

Fourth Quarter Accelerated Curriculum:

Montessori Binomial and Trinomial Squares and Cubes

Albanesi Cards: 41.E; 44.A-H; 45.A-E; 47.A-B

Solving Two-Step Equations:

POW (06-07): Week 34

Glencoe: 9-5, 9-5b

c. Solve for the unknown in a one-step inequality

Montessori Lessons:


d. Identify or graph solutions of a one-step inequality on a number line.

Montessori Lessons:


e. Apply given formulas to a problem solving situation

Montessori Lessons:



Grade 4

Grade 5

Grade 6

Topic1.C. Numeric and Graphic Representations of Relationships

Topic 1.C. Numeric and Graphic Representations of Relationships

Topic 1.C. Numeric and Graphic Representations of Relationships

1.C.1 Locate points on a number line and in a coordinate grid

Quarter 1 – 1.C.1.b and c

Quarter 2- 1.C.1.a

1.C.1. Locate points on a number line and in a coordinate grid

Quarter 1 – 1.C.1.b

Quarter 2- 1.C.1.a

1.C1. Locate points on a number line and in a coordinate plane

Quarter

1

a. Represent mixed numbers and proper fractions on a number line

Assessment limit: Use proper fractions with a denominators of 6, 8, or 10


History of Numbers; Classification of Numbers

POW (06-07): Week 17

SFAW 10-4; TE 4

DIS: H-29; p. 57-58, 115

a. Represent decimals and mixed numbers on a number line

Assessment limit: Use decimals with no more than two decimal places (0 – 100) or mixed numbers with denominators of 2, 3, 4, 5, 6, 8, or 10 (0 - 10)


History of Numbers; Classification of Numbers

SFAW: 7-5; TE 3

DIS: H-23 p. 45-46, 109

SFAW: 7-14; TE 3


Use integers -20 to 20.

POW(06-07): Week 37, 38

a. Represent rational numbers on a number line

Assessment limit: Use integers (-20 to 20)


History of Numbers; Classification of Numbers; Negative Snake Game; Integers Lessons; Social Studies Cross-Curricular Lesson: BC/CE Timeline

Albanesi Cards:

38.A – K; 39.A – C; 42.A- H; 46.A – B

Glencoe: 8-1


Grade 4

Grade 5

Grade 6

b. Identify positions in a coordinate plane

Assessment limit: Use the first quadrant and ordered pairs of whole numbers (0 - 20)

Montessori Lessons:

Integrated Lessons in Science and Geography (latitude and longitude)

Albanesi Cards:

101.D – I

SFAW 4-9; TE 2

DIS: L-4; p. 7-8, 66

MSA Finish Line:

Pages 24-27

b. Create a graph in a coordinate plane

Assessment limit: Use the first quadrant and ordered pairs of whole numbers (0 – 50)

Montessori Lessons:


Albanesi Cards:

25.J – O

POW (06-07): Week 2

SFAW: 3-14

MSA Finish Line:

Pages 24-27

Fourth Quarter Accelerated Curriculum: Introduce coordinate grid with four quadrants.

SFAW: 12-9; TE 4

b. Graph ordered pairs in a coordinate plane.

Assessment limit: Use no more than 3 ordered pairs of integers (-20 to 20) or no more than 3 ordered pairs of fractions/mixed numbers with denominators of 2 (-10 to 10)

Montessori Lessons:


Glencoe: 8-6

MSA Finish Line:

Pages 24-27


Glencoe: 9-5, 9-7

c. Represent decimals on a number line

Fourth Quarter


Montessori Lessons: Command Cards

SFAW 7-14, TE 3

c. Graph linear data from a function table

Fourth Quarter


Montessori Lessons: Story Problems; Command Cards

Albanesi Cards: 41.A-D

Glencoe: 9-5, 9-7

POW: Week 26

1.C.2. Analyze linear relationships

Quarter

1


Grade 4

Grade 5

Grade 6

a. Identify and describe the change represented in a graph

Assessment limit: Identify increase, decrease, or no change

Montessori Lessons:

Student Surveys, Student Created Graphs, Integrated Lessons in Science

Glencoe: 2-8

MSA Finish Line:

Pages 28-31

b. Translate the graph of a linear relationship onto a table of values that illustrates the type of change

Montessori Lessons:

Student Surveys, Student Created Graphs, Integrated Lessons in Science

QUARTER 2

REVIEW

MSA Finish Line of Algebra, Patterns, and Functions:

Pages 7, 28-30

QUARTER 2

REVIEW


Pages 7, 28-30

QUARTER 2

REVIEW


Pages 7, 32-34

VSC-Mathematics-Standard 2.0 Knowledge of Geometry: Students will apply the properties of one-, two-, or three-dimensional geometric figures to describe, reason, or solve problems about shape, size, position, or motion of objects

Grade 4

Grade 5

Grade 6

Topic 2.A. Plane Geometric Figures

Topic2. A. Plane Geometric Figures

Topic 2.A. Plane Geometric Figures

2.A.1. Analyze the

properties of plane

geometric figures

Quarter

2

2.A.1. Analyze the

properties of plane

geometric figures

Quarter

2

2.A.1. Analyze the

properties of plane

geometric figures

Quarter

2

a. Identify properties of

angles using

manipulative

and pictures

Montessori Lessons:

Geometry Nomenclature

Cards: Three Period

Lessons; Angle Search in

the Classroom / Angle

Search in Yarn Webs;

Geometric Stick Box

SFAW 8-3; TE 3

DIS: K-46; p. 91-92, 160

a. Identify and describe

relationships of lines

and line segments in

geometric figures or

pictures

Assessment limit: Use parallel or perpendicular lines and line segments

Montessori Lessons:

Geometry Nomenclature Cards: Three Period Lessons; Line Treasure Hunt in Classroom / Yarn Webs; Geometric Stick Box

POW (06-07): Week 8

SFAW 6-1; TE 2

DIS: K-46; p. 91-92, 160

a. Identify, describe, and

label points, lines, rays,

line segments, vertices,

angles, and planes

using correct symbolic

notation

Montessori Lessons:

Geometry Nomenclature Cards; Geometric Stick Box; Drawing and labeling points, lines, rays, vertices, and angles using rulers and protractors.

Glencoe: 13-1, 13-2

b. Identify, compare,

classify, and describe

angles in relationship

to another angle

Assessment limit: Use acute, right, or obtuse angles

Montessori Lessons:

Geometry Nomenclature Cards; Geometric Stick Box

POW (06-07): Week 10

SFAW 8-4; TE 3

DIS: K-41, K-42; p. 81-84, 155-156

MSA Finish Line:

Pages 32-35

b. Identify polygons within

a composite figure

Assessment limit: Use polygons with no more than 8 sides as part of a composite figure comprised of triangles or quadrilaterals

Montessori Lessons:

Geometry Nomenclature Cards; Constructive Triangles; Geometric Cabinet

SFAW 6-6; TE 2

DIS: K-5; p.101-102, 165

MSA Finish Line:

Pages 32-35

b. Identify and describe

line segments

Assessment limit: Use diagonal line segments

Montessori Lessons:

Geometry Nomenclature Cards

Glencoe: 13-3a

MSA Finish Line:

Pages 36-39


Grade 4

Grade 5

Grade 6

c. Identify parallel and

intersecting line

segments

Montessori Lessons:

Geometry Nomenclature Cards; Geometric Stick Box

SFAW 8-3; TE 3

c. Identify and describe

the radius and diameter

of a circle

Montessori Lessons:

Geometry Nomenclature Cards; Circle Search in the Classroom; Linear Parts of a Circle; Stick Box

c. Identify and describe the

parts of a circle

Assessment limit: Use radius, diameter, or

Montessori Lessons:

Geometry Nomenclature Cards; Parts of a Circle Chart; Concentric Circles; Linear Parts of a Circle: Red Fraction Inset Material


Parts of a circle.

Montessori Lessons: Geometry Nomenclature Cards; Circle Search in the Classroom; Linear Parts of a Circle

POW (06-07): Week 38

SFAW 8-5

MSA Finish Line:

Pages 32-33

circumference

Glencoe: 4-6

PGCPS 6th CFPG:

Supplemental Lesson 2

2.A.2. Analyze geometric

relationships

Quarter

2

2.A.2. Analyze geometric

Relationships

Quarter

2


Grade 4

Grade 5

Grade 6

a. Compare and classify

quadrilaterals by length

of sides and types of

angles (Include the

angle symbol

Assessment limit: Use squares, rectangles, rhombi, parallelograms, and trapezoids

Montessori Lessons:

Stick Box, Quadrilateral Who Am I? Game, GEO Boards, Geometric Cabinet, Nomenclature Cards

POW (06-07): Week 9

SFAW 6-9; TE 2

DIS: K-48; p. 95-96, 162

MSA Finish Line:

Pages 36-39

a. Compare and classify

triangles by sides

Assessment limit: Use scalene, equilateral, or isosceles

Montessori Lessons:

Constructive Triangles, Stick Box, Triangle Logical Adjective Game, GEO Boards, Geometric Cabinet, Geometry Nomenclature Cards

Glencoe: 13-4

b. Compare triangles by

sides

Montessori Lessons:


b. Compare and classify

triangles by angle

measure

Assessment limit: Use equiangular, obtuse, acute, or right

Montessori Lessons:


MSA Finish Line:

Pages 44-47

c. Determine a third angle

measure of a triangle given two angle measures

Montessori Lesson:

Sum of the angles of a triangle

Assessment limit: Use the concept of the sum of angles in any triangle is 180° without using a diagram

POW (06-07): Week 22

Glencoe: 13-4b

MSA Finish Line:

Pages 48-51


Grade 4

Grade 5

Grade 6

d. Identify and compare

the relationship

between parts of a

circle

Assessment limit: Use radius, diameter and circumference (=3.14)

Montessori Lessons:

Circle as a “Regular Polygon,” Sensorial Exploration of Circumference; Geometry Nomenclature Cards

Glencoe: 4-6

MSA Finish Line:

Pages 40-43

Topic 2.B. Solid Geometric Figures

Quarter

2


Quarter

2


2.B.1. Analyze the properties of solid geometric figures

2.B.1. Analyze the properties of solid geometric figures

a. Identify cones,

cylinders, prisms, and

pyramids

Assessment limit: Use cones or cylinders

Montessori Lessons:

Sensorial Classification of Geometric Solids, Geometric Nomenclature Cards, Solid Geometry Classroom Scavenger Hunt

SFAW: 8-1

DIS: K-38, p. 75-76, 152

a. Identify and classify

pyramids and prisms by

the number of edges,

faces, or vertices

Assessment limit: Use triangular pyramids, rectangular pyramids, triangular prisms, or rectangular prisms

Montessori Lessons:

Sensorial Classification Geometric Solids, Geometric Nomenclature Cards, Solid Geometry Classroom Scavenger Hunt

SFAW 10-1; TE 4

DIS: H-28; p. 55-56, 114


Grade 4

Grade 5

Grade 6

b. Describe solid

geometric figures by

the number of edges,

faces, or vertices

Assessment limit: Use triangular pyramids, rectangular pyramids, triangular prisms, or rectangular prisms

Montessori Lessons:

Sensorial Classification of Geometric Solids, Geometric Who Am I? Game, Geometric Solids Scavenger Hunt

SFAW 8-1; TE 3

DIS: K-38; p. 75, 75, 152

b. Identify and classify

pyramids and prisms by

the base

Assessment limit: Use triangular prisms and pyramids or rectangular prisms and pyramids

Montessori Lessons:


POW (06-07): Week 17

SFAW 10-2; TE 4

DIS: H-29; p. 57-58, 113


Grade 4

Grade 5

Grade 6

2.B.2. Analyze the relationship between plane geometric figures and surfaces of solid geometric figures

Quarter

2

2.B.2. Analyze the relationship between plane geometric figures and faces of solid geometric figures

Quarter

2

a. Compare a plane figure

to surfaces of solid

geometric figure

Assessment limit: Analyze or identify the number or arrangement of squares needed to make a cube and triangles/rectangles needed to make a triangular pyramid or rectangular pyramid.

Montessori Lessons:


POW (06-07): Week 9

SFAW: 8-1 cont’d, 8-2

DIS: K-45, p. 89-90, 159

MSA Finish Line:

Pages 36-39

a. Compare a plane figure

to faces of solid

geometric figure

Assessment limit: Analyze and identify the number or arrangement of rectangles needed to make a rectangular prism, number of triangles/rectangles needed to make a triangular prism, and the number of circles/rectangles needed to make a cylinder.

Montessori Lessons:

Sensorial Classification of Geometric Solids, Geometric Who Am I? Game, Geometric Solids Scavenger Hunt, Creating Nets for Geometric Solids

MSA Finish Line:

Pages 40-43


Grade 4

Grade 5

Grade 6

Topic 2.C. Representation of Geometric Figures



2.C.1. Represent plane

geometric figures

Quarter

2


geometric figures

Quarter

2


geometric figures

Quarter

2

a. Sketch acute, right,

obtuse angles, and

parallel and

intersecting line

segments

Montessori Lessons:

Geometry Nomenclature Cards: Students create booklet; Geometry command cards

a. Identify, describe, and

draw angles, parallel

line segments, and

perpendicular line

segments

Assessment limit: Provide their dimensions as whole numbers (0 - 20) or angle measurements (0° - 179°)

Montessori Lessons:

Sensorial Exploration of Angles with Montessori Protractor and Red Circle Fractions, Stick Box, Traditional Protractor; Geometry Nomenclature cards: Student created booklets; Geometry command cards

SFAW: 6-2

DIS: K-49, p. 97-98, 163

MSA Finish Line:

Pages 32-25

a. Draw geometric figures using a variety of tools

Assessment limit: Draw triangles given the measures of 2 sides and one angle or 2 angles and 1 side using whole numbers (0-20) and angle measures (0°-179°)

Montessori Lessons:

Traditional Protractor; Standard and Metric Rulers; Geometry Nomenclature Cards: Student created booklets; Geometry Command Cards

Glencoe: 13-4, 13-4b

b. Identify, describe, or

draw a polygon

Assessment limit: Use the first quadrant given no more than six coordinates

Montessori Lessons:

Traditional Protractor; Standard and Metric Rulers; Geometry Nomenclature Cards: Student created booklets; Geometry command cards



Grade 4

Grade 5

Grade 6

b. Identify or describe

angle relationships

Assessment limit: Use perpendicular bisectors or angle bisectors

Montessori Lessons:

Geometry Nomenclature: Supplementary and Complementary Angles; Bisecting Angles with a Compass

POW (06-07): Week 21

Glencoe: 13-1, 13-3

MSA Finish Line:

Pages 52-55


Grade 4

Grade 5

Grade 6

Topic 2.D. Congruence



2.D.1. Analyze geometric figures

Quarter

2

2.D.1. Analyze similar figures to

Quarter

2

2.D.1. Analyze congruent figures

Quarter

2


geometric figures as

congruent

Assessment limit: Identify the result in a transformation as being congruent to the original figure

Montessori Lessons:

Constructive Triangles, Stick Box, Geometric Equivalence Materials

SFAW 8-6, TE 3

DIS: K-43, K-48, p. 85-86, 95-96, 157, 162

a. Identify or describe

geometric figures as similar

Assessment limit: Use same shape and different size

Montessori Lessons:


SFAW: 6-9

DIS: K-48, p. 95-96, 162

MSA Finish Line:

Pages 44-47


congruent polygons and

their corresponding

parts

Montessori Lessons:


POW (06-07): Week 36


Grade 4

Grade 5

Grade 6

Topic 2.E. Transformations



1. Analyze a transformation

Quarter

2

1. Analyze a transformation

Quarter

2

1. Analyze a transformation on a coordinate plane

Quarter

2


the results of

translations, reflections,

and rotations

Assessment limit: Use a horizontal line translation, reflection over a vertical line, or rotation of 90° clockwise around a given point of a geometric figure or picture

Montessori Lessons:

Blue Constructive Triangles, GEO Boards

POW (06-07): Week 11

SFAW 8-7,TE 3

DIS: K-44 p. 87-88, 158

MSA Finish Line:

Pages 40-43


the results of

translations, reflections,

and rotations of

geometric figures

Assessment limit: Use translation along a vertical line, reflection over a horizontal line, or rotation 90° or 180° around a given point

Montessori Lessons:

Blue Constructive Triangles, GEO Boards

SFAW: 6-10

DIS: K-52, p. 103-104, 166

MSA Finish Line:

Pages 48-51

a. Plot the result of one

transformation

(translation, reflection,

rotation) on a coordinate plane

Montessori Lessons:

Grid Paper, Command Cards

POW (06-07): Week 23


QUARTER 2

REVIEW or Geometry

MSA Finish Line

Pages 31, 44-46

QUARTER 2

REVIEW or Geometry

MSA Finish Line

Pages 31, 52-54

QUARTER 2

REVIEW or Geometry

MSA Finish Line

Pages 35, 56-58

VSC Mathematics Standard 3.0 Knowledge of Measurement: Students will identify attributes, units, or systems of measurements or apply a variety of techniques, formulas, tools or technology for determining measurements

Grade 4

Grade 5

Grade 6

Topic 3.A. Measurement Units

Topic 3.A. Measurement Units

Topic 3. A. Measurement Units

3.A.1. Read customary and metric measurement units

Quarter 2- 3.A.1.a

Quarter 3- 3.A.1.b and c

3.A.1 Read customary and metric measurement units

Quarter

3

3.A.1. Read customary and metric measurement units

Quarter

3

a. Estimate and determine length and height

Assessment limit: Use the nearest millimeter or ¼ inch

Montessori Lessons:

Measuring Object Boxes

Albanesi Cards:

(See Appendices – Measurement Activities)

SFAW 10-8, TE 4

DIS: K-1, p. 1-2, 115

SFAW 10-7, TE 4

DIS: K-2, p. 3-4, 116

Quarter 4


SFAW 10-8, TE 4

DIS: K-3, p. 5-6, 117

SFAW 10-10, TE 4

DIS: K-8, p. 15-16, 122

SFAW 10-11, TE 4

DIS: K-4, p. 7-8, 116

a. Estimate and determine weight or mass

Assessment limit: Use the nearest ounce for weight and the nearest gram for mass

Montessori Lessons:

Scales: Balance, Spring

Albanesi Cards:


SFAW 9-8, TE 3

DIS: K-28, p. 55-56, 142

MSA Finish Line:

Pages 56-59


Grade 4

Grade 5

Grade 6

b. Estimate and determine weight or mass

Montessori Lessons:

Scales: Balance, Spring

Albanesi Cards:


POW(06-07): Week 36

Quarter 4


SFAW 10-11, TE 4

DIS: K-4, p. 7-8, 116

Revisit SFAW11-2, TE 4

DIS: I-5, p. 9-10, 97

b. Estimate and determine capacity

Assessment limit: Use the nearest ounce

Montessori Lessons:

Sensorial Exploration using household containers, graduated Cylinder material, Scales: Balance, Spring

Albanesi Cards:


SFAW 10-6, TE 4

SFAW 10-7, TE 5

c. Estimate and determine capacity

Montessori Lessons:

Graduated Cylinders in Multiple Sizes

Albanesi Cards:


SFAW 10-9, TE 4


Grade 4

Grade 5

Grade 6

Topic 3.B. Measurement Tools



3.B.1. Measure in customary and metric units

Quarter

2


Quarter

2


Quarter

2

a. Select and use appropriate tools and units

Assessment limit: Use the nearest millimeter or ¼ inch with a ruler

Montessori Lessons:

The Story of Standard Measurement

Albanesi Cards:


POW(06-07): Week 18 and 19

SFAW 11-9, TE 4

DIS: K-5, p. 9-10, 119

SFAW 11-12, TE 4

(metric)

DIS: K-5, p. 9-10, 119

MSA Finish Line:

Pages 48-51

Quarter 4


SFAW 10-9, TE 4

DIS: K-6, p. 11-12, 120

Measure Angles:

SFWA 8-3, TE 3

Enrichment

Activity, p. 443

DIS: K-49, p. 97-98, 163


Assessment limit: Measure length to 1/8 inch with a ruler

Montessori Lessons:

The Story of Standard Measurement; Intro to the Metric System, Sensorial Exploration using yardsticks, meter sticks, and dual sided rulers.

Albanesi Cards:


POW(06-07): Week 14

SFAW 9-2, TE 3

DIS: K-3 p.5-6, 117


Assessment limit: Measure length to the nearest 1/16 inch with a ruler

Montessori Lessons:

The Story of Standard Measurement; Intro to Metric System

Albanesi Cards:


Glencoe: 12-2, 12-3, 12-3b, 12-4, 12-6

MSA Finish Line:

Pages 60-63


Grade 4

Grade 5

Grade 6

3.B.2. Compare right angles to a corner

Quarter

2

3.B.2. Measure angles

Quarter

2

3.B.2. Measure angles in polygons

Quarter

2

Montessori Lessons:

Constructive Triangles

Quarter 4


Refer to SFAW 8-3, TE 3

a. Measure a single angle and angles in regular polygons

Assessment limit: Measure an angle between 0 and 180 to the nearest degree

Montessori Lessons:

Constructive Triangles

SFAW 6-4, TE 2

DIS: K-45 p. 89-90, 159

See Sample Lesson Plan

Investigation TE 2 p.326

MSA Finish Line:

Pages 60-63

Montessori Lessons:

Equivalence Material, Yellow area material, Constructive Triangles


Quarter 4


Montessori Lessons: Bisecting angles, Addition and Subtraction of angles

Topic 3.C. Applications in Measurement



3.C.1. Apply measurement concepts

Quarter

3

3.C.1. Estimate and apply measurement formulas

Quarter

2

3.C.1. Estimate and apply measurement formulas

Quarter

2


a. Determine perimeter

Assessment limit: Use polygons with no more than 6 sides given the length of the sides in whole numbers (0 – 100)

Montessori Lessons:

Sensorial Exploration of Perimeter, Constructive Triangles, Equivalence Materials, GEO Boards, Real World Problems, Measurement Command Cards

Albanesi Cards:

(See Appendices, Measurement Cards: 69.Q)

SFAW 8-10, TE 3

DIS: K-26, p. 51-52, 140

MSA Finish Line:

Pages 52-55

Quarter 4


Revisit

SFAW 8-10, TE 3

DIS: K-31, p. 61-62, 145

a. Determine perimeter

Assessment limit: Use polygons with no more than 8 sides and whole numbers (0 –500)

Montessori Lessons:

Sensorial Exploration of Perimeter, Constructive Triangles, Equivalence Materials, GEO Boards, Real World Problems, Measurement Command Cards

Albanesi Cards:

(See Appendices, Measurement Cards: 69.Q)

POW(06-07): Week15

SFAW 9-5, TE 3

DIS: K-26 p.51-52, 140

a. Estimate and determine the area of a polygon

Assessment limit: Use triangles and whole number dimensions (0 – 200)

Montessori Lessons:

Yellow area material, Equivalence material

Albanesi Cards:

(See Appendices)

POW(06-07): Week 18

Glencoe: 1-8, 12-1a, 14-1, 14-2, 14-2a, 14-2b

MSA Finish Line:

Pages 64-67

Quarter 4


Montessori Lessons: Area for Rhombus, and regular polygon, area of a circle material, use of equivalence Material, Pythagorean Theorem lesson with sensorial Pythagoras material

Grade 4

Grade 5

Grade 6

b. Determine area

Assessment limit: Use rectangles with the length of the sides in whole numbers (0 – 100)

Montessori Lessons:

Egyptian Rope Stretchers, Yellow Area Material, Equivalence Material, Geo Boards

Albanesi Cards:

(See Appendices, Measurement Cards: 36.T)

POW(06-07): Week 12

SFAW 8-11, Investigation

TE 3 (432J)

DIS: K-25, p. 49-50, 140

MSA Finish Line:

Pages 56-59

Quarter 4


SFAW 8-11, TE 3

DIS: K-31, p. 61-62, 145

b. Determine area

Assessment limit: Use rectangles and whole numbers (0 – 200)

Montessori Lessons:

Egyptian Rope Stretchers, Yellow Area Material, Equivalence Material, Geo Boards

Albanesi Cards:

(See Appendices, Measurement Cards: 36.T)

SFAW 9-7, TE 3

(Re-teaching Lesson: TE

p.548B)

DIS: K-25 p.4-50, 139

MSA Finish Line:

Pages 64-67

b. Estimate and determine the volume of a rectangular prism

Assessment limit: Use rectangular prisms and whole number dimensions (0 – 1000)

Montessori Lessons:

Yellow Volume Material, Volume Cube Box

Story of Archimedes

POW(06-07): Week 19

Glencoe: 14-5, 14-6a

MSA Finish Line:

Pages 68-71

Quarter 4


Montessori Lessons: Volume and surface area of hexagonal, trapezoidal , and rhomboid prisms, pyramids, cylinders, and cones, Materials: Whole and divided rhomboid, hexagonal prisms, hollow volume material

POW(06-07): Week 39 and 40

Glencoe: 14-6


Grade 4

Grade 5

Grade 6

c. Determine start time, elapsed time, and end time

Assessment limit: Use hour and half hour intervals

Montessori Lessons:

Flash Cards, Clocks

Albanesi Cards:

107.A-D, (See Appendices, Measurement: 69.N.9)

POW(06-07): Week 5

SFAW 4-2, TE 2

DIS: K-14, p. 27-28, 128

SFAW 4-3, TE 2

DIS: K-16, p. 31-32, 130

MSA Finish Line:

Pages 60-63

c. Find the area and the perimeter of any closed figure on a grid

Assessment limit: Use whole and partial units (0-50)

Montessori Lessons:

Geo Board Activities, Grid Paper Lessons,

See Attached

Lesson Plan

SFAW 9-7

c. Estimate and determine the area of a composite figure

Assessment limit: Use composite figures with no more than four polygons (triangles or rectangles) and whole number dimensions (0 – 500)

Montessori Lesson:

Constructive Triangles, Yellow area Material

PGCPS 6th CFPG

Supplemental Lesson 3

MSA Finish Line:

Pages 72-75

d. Estimate and determine volume by counting

Montessori Lessons:

Story of Archimedes

Volume Cubes

SFAW 10-5, TE 4

d. Determine missing dimension of a quadrilateral given the perimeter length

Assessment limit: Find length in a quadrilateral given the perimeter with whole number dimensions (0 – 200)

Montessori Lessons:

See Appendices, Story Problems

POW(06-07): Week 17

MSA Finish Line:

Pages 76-79


Grade 4

Grade 5

Grade 6

e. Determine the missing dimension of rectangles

Assessment limit: Find length in a square or rectangle given the area and whole number dimensions (0 – 200)

Montessori Lessons:

See Appendices, Story Problems

MSA Finish Line:

Pages 76-79

3.C.2. Calculate equivalent measurements

Quarter 2 – 3.C.2.a

Quarter 3 – 3.C.2.b,c

3.C.2. Calculate equivalent measurements

Quarter

3

a. Determine equivalent units of length

Assessment limit: Use 36 inches = 1 yard and whole numbers (0-100)

Montessori Lessons:

Sensorial Exploration

SFAW 10-11, TE 4

(customary)

only length

DIS: K-19, p. 37-38,133

MSA Finish Line:

Pages 64-67

a. Determine start, elapsed, and end time

Assessment limit: Use the nearest minute

Montessori Lessons:

Flash Cards, Clocks

Albanesi Cards:

(See Appendices, Measurement: 69.N.9)

POW(06-07): Week 26

SFAW 9-13, TE 3

DIS: K-16,17 p.31-34,130-131

MSA Finish Line:

Pages 68-71


Grade 4

Grade 5

Grade 6

b. Determine equivalent units of time

Montessori Lessons:

Sensorial Exploration Sundial Observation, Memorization Games

b. Determine equivalent units of measurement

Assessment limit: Use seconds, minutes, and hours or pints, quarts, and gallons

Montessori Lessons:

Sensorial Exploration using Household Containers

POW(06-07): Week16

SFAW 9-12, TE 3

DIS: K-14 p.27-28, 128

SFAW 10-6, TE 3

DIS: K-6 p.11-12, 120

MSA Finish Line:

Pages 72-75

c. Determine equivalent units of capacity and weight within the same system

Albanesi Cards:

(See Appendices - Measurement)

REVIEW

MSA FINISH LINE

Pages 47, 68-70

REVIEW

MSA FINISH LINE

Pages 55, 76-78

REVIEW

MSA FINISH LINE

Pages 59, 80-82

VSC – Mathematics Standard 4.0 Knowledge of Statistics: Students will collect, organize, display, analyze, or interpret data to make decisions or predictions.

Grade 4

Grade 5

Grade 6

Topic 4.A. Data Displays



4.A.1. Collect, organize, and display data

Quarter

1

4.A.1. Collect, organize, and display data

Quarter

1

4.A.1. Organize and display data

Quarter

1

a. Collect data by conducting surveys to answer a question

Montessori Lessons:

Student Generated Surveys; Student Created Graphs; Statistics Command Cards (See Appendix)

Albanesi Cards:

101.A-C

25.A

SFAW 4-4, TE 2

DIS: M-19, p. 37-38, 111

SFAW 4-6; TE 2

DIS: L-2, p. 3-4, 64

a. Collect data by conducting surveys to answer a question

Montessori Lessons:

Student Generated Surveys; Student Created Graphs; Statistics Command Cards (See Appendix)

SFAW: 5-1, TE 2

DIS: H-37, p. 73-74, 123

a. Organize and display data to make frequency tables

Assessment limit: Use no more than 5 categories or ranges of numbers and total frequencies of no more than 25

Montessori Lessons:

Student Generated Surveys; Student Created Graphs; Statistics Command Cards (See Appendix); Cross-Curricular Lessons: Science Fair

Albanesi Cards:

62.A-B

Glencoe: 2-1, 2-2a

b. Organize and display data in line plots and frequency tables using a variety of categories and sets of data

Assessment limit: Use line plots with no more than 20 pieces of unorganized data and a range of no more than 10 and whole numbers (0 – 100)

Montessori Lessons:

Student Generated Surveys; Student Created Graphs; Statistics Command Cards; Cross-Curricular Lessons: Science Fair

POW(06-07): Week 3

SFAW 4-13, TE 2

SFAW 4-14, TE 2

b. Organize and display data in stem-and-leaf plots

Assessment limit: Use no more than 20 data points and whole numbers (0 – 100)

Montessori Lessons:


SFAW 5-4, TE 2

DIS L-28, pg. 55-56, 90

b. Organize and display data to make stem-and-leaf plots

Assessment limit: Use no more than 20 data points and whole numbers (0–999)

Montessori Lessons:


POW(06-07): Week 4

Glencoe: 2-5

MSA Finish Line:

Pages 88-91


Grade 4

Grade 5

Grade 6

c. Organize and display data in line plots

Assessment limit: Use no more than 20 pieces of data with a range of no more than 20 and whole numbers (0 – 200)

Montessori Lessons:


SFAW: 5-5, TE 2

c. Organize and display data using a back-to-back stem-and-leaf plot

Montessori Lessons:


Quarter 4


Box and Whisker plot

POW(06-07): Week 30

Glencoe: 2-7b

d. Organize and display data in double bar graphs

Assessment limit: Use no more than 4 categories and intervals of 1, 2, 5, or 10 and whole numbers (0 – 100)

Montessori Lessons:

Student Generated Surveys; Student Created Graphs; Statistics Command Cards

Albanesi Cards:

25.B-H

SFAW: 5-2, TE 2

DIS: L-3, p. 5-6, 65


Grade 4

Grade 5

Grade 6

e. Organize and display data in line graphs

Assessment limit: Use y-axis with intervals of 1, 2, 4, 5, or 10 and x-axis with no more than 10 time intervals and whole numbers (0 – 100)

Montessori Lessons:


Albanesi Cards:

25.I

SFAW 5-3, TE 2

DIS: L-6, pg. 11-12, 68

f. Determine the appropriate type of graph to effectively display data

Montessori Lessons:


SFAW 5-8, TE 2


Grade 4

Grade 5

Grade 6

Topic 4.B. Data Analysis



4.B.1. Analyze data

Quarter

1

4.B.1. Analyze data

Quarter

1

4.B.1. Analyze data

Quarter

1

a. Interpret line plots

Assessment limit: Use no more than 20 pieces of data with a range no more than 10 and whole numbers (0 – 100)

Montessori Lessons:

Integrated Lessons in Science and Social Studies;

Statistics Command Cards; Analyze data displays encountered in classroom periodicals such as “Weekly Reader,” “Scholastic News,” “Time for Kids,” etc.

SFAW 4-7, TE 2

DIS: L-25, 49-50, 87

MSA Finish Line:

Pages 72-75

a. Interpret and compare data in stem & leaf plot

Assessment limit: Use no more than 20 data points and whole numbers (0 – 100)

Montessori Lessons:



POW(06-07): Week 6

SFAW 5-4, TE 2

MSA Finish Line:

Pages 80-83

a. Interpret frequency tables

Assessment limit: Use no more than 5 categories or ranges of numbers and frequencies of no more than 25

Montessori Lessons:



POW(06-07): Week 3 and 15

Glencoe: 2-1

MSA Finish Line:

Pages 84-87

VSA – Mathematics Standard 4.0 Knowledge of Statistics: Students will collect, organize, display, analyze, or interpret data to make decisions or predictions.

Grade 4

Grade 5

Grade 6

b. Interpret line graphs

Assessment limit: Use the x-axis representing no more than 6 time intervals, the y-axis consisting of no more than 10 intervals with scales as factors of 100 using whole numbers (0 – 100)

Montessori Lessons:



SFAW 4-10; TE 2

DIS: L-5, p. 9-10, 67

SFAW 4-11, TE 2

DIS: M-31, p. 61-62, 123

MSA Finish Line:

Pages 76-79

b. Interpret and compare data in line plots

Assessment limit: Use no more than 20 pieces of data with a range of no more than 20 and whole numbers (0 – 100)

Montessori Lessons:



POW(06-07): Week 5

MSA Finish Line:

Pages 84-87

b. Read and analyze circle graphs

Assessment limit: Use no more than 5 categories using data in whole numbers or percents (0 – 1000)

Montessori Lessons:



POW(06-07): Week 3

Glencoe: 2-3

MSA Finish Line:

Pages 92-95

QUARTER 4

Accelerated Curriculum;

Making Circle Graphs Glencoe: 14-3b


Grade 4

Grade 5

Grade 6

c. Interpret and compare data in double bar graphs

Assessment limit: Use no more than 4 categories and intervals of 1, 2, 5, or 10 and whole numbers (0 – 1000)

Montessori Lessons:



MSA Finish Line:

Pages 88-91

c. Interpret data from a stem-and-leaf plot

Montessori Lessons:



d. Interpret and compare data in double line graphs

Assessment limit: Use y-axis with intervals of 1, 2, 5, or 10 and x- axis with no more than 10 time intervals and whole numbers (0-100)

Montessori Lessons:

Integrated Lessons in Science Social Studies; Statistics Command Cards; and Analyze data displays encountered in classroom periodicals such as “Weekly Reader,” “Scholastic News,” “Time for Kids,” etc.

SFAW: 5-8, TE 2

(Extension on page 291)

SFAW Chapter 5 Review

(Page 294)

MSA Finish Line:

Pages 92-95

Quarter 4


Bar Graphs and Line Graphs:

Glencoe: 2-2

Making Bar Graphs and Line Graphs using a Spreadsheet

Glencoe: 2-2b

Making Predictions:

Glencoe: 2-4

Analyzing Data:

Glencoe: 2-8


Grade 4

Grade 5

Grade 6

e. Read circle graphs

Assessment limit: Use no more than 4 categories and data in whole numbers or percents which are multiples of 5 and whole numbers (0 – 100)

Montessori Lessons:



SFAW 5-7, TE 2

MSA Finish Line:

Pages 96-99


Grade 4

Grade 5

Grade 6

4.B.2. Describe a set of data

Quarter

1

4.B.2. Describe a set of data (mean, median, mode)

Quarter

1

4.B.2. Describe a set of data

Quarter

1

a. Determine median, mode, and range

Assessment limit: Use no more than 8 pieces of data and whole numbers (0 – 100)

Montessori Lessons:

Statistics Command Cards; Cross-Curricular Lessons: Science Fair

POW(06-07): Week 4

SFAW 4-12; TE 2

DIS: L-26, p. 51-52, 88

a. Determine the mean of a given data set or data display

Assessment limit: Use no more than 8 pieces of data and whole numbers without remainders (0 – 1000)

Montessori Lessons:


SFAW 5-6, TE 2

MSA Finish Line:

Pages 100-103

a. Apply measures of central tendency (mean, median, mode)

Montessori Lessons:


Albanesi Cards:

62.C-G

MSA Finish Line:

Pages 80-83

Glencoe: 2-6, 2-7

QUARTER 4


Spreadsheets and Mean, Glencoe 2-6b

b. Model the mean of a set of data

Montessori Lessons:

Statistics Command Cards

SFAW 7-12, TE 3

b. Apply the range and measures of central tendency to solve a problem or answer a question

Montessori Lessons:

Statistics Command Cards; Story Problem Cards

QUARTER 1

Review of Statistics

MSA Finish Line

Pages 71, 84-86

QUARTER 1


MSA Finish Line

Pages 79, 104-106

QUARTER 1


MSA Finish Line

Pages 83, 96-98

VSC –Mathematics-Standard 5.0 Knowledge of Probability: Students will use experimental methods or theoretical reasoning to determine probabilities to make predictions or solve problems about events whose outcomes involve random variation.

Grade 4

Grade 5

Grade 6

Topic 5. A. Sample Space

Topic 5.A. Sample Space

Topic 5.A. Sample Space

5. A.1. Identify possible outcomes

Quarter

3

a. Determine possible outcomes of independent events

Assessment limit: Use two independent events with no more than 4 outcomes each and an organized list or tree diagram

Montessori Lessons:

Probability Problem Solving Cards (See Appendix); Small Group Experiments

POW (06-07): Week 7

SFAW 5-10, TE 2

DIS: L-16, pg. 31-32, 78

SFAW 5-11, TE 2

MSA Finish Line

Pages 108-111


Grade 4

Grade 5

Grade 6

Topic 5.B. Theoretical Probability

Topic 5.B. Theoretical Probability

Topic B. Theoretical Probability

5.B.1. Determine the probability of one simple event comprised of equally likely outcomes

Quarter

3


Quarter

3


Quarter

3

a. Express the probability as a fraction

Assessment limit: Use a sample space of no more than 6 outcomes

Montessori Lessons:

Probability Problem Solving Cards (See Appendix)

POW (06-07) Week: 26,30

SFAW 12-7, TE 4

DIS: l-12, pg. 23-24, 75

MSA Finish Line:

Pages 88-91

a. Make predictions and express the probability as a fraction

Assessment limit: Use a sample space of no more than 20 outcomes

Montessori Lessons:


SFAW 5-12, TE 2

Investigation from TE Page 258 J

MSA Finish Line

Pages 112-115

a. Express the probability of an event as a fraction.

Montessori Lessons:


Glencoe: 11-1, 11-2

b. Express the probability of an event as a decimal

Assessment limit: Use a sample space of 10, 20, 25, or 50 outcomes

Montessori Lessons:

Probability Problem Solving Cards (SeeAppendix); Small Group Experiments

Glencoe: 11-1, 11-2

MSA Finish Line

Pages 100-103


Grade 4

Grade 5

Grade 6

c. Express the probability of an event as a percent

Montessori Lessons:

Probability Problem Solving Cards (See Montessori Math Supplement); Small Group

Experiments

POW (06-07): Week 14

Glencoe: 11-1, 11-2


Probability and Area:

Glencoe: 11-4

Probability of Independent Events: Glencoe: 11-Problem Solving with Probability: Glencoe 11-5a


Grade 4

Grade 5

Grade 6

Topic 5.C. Experimental Probability



1. Analyze the results of a probability experiment

Quarter

3

a. Make predictions and express the experimental

HYPERLINK "javascript:openPopup('/share/vsc/glossary/mathematics/probability.html',200,500)" probability as a fraction, a decimal, or a percent

Assessment limit: Use no more than 30 results in the sample space

Montessori Lessons:

Probability Problem Solving Cards (See Montessori Math Supplement); Small Group Experiments

POW (06-07): Week 13

Glencoe: 11-1b, 11-3

MSA Finish Line

Pages 104-107

2. Conduct a probability experiment

Montessori Lessons:

Probability Problem Solving Cards (See Montessori Math Supplement); Small Group Experiments

3. Compare outcomes of theoretical probability with the results of experimental

HYPERLINK "javascript:openPopup('/share/vsc/glossary/mathematics/probability.html',200,500)" probability

Glencoe: 11-1b

4. Describe the difference between theoretical and experimental

HYPERLINK "javascript:openPopup('/share/vsc/glossary/mathematics/probability.html',200,500)" probability

Glencoe: 11-1b


QUARTER 3

REVIEW

MSA Finish Line

Pages 87, 92-94

QUARTER 3

REVIEW

MSA Finish Line

Pages 107, 116-118

QUARTER 3

REVIEW

MSA Finish Line

Pages 99, 108-110

VSC – Mathematics-Standard 6.0 Knowledge of Number Relationships and Computation/Arithmetic: Students will describe, represent, or apply numbers or their relationships or will estimate or compute using mental strategies, paper/pencil or technology.

Grade 4

Grade 5

Grade 6

Topic 6.A. Knowledge of Number and Place Value



6.A.1. Apply knowledge of whole numbers and place value

Quarter

1

6.A.1. Apply knowledge of fractions, decimals, and place value

Quarter 2 – 6.A.1.a,c,d

Quarter 3 – 6.A.1.b,e

6.A.1. Apply knowledge of rational numbers and place value

Quarter 1 – 6.A.1.a, b, e

Quarters 2 and 3– 6.A.1.c,d

a. Read, write, and represent whole numbers using symbols, words, and models

Assessment limit: Use whole numbers (0 - 1,000,000)

Montessori Lessons:

Golden Beads, Wooden Hierarchical Material, Long Bead Frame, Infinity Street, Golden Mat with Bead Bars

Albanesi Cards:

92.A-M

6.A-E

SFAW 1-1, TE 1

DIS: F-7, pg. 13-14, 85

a. Read, write, or represent fractions or mixed numbers using symbols, models, and words

Assessment limit: Use denominators that are factors of 24 and numbers (0 – 200)

Montessori Lessons:

Red Fraction Materials, Story Problem Cards, Student Created Models

Albanesi Cards:

104.A-F

1.A-B

SFAW 7-3, TE 3

DIS: H-15, pg. 29-30, 101

MSA Finish Line:

Pages 120-123

a. Read, write, and represent whole numbers

Assessment limit: Use exponential form with powers of 10 (0 - 100,000)

Montessori Lessons:

Powers of Two, Wooden Squaring Material, Scientific Notation ; Exponential Notation, Paper and Pencil Abstract Lessons

Albanesi Cards:

92.A-P; 6.A-1; 7.A

Glencoe: 4-1

MSA Finish Line:

Pages 1112-115


Exponential Form

Albanesi Cards:

POW (06-07): Week 29

Glencoe: 1-4

VSC – Mathematics-Standard 6.0 Knowledge of Number Relationships and Computation/Arithmetic: Students will describe, represent, or apply numbers or their relationships or will estimate or compute using mental strateg

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