Hawken School - Mathematics Curriculum Map Concept

HAWKEN ACADEMIC PROFILE SERIES

I Mathematics: Kindergarten - Grade 5

No problem can be solved until it is understood.

Your guide to the philosophy, highlights, curriculum and content of the Hawken School Mathematics Program Kindergarten-Grade 5

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“THAT THE BETTER SELF SHALL PREVAIL AND EACH GENERATION INTRODUCE ITS SUCCESSOR TO A HIGHER PLANE OF LIFE.” - James A. Hawken Founder and Headmaster, 1915-1924

AN INTRODUCTION TO HAWKEN SCHOOL

Purpose, Promise and Principles.

When Hawken School was established in 1915 by James A. Hawken, his foremost purpose was to prepare his students for the real world. As Hawken nears its centennial mark as a school, we find ourselves in a greatly changed world; however our commitment to forward-focused education has withstood the test of time.

At Hawken, students are taught and encouraged to think creatively and critically, to explore their passions and interests, and to voice their opinions as members of a diverse and vibrant community. Our students experience an education focused not only on knowledge, but the skills and values that will prepare them for fulfilling and purposeful careers and lives. To describe Hawken’s approach to teaching, learning, and the development of character, faculty and administrators developed The Hawken Method. The Hawken Method represents the application of Hawken’s Purpose, Promise and Principles and is based on six core ideas that fundamentally shape the Hawken Experience and the school’s expectations of students. These six core ideas are as follows: 1. Inspiring Relationships Respect and inspiring relationships are the cornerstone of the educational experience at Hawken.

2. Essential Skills Hawken’s program develops the skills essential for academic success, especially those that stress critical and creative inquiry and expression.

3. Meaningful Learning Hawken believes that learning should be meaningful. Teachers construct lessons and curriculum that clarify and expand upon students’prior knowledge.

4. Student Assessment Student assessment is used both to measure and guide student learning.

5. Intentional Use of Time Hawken respects student time, using it in intentional ways to maximize educational outcomes.

6. Culture as a Teaching Tool Hawken’s culture conveys its values and is among the school’s most important teaching tools.

These six core ideas, The Hawken Method, and Hawken’s Purpose, Promise and Principles guide all our efforts nd are woven into the fabric of our curriculum.

By the time our students graduate from Hawken, they will be ready for all the opportunities the world offers.

D. Scott Looney Hawken Head of School 1

OUR PHILOSOPHY

I Early Childhood and Lower School

Early Childhood (Preschool - Grade 2) Hawken’s forward-focused mission of preparation through the development of character and intellect applies to even our youngest students. Our dual commitment to academic and social curricula puts students at the center of learning, teaching them in developmentally appropriate ways to make choices, manage time, and think critically and creatively. At the same time, our programs help develop and encourage critical character skills, such as individual ownership of learning and empathy for others. In all of our endeavors, we seek to foster joy in learning and the importance of being a significant member of a community.

Hawken’s early childhood experts know young children thrive in nurturing environments that encourage and support discovery and the construction of knowledge through exploration and experimentation in a variety of settings. In our classrooms, the play setting has the most integrity for young children. As students reconstruct and experience their own worlds, genuine learning results.

The Early Childhood Center provides our students with a state of the art environment specifically designed to facilitate and encourage early childhood learning.This new space enhances programming by inspiring exploration, supporting a variety of social learning experiences, and encouraging development of motor skills. Hands-on activities provide meaningful, creative experiences while fostering self-confidence and an excitement for learning. This unique learning environment provides rich and varied opportunities for in-depth exploration and discovery while incorporating the broader goals of language development, science inquiry, math awareness, creative arts exploration, and social and emotional growth.

In a day’s time, students have the opportunity to interact with teachers from a wide spectrum of subjects, benefitting from a seamless interdisciplinary approach to learning.

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Lower School (Grades 3-5) At Hawken, education revolves around the central premise that young people’s talents can be maximized through a comprehensive and balanced curriculum coupled with challenging and diverse assessment. We are committed to providing an effective learning experience for our students, where classroom experience has practical life applications. Hawken’s Lower School offers a rich and varied program emphasizing the many facets of a child’s development. The Hawken classroom applies developmentally appropriate practice in an atmosphere that celebrates the joys of teaching and learning. Our faculty presents curriculum through multiple lenses and perspectives to maximize individual growth. Flexible grouping and focus on individual learning styles are utilized to achieve each student’s potential.

In a day’s time, students have the opportunity to interact with teachers from a wide spectrum of subjects, benefiting from a seamless interdisciplinary approach to learning. With an emphasis on collaboration and the development of effective communication skills, Lower School students are encouraged to question, problem solve and demonstrate their understanding through verbal and written expression. Academic expectations are high, yet we understand that effective education must be cognizant of developmentally appropriate practice, and, at times, retain a flexibility to ensure each student is challenged in the most effective way.

Character development is an integral component of the Hawken education.

The Lower School utilizes the Responsive Classroom approach, which places equal value on the development of academic and social skills. Building community is not a theory at Hawken, but has practical, every day application.

It is exemplified by Morning Meetings, classroom expectations, and our school-wide standard of purposeful and respectful language. Multicultural understandings are woven into the fabric of the day through intentional choices of curricular content, teaching materials and opportunities for interaction and dialogue.

CENTRAL TO HAWKEN’S MISSION IS OUR PROMISE TO “PREPARE STUDENTS TO NAVIGATE A COMPLEX AND DYNAMIC WORLD WITH SELFCONFIDENCE AND DETERMINATION; EMBRACE CHALLENGES WITH DISCIPLINED ANALYSIS AND CREATIVITY; AND ENGAGE OTHERS WITH EMPATHY AND INTEGRITY.”

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MATHEMATICS HIGHLIGHTS

I Early Childhood and Lower School

Kindergarten Counts beyond 20 in daily activities and play • Identifies and names numerals 0-20 • Makes parts to whole comparisons on a consistent basis • Compares and orders whole numbers to 20 • Compares, constructs and deconstructs sets of objects representing whole numbers • Models addition and subtraction processes up to 10 • Uses numbers and counting for problem solving and quantity • Identifies, creates and sorts two-and three-dimensional shapes • Uses unit of time vocabulary with accuracy,and recognizes various devices used to measure time • Measures length,volume and weight using standard and non-standard units of measure • Demonstrates a problem situation with physical materials and then translates it to a descriptive number sentence • Collects data through questions, observations,interviews and surveys to organize in chart and graph form Grade 1 Counts up to 100 • Uses place value concepts • Reads and writes the numerals for numbers to 100 • Represents fractions using words,numerals,and physical models • Uses ordinal numbers to order objects • Models,represents and explains multiple strategies for addition and subtraction processes up to 10 • Incorporates a variety of strategies to solve mathematical problems (including estimation) and explains to others the process used • Identifies,creates,compares,and sorts two- and three-dimensional shapes while using attributes to describe them • Tells time to the hour and half hour on digital and analog timepieces • Estimates and measures length,volume and weight using non-standard and standard units of measure • Sorts and classifies objects by multiple attributes • Creates and extends more complex shaped and number patterns • Describes and models a problem situation using words,objects,and number sentences • Discusses possible outcomes of a math problem or scenario and predicts whether they are likely to occur Grade 2 Counts beyond 100 • Uses place value concepts to represent,compare,add,subtract and order whole numbers using physical models,numerals and words • Reads and writes numbers beyond 100 • Represents fractions using words,numerals and physical models on a consistent basis and compares equivalent fractions • Models,represents and explains multiplication as repeated addition,rectangular arrays,and skip counting • Models,represents and explains multiple strategies for addition and subtraction processes up to 18 • Identifies and determines whether two-dimensional shapes are congruent or similar by copying or using superposition • Tells time to the minute on both analogue and digital timepieces and calculates elapsed time • Sorts objects and explains the classification process • Determines appropriate strategies to solve mathematical problems and communicates the steps involved in the process Grade 3 Constructs and verbalizes a variety of materials and strategies to solve problems • Applies mathematical vocabulary in written and oral explanations • Demonstrates numbers sense and accuracy in computation • Observes patterns using the 100 chart • Grasps multiplication facts through 10 • Uses multiplication or division notation to correctly write number sentences Grade 4 Demonstrates fluency in adding,subtracting,multiplying and dividing • Analyzes and solves multi-step problems • Uses associative and distributive properties • Identifies and generates equivalent forms of fractions • Represents and interprets data using graphs • Uses models and words to describe patterns and relationships • Writes,solves and verifies solutions to multi-step problems using measurement Grade 5 Compares and orders whole and decimal numbers • Computes long division,addition,subtraction and multiplication of decimals • Identifies fraction,percent and decimal equivalencies • Simplifies and adds fractions • Employs and communicates orally and in writing,various problem solving strategies

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Mathematics Curriculum Maps Comprehensive content for Hawken School Mathematics Kindergarten-Grade 5

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CURRICULUM MAP

I Early Childhood Kindergarten

Mathematics Content

September

October

November

December

Unit 1

Unit 2

Unit 3

Unit 4

A. Sorting and Classifying • Single Multiple Attributes B. Measurement • Non Standard Units • Comparative Language (longer, shorter, taller, bigger, smaller, more, less) C. Graphing and Recording • Bar graphs • Data • Count/Understand“how many”in set • Concrete/Pictorial/Verbal Numeracy • Venn Diagram (compare and contrast) • Pictorial Information D. Patterns • Simple Patterns (ab, abb, aab, abc) E. Counting • Zero • Objects (1-10) 1 to 1 Correspondence • Records (1-10) F. Equations • Simple Addition • Vocabulary: (add, join, more, altogether) G. Exploration Center • Pattern Blocks/Templates • Money • Number Board (1-10)

A. Sorting and Classifying • By Criteria (various) • Attribute Charts B. Measurement • Non-Standard Units • Comparative Language (heavier, lighter, more less) • Weight (balance scales) C. Graphing and Tallying • Surveys/Results (pictorial, bar chart) • Tally Marks D. Patterns • Simple Patterns (ab, abb, aab, abc) • Suggestion/Continuation (extend) E. Counting • Numbers to 10 • Forward 0-10 • Forward 0-21 • Continuation from Given Number • Number Formation 0-21 (trace and write) F. Equations • Manipulatives for Simple Equations G. Exploration Center • Pattern Blocks/Templates • Weighing Scales • Money Match Game • 1 Cent Buying Power

A. Measurement • Longer/Shorter,Taller/Smaller • Measure/Weight (follow recipes) • Standard Units B. Graphing and Tallying • Collection/Record of Data • Tally/Group Numbers through 20 C. Equations/ Numbers • 0-50 • Backwards 12-0 • Double Digit (10+ Digits] • Addition and Subtraction • Continuation from Given Number • Monster Squeeze Game • Match Objects to Number D. Geometry • Shape Patterns • 3-D Shapes from 2-D Shapes E. Time/Money • Birthday Calendar (months) • Days and Months Order • Calendar • Making Change Using Pennies F. Exploration Center • Candles Cakes • Boxes • Party Supplies

Resources • Manipulatives • Venn Diagram • Pattern Blocks • Number Template • Calendar • 1-100 Square • Money Sorter • Number Boards 1-10 • Calendar • 1-100 Square • Money Sorter

Resources • Manipulatives • Pattern Blocks • 0-100 Chart • Calendar • Money • Timer • Scales • Money Match Game • Attribute Blocks

A. Measurement • Non-Standard Units • Comparative Language • Weight (rocker scales) • Estimation B. Graphing and Tallying • Collection/Record of Data (tally, bar chart) C. Patterns • Creation with 2+ More Elements D. Counting • Double Digits • Forward 0-35 • Read 1-15 • Teen Numbers (10 + digit) • One More/One Less E. Equations • Subtraction Vocabulary (less than, difference, take away, separate) • Story Problems F. Geometry • 2-D Shapes • Symmetry G. Time/Money • Penny Combination - Totals • O’Clock (big hand on 12) H. Exploration Center • Shape Templates • Number Story Boards • Straws and Connectors Resources • Manipulatives • Pattern Cards • 0-100 Chart • Money • Scales • 2-D Shapes (attribute blocks) • Mirrors • Number Story Boards • Straws and Connectors

Resources • Recipes/cups and spoons • Calendar • 0-100 Chart • Play Money • 2-D & 3-D Shapes • Boxes

Note: While units described are depicted monthly for organizational ease, coursework may progress transitionally according to class dynamics and the educators’discretion.

Kindergarten Mathematics / Displayed Core Competencies: Counts beyond 20 in daily activities and play • Identifies and names numerals 0-20 • Makes parts to whole comparisons on a consistent basis • Compares and orders whole numbers to 20 • Compares,constructs and deconstructs sets of objects representing whole numbers • Models addition and subtraction processes up to 10 • Uses numbers and counting for problem solving and quantity • Identifies,creates and sorts two-and three-dimensional shapes • Uses unit of time vocabulary with accuracy,and recognizes various devices used to measure time • Measures length,volume and weight using standard and non-standard units of measure • Demonstrates a problem situation with physical materials and then translates it to a descriptive number sentence • Collects data through questions,observations,interviews and surveys to organize in chart and graph form

January

February

March

April

May

Unit 5

Unit 6

Unit 7

Unit 8

Unit 9

A. Sorting and Classifying • Objects by own criteria B. Measuring/Weighing • Ordering by length • Explore measuring tools • How big is a foot?

• Standard Units - inches • Weighing for cookings • Estimation - measurement C. Graphing and Tallying • Surveys • Tallying Responses D. Patterns & Geometry • Counting Patterns (100 square) • Copy Cat Building • Shape Exploration (2-D and 3-D) E. Counting • Estimating • Grouping into tens and ones • Skip Counting - calculator • Skip Counting - 2’s, 5’s, 10’s • Forward 0-70; Back from 15-0 • Money - Dimes, Nickels, Pennies F. Equations • Word Problems • Function Machine • Mental Math Challenges • Missing Numbers • Inverse Operations (+ & -) • What’s My Operation? (+ or -) G. Time/Money • Clock Making • Clock Bingo • Elapsed Time • Identify Dime and Nickel • Characteristics of Nickel • Purchasing (Dime, Nickel, Penny) H. Exploration Center • Inventor’s Closet • Clocks • Function Machine • Measuring Tools

A. Sorting and Classifying • Venn Diagrams • What’s My Rule Game?

B. Measuring/ Weighing • Area (Unifix Cubes) • Comparative Weights • Capacity (various containers) C. Graphing and Tallying • Graphing (computer) • Reading Tally Charts D. Patterns & Geometry • Weaving & Repeating Patterns • Symmetry • Tangrams E. Counting • Estimating • Grouping in 10’s • Abacus • Number Lines • Skip Counting 2’s, 5’s, 10’s • Count 0-90; Back 15-0 F. Equations • Tachyscope Equations • Ordinal Numbers • Magic Squares • Missing Numbers • Place Value ( 1’s and 10’s) G. Time/Money • Money Bingo • Counting Money ( 1’s, 5’s, 10’s) • Sorting Money • Estimate/Count • Exchanging Pennies • Explore Quarter • Read to Hour (analog clock) H. Exploration Center • Calculators • Rocker Scale • Pattern Blocks • Sorting Trays - Money • Tangrams • Abacus

A. Sorting and Classifying • Sequencing Growth • Sequencing Numbers • Construct 0-100 Chart B. Measuring/Weighing • Standard Unit (inch, foot) • Circumferences (with string) • Intro. to Foot Measure (standard) • Comparative Language C. Graphing and Tallying • Tally Charts • Bar Graph • Absence Graph D. Patterns & Geometry • Fractions (Explore 1/2) • Shapes Explored Through Print • Divide into Groups Equally • Review Shapes E. Counting • Counting Patterns (2, 5,10) • Odd & Even Numbers • Counting On Number Line • Race to 100 • Ordinal Numbers • Count 0-115; Back 20-0 F. Equations • Word Problems (Vocabulary) • Fact Families - 10 • Selecting Operations • Subtraction Stories • Mental Math Challenges G. Time/Money • Using Money (Purchasing) • Counting On (Dime, Nickel, Penny) • Time 1 Hour + 1/2 Hour • Time Bingo (Hour, 1/2 Hour) H. Exploration Center • 100’s Chart • Measuring Tools • Fraction Blocks • Play-Money

A. Sorting and Classifying • Venn Diagrams • Ordering from longest to shortest • Ordinal Numbers (1-12) • Co-Ordinates B. Measurement • Temperature (bar graph) • Follow simple recipe • Compare volume (containers) C. Graphing and Tallying • Surveys and Tallys D. Patterns & Geometry • Fraction stories • Pattern Block design • Tangrams • Complex Patterns E. Counting • Grouping and Counting 10’s • Skip counting, 2’s, 5’s, 10’s • Record 2 + 3 digit numbers • Greater Than/Less Than • Estimate and Count • Number Lines • Grouping 10’s and 1’s • Odd and even numbers • Count 0-115; Back 20-0 • Record Numbers 20-0 F. Equations • Equations (+ and -) • Word Problems • Missing Numbers • Function Rules (Operations) • Fact Families G. Time/Money • Comparative Time • Time (analog and digital) • Dollar Recognition • Money (exchanges and counting) H. Exploration Center • Money Clocks • Function Machine • Thermometer • Volume (water and sand) • Pattern Blocks • Tangrams

A. Sorting and Classifying • Probability • Calendar Questions • Co-Ordinates B. Measurement • Measure Height/Length in Inches • Measure Perimeter • Volume (water) C. Graphing and Tallying • Bar Graph • Tally Shapes • Sort and Graph D. Patterns & Geometry • Review 2D Shapes • Solid Shapes • Compare 4-Sided Shape • Symmetry • Repeating Patterns (Music) • Shape Attributes E. Counting • Digit Reversal • Make Double,Triple Digit Numbers • Skip Counting (2, 5, 10) • Ordering Numbers • Read, Display Numbers (10’s + 1’s) • Count Back From (20-0) • Recording Numbers F. Equations • Missing Numbers & Operations • Number Walls • Mental Math • Fact Families • Word Problems • Divide into 1/2 G. Time/Money • Purchasing Power • Time (digital and analog) • Money Exchanges • Recognize Dollar & Quarter H. Exploration Center • Money (quarters and bills) • Symmetry (mirrors) • Water Containers • Pattern Blocks (Tessellation Tray)

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CURRICULUM MAP

I Lower School Grade 1

Mathematics Content

September

October

November

December

Unit 1

Unit 2

Unit 3

Unit 3 (continued)

A. Numbers • Counting • Writing • Recognition

A. Numbers • Writing • Recognition

A. Patterns • Even/Odd patterns • Visual patterns

A. Patterns • Even/Odd patterns • Visual patterns • Dominos

B. • • •

B. Numbers • Number line counting • Word problems

B. • • •

Manipulatives Pattern Blocks Base-10 Blocks Geoboards

C. Patterns • Templates Resources • Everyday Mathematics

Money Nickels, Dimes, Quarters Money Exchange Coin Combinations

C. Addition/Subtraction • Math Facts • Addition Number Stories • Greater than/Less than Resources • Everyday Mathematics

C. Time • Time to the hour/half-hour

B. Numbers • Number line counting • Word problems C. Time • Time to the hour/half-hour

D. Frames and arrows routine E. Money • Dimes • Coin combinations

D. Money • Dimes and Coin combinations • Money exchange

F. Addition/Subtraction • Math minute tests • Math facts

E. • • •

Addition/Subtraction Math minute tests Math facts Frames and Arrows

Resources • Everyday Mathematics

F. Graphs • Data collection G. Measurement • Thermometers • Linear Measure (feet and inches) Resources • Everyday Mathematics

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Note: While units described are depicted monthly for organizational ease, coursework may progress transitionally according to class dynamics and the educators’discretion.

Grade 1 Mathematics / Displayed Core Competencies: Counts up to 100 • Uses place value concepts • Reads and writes the for numbers to 100 • Represents fractions using words,numerals,and physical models • Uses ordinal numbers to order objects • Models,represents and explains multiple strategies for addition and subtraction processes up to 10 • Incorporates a variety of strategies to solve mathematical problems (including estimation) and explains the process to others • Identifies,creates,compares,describes and sorts two- and three-dimensional shapes • Tells time to the hour and half hour on digital and analog timepieces • Estimates and measures length,volume and weight using non-standard and standard units of measure • Sorts and classifies objects by multiple attributes • Creates and extends more complex shaped and number patterns • Describes and models a problem situation using words,objects,and number sentences • Discusses possible outcomes of a math problem or scenario and predicts whether they are likely to occur

January

February

March

April

May

Unit 4

Unit 5

Unit 5 (continued)

Unit 6

Unit 6

A. Patterns • Even/Odd patterns • Visual patterns

A. Patterns • Even/Odd patterns • Visual patterns

B. Numbers • Number line counting • Word problems

A. Patterns • Even/Odd patterns • Visual patterns • Spheres, Cylinders and Rectangular Prisms • Pyramids, Cones and Cubes • Symmetry

A. Patterns • Even/Odd patterns • Visual patterns • Spheres, Cylinders and Rectangular Prisms • Pyramids, Cones and Cubes • Symmetry

C. Time • Time to the hour/half-hour • Time to the quarter-hour

B. Numbers • Number line counting • Word problems • Comparison number stories • Relations (greater than, less than, and equal to) • Place Value (tens and ones)

A. Patterns • Even/Odd patterns • Visual patterns • Making Polygons • Spheres, Cylinders and Rectangular Prisms • Pyramids, Cones and Cubes • Symmetry

D. Money • Dimes, nickels, pennies • Money exchanges • Coin combinations

C. Time • Time to the hour/half-hour • Time to the quarter hour • Minutes and Seconds

B. Numbers • Number line counting • Word problems • Comparison number stories • Relations (greater than, less than and equal to) • Place Value (hundreds, tens, ones) • Fraction parts of the whole

B. Numbers • Number line counting • Word problems • Comparison number stories • Relations (greater than, less than and equal to) • Place Value (hundreds, tens, ones) • Fraction parts of the whole

E. Addition/Subtraction • Math minute tests • Math facts • Frames and Arrows routine

D. Money • Dimes, nickels, pennies • Money exchanges • Coin combinations • Quarters

C. Time • Time to the hour/half-hour • Time to the quarter hour • Seconds

C. Time • Time to the hour/half-hour • Time to the quarter hour • Seconds • Fast Fives

C. Time • Time to the hour/half-hour • Time to the quarter hour • Seconds • Fast Fives

D. Money • Quarters, dimes, nickels, pennies • Money exchanges • Coin combinations • Dollars

D. Money • Quarters, dimes, nickels, pennies • Money exchanges • Coin combinations • Dollars

D. Money • Quarters, dimes, nickels, pennies • Money exchanges • Coin combinations • Dollars

E. Addition/Subtraction • Math minute tests • Math facts • Frames and Arrows routine • Turn-around-facts • “What’s my Rule?”routine • Addition/Subtraction fact table • Fact families and triangles • Double-digit addition

E. Addition/Subtraction • Math minute tests • Math facts • Frames and Arrows routine • Turn-around-facts • “What’s my Rule?”routine • Addition/Subtraction fact table • Fact families and triangles • Double-digit addition/subtraction

E. Addition/Subtraction • Math minute tests • Math facts • Frames and Arrows routine • Turn-around-facts • “What’s my Rule?”routine • Addition/Subtraction fact table • Fact families and triangles • Double-digit addition/subtraction

F. Measurement • Standard foot and inches • Ruler and tape measure • Centimeters • Height and Width

F. Measurement • Standard foot and inches • Ruler and tape measure • Centimeters • Height and Width

F. Measurement • Standard foot and inches • Ruler and tape measure • Centimeters • Height and Width

Resources • Everyday Mathematics

Resources • Everyday Mathematics

Resources • Everyday Mathematics

G. Measurement • Personal“foot”vs. standard foot • Inches • Rulers and tape measures Resources • Everyday Mathematics

E. Addition/Subtraction • Math minute tests • Math facts • Frames and Arrows routine • Turn-around-facts • “What’s my Rule?”routine • Addition/subtraction fact table • Fact families • Fact triangles F. Measurement • Standard foot and inches • Ruler and tape measure • Centimeters Resources • Everyday Mathematics

B. • • • •

Numbers Number line counting Word problems Comparison number stories Relations (greater than, less than and equal to) • Place Value (hundreds, tens, ones) • Fraction parts of the whole

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2

CURRICULUM MAP

I Lower School Grade 2

Mathematics Content

September

October

November

December

Unit 1

Unit 2

Unit 3

Unit 3 (continued)

A. Measurement • Nearest inch

A. Measurement • Nearest inch

A. Place Value • Two & three digit numbers

B. Money • Coin values • Totals to one dollar

B. Addition with Sums: 1-20 • Fact families • Simple number stories • Frames and arrows • “What’s my Rule?”tables

B. Money • Change

A. Temperature • Temperatures in degrees Fahrenheit and Celsius • Appropriate temperature

C. Subtraction w/Differences: 1 through 20 • Fact families • Simple subtraction stories • Frames and arrows • “What’s my Rule?”tables

D. Two digit Addition and Subtraction • Sums and differences: 1 through 20 • Two rule frames and arrows • Multiples of ten

D. Place Value • Two & three digit numbers

Resources • Everyday Mathematics

C. Addition D. Place Value • Ones, tens, hundreds E. Comparison • Greater than/Less than • Equal to • Equivalent names F. Number Sense • Tally marks to one hundred

E. Money Resources • Everyday Mathematics

F. Time • Five minute intervals Resources • Everyday Mathematics

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C. Time • Five minute intervals

B. Subtraction of two digit numbers • Multiples of ten • Differences of two digit numbers C. Estimation • Costs • Sums D. Geometry • Common attributes of shapes • Two dimensional shapes • Symmetrical shapes E. Sums and Differences: 1 through 20 • Timed tests Resources • Everyday Mathematics

Note: While units described are depicted monthly for organizational ease, coursework may progress transitionally according to class dynamics and the educators’discretion.

Grade 2 Mathematics / Displayed Core Competencies: Counts beyond 100 • Uses place value concepts to represent,compare,add,subtract and order whole numbers using physical models,numerals and words • Reads and writes numbers beyond 100 • Represents fractions using words,numerals and physical models on a consistent basis and compares equivalent fractions • Models,represents and explains multiplication as repeated addition,rectangular arrays,and skip counting • Models,represents and explains multiple strategies for addition and subtraction processes up to 18 • Identifies and determines whether two-dimensional shapes are congruent or similar by copying or using superposition • Tells time to the minute on both analogue and digital timepieces and calculates elapsed time • Sorts objects and explains the classification process • Determines appropriate strategies to solve mathematical problems and communicates the steps involved in the process

January

February

March

April

May

Unit 4

Unit 4-5

Unit 5

Unit 6

Unit 7

A. Whole-Number Operations • Addition with Several Addends • Trade-First Subtraction Algorithm • Multiplication

A. Fractions • Equal Parts of One • Equivalent Fractions • Fraction Comparison • Fraction Number Stories

A. Measurement • Linear Measures • Fractional Units of Length • Perimeter • Area • Capacity • Weight

A. Place Value • Ten-Thousands

A. Calendar • Skill Review

B. Addition and Subtraction • Groups with Parentheses

B. Time • Skill Review

C. Addition and Subtraction Number Stories • Dollars and Cents

C. Multiplication Facts

B. Median B. Number Stories • Addition and Subtraction Stories • Multiplication-Array • Division C. Patterns in Counting • Number Grid • Arrow Paths • Doubles and Halves D. Sums and Differences: 1 through 20 • Timed Tests Resources • Everyday Mathematics

C. Measurement • Yards • Meters D. Sums and Differences: 1 through 20 • Timed Tests Resources • Everyday Mathematics

B. Money • Decimal Notation for Pennies and Dimes • Amounts with Calculators • Estimation and Exact Costs • Change C. Sums and Differences: 1 through 20 • Timed Tests Resources • Everyday Mathematics

D. Division • Number Models • Division Facts • Fact Families

D. Sums and Differences: 1 through 20 • Timed Tests Resources • Everyday Mathematics

E. Multiplication • Multiples of Equal Groups • Multiplications Facts • Fact Families F. Sums and Differences: 1 through 20 • Timed Tests Resources • Everyday Mathematics

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3

CURRICULUM MAP

I Lower School Grade 3

Mathematics Content

September

October

November

December

Unit 1: Routines, Review and Assessment

Unit 2: Adding and Subtracting Whole Numbers

Unit 3: Linear Measures and Area (continued)

Unit 4: Multiplication and Division (continued)

A. Four Types of Numbers: Counting, Measuring, Codes, Reference Frames

A. Fact Families

D. Perimeter

E. Multiplication Fact Power and Shortcuts

B. Addition and Subtraction Fact Extensions

E. Area

B. Number Grids and Differences C. Place Value through Thousands

C. “What's My Rule?”Problems

D. Student Reference Book

D. Parts-and-Total Number Stories

E. Measurement • Time to nearest minute • Length to nearest centimeter and half inch

E. Change Number Stories

F. Number Models for Area

F. Multiplication/Division Fact Tables and Fact Families

G. Diameter and Circumference

G. Multiplication Fact Practice for Fluency

H. Review and Assessment

H. Estimation of Distances Using Map Scale

Unit 4: Multiplication and Division I. Review and Assessment

F. Comparison Number Stories A. Multiples of Equal Groups G. Partial-Sums Algorithm B. Multiplication Arrays

F. Graphs H. Trade-First Subtraction Algorithm G. Equivalent Names I. Addition with Three or More Addends

C. Division as Equal Shares and Equal Groups

I. Calculator Skills Unit 3: Linear Measures and Area J. Money • Notation • Comparison • Story problems • Estimation versus exact answers K. Number Patterns L. Length-of-Day Project • Elapsed time

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A. Standard Units for Measure B. Measurement to Nearest 1/4 Inch C. U.S. Customary and Metric Units of Length

D. Relationship between Division and Multiplication

Note: While units described are depicted monthly for organizational ease, coursework may progress transitionally according to class dynamics and the educators’discretion.

Grade 3 Mathematics / Displayed Core Competencies: Constructs and verbalizes a variety of materials and strategies to solve problems • Applies mathematical vocabulary in written and oral explanations • Demonstrates numbers sense and accuracy in computation • Observes patterns using the 100 chart • Grasps multiplication facts through 10 • Uses multiplication or division notation to correctly write number sentences

January

February

March

April

May

Unit 5: Place Value in Whole Numbers and Decimals

Unit 6: Geometry

Unit 7: Multiplication and Division

Unit 8: Fractions

Unit 9: Multiplication and Division

A. Place Value through Millions • Read, write and order numbers B. Place Value in Decimals • Read, write, and order decimals through hundredths • Exchange between tenths and hundredths • Introduce thousandths

A. Line segments, Lines and Rays B. Angles and Turns • Identification • Measurement

A. Multiplication and Division Patterns; Square Numbers

A. Fractional Parts: Naming Fractional Parts of Regions and Sets

B. Development of Multiplication Fact Power

B. Identifying Fractions On a Number Line

C. Number Models with Parentheses

C. Equivalent Fractions

C. Multi-digit Numbers • Partial-products algorithm • Lattice method • Traditional algorithm D. Factors of a Number

C. Triangles

D. Comparing Fractions

D. Quadrangles E. Polygons F. Symmetry G. Polyhedrons

D. Extended Multiplication and Division Facts • Multiply by multiples of 10, 100 and 1,000 • Divide such multiples by 1-digit numbers E. Estimating • Sums, products and estimates F. Extended Multiplication • Facts to tens times tens G. Review and Assessment

E. Fractions Greater than One

E. Interpreting Remainders in Division Problems F. Positive and Negative Numbers

F. Fractions in Number Stories G. Review and Assessment Unit 9: Multiplication and Division

Unit 10/11: Measurement, Data and Probability A. Volume B. Mean and Median

A. Multiplication and Division with Multiples of 10, 100, and 1,000 B. Mental Math: Multiplying 1-digit by Multi-digit Numbers

C. Measures of Weight and Capacity D. Chance Events E. Probability • Use fractions to record probability • Collect and organize data to predict outcomes

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4

CURRICULUM MAP

I Lower School Grade 4

Mathematics Content

September

October

November

December

Unit 1

Unit 1 (continued)

Unit 2

Unit 2 (continued)

A. Naming and Constructing Geometric Figures • Points, line segments, lines and rays • Angles, triangles and quadrangles • Parallelograms • Polygons • Circles

A. Multiplication and Division • Facts

A. Distance in Miles/Hours Traveling

A. Distance in Miles/Hours Traveling

B. Elevations/Population/Weather

B. Elevations/Population/Weather

C. Big Numbers, Estimation and Computation • Estimating Sums • Powers of 10 • Rounding

C. Big Numbers, Estimation and Computation • Estimating Sums • Powers of 10 • Rounding

D. Division • Number Stories • Remainders

D. Division • Number Stories • Remainders

E. Time Tests • Multiplication/Division

E. Time Tests • Multiplication/Division

Resources • Everyday Math • Daily Math for Fourth Grade

Resources • Everyday Math • Daily Math for Fourth Grade

B. Using Numbers and Organizing Data • Place value for numbers: • Median • Addition of multi-digit numbers C. Time Tests • Addition/Subtraction • Multiplication/Division

B. Number Sentences and Algebra • Strategies • True or False Sentences • Open Sentences • Logic Problems C. Decimals and Their Uses • Addition/Subtraction • Estimating • Place Value • Money D. Time tests • Multiplication/Division Resources • Everyday Math • Daily Math for Fourth Grade

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Note: While units described are depicted monthly for organizational ease, coursework may progress transitionally according to class dynamics and the educators’discretion.

Grade 4 Mathematics / Displayed Core Competencies: Demonstrates fluency in adding,subtracting,multiplying and dividing • Analyzes and solves multi-step problems • Uses associative and distributive properties • Identifies and generates equivalent forms of fractions • Represents and interprets data using graphs • Uses models and words to describe patterns and relationships • Writes,solves and verifies solutions to multi-step problems using measurement

January

February

March

April

May

Unit 3

Unit 3 (continued)

Unit 4

Unit 5

Unit 5 (continued)

A. Decimals • Adding and subtracting • Comparing • Money • Place values

D. Division • Strategies • Interpreting remainders • Expressing remainders as fractions

A. Perimeter • Scale drawings • Formula for perimeter

C. Symmetry • Properties • Identifying lines of symmetry • Reflections

B. Metric Units of Length • Meters • Decimeters • Centimeters • Millimeters • Conversions

E. • • •

A. Fractions • Sets • Adding and subtracting • Equivalent • Comparing • Probability • Decimals • Fractions to percentages

C. Division • Strategies • Interpreting remainders • Expressing remainders as fractions

Angles Circular protractor Rotations Ordered pairs and grids

Resources • Everyday Math • Daily Math for Fourth Grade

B. Decimals • Multiplication • Division • Percentages Resources • Everyday Math • Daily Math for Fourth Grade

B. Area • Formula for rectangle • Formula for triangle • Measurements Resources • Everyday Math • Daily Math for Fourth Grade

D. Positive/Negative Numbers • Adding and subtracting E. Volume Resources • Everyday Math • Daily Math for Fourth Grade

E. Time tests • Multiplication/division Resources • Everyday Math • Daily Math for Fourth Grade

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5

CURRICULUM MAP

I Lower School Grade 5

Mathematics Content

September

October

November

December

Unit 1: Number Theory

Unit 2: Estimation and Computation

Unit 3: Geometry Explorations

Unit 5: Fractions, Decimals, and Percents

A. Rectangular Arrays

A. Addition and Subtraction Number Stories

A. Congruent Triangles

B. Factors

A. Fraction Review B. Properties of Polygons

B. Estimating Time, Distance and Length C. Divisibility

B. Mixed Numbers C. Regular Tessellations

C. Chance Events D. Prime and Composite Numbers

C. Ordering Fractions D. Angles of Polygons

D. Estimating Products E. Square Numbers and Square Roots F. Factor Strings and Prime Factorization

E. Multiplication of Whole Numbers and Decimals

Unit 2: Estimation and Computation

F. Comparing Millions, Billions and Trillions

D. Finding Equivalent Fractions E. Solving Problems Using the Geometry Template

E. Converting Fractions to Decimals F. Converting Fractions to Percents

Unit 4: Division G. Bar and Circle Graphs A. Division Facts and Extensions

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A. Addition & Subtraction of Whole Numbers and Decimals

Unit 3: Geometry Explorations

B. Division Algorithms

E. Spelling

A. Exploring Angle Measures

C. Division of Decimal Numbers

Resources • Everyday Mathematics

B. Using a Protractor and Compass

D. Interpreting Remainders

Resources • Everyday Mathematics

Resources • Everyday Mathematics

H. The Percent Circle: Reading & Making Circle Graphs Resources • Everyday Mathematics

Note: While units described are depicted monthly for organizational ease, coursework may progress transitionally according to class dynamics and the educators’discretion.

Grade 5 Mathematics / Displayed Core Competencies: Compares and orders whole and decimal numbers • Computes long division,addition,subtraction and multiplication of decimals • Identifies fraction,percent and decimal equivalencies • Simplifies and adds fractions • Employs and communicates orally and in writing,various problem solving strategies

January

February

March

April

May

Unit 6: Using Data; Addition and Subtraction of Fractions

Unit 7: Exponents and Negative Numbers

Unit 8: Fractions and Ratios (continued)

Unit 10: Algebra Concepts and Skills

Unit 12: Probability, Ratios and Rates

A. Exponential Notation

E. Finding a Percent of a Number

A. Algebraic Expressions

A. Factor Trees

B. Rules,Tables and Graphs

B. Choices,Tree Diagrams and Probability

A. Organizing Data B. Powers of 10 B. Stem-and-Leaf Plots C. Scientific Notation C. Line Plots

F. Using Unit Fractions and Unit Percents to Find a Whole

D. Order of Operations D. Sample Size and Analysis of Sample Data E. Using a Slide Rule to Add and Subtract Fractions

C. Circumference of a Circle C. Ratios of Parts to Wholes D. Areas of Circles

G. Fraction Division E. Adding and Subtracting Positive and Negative Numbers

D. Number Models for Ratio Number Stories Unit 11: Volume

Unit 9: Coordinates, Area, Volume and Capacity

E. Finding Rates A. Geometric Solids

Unit 8: Fractions and Ratios F. Common Denominators

A. Coordinate Graphs A. Comparing Fractions

Resources • Everyday Mathematics

B. Adding and Subtracting Mixed Numbers

B. Areas of Rectangles, Triangles and Parallelograms

C. Fractions of Fractions

C. Volume of Prisms

D. Multiplication of Fractions, Whole Numbers and Mixed Numbers

D. Capacity: Liter, Milliliter, and Cubic Liter

B. Volume of Cylinders, Pyramids and Cones C. Capacity and Weight

F. Collecting, Graphing and Interpreting Data Resources • Everyday Mathematics

D. Surface Area

Resources • Everyday Mathematics

Resources • Everyday Mathematics

Resources • Everyday Mathematics

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ACADEMIC PERSPECTIVE

I Early Childhood and Lower School

The acquisition of basic skills is an important component of a rich and well-rounded primary program. With this foundation, students become more confident learners and effective problem solvers. In an atmosphere that promotes taking safe risks, girls and boys learn to share their understanding and be receptive to creative problem solving - the idea that there is more than one way to come to a solution. Students learn specific problem solving strategies that can be applied and connected to the real world through a variety of experiential learning opportunities.

We believe an exemplary program challenges students to develop self-awareness as independent learners, assume personal responsibility for academic learning and social behavior, and balance self-interest with active membership in the larger community. With this in mind, the educational experience for Hawken students is organized into Three Pillars: Childhood toward Pre-Adolescence; Concrete Operational Thinking toward Abstract Thinking; and Guided Apprenticeship toward Independent Practice.

Our ‘Three Pillars’ of Educational Experience 1. Childhood toward Pre-Adolescence (Social/Emotional Development) Students begin to exhibit pre-adolescent attitudes and behaviors, exhibiting an increased awareness of themselves and of the social world around them. These new perspectives yield deep changes in the ways in which students view (and understand/ regulate) themselves, interact with others, and approach learning challenges.

2. Concrete Operational Thinking toward Abstract Thinking (Cognitive Development) Students’cognitive processes reflect concrete operational thought. Students demonstrate a greater ability to reason logically, apply mental concrete operations to everyday situations and problem solve. Students organize information in more complex ways and can now apply principles or hierarchical classification to the world around them. Some students demonstrate threads of abstract thinking, which will develop more fully as they move into the Middle School years.

3. Guided Apprenticeship toward Independent Practice (Approaches to Learning) Students expand their repertoire of tools and strategies for learning. With supportive instruction and gains in complex cognitive capacity, they begin to access and utilize appropriate strategies in varied learning situations. Students practice skills with greater efficiency and accuracy, approaching learning with increased sophistication and independence.

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AT HAWKEN, STUDENTS EXPERIENCE AN EDUCATION FOCUSED NOT ONLY ON KNOWLEDGE BUT ON THE SKILLS AND VALUES THAT WILL PREPARE THEM FOR FULFILLING AND PURPOSEFUL CAREERS AND LIVES.

Our Higher Challenge Founded in 1915, Hawken School is an independent, coeducational college preparatory day school serving 941 students in preschool through grade 12 from nine counties in Northeast Ohio.

For more information about Mathematics and other academic programs at Hawken School, please contact:

Central to Hawken’s mission is our promise to “prepare students to navigate a complex and dynamic world with self-confidence and determination; embrace challenges with disciplined analysis and creativity; and engage others with empathy and integrity.” The fulfillment of this promise has earned Hawken a national reputation for educational excellence and innovative programming.

Bradley Gill Director of the Lower School

At Hawken School, we are committed to providing an atmosphere where the timeless values of character, empathy, and respect are just as important and expected as academic excellence.

P 440.423.2044 mhilb@hawken.edu

HAWKEN s

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Lyndhurst Campus Lower School: Preschool - Grade 5 Middle School: Grades 6 - 8 5000 Clubside Road Lyndhurst, Ohio 44124 440.423.2950

P 440.423.2122 bgill@hawken.edu Mary Beth Hilborn Director of Early Childhood

Gates Mills Campus Upper School: Grades 9 -12 PO Box 8002 Gates Mills, Ohio 44040 440.423.2955

WWW.HAWKEN.EDU

I Get Ready.