LEARNING GUIDELINE



Brockton Public Schools

Mathematics

Curriculum, Pre-K-8

2006-2007

Brockton Public Schools

Mathematics Curriculum, Pre-K-8

2006-2007

Basan Nembirkow, Superintendent

Catherine F. Brine, Executive Director, Office of Teaching and Learning, K-6

John J. Jerome, Executive Director of Office of Teaching and Learning, 7-8

Linda A. Santry, Coordinator of Math and Science, K-8

Barbara M. Lee, Coordinator of Early Childhood Education

Mary H. Sundstrom, Department Head for Math, Pre-K-8

Mathematics Committee

|Linda Jordan |Math Coach–Central Office | |Courtney Vasquez |Teacher, Brookfield Elementary |

|Marguerite Masson |Math Coach–Central Office | |Richard Webb |Teacher, Brookfield Elementary |

|Maxine Richardson |Math Coach–Central Office | |Michael Sheehan |Teacher, Hancock Elementary |

|Glenn Young |Math Coach–Central Office | |Amy Simon |Teacher, Hancock Elementary |

|David Cournoyer |IRS, Arnone Elementary | |Joan White |Teacher, Hancock Elementary |

|Patricia Medis |IRS, Gilmore Elementary | |Michelle Bernstein |Teacher, Goddard Kindergarten |

|Kathleen Flaherty-Sites |IRS, Franklin Elementary | |Susan Silva |Teacher, Kennedy Elementary |

|Kathryn McMenamy |Teacher, East Junior High | |Joyce Meaden |Teacher, East Junior High |

|Jocelyn Young |Teacher, Angelo Elementary | |Joan Farrington |IRS, South Junior High |

|Violet LeMar |Ass’t. Princ., Arnone Elementary | |Judith Green |Teacher, South Junior High |

|Diane Tarbet |Teacher, Ashfield School | |Diane Behan |Teacher, North Junior High |

|Jennifer Giannaros |Teacher, Belmont Elementary | |Richard Castle |Teacher, West Junior High |

|Chanda Lavigne |Teacher, Brookfield Elementary | |Linda Monkevicz |Teacher, South Junior High |

| | | |Matthew Murphy |Teacher, South Junior High |

Table of Contents

|Mathematics Program Philosophy |1 | |Strand: Patterns, Relations, and Algebra |78 |

|Best Practices in Mathematics |3 | |Strand: Geometry |80 |

|Pre-Kindergarten Mathematics | | |Strand: Measurement |82 |

|Number Sense |5 | |Strand: Data Analysis, Statistics, and Probability |84 |

|Patterns & Relations |10 | |Grade 5 | |

|Shapes and Spatial Sense |12 | |Strand: Number Sense and Operations |88 |

|Measurement |15 | |Strand: Patterns, Relations, and Algebra |92 |

| Data Analysis, Statistics, and Probability |16 | |Strand: Geometry |94 |

|Kindergarten | | |Strand: Measurement |96 |

|Strand: Number Sense and Operations |18 | |Strand: Data Analysis, Statistics, and Probability |98 |

|Strand: Patterns, Relations, and Algebra |23 | |Grade 6 | |

|Strand: Geometry |26 | |Strand: Number Sense and Operations |100 |

|Strand: Measurement |29 | |Strand: Patterns, Relations, and Algebra |108 |

|Strand: Data Analysis, Statistics, and Probability |30 | |Strand: Geometry |111 |

|Grade 1 & 2 | | |Strand: Measurement |115 |

|Strand: Number Sense and Operations |32 | |Strand: Data Analysis, Statistics, and Probability |119 |

|Strand: Patterns, Relations, and Algebra |41 | |Grade 7 | |

|Strand: Geometry |47 | |Strand: Number Sense and Operations |122 |

|Strand: Measurement |51 | |Strand: Patterns, Relations, and Algebra |126 |

|Strand: Data Analysis, Statistics, and Probability |54 | |Strand: Geometry |129 |

|Grade 3 | | |Strand: Measurement |131 |

|Strand: Number Sense and Operations |59 | |Strand: Data Analysis, Statistics, and Probability |133 |

|Strand: Patterns, Relations, and Algebra |64 | |Grade 8 | |

|Strand: Geometry |66 | |Strand: Number Sense and Operations |135 |

|Strand: Measurement |68 | |Strand: Patterns, Relations, and Algebra |139 |

|Strand: Data Analysis, Statistics, and Probability |70 | |Strand: Geometry |146 |

|Grade 4 | | |Strand: Measurement |148 |

|Strand: Number Sense and Operations |72 | |Strand: Data Analysis, Statistics, and Probability |150 |

Program Philosophy

The Brockton Public Schools’ Mathematics Program, PreK-8, will provide all students access to the richness of mathematical and technological resources. Through hands-on learning, students will be able to apply mathematical principles to solve problems in their daily lives.

The program goals are to

• promote excellence in the teaching and learning of mathematics.

• implement the Massachusetts Mathematics Curriculum Framework.

• increase awareness and use of technology in the learning process.

• enhance systemic change in the school district by implementing methodologies and strategies to embrace all learning styles.

In mathematics, students concentrate on making connections and using principles of mathematics to communicate, reason, and solve problems. Students engage in projects that require them to apply number systems, operations, and forms in real-world contexts. The use of manipulatives and technology further supports student learning. Brockton’s Mathematics Program allows students to explore the world of numbers, algorithms, patterns, shapes, data, and spatial sense. Students engage in activities that require them to make sense of real-world data, use manipulatives as representative objects, conceptualize the symbolic value of numbers in various forms, perform operations with numbers, and articulate and justify solutions to problems. The program emphasizes the need for students to make connections and use mathematical principles to communicate, reason, and solve problems.

The Brockton Public Schools Mathematics Program, PreK-8, adopts the vision of the Massachusetts Mathematics Curriculum Framework that “all students in the Commonwealth will achieve mathematical power through problem solving, communication, reasoning, and connections.” The program also embraces the Framework’s Guiding Principles.

Guiding Principles

• Students will explore mathematical ideas in ways that maintain their enjoyment of and curiosity about mathematics and that help

them develop a depth of understanding. Students will also reflect on real world applications of mathematical principles.

• All students will have access to high quality mathematics programs.

• Mathematics learning is a lifelong process that begins and continues in the home and extends to school and community settings.

• Mathematics instruction will connect with other disciplines and move toward integration of mathematical domains.

• Students will work together in teams and groups to enhance mathematical learning, communicate effectively, and develop social and mathematical skills.

• Technology will be used as an essential tool for effective mathematics education.

• Mathematics assessment will monitor student performance, improve instruction, enhance learning, and encourage student self reflection.

Students as Active Learners

In order to encourage students to take an active role in their mathematics learning, teachers must establish an environment in which students can investigate and experiment with mathematics in authentic ways. Teachers will, therefore, provide students of all ages and learning styles a wide variety of models, materials, activities, demonstrations, games, investigations, interesting problems and conversations in the mathematical content being explored. Thus, students will spend daily-sustained time engaged in authentic mathematical activities. Students will work cooperatively to share ideas, solutions and strategies and confirm that there are multiple ways to solve problems. Learning Centers will be set up accordingly. An appreciation of the importance of learning from one another and the importance of reflection, guided by the teacher, will enhance the learning process.

Instructional Groupings

In order to achieve the goals of the mathematics curriculum, a multiplicity of grouping strategies—including whole group, small group and individual work—must be utilized. Teachers will use a variety of grouping practices, including cooperative and flexible groupings, to meet the differences in their students’ learning styles and rates. The reconfiguration of groups should be based on teachers’ ongoing assessment of students’ needs. Learning Centers will be designed to meet the needs of diverse learners as well as facilitate the mathematics program.

Importance of Manipulatives

Active learning necessitates the extensive and thoughtful use of physical materials to foster the development of abstract ideas, encouraging less teacher direction and more student involvement. Manipulatives and activity-based lessons are necessary to address the different learning styles of our students. Their use will help connect mathematics to the real world. All students, PreK-8, should have frequent, ongoing opportunities to use manipulatives to develop an understanding of mathematical concepts and content.

Assessment and Evaluation

Assessment and evaluation are an integral part of the teaching of mathematics and, therefore, should be a daily occurrence within the mathematics classroom. Assessment and evaluation determine instructional decisions and must incorporate teacher observation of the students at work, both individually and in groups. The classroom culture should reinforce the belief that errors are opportunities for learning and that students should be encouraged to take risks without fear of embarrassment or failure.

Traditionally, quizzes and tests have been administered at regular intervals to ascertain student mastery. Today’s battery of assessment devices will also include the teacher’s daily observation of student performance. Teachers must look at the strategies students use to solve problems as well as the solutions they generate. Teachers will also develop rubrics and other assessment techniques and tools which are based on current research, the National Council of Teachers of Mathematics Standards and the Massachusetts Mathematics Curriculum Framework. Additional student assessments include interviews, daily journal writing, other forms of writing about mathematics, student/teacher conferencing, student self assessment and work samples.

Technology

The Brockton Public Schools’ Five Year Plan for Instructional Technology calls for the phasing in of instructional learning systems and software in all schools. Initially, each student will be assessed to determine an accurate instructional level. Thereafter, students will work on their individualized mathematics programs. Research indicates that students will show significant gain in specific skill areas when the software is used appropriately and consistently. Documentation of student progress provided through this software thus becomes part of each student’s ongoing assessment as well as that of the Brockton Public Schools’ Mathematics Program.

Calculators will also be used in the mathematics program. Neither calculators nor computers replace the need to learn basic facts, to compute mentally or to do paper and pencil computation. Rather, they enhance the learning process and allow the student the opportunity to use technology intelligently to become a confident and knowledgeable decision maker.

Best Practices in Mathematics

Teachers at each grade level, K-6, will begin each day with The Every Day Counts calendar program from Houghton Mifflin.

In grades 7 and 8 each mathematics class will begin with a dialogue, which will bring the lesson of the day into a real life situation. The core program must be utilized to ensure that prior knowledge, developmental and ongoing assessment options are included in each lesson. In addition, writing about mathematical processes and the use of hands-on, activity-based strategies should be incorporated into lessons to ensure that all learning styles are addressed.

Each daily K-8 mathematics lesson should include the following components:

• objective(s)

• a stated purpose for achieving the objective

• core program materials with appropriate page numbers

• other materials/manipulatives

• authentic and engaging independent/group work

• vocabulary/reading/writing strategies

• assessment, when applicable

Students will

• engage in authentic mathematics activities daily.

• write daily.

• participate in small group discussions several times a week.

• participate in cooperative learning several times a week.

• engage in group problem solving, negotiation and consensus development several times a week.

• engage in solving multi-step problems several times a week.

• engage in “hands on” learning activities (e.g., lab assignments, manipulatives) several times a week.

• respond to open-ended and open response questions several times a week.

• participate in various forms of assessment weekly.

• use calculators as part of lessons several times a month.

• take multiple choice/short answer tests several times a month.

• work on group projects monthly.

• work on share projects with the rest of the school several times a year.

• make oral presentations.

• use computers and other technology as part of lessons.

Teachers will

• directly teach and model mathematics strategies daily.

• engage students in authentic mathematics activities daily.

• engage students in solving multi-step problems.

• function as coach and facilitator daily.

• emphasize the practical real world application of course materials daily.

• use interdisciplinary teaching materials.

• use alternative, performance based assessments weekly.

• use rubrics as part of all assessments.

• use portfolios of students’ work as indicators of student success several times a year.

• plan and implement strategies to increase parent involvement several times a year.

|LEARNING GUIDELINE |STATE STANDARD |PRE-K |LEARNING EXPERIENCE |RESOURCES |

| | |Progress Indicators | | |

|2. Connect many |K.N.2 |Create sets of objects to |Arrange and count a variety of different kinds of objects to |Everyday Counts: September –June |

|kinds/quantities of concrete |Match quantities up to at least|repre-sent quantities from 1-5. |explore the consistency of quantities (e.g., to build |Mathematics Their Way: 166-178 |

|objects and actions to numbers.|10 with numerals and words. | |understanding of what "3" looks like, whether you are |Workjobs: 130-179 |

| | |Recognize numeric symbols for |counting blocks, beads or pinecones). | |

| | |quantities from 1-5. | | |

| | | |Participate in finger plays and action rhymes that associate | |

| | | |number concepts with concrete actions (e.g., Five Little |LAP-D Cognitive Counting: 13, 14 |

| | | |Monkeys Jumping on the Bed). |Workjobs: 130-179 |

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| | | |Use concrete objects, actions, or drawings to represent | |

| | | |quantities (e.g., jump two times; stack four unit blocks; | |

| | | |string three beads, hold up two fingers, get three blocks on | |

| | | |request). |LAP-D Cognitive Counting: 15 |

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|3. Use positional |K.N.3 |Use ordinal numbers 1st, 2nd, 3rd|Place concrete objects such as nesting or stacking cups, |Everyday Counts: January - June |

|language and ordinal numbers |Identify position of objects in|verbally to identify position. |boxes, or dolls in a row and identify their position as |Young Children in Action: 222-224 |

|(first, second, third) in |sequences (e.g., first, second)| |first, second, third. | |

|everyday activities. |up to fifth. | | | |

| | | |Arrange materials in order (seriate) from small to large; |Young Children in Action: 222-224 |

| | | |short to long, etc | |

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| | | |Use ordinal numbers and positional words (e.g., before/after;|Everyday Counts January - June |

| | | |first, second, third) to describe the order of daily |Young Children in Action: 222-224 |

| | | |activities. | |

| | | | |Workjobs: 21 |

| | | |Arrange illustrations from a story or photographs of class | |

| | | |events or daily routines in sequence. | |

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|4. Use concrete |K.N.4 |Order the numerals |Distribute and compare concrete objects in meaningful ways |Everyday Counts: November, December, January, March, |

|objects to solve simple |Compare sets of up to at least |1-5. |(e.g., which bucket has more rocks in it; how many more |June |

|addition and subtraction |10 concrete objects using | |napkins are needed for everyone at the table). |Mathematics Their Way: 116-118 |

|problems using comparative |appropriate language (e.g., |Determine whether a group of | |LAP-D Cognitive Concepts 10, 20, 26, 27, 29 |

|language (more than, fewer |none, more than, fewer than, |objects being changed is getting |Sing songs and do finger plays that involve adding and taking| |

|than, same number of). |some number of, one more than) |“more” or “less”. |away (e.g., Two Little Blackbirds). |LAP-D Cognitive Counting 10 |

| |and order numbers. | | |Young Children in Action: 230-232 |

| | | |Use pictorial recipes and discuss how many more cups of cups | |

| |K.N.7 | |of flour need to be added to the cookie dough. |Mathematics Their Way: 116-118 |

| |Use objects and drawings to | | | |

| |model and solve related | |Make pictorial menus or shopping lists; identify the amount | |

| |addition and subtraction | |of money needed to "buy products" in various play areas. | |

| |problems to ten. | | |Mathematics Their Way: 116-118 |

| | | |Figure out how many blocks they have altogether when they | |

| | | |join two sets or how many blocks are needed to make two | |

| | | |towers the same size. | |

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| | | |See and discuss meaningful examples of the concept of "none" |Mathematics Their Way: 116-118 |

| | | |(e.g., you have two cookies left, I have none). | |

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| | | | |Mathematics Their Way: 116-118 |

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|5. Observe and |K.N.5 |Identify if something cut into |Cut food into two equal parts for snacks. |Everyday Counts: November |

|manipulate concrete examples of|Understand the concepts of |two pieces has created equal | | |

|whole and half. |whole and half. |parts or “fair share”. |Match whole objects to similar objects that have been broken | |

| | | |or cut in half. |Everyday Counts: November |

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| | | |Divide a set of objects into two equal parts (e.g., two for | |

| | | |you and two for me). |Everyday Counts: November |

|6. Examine, |K.N.6 |Identify pennies and count them |Create a grocery store or shoe store in the dramatic play |Everyday Counts: September – February |

|manipulate, and identify |Identify U.S. coins by name. |by ones, (1-5). |area and use play money to pay for items. | |

|familiar U.S. coins (penny, | | | | |

|nickel, dime, quarter) in play | |Match and label “penny”, |Listen to age appropriate books about money and identify the | |

|activities. | |“nickel”, “dime”, and “quarter”. |coins. |Everyday Counts: September – February |

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| | |Use the word “add” as a synonym |Separate coins by color and size. | |

| | |for “getting more”. | | |

| | | | |Everyday Counts: September - February |

| | |Identify the “+” sign to indicate| | |

| | |“getting more”. | | |

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| | |Draw a model to represent simple | | |

| | |addition problems to 5. | | |

|LEARNING GUIDELINE |STATE STANDARD |PRE-K |LEARNING EXPERIENCE |RESOURCES |

| | |Progress Indicators | | |

|8. Sort, categorize, |K.P.2 |Sort and classify objects, giving|Sort parquetry blocks or string beads by size, shape,|Everyday Counts: December - June |

|or classify objects by more |Sort and classify objects by |reasons why they are alike or |color, or texture (e.g., big circles/small circles; |Mathematics Their Way: 60-87 |

|than one attribute. |color, shape, size, number, and|different. |blue squares/blue circles; big yellow squares/ small |Young Children in Action: 200-206 |

| |other properties. | |yellow squares). | |

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|9. Recognize, |K.P.3 |Reproduce and extend a color, |Repeat clapping or drumbeat patterns. |Everyday Counts: October – June |

|describe, reproduce, extend, |Identify, reproduce, describe, |rhythmic, shape, number, and | | |

|create, and compare repeating |extend, and create color, |letter simple repeating pattern |Use pattern cards to reproduce patterns with concrete| |

|patterns of concrete materials.|rhythmic, shape, number, and |(ABAB). |objects such as beads, colored cubes, mosaic tiles |Mathematics Their Way: 21-2-42 |

| |letter repeating patterns with | |with pattern cards. |LAP-D Cognitive Matching 7, 10 |

| |simple attributes (e.g., | | | |

| |ABABAB). | |Find patterns in their everyday environment (plaid, | |

| | | |stripes, checks on clothing, floors or walls). | |

| | | | |Everyday Counts: November, December, April, May – June |

| | | |Repeat a pattern/sequence in a variety of ways (e.g.,| |

| | | |an ABAB pattern with stickers, blocks, or stamps). | |

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| | | |Manipulate objects in and out of patterns. |Everyday Counts: November-June |

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| | | |recognize and predict word patterns in familiar | |

| | | |rhythms, music or stories. | |

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| | | |Note: The ability to recognize and create patterns |Everyday Counts: February, April, June |

| | | |generally develops over time. The ability to | |

| | | |distinguish multiple attributes also grows over time.| |

| | | | |Everyday Counts: November - February |

|LEARNING GUIDELINE |STATE STANDARD |PRE-K |LEARNING EXPERIENCE |RESOURCES |

| | |Progress Indicators | | |

|11. Explore and |K. G. 4 |Identify positions of objects in |Illustrate position and relative distance among objects/ |Everyday Counts: September – June |

|identify space, |Identify positions of objects |space and use appropriate |locations using classroom materials or outdoor equipment |Everyday Counts: LAP-D Cognitive Counting 2, 9 |

|direction, |in space, and use appropriate |language (e.g., inside, outside, |(e.g., up, down, high, low, above, below, in front of, |LAP-D Cognitive Matching 11, 14 |

|movement, |language (e.g., beside, inside,|under, over, next to) to describe|behind, beside, near, far, next to, apart, together). | |

|relative position, |next to, close to, above, |and compare their |Move their bodies in space by | |

|and size using |below, apart) to describe and |relative positions. |following verbal instructions through | |

|body movement |compare their relative | |an obstacle course (e.g., crawl under |Young Children in Action: 248-261 |

|and concrete |positions. | |the table, walk around the jungle | |

|objects. | | |gym; jump over the block). | |

| | | |Follow or use directional language related to daily | |

| | | |routines and activities or in dance recordings (e.g., "Put | |

| | | |your hands up, down, over your head."). |LAP-D Cognitive Counting 2, 9 |

| | | |Locate objects based on directional words (e.g., it's next | |

| | | |to the ball; under the basket). | |

| | | |Play with puzzles of increasing complexity as skills | |

| | | |develop. | |

| | | |Figure out how much space is needed for a task (e.g., to |LAP-D Cognitive Counting 2, 9 |

| | | |build a construction using large interlocking panels, or | |

| | | |whether two children can fit inside a cardboard box). | |

| | | |Identify shapes in different orientations (a triangle is |Young Children in Action: 248-261 |

| | | |still a triangle even though it's turned in different | |

| | | |directions). |Young Children in Action: 248-261 |

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| | | | |Young Children in Action: 248-261 |

|12. Listen to and use |K.M.1 |Use words that describe amounts |Compare and describe objects according to a single |Everyday Counts March – Jun |

|comparative words to describe |Recognize and compare the |appropriately, e.g., longer, |attribute (e.g., which is bigger, smaller, taller, longer, |Mathematics Their Way: 116-139 |

|the relationships of objects to|attributes of length, |taller, shorter, same length, |shorter, same length, wider, narrower, thicker, thinner, |LAP-D Cognitive Counting 11 |

|one another. |volume/capacity, weight, area, |heavier, lighter, same weight, |deeper, shallower, lighter, heavier, holds less, or holds |Young Children in Action: 135-136 |

| |and time using appropriate |holds more, holds, less, holds |the same amount). | |

| |language, e.g., longer, taller,|the same amount. | | |

| |shorter, same length, heavier, | |Measure sand, water, or rice using variety of containers | |

| |lighter, same weight, holds | |and compare the amounts. | |

| |more, holds less, holds the | | |Mathematics Their Way: 116-139 |

| |same amount. | |Make objects of play dough and compare their size. | |

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| | | |Build structures with blocks and compare their length or | |

| | | |height. |Young Children in Action: 135-136 |

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| | | |String beads and compare the length of two necklaces. | |

| | | | |Young Children in Action: 135-136 |

| | | |Use simple balance scales to compare the weight of | |

| | | |classroom materials. | |

| | | | |Young Children in Action: 135-136 |

| | | |Compare the size of various everyday objects (e.g., put | |

| | | |various people's shoes side by side to see which is | |

| | | |longest. |Young Children in Action: 135-136 |

| | | |Note: Younger preschool children should focus on a single | |

| | | |attribute at a time. | |

| | | | |Young Children in Action: 135-136 |

|LEARNING GUIDELINE |STATE STANDARD |PRE-K |LEARNING EXPERIENCE |RESOURCES |

| | |Progress Indicators | | |

|14. Use nonstandard |K.M.3 |Use non-standard units to measure|Measure the circumference of a pumpkin or watermelon using |Everyday Counts: March – June |

|units to measure length, weight, and |Use non-standard units to |length, area, weight, and |a piece of string. | |

|amount of content in familiar |measure length, area, weight, |capacity. | | |

|objects. |and capacity. | |Measure the length of a table using their hands. | |

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| | | |Measure the width of the sandbox with footsteps. | |

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| | | |Measure a child's height using large cardboard blocks. | |

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| | | |Compare the length of two play dough snakes or the height | |

| | | |of two block towers using their hands. | |

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| | | |Compare the capacity of two different containers in the | |

| | | |sand or water table. | |

|LEARNING GUIDELINE |STATE STANDARD |PRE-K |LEARNING EXPERIENCE |RESOURCES |

| | |Progress Indicators | | |

Pre Kindergarten Curriculum Resources

Every Day Counts: Every Day in Pre-K Math. 2002/Great Source Education Group.

LAP-D (Learning Accomplishment Profile) Planning Cards 1996/Kaplan Early Learning Company

Mathematics Their Way Barrata-Lorton, Mary. 1995/Dale Seymour Publications

Workjobs II: Number Activities for Early Childhood. Barrata-Lorton, Mary 1987/Pearson Learning.

Young Children in Action: A Manual for Preschool Educators. Hohman, Mary. 1983/High Scope Press.

|Additional Resources |

|The following are Pre K – 8 Resources to be used to supplement the core programs where needed |

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|Question of the Day, Lakeshore Publishing – K only |

|Every Day Counts Pattern Games – K-3 only – Great Source |

|Games for Number Sense – Great Source – K Only |

|Playing Math Games – Teacher Resource Center – K Only |

|Developing Number Concepts: Counting, Comparing and Patterns – Dale Seymour Publications – K Only |

|Super Source K-8 – All Grades - ETA Cuisenaire |

|Base Ten Blocks |

|Color Tiles |

|Geoboards |

|Pattern Blocks |

|Snap Cubes |

|Tangrams |

|Hundred Chart – ETA Cuisenaire |

|Analog Clocks – ETA Cuisenaire |

|Equa Beam – ETA Cuisenaire |

|Hands-On Equations – ETA Cuisenaire |

|Fraction Strips – ETA Cuisenaire |

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|Math to Learn – Grades 1&2 – Great Source Educational Group |

|Math to Know – Grades 3&4 – Great Source Educational Group |

|Math at Hand – Grades 5&6 – Great Source Educational Group |

|Math on Call – Grades 6-8 – Great Source Educational Group |

|Algebra to Go – Grade 8 – Great Source Educational Group |

|Strand: Number Sense and Operations |

|DOE |State Standard |Pre-Kindergarten |Kindergarten |Resources |

|Standard number | |Progress Indicators |Progress Indicators | |

|K.N.2 |Match quantities up to at least 10 with |Create sets of objects to represent |Create sets of objects to represent |Mathematical Thinking in Kindergarten |

| |numerals and words. |quantities from 1-5. |quantities from 0-10. |Investigation 1, 4-23 |

| | | | |Investigation 2, 26-39 |

| | |Recognize numeric symbols for quantities |Recognize and write numeric symbols for |Collecting, Counting, and Measuring |

| | |from 1-5. |quantities from 0-10. |Investigation 1, 2-21 |

| | | | |Investigation 2, 22-35 |

| | | |Represent an empty set with the numeral |Investigation 3, 36-51 |

| | | |“0”. |Investigation 4, 52-65 |

| | | | |Investigation 5, 66-77 |

| | | | |Investigation 6, 78-97 |

| | | | |Counting Ourselves and Others |

| | | | |Investigation 1, 2-35 |

| | | | |Investigation 4, 76-91 |

| | | | |How Many In All? |

| | | | |Investigation 1, 2-27 |

| | | | |Every Day Counts |

| | | | |September-June |

| | | | |Digi-Blocks |

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| | | | |Supplement with: |

| | | | |- Super Source – Color Tiles |

| | | | |Creating Patterns, p. 22 |

| | | | |- Developing Number Sense Book 1, |

| | | | |pp. 50-52 |

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|K.N.3 |Identify position of objects in sequences |Use ordinal numbers 1st, 2nd, 3rd verbally|Use ordinal numbers, 1st, 2nd, 3rd, 4th, |Collecting, Counting, and Measuring |

| |(e.g., first, second) up to fifth. |to identify position. |and 5th verbally to identify positions. |Investigation 5, 66-77 |

| | | | |Investigation 6, 78-97 |

| | |Order the numerals 1-5. |Order the numerals 0-10. |Every Day Counts |

| | | | |September-June |

| | | | |Digi-Blocks |

| | | | | |

| | | | |Supplement with: |

| | | | |- Super Source – Color Tiles |

| | | | |Line Up Four, pg. 62 |

| | | | |- Super Source – Snap Cubes |

| | | | |Make A Copy, pg. 38 |

|K.N.4 |Compare sets of up to at least 10 concrete|Determine whether a group of objects being|Determine whether a group of objects being|Mathematical Thinking in Kindergarten |

| |objects using appropriate language (e.g., |changed is getting “more” or “less”. |changed is getting “more,” “less” or |Investigation 4, 54-60 |

| |none, more than, fewer than, some number | |“staying the same.” |Collecting, Counting, and Measuring |

| |of, one more than) and order numbers. | | |Investigation 4, 52-65 |

| | | |Represent two equal sets containing up to |Investigation 5, 66-77 |

| | | |10. |Investigation 6, 78-97; |

| | | | |Every Day Counts |

| | | |Compare sets of at least 10 objects using |September-June |

| | | |appropriate language. |Digi-Blocks |

| | | | | |

| | | | |Supplement with: |

| | | | |- Developing Number Concepts Book 1, |

| | | | |pp. 45-46, 48 |

| | | | | |

| | | | | |

| | | | | |

|K.N.5 |Understand the concepts of whole and half.|Identify if something cut into two pieces |Identify if something cut in 2 pieces has |May be used in conjunction with the Making Shapes and Building |

| | |has created equal parts or “fair share”. |been fairly cut in half. |Blocks |

| | | | |Unit |

| | | |Tell or show how to cut something equally |Every Day Counts |

| | | |in half. |None |

| | | | | |

| | | | |Supplement with: |

| | | | |- Super Source – Color Tiles |

| | | | |Half and Half, pg. 46 |

| | | | |- Super Source – Snap Cubes |

| | | | |Make A Copy, pg. 38 |

|K.N.6 |Identify U.S. coins by name. |Identify pennies and count them by ones, |Identify U.S. coins by name. |See Grade 1 |

| | |(1-5) | |Number Games and Story Problems |

| | | |Match coins to their correct value (i.e. a|Investigation 2, p. 69. |

| | |Match and label “penny”, “nickel”, “dime”,|nickel = 5 cents) |Every Day Counts |

| | |and “quarter”. | |February-April |

| | | | | |

| | | | |Supplement with: |

| | | | |- Games for Number Sense pp. S27-S28 |

| | | | |- Math By All Means (Gr. 1 & 2), |

| | | | |Menu Activities |

| | | | | |

| | | | | |

| | | | | |

| | | | | |

| | | | | |

| | | | | |

| | | | | |

|K.N.7 |Use objects and drawings to model and |Use the word “add” as a synonym for |Interpret number sentences for addition |How Many In All? |

| |solve related addition and subtraction |“getting more”. |and subtraction problems using numbers |Investigation 2, 28-51 |

| |problems to ten. | |0-10 with manipulatives (e.g., with number|Investigation 3, 52-73 |

| | |Identify the “+” sign to indicate “getting|tiles, counters). |Investigation 4, 74-95 |

| | |more”. | |Every Day Counts |

| | | |Create and interpret simple stories that |February-April |

| | |Draw a model to represent simple addition |can be solved using addition or |Digi-Blocks |

| | |problems to 5. |subtraction. | |

| | | | | |

| | | |Use objects and drawings to model and | |

| | | |solve related addition and subtraction | |

| | | |problems to ten. |Supplement with: |

| | | | |- Games for Number Sense – Domino |

| | | | |sums – pg. 57 |

| | | | |- Super Source – Color Tiles |

| | | | |Very Busy Animals, pg. 78 |

|K.N.8 |Estimate the number of objects in a group |Put sets of objects in order from least to|Use the strategy of “guess and check” to |Counting Ourselves and Others Investigation 1, 2-35 |

| |and verify results. |greatest, shortest to longest, etc., using|estimate with like objects from 0-10 and |Every Day Counts |

| | |visual clues. |verify results. |None |

| | | | |Digi-Blocks |

| | | | | |

| | | | |Supplement with: |

| | | | |- Developing Number Concepts |

| | | | |Book 1, pg. 62 |

|Strand: Patterns, Relations, and Algebra |

|DOE |State Standard |Pre-Kindergarten |Kindergarten |Resources |

|Standard number | |Progress Indicators |Progress Indicators | |

|K.P.2 |Sort and classify objects by color, shape,|Sort objects by matching color, shape, and|Sort and classify objects, giving reasons |Mathematical Thinking in Kindergarten |

| |size, number, and other properties. |size. |why they are alike or different. |Investigation 1, 4-23 |

| | | | |Pattern Trains and Hopscotch Paths |

| | | | |Investigation 1, 2-23 |

| | | | |Counting Ourselves and Others |

| | | | |Investigation 1, 2-35 |

| | | | |Investigation 2, 36-55 |

| | | | |Investigation 3, 56-75 |

| | | | |Every Day Counts |

| | | | |September-June |

| | | | |Digi-Blocks |

| | | | | |

| | | | | |

| | | | | |

| | | | |Supplement with: |

| | | | |- Developing Number Concepts |

| | | | |Book 1, pg. 67 |

| | | | |- Games and Number Sense, pp. 46-47 |

|K.P.3 |Identify, reproduce, describe, extend, and|Reproduce and extend a color, rhythmic, |Identify, reproduce, describe, extend, and|Mathematical Thinking in Kindergarten |

| |create color, rhythmic, shape, number, and|shape, number, and letter simple repeating|create color, rhythmic, shape, number, and|Investigation 1, 4-23 |

| |letter repeating patterns with simple |pattern (ABAB). |letter repeating patterns with simple |Pattern Trains and Hopscotch Paths |

| |attributes (e.g., ABABAB). | |attributes (e.g., ABABAB). |Investigation 1, 2-23 |

| | | | |Counting Ourselves and Others |

| | | | |Investigation 1, 2-35 |

| | | | |Investigation 2, 36-55 |

| | | | |Investigation 3, 56-75 |

| | | | |Every Day Counts |

| | | | |September-June |

| | | | |Digi-Blocks |

| | | | | |

| | | | |Supplement with: |

| | | | |- Super Source, Pattern Blocks, Antwalks |

| | | | |p.18, Sping to Win p.88, Who Caught |

| | | | |the Biggest Fish? p.86 |

| | | | |- Developing MathConcepts |

| | | | |Book 1, pg. 91-124 |

| | | | |- Games and Number Sense, pp. 46-47 |

| | | | | |

| | | | | |

| | | | | |

| | | | | |

| | | | | |

|K.P.4 |Count by fives and tens at least up to 50.|Count by tens to 50. |Count by fives and tens at least up to 50.|Mathematical Thinking in Kindergarten |

| | | | |Investigation 1, 4-23; |

| | | | |Pattern Trains and Hopscotch Paths |

| | | | |Investigation 1, 2-23 |

| | | | |Counting Ourselves and Others |

| | | | | |

| | | | |Supplement with: |

| | | | |- Games for Number Sense, p.26-27,88-89 |

| | | | |Investigation 1, 2-35 |

| | | | |Investigation 2, 36-55 |

| | | | |Investigation 3, 56-75 |

| | | | |Every Day Counts |

| | | | |November, February, March May/June Digi-Blocks |

|Strand: Geometry |

|DOE |State Standard |Pre-Kindergarten |Kindergarten |Resources |

|Standard number | |Progress Indicators |Progress Indicators | |

|K.G.2 |Describe the attributes of two-dimensional|Count the number of sides and corners on a|Describe the attributes of two-dimensional|Mathematical Thinking in Kindergarten |

| |shapes (e.g., number of sides, number of |triangle, square, and rectangle. |shapes (e.g., number of sides, number of |Investigation 1, 4-23 |

| |corners). | |corners). |Making Shapes and Building Blocks |

| | | | |Investigation 1, 2-25 |

| | | | |Investigation 2, 26-37 |

| | | | |Investigation 3, 38-59 |

| | | | |Investigation 4, 60-81 |

| | | | |Every Day Counts |

| | | | |September, March, April |

| | | | |Digi-Blocks |

| | | | | |

| | | | |Supplement with: |

| | | | |- Super Source – Geoboards |

| | | | |Four in a Row, p. 30 |

| | | | | |

|K.G.3 |Name and compare three-dimensional shapes.|Match and sort three-dimensional shapes. |Name and compare three-dimensional shapes |Mathematical Thinking in Kindergarten |

| | | |(e.g., sphere, cube). |Investigation 1, 4-23 |

| | | | |Making Shapes and Building Blocks |

| | | | |Investigation 1, 2-25 |

| | | | |Investigation 2, 26-37 |

| | | | |Investigation 3, 38-59 |

| | | | |Investigation 4, 60-81 |

| | | | |Every Day Counts |

| | | | |September, December, May/June |

| | | | |Digi-Blocks |

| | | | | |

| | | | |Supplement with: |

| | | | |- Super Source – Geoboards |

| | | | |Farm Fences, p. 26 |

| | | | | |

|K.G.4 |Identify positions of objects in space, |Identify positions of objects in space and|Identify positions of objects in space, |Mathematical Thinking in Kindergarten |

| |and use appropriate language (e.g., |use appropriate language (e.g., inside, |and use appropriate language (e.g., |Investigation 1, 4-23 |

| |beside, inside, next to, close to, above, |outside, under, over, next to) to describe|beside, inside, next to, close to, above, |Making Shapes and Building Blocks |

| |below, apart) to describe and compare |and compare their relative positions. |below, apart) to describe and compare |Investigation 1, 2-25 |

| |their relative positions. | |their relative positions. |Investigation 2, 26-37 |

| | | |See Math Frameworks, Nov. 2000, p. 37. |Investigation 3, 38-59 |

| | | | |Investigation 4, 60-81 |

| | | | |Every Day Counts |

| | | | |None |

| | | | |Digi-Blocks |

| | | | | |

| | | | |Supplement with: |

| | | | |- Super Source – Geoboards |

| | | | |Inside, Outside, p. 42 |

|Strand: Measurement |

|DOE |State Standard |Pre-Kindergarten |Kindergarten |Resources |

|Standard number | |Progress Indicators |Progress Indicators | |

|K.M.2 |Make and use estimates of measurements |Demonstrate a strategy. |Make and use estimates of measurements |Collecting, Counting, and Measuring |

| |from everyday experiences. | |from everyday experiences. |Investigation 3, 36-51 |

| | | | |How Many In All? |

| | | | |Investigation 1, 2-27; |

| | | | |Every Day Counts |

| | | | |November, December, January |

| | | | |Digi-Blocks |

| | | | | |

| | | | |Supplement with: |

| | | | |- Super Source – Shape Cubes |

| | | | |How Long Is It? p. 30 |

| | | | |Puzzles, p. 54 |

| | | | |- Super Source – Geoboards |

| | | | |Tell Me About That p. 70 |

|K.M.3 |Use non-standard units to measure length, |Use non-standard units to measure length, |Use non-standard units to measure length, |Collecting, Counting, and Measuring |

| |area, weight, and capacity. |area, weight, and capacity. |area, weight, and capacity. |Investigation 3, 36-51 |

| | | | |How Many In All? |

| | | | |Investigation 1, 2-27 |

| | | | |Every Day Counts |

| | | | |November-January |

| | | | |Digi-Blocks |

| | | | | |

| | | | |Supplement with: |

| | | | |- Super Source – Geoboards |

| | | | |From A to Z p. 34 |

| | | | | |

| | | | | |

| | | | | |

|Strand: Data Analysis, Statistics, and Probability |

|DOE |State Standard |Pre-Kindergarten |Kindergarten |Resources |

|Standard number | |Progress Indicators |Progress Indicators | |

|Additional Resources |

|The following are Pre K – 8 Resources to be used to supplement the core programs where needed |

| |

|Question of the Day, Lakeshore Publishing – K only |

|Every Day Counts Pattern Games – K-3 only – Great Source |

|Games for Number Sense – Great Source – K Only |

|Playing Math Games – Teacher Resource Center – K Only |

|Developing Number Concepts: Counting, Comparing and Patterns – Dale Seymour Publications – K Only |

|Super Source K-8 – All Grades - ETA Cuisenaire |

|Base Ten Blocks |

|Color Tiles |

|Geoboards |

|Pattern Blocks |

|Snap Cubes |

|Tangrams |

|Hundred Chart – ETA Cuisenaire |

|Analog Clocks – ETA Cuisenaire |

|Equa Beam – ETA Cuisenaire |

|Hands-On Equations – ETA Cuisenaire |

|Fraction Strips – ETA Cuisenaire |

| |

|Math to Learn – Grades 1&2 – Great Source Educational Group |

|Math to Know – Grades 3&4 – Great Source Educational Group |

|Math at Hand – Grades 5&6 – Great Source Educational Group |

|Math on Call – Grades 6-8 – Great Source Educational Group |

|Algebra to Go – Grade 8 – Great Source Educational Group |

|Strand: Number Sense and Operations |

|DOE |State Standard |Grade 1 |Grade 2 |Resources |

|Standard Number | |Progress Indicators |Progress Indicators | |

|2.N.2 |Identify and distinguish among multiple |Distinguish between cardinal (“there are |Identify and distinguish among multiple |Grade 1 |

| |uses of numbers including cardinal (to |2”) and ordinal (“it’s the second one”) |uses of numbers including cardinal (to |Mathematical Thinking at Grade 1 Investigation 2, 24-59 |

| |tell how many) and ordinal (to tell which |numbers verbally. |tell how many, 1-1000) and ordinal (to |Bigger, Taller, Heavier, Smaller |

| |one in an ordered list), and numbers as | |tell which one in an ordered list, to |Investigation 3, 60-81 |

| |labels and as measurement. |Use ordinal numbers |1000th), and numbers as labels and as |Every Day Counts |

| | |(1st-10th). |measurement. |Sept., Oct., Nov., Dec., Feb., March, April, May, June |

| | | | |Digi-Blocks |

| | |Measure common objects using |Use a standard ruler to measure to nearest|CCC Lab – Ordinal Numbers |

| | |non-standards units of measure. |half-inch. |Grade 2 |

| | | | |Mathematical Thinking at Grade 2 |

| | |Measure common objects using a ruler to | |Investigation 1, 2-19 |

| | |nearest inch. | |Investigation 2, 20-51 |

| | | | |Every Day Counts |

| | | | |All months |

| | | | |Digi-Blocks |

| | | | | |

| | | | | |

| | | | | |

| | | | | |

| | | | | |

| | | | | |

| | | | | |

| | | | | |

| | | | | |

| | | | | |

|2.N.3 |Identify and represent common fractions |Identify fair shares in halves, thirds |Identify and represent common fractions |Grade 1 |

| |(1/2, 1/3, 1/4) as parts of wholes, parts |and fourths. |(1/2 to 7/8) as parts of wholes, parts of |Additional resources needed |

| |of groups, and numbers on the number line.| |groups, and numbers on the number line. |Every Day Counts |

| | |Describe one unit of a fraction as | |Feb. |

| | |“one-half”, “one-third” or “one-fourth” |Use the terms “numerator” or “denominator”|CCC Lab |

| | |(1/2, 1/3, 1/4). |correctly. |- Super Source – Pattern Blocks |

| | | | | |

| | | |Add simple fractions with like |Grade 2 |

| | | |denominators using manipulatives |Shapes, Halves, and Symmetry |

| | | |(1/4 + 2/4 +3/4). |Investigation 3, 72-93 |

| | | | |Every Day Counts |

| | | | |Oct., March |

|2.N.4 |Compare whole numbers using terms and |Compare whole numbers to 100 using terms |Read, write, compare |Grade 1 |

| |symbols (e.g., less than, equal to, |and symbols (e.g. less than, equal to, |(>, ................
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