roosevelt public school district math curriculum revised ... · 2a school lane. p.o. box 160...

2a School Lane. P.O. Box 160 Roosevelt, NJ 08555-0160

T 609.448.2798 F 609.448.2681

Shari Payson,

Principal

www.rps1.org

Roosevelt Public School District

Math Curriculum

Revised 2008-2009

Committee Members

Shari Payson

Donna Gazzani

Scot Gershman

ROOSEVELT SCHOOL DISTRICT Mathematics Curriculum – Grade K

Everyday Math, 2007

Objectives/Goals

Materials

Assessment/Evaluation

1

Standard 4.1 Number and Numerical Operation All students will develop number sense and will perform standard

numerical operations and estimations on all types of numbers in a variety of ways using real life experiences.

4.1.A Number Sense Essential Questions How can we compare and contrast numbers? How can counting, measuring or labeling help to make sense of the world around us? • Move flexibly between concrete and abstract representations of

mathematical ideas in order to solve problems, model mathematical ideas, and communicate solution strategies

• Understand that numbers have a variety of uses • Make and use a variety of models for "number". • Break numbers into parts • Utilize calculator • Use numbers throughout the school day as they discuss the date,

attendance, calendar, time, snacks, money, etc. • Use a balance to find combinations of numbered weights that will pan

balance an object that will be greater or less than a given weight • Count by 1s to 100; count by 2s, 5s, and 10s and count backwards by

1s • Count 20 or more objects, estimate the number of objects in a

collection • Model numbers using manipulatives; use manipulatives to exchange

1s for 10s and 10s for 100s; read numbers up to 30. • Use manipulatives to model half or a region or a collection • Compare and order whole numbers up to 20.

LCD Projector Document Camera Overhead AppleWorks KidPix Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Chips Popsicle Sticks Games

Formative Assessments Math Message Mental Math Math Boxes Use of White Boards Individual Profile of Progress Questions & Answers Think, Pair, Share Home Links Math Journals Math Masters Math Minutes On-line Math Facts Games Teach Observation Problem of the Day Informal observation/ student presentation Oral assessment of individual students Discussion of yes/no questions. Which one has more/less Summative Assessments Unit Assessments Teacher Prepared Assessments


Everyday Math, 2007

Objectives/Goals

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2

4.1.B Numerical Operations and Computation Essential Question What makes a computational strategy both effective and efficient? • Solve problems involving the addition and subtraction of 1-digit whole

numbers • Use a variety of strategies to solve simple verbal story problems

involving numbers 0 to 10 • Identify join and take-away situations 4.1.C Estimation Essential Question How can we decide when to use an exact answer and when to use an estimate? • Use words, actions, pictures, or manipulatives to solve problems • Judge without counting whether a set of objects has less than or more

than the number of objects in a reference set • Explain the reasonableness of a solution

White boards Singapore Math Marbles Other manipulatives Abacus Geoboard Attribute Blocks Meter Stick Ruler Centimeter Cube Thermometer Paper Clock Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models

Additional Assessments Open Ended Questions – Scored Using Rubric Multiple Choice questions Creative Story Writing Counters to make a set equal to greater than or less than Use dot pattern cards or dominoes to practice more, less, and same. Students can label the sets with cards that show the appropriate words. With dominoes, students work in pairs to compare the dots on the two halves and state which is more and by how much. Broken Calculator Key Game Students play the card game Top-It with either dot cards or with a deck of regular playing cards minus the face cards. Every now and then, the rule changes so that the student with the card that is less wins the play Students play Guess the Point. A long number line with endpoints of 20 and 75, for example, is drawn on the board where all of the intermediary points are labeled above the line. The labels are then covered by a long piece of paper that can be lifted to reveal them. A


Everyday Math, 2007

Objectives/Goals

Materials


3

Standard 4.2 Geometry and Measurement All students will develop spatial sense and the ability to use geometric

properties, relationships, and measurement to model, describe and analyze phenomena.

4.2.A Geometric Properties Essential Questions How can spatial relationships be described by careful use of geometric language? How can we best represent and verify geometric/algebraic relationships? • Specify locations and describe spatial relationships (use directional

terms in a variety of situations: over, under forward, backward, between, right and left

• Combine shapes to fill an area • Identify and describe 2D and 3D figures including circles, triangles,

squares, rectangles, spheres, and cubes. • Identify shapes having line symmetry • Use simple shapes to make designs, patterns and pictures 4.2.B/C Transforming Shapes/Coordinate Geometry Essential Question What situations can be analyzed using transformations and symmetries? • Sort, describe, compare and contrast 2-D and 3-D shapes according to

their attributes • Manipulate shapes so that they fill an outline (e.g., flip a pattern block

so it will complete a missing space of a given outlined area)

Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Chips Popsicle Sticks Games White boards Singapore Math Marbles Other manipulatives Abacus Geoboard Attribute Blocks Meter Stick Ruler Centimeter Cube Thermometer

student places a finger somewhere on the line and others must estimate the numerical label of the point chosen. The paper is then lifted to check the accuracy of their responses. Students play Guess the Point. A long number line with endpoints of 20 and 75, for example, is drawn on the board where all of the intermediary points are labeled above the line. The labels are then covered by a long piece of paper that can be lifted to reveal them. A student places a finger somewhere on the line and others must estimate the numerical label of the point chosen. The paper is then lifted to check the accuracy of their responses. “Train Games” with centers adding and subtracting based on dice with + or – signs. Find the line of symmetry of a given 2-D shape (e.g., drawing a line down the middle of a circle to create two equal halves or folding a paper circle in half so that the edges match without any overlap)


Everyday Math, 2007

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4

4.2.D/E Units of Measurement/Measuring Objects Essential Question How can measurements be used to solve problems? • Students will be able to identify the tool use to measure an object with

(eg. Ruler measures length of a book and a scales tell you the weight of an object)

• Use words to describe time (eg. Day, night, morning, afternoon, yesterday, today, tomorrow)

• Use words to describe temperature (eg. Hot, warm, cool, cold) • Tell time to the hour • Recognize the thermometer as a way of measuring temperature • Recognize the calendar as a way of measuring time)

Paper Clock Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models

Symmetrical paintings “What’s My Rule Game” Kindergarten students play the hide the pennies game. The first player places a number of pennies (say 7) on the table and lets the other player count them. The first player covers up a portion of the pennies, and the second player must determine how many are covered. They may represent the situation with markers or pictures to help them. Students are given a bag with Unifix Cubes. They are told that the bag and 2 cubes balance 7 cubes. They use a balance scale to find how many cubes are in the bag. Describe daily weather and temperature


Everyday Math, 2007

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5

Standard 4.3 Patterns and Algebra All students will represent and analyze relationships among variable

quantities and solve problems involving patterns, functions, and algebraic concepts and processes.

4.3.A,B,C Patterns, Functions and Algebra Essential Questions How can change be best represented mathematically? How are patterns of change related to the behavior of functions? How can patterns be represented graphically, symbolically or verbally? How can we use physical models to understand mathematics? How do algebraic and numeric procedures interconnect and build on one another to produce a coherent whole? • Copy and construct repeating patterns • Compare and describe repeating patterns • Record repeating patterns using objects, drawings, and/or words • Determine what comes next in a repeating pattern • Distinguish between patterns and non-patterns • Construct a variety of patterns using the same elements • Compare and contrast different kinds of patterns • Identify the unit of a repeating pattern (e.g., in a red, blue, red, blue

pattern, red, blue is the unit) • Count the number of units in a repeating pattern • Extend a repeating pattern by adding on units to the pattern • Keep track of a growing set of objects • Recognize and describe change in quantities • Construct and solve simple open sentences involving addition or

subtraction (e.g., 4 + 1 = __, 5 – 2 = __)

Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Chips Popsicle Sticks Games White boards Singapore Math Marbles Other manipulatives Abacus Geoboard Attribute Blocks Meter Stick Ruler

Formative Assessments Math Message Mental Math Math Boxes Use of White Boards Individual Profile of Progress Questions & Answers Think, Pair, Share Home Links Math Journals Math Masters Math Minutes On-line Math Facts Games Teach Observation Problem of the Day Informal observation/ student presentationOral assessment of individual students. Summative Assessments Unit Assessments Teacher Prepared Assessments Additional Assessments Open Ended Questions – Scored Using Rubric Multiple Choice questions Creative Story Writing Counters to make a set equal to greater than or less than Making patterns with markers, beads, chains


Everyday Math, 2007

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6

Standard 4.4 Data Analysis, Probability and Discrete Mathematics All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to

model situations, solve problems, and analyze and draw appropriate inferences from data.

4.4.A Data Analysis Essential Questions How can the collection, organization, and display of data be used to answer questions? How can experimental probabilities be used to make predictions or draw conclusions? How can attributes be used to classify data/objects? What is the best way to solve this? What counting strategy works best here? • Collect and organize data to create class-constructed tally charts,

tables and bar graphs • Use graphs to answer simple questions • Students collect objects such as buttons, books, blocks, counters, etc.

which can be sorted by color, shape, or size. They classify the objects and color one square of a bar graph for each item using different colors for each category. Then they compare the categories and discuss the relationships among them.)

• Describe events using certain, possible, impossible and other basic probability terms

• Use Venn diagrams to analyze data

Centimeter Cube Thermometer Paper Clock Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Chips Popsicle Sticks Games White boards Singapore Math

Formative Assessments Math Message Mental Math Math Boxes Use of White Boards Individual Profile of Progress Questions & Answers Think, Pair, Share Home Links Math Journals Math Masters Math Minutes On-line Math Facts Games Teach Observation Problem of the Day Informal observation/ student presentationOral assessment of individual students. Summative Assessments Unit Assessments Teacher Prepared Assessments Additional Assessments Open Ended Questions – Scored Using Rubric Multiple Choice questions


Everyday Math, 2007

Objectives/Goals

Materials


7

Standard 4.5 Mathematical Processes All students will use mathematical processes of problem solving,

communication, connections, reasoning, representations, and technology to solve problems and communicate mathematical ideas.

4.5.A Problem Solving • Learn mathematics through problem solving, inquiry, and discovery • Solve problems:

o Open-ended problems o Non-routine problems o Problems with multiple solutions

• Select and apply a variety of appropriate problem-solving strategies (e.g., “try a simpler problem” or “make a diagram”) to solve problems

• Pose problems of various types and levels of difficulty 4.5.B Communication • Use communication to organize and clarify mathematical thinking • Communicate mathematical thinking coherently and clearly to peers,

teachers, and others, both orally and in writing • Analyze and evaluate the mathematical thinking and strategies of

others • Use the language of mathematics to precisely express mathematical ideas 4.5.C Connections • Recognize recurring themes across mathematical domains (e.g., patterns

in number, algebra, and geometry) • Use connections among mathematical ideas to explain concepts (e.g.,

two linear equations have a unique solution because the lines they

Marbles Other manipulatives Abacus Geoboard Attribute Blocks Meter Stick Ruler Centimeter Cube Thermometer Paper Clock Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models

Creative Story Writing Counters to make a set equal to greater than or less than Individual bar graphs with data


Everyday Math, 2007

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represent intersect at a single point) • Trace the development of mathematical concepts over time and across

cultures (cf. world languages and social studies standards) • Understand how mathematical ideas interconnect and build on one

another to produce a coherent whole 4.5.D Reasoning • Recognize that mathematical facts, procedures, and claims must be

justified • Use reasoning to support mathematical conclusions and problem

solutions • Select and use various types of reasoning and methods of proof • Rely on reasoning, rather than answer keys, teachers, or peers, to

check the correctness of problem solutions • Evaluate examples of mathematical reasoning and determine whether

they are valid 4.5.E Representations • Recognize that mathematical facts, procedures, and claims must be

justified • Use reasoning to support mathematical conclusions and problem

solutions • Select and use various types of reasoning and methods of proof • Rely on reasoning, rather than answer keys, teachers, or peers, to

check the correctness of problem solutions • Evaluate examples of mathematical reasoning and determine whether

they are valid


Everyday Math, 2007

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9

4.5.F Technology • Use technology to gather, analyze, and communicate mathematical

information • Use computer software to make and verify conjectures about geometric

objects • Use calculators as problem-solving tools (e.g., to explore patterns, to

validate solutions) • Use computer-based laboratory technology for mathematical

applications in the sciences

LCD Document Camera AppleWorks KidPix On-line Games/Websites EDM Games

ROOSEVELT PUBLIC SCHOOL DISTRICT Mathematics Curriculum – Grade 1

Everyday Math, 2007

Objectives/Goals

Materials


1

Standard 4.1 Number and Numerical Operation All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a

variety of ways using real life experiences.

4.1.A Number Sense Essential Questions How do mathematical ideas interconnect and build on one another to produce a coherent whole? How can we compare and contrast numbers? How can counting, measuring, or labeling help to make sense of the world around us? What makes a computational strategy both effective and efficient? • Count by 1s, 2s, 5s, and 10s past 100, and back by 1s from any • number less than 100 with and without number grids, number

lines or calculators • Count collection of object accurately • Read, write and model numbers up to 1000 with

manipulatives; identify the place value of digits • Use manipulatives and drawings to model halves, thirds and

quarters as equal parts of a region or a collection. • Identify odd and even numbers • Compare and order numbers up to 100 • Understand numbers, have a variety of uses

LCD Projector Document Camera Overhead AppleWorks KidPix Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Chips Popsicle Sticks

Formative Assessments Math Message Mental Math Math Boxes Use of White Boards Individual Profile of Progress Questions & Answers Think, Pair, Share Home Links Math Journals Math Masters Math Minutes On-line Math Facts Games Teacher Observation Problem of the Day Summative Assessments Unit Assessments Teacher Prepared Assessments Additional Assessments Open Ended Questions – Scored Using Rubric Multiple Choice questions


Everyday Math, 2007

Objectives/Goals

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2

4.1.B Numerical Operations Essential Question How do operations affect numbers? • Demonstrate with proficiency the fact families of addition and

subtraction up to 10. • Understand and use the inverse relationship of addition and

subtraction • Use manipulatives, number grids, mental math and calculators

to solve problems involving the addition and subtractions of 1-digit whole numbers with a 1- or 2-digit whole number

• Calculate and compare the values of combinations of coins up to one dollar

• Identify change- to- more, or change -to -less, comparison and parts-and total situations

• Develop the meaning of addition and subtraction by joining, separating and comparing

• Select paper-pencil, mental math, or the use of a calculator as the best means in solving a problem

4.1.C Estimation

Essential Question How can we decide when to use an exact answer and when to use an estimate? • Judge without counting whether a set or collection has more

than, less than or equal to a reference set. • Determine the reasonableness of an answer through estimation • Explore a variety of methods for estimating ( eg. number of

marbles in a marble jar)

Games White boards Singapore Math Marbles Other manipulatives Abacus Geoboard Meter Stick Ruler Centimeter Cube Thermometer Paper Clock Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models Spinner Manipulatives White board

Creative Story Writing Broken Key Calculator Game See text for additional math games. What’s My Rule Frames & Arrows


Everyday Math, 2007

Objectives/Goals

Materials


3

Standard 4.2 Geometry and Measurement All students will develop spatial sense and the ability to use

geometric properties, relationships, and measurement to model, describe and analyze phenomena.

4.2. A. Geometric Properties Essential Questions How can spatial relationships be described by careful use of geometric language? How do geometric relationships help us to solve problems and/or make sense of phenomena? What situations can be analyzed using transformations and symmetries? How can we best represent and verify geometric/algebraic relationships? • Identify and describe spatial relationships among objects in

space according location (inside/outside), size (larger than, smaller than) and if they are congruent

• Identify and discriminate between 2-D and 3-D figures • Label points, faces, edges, sides and vertices • Recognize, describe and extend patterns • Locate lines of symmetry • Use simple shapes to make designs and patterns • Use smaller shapes to make a larger shape • Give and follow directions from getting from one point to

another on a map or grid

Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Chips Popsicle Sticks Games White boards Singapore Math Marbles Other manipulatives Abacus Geoboard Attribute Blocks Meter Stick Ruler

Formative Assessments Math Message Mental Math Math Boxes Use of White Boards Individual Profile of Progress Questions & Answers Think, Pair, Share Home Links Math Journals Math Masters Math Minutes On-line Math Facts Games Teach Observation Problem of the Day Summative Assessments Unit Assessments Teacher Prepared Assessments Additional Assessments Open Ended Questions – Scored Using Rubric Multiple Choice questions Creative Story Writing Broken Key Calculator Game See text for additional math games.


Everyday Math, 2007

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4

4.2. B.C Transforming Shapes/Coordinate Geometry Essential Question What situations can be analyzed using transformations and symmetries? • Explore how shapes can be combined to make other shapes • Cover a region without gaps or overlaps using multiple shapes • Match a 3-D object to a 2-D outline of one of its faces or a

picture • Compare and contrast attributes of a group of shapes • See relationships between squares and triangles • Explore how shapes can be combined to make other shapes • Cover a region without gaps or overlaps using multiple shapes

4.2.D Units of Measurement Essential Question How can measurements be used to solve problems? • Use nonstandard tools and techniques to estimate and compare

weight and length: measure length with standard measuring tools to the nearest inch and the nearest centimeter

• Identify a measurement tool that would be used to measure a specified item (eg. That tool would be used to measure the length of a door?)

• Be able to determine the weight of an object to the use of a nonstandard unit of items (eg. How many paper clips will it take to make the weight of a block on a pan balance)

• Identify liquid measurement of cup, pint, quart and gallon • Identify a thermometer as a tool for measuring temperature;

read temperatures on Fahrenheit and Celsius thermometers to the nearest 10 degrees

Centimeter Cube Thermometer Paper Clock Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models Metersticks Rulers Scales Measuring cups Containers of Pint, Quart, and Gallon Thermometer

What’s My Rule Frames & Arrows


Everyday Math, 2007

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5

• Use a calendar to identify days, weeks, months and dates; tell and show time to the nearest half and quarter hour on an analog clock

• Measure the perimeter of a simple 2-D shape • State the area of a 2-D figure by counting its square units

Calendars Graph paper


Everyday Math, 2007

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6

Standard 4.3 Patterns and Algebra All students will represent and analyze relationships among variable quantities and solve problems involving patterns,

functions, and algebraic concepts and processes.

4.3.A,B Patterns/Functions Essential Questions How can change be best represented mathematically? How can patterns, relations, and functions be used as tools to best describe and help explain real-life situations? • Identify what comes next in a repeating pattern • Use the word pattern to describe some kind of regularity in a

sequence • Represent a repeating unit in more than one way (representing

red-blue-red cube pattern with the movement clap-slap knees-clap-slap knees)

• Associate counting numbers with the elements of a repeating pattern

• Identify what comes several steps beyond the visible part of a repeating pattern

• Determine the element of a repeating pattern associated with a particular counting number

• Compare repeating and non-repeating sequencing • Describe a repeating pattern as a sequence built from a part that

repeats over and over called a unit • Identify the unit of a repeating pattern • Extend a repeating pattern by adding on units to the pattern • Students represent data in various ways such as equations and

different types of graphs

Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Chips Popsicle Sticks Games White boards Singapore Math Marbles Other manipulatives Abacus Geoboard Attribute Blocks Meter Stick Ruler Centimeter Cube Thermometer Paper Clock

Formative Assessments Math Message Mental Math Math Boxes Use of White Boards Individual Profile of Progress Questions & Answers Think, Pair, Share Home Links Math Journals Math Masters Math Minutes On-line Math Facts Games Teach Observation Problem of the Day Summative Assessments Unit Assessments Teacher Prepared Assessments Additional Assessments Open Ended Questions – Scored Using Rubric Multiple Choice questions Creative Story Writing


Everyday Math, 2007

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7

4.3. C,D Modeling/Procedures Essential Question How can we use mathematical models to describe physical relationships? • Recognize and describe changes over time (e.g. temperature,

height) • Construct and solve simple open sentences involving addition

or subtraction (part unknown in an equation) • Understand and apply the following properties of addition

(commutative, associative, and zero as the identity element)

Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models Thermometer

Broken Key Calculator Game See text for additional math games. What’s My Rule Frames & Arrows Games


Everyday Math, 2007

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8

Standard 4.4 Data Analysis, Probability, and Discrete Mathematics

All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete

mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from

data.

4.4.A Data Analysis Essential Question How can the collection, organization, and display of data be used to answer questions? • Judge without counting whether a set or collection has more

than, less than or equal to a reference set • Describe attributes of objects • Use attributes to sort a set of objects • Interpret results of a data investigation • Sort objects into groups considering their attributes • Collect and organize data to create tally charts, tables, bar

graphs and line plots • Use graphs to answer simple questions and draw conclusions;

find the maximum, minimum and range of a set of data • Organize data in numerical order • Use data to compare how two groups are similar or different 4.4. B Probability

Essential Question How can experimental and theoretical probabilities be used to make predictions or draw conclusions?

Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Chips Popsicle Sticks Games White boards Singapore Math Marbles Other Spinners Manipulatives Abacus Geoboard Attribute Blocks Meter Stick Ruler Centimeter Cube Thermometer

Formative Assessments Math Message Mental Math Math Boxes Use of White Boards Individual Profile of Progress Questions & Answers Think, Pair, Share Home Links Math Journals Math Masters Math Minutes On-line Math Facts Games Teach Observation Problem of the Day Summative Assessments Unit Assessments Teacher Prepared Assessments Additional Assessments


Everyday Math, 2007

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• Collect, generate and record data from the use of a simple spinner

• Describe events using certain, likely, unlikely, possible and impossible in basic probability terms

• Write the probability of choosing an object out of a bag in fractional format

4.4 C.D Discrete Mathematics - Systematic Listing and Counting/ Vertex-Edge Graphs and Algorithms Essential Questions How can attributes be used to classify data/objects? What is the best way to solve this? What counting strategy works best here? • Sort and classify objects according to attributes • Generate all possibilities in a simple situation (2 shirts and 2

pairs of pants) • To get from one point to another by exploring concrete models

of vertex-edge graphs • Recognize symmetrical objects • Color simple maps with the smallest number of colors • Use pictures and multiple strategies to solve problems

Paper Clock Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models Buttons Paper dolls and clothes Reflective forms Maps Singapore Math

Open Ended Questions – Scored Using Rubric Multiple Choice questions Creative Story Writing Broken Key Calculator Game See text for additional math games What’s My Rule Frames & Arrows Venn Diagram


Everyday Math, 2007

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10

Standard 4.5 Mathematical Processes All students will use mathematical processes of problem

solving, communication, connections, reasoning, representations, and technology to solve problems and

communicate mathematical ideas.

4.5. A Problem Solving • Learn mathematics through problem solving, inquiry, and

discovery • Solve problems:


• Judge without counting whether a set or collection has more than, less than or equal to a reference set.

• Select and apply a variety of appropriate problem-solving strategies (e.g., “try a simpler problem” or “make a diagram”) to solve problems

• Pose problems of various types and levels of difficulty 4.5. B Communication

• Write and discuss mathematical thinking and the use of their

strategies to others • Use communication to organize and clarify mathematical

thinking • Communicate mathematical thinking coherently and clearly to

peers, teachers, and others, both orally and in writing • Analyze and evaluate the mathematical thinking and strategies

of others

Problem of the day Singapore math Problem solving techniques Math Journals

Open ended test response Class discussion Open ended test response Rubric for math responses


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• Use the language of mathematics to express mathematical ideas precisely

4.5.C Connections • Recognize that mathematics is used in a variety of context

outside of mathematics • Use communication to organize and clarify mathematical

thinking • Communicate mathematical thinking coherently and clearly to

peers, teachers, and others, both orally and in writing • Use connections among mathematical ideas to explain concepts • Use the language of mathematics to express mathematical ideas

precisely

4.5.D Reasoning • Rely on reasoning to infer if the solution, or method of solving

an equation makes math sense • Use reasoning to support mathematical conclusions • Select and use various types of reasoning and methods of proof • Rely on reasoning, rather than answer keys, teachers, or peers,

to check the correctness of their problem solutions 4.5.E Representations • Create and use representations to organize, record, and

communicate mathematical ideas o Concrete representations (e.g., base-ten blocks or algebra

tiles) o Pictorial representations (e.g., diagrams, charts, or

Everyday math journal Problem of day Manipulatives Charts Everyday math reference book Singapore math Problem solving techniques Base-ten blocks Graph paper

Class discussion Problem of Day Rubrics Open ended math tests


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tables) o Symbolic representations (e.g., a formula) o Graphical representations (e.g., a line graph) o Select, apply, and translate among mathematical

representations to solve problems

4.5.F Technology • Use technology to gather, analyze, and communicate

mathematical information • Use computer software to make and verify conjectures about

geometric objects • Use calculators as problem-solving tools (e.g., to explore

patterns, to validate solutions) • Use computer-based laboratory technology for mathematical


Number line LCD Document Camera AppleWorks KidPix On-line Games/Websites EDM Games Calculators

Teacher Observations


Everyday Math, 2007

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Standard 4.1 Number and Numerical Operations

All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a

variety of ways.

4.1.2. A Number Sense Essential Questions How do mathematical ideas interconnect and build on one another to produce a coherent whole? How can we compare and contrast numbers? How can counting, measuring, or labeling help to make sense of the world around us? • Count using number grids, number lines and calculators • Count backwards from one-thousand by ones, twos, fives, tens, twenty-

fives and hundreds • Count on by ones, twos, fives, tens, twenty-fives and hundreds past

one-thousand • Count without using number grids, number lines and calculators • Develop skills involving rote counting • Develop skills involving place-value • Read, write, and model with manipulatives whole numbers to ten-

thousand • Identify place values in numbers up to ten-thousand • Read and write money amounts in dollar and cents notation • Use manilpulatives and drawings to model fractions as equal parts of a region or a collection • Describe the models and name the fractions • Use tally marks, arrays, and numerical expressions • Use addition and subtraction to give equivalent names for whole

numbers • Recognize numbers as odd or even

LCD Projector Document Camera Overhead AppleWorks KidPix Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Chips Popsicle Sticks Games White boards

Formative Assessments Math Message Mental Math Math Boxes Use of White Boards Individual Profile of Progress Questions & Answers Think, Pair, Share Home Links Math Journals Math Masters Math Minutes On-line Math Facts Games Teach Observation Problem of the Day Summative Assessments Unit Assessments Teacher Prepared Assessments Additional Assessments Open Ended Questions – Scored Using Rubric Multiple Choice questions Creative Story Writing Math Journals Venn Diagram


Everyday Math, 2007

Objectives/Goals

Materials


• Develop meanings and uses of fractions • Find equivalent names fractions, decimals, and percents • Use manipulatives and drawings to model equivalent names for one-

half • Compare and order whole numbers up to ten-thousand • Use area models to compare fractions • Check the reasonableness of results of computation • Use the number line and 100 chart to understand the place value

system and model addition and subtraction • Use the number line to reason about, and keep track of information

about, the magnitude and relationship of numbers • Solve problems with unknown change • Combine coins to a total of 50 cents • Solve an addition story problem by counting on or breaking numbers

apart • Consider whether reordering three addends results in the same total • Consider a generalization about reordering addends for all numbers • Identify coins and their values and uses coin equivalencies • Add 2-digit numbers • Understand that any number that can be divided into groups of two can

also be divided into two equal groups (and vice versa) • Characterize even and odd numbers as those that do or do not make

groups of two (partners) and two equal groups (teams) • Consider whether observation about even or odd numbers apply to all

even numbers or all odd numbers • Look at patterns and developing fluency with skip counting by 2s, 5s,

and 10s • Use the calculator as a mathematical tool • Add tens and ones to combine 2-digit numbers • Understand the value of the tens place when a multiple of 10 is added

or subtracted • Develop fluency with the sequence of numbers from 1 to 100 • Find and use patterns in the sequence of numbers

Marbles Other manipulatives Abacus Geoboard Meter Stick Ruler Centimeter Cube Thermometer Paper Clock Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models


Everyday Math, 2007

Objectives/Goals

Materials


• Recognize the equivalence of different fourths of the same object • Identify halves, thirds, and fourths of regions • Identify and name fractional parts that have numerators greater than 1

(e.g., 2/3, 2/4, 3/4) • Find fractions of sets • Solve problems about finding halves in different contexts • Solve problems that result in mixed numbers • Learn the fraction terms and notation 1/2, 1/3, and 1/4 • Learn the terms and notation for mixed numbers (1 !) 4.1.2. B Numerical Operations Essential Questions What makes a computational strategy both effective and efficient? How do operations affect numbers? • Demonstrate automaticity with addition and subtraction facts involving

zero or one • Demonstrate automaticity with addition and subtraction facts involving

doubles and sum-equals-tens facts • Develop procedures for using addition and subtraction facts • Use manipulatives, number grids, tally marks, mental arithmetic, paper

and pencil, and calculators to solve problems involving addition and subtraction of two digit numbers

• Describe the strategies used • Calculate and compare the values of coin and bill combinations • Identify and describe change using comparison and parts and total

situations • Use repeated addition, arrays, and skip counting to model

multiplication • Use equal sharing and equal grouping to model division • Visualize, retell, and model the action of addition and subtraction (as

removal) situations


Everyday Math, 2007

Objectives/Goals

Materials


• Use known combinations (i.e. combinations that make 10) to compose,

decompose, and combine numbers • Subtract a quantity from a whole of up to 30 • Solve addition and subtraction (as removal) story problems • Find two addends that make 10 • Find the missing addend to make a total of 10 • Develop fluency with the doubles combinations • Establish use of tools, routines, and, expectations for math class • Use standard notation (>,<,+,-,=) to describe arrangement of cubes, to

record expressions that equal a given number, to compare quantities, to represent addition and subtraction situations, and to represent doubling

• Use the number line to reason about, and keep track of information about, the magnitude and relationship of numbers

• Record strategies for solving problems, including addition and subtraction story problems

• Connect standard notation for addition and subtraction (+,-,=) to the quantities and actions that the signs and symbols represent

• Use known combinations to add two or more numbers • Compare a number to 20 to find the difference • Develop strategies for solving a variety of addition and subtraction

story problems and recording work • Solve problems with unknown change • Add 2-digit numbers by adding tens and ones • Solve place value problems when 2-digit numbers with a sum over 100

are combined • Explore the meanings of multiplication and division by modeling and

discussing problems • Check the reasonableness of results of computations


Everyday Math, 2007

Objectives/Goals

Materials


4.1.2. C Estimation Essential Question How can we decide when to use an exact answer and when to use an estimate? Develop procedures for forming computational estimates • Make reasonable estimates for whole number addition and subtraction

problems • Make predictions about data to be collected • Cover a region, without gaps or overlaps, with a single shape or

multiple shapes • Cover a region, without gaps or overlaps, using different shapes • Explain how the estimates were obtained


Everyday Math, 2007

Objectives/Goals

Materials


Standard 4.2 Geometry and Measurement

All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze

phenomena.

4.2.2. A Geometric Properties Essential Questions How can spatial relationships be described by careful use of geometric language? How do geometric relationships help us to solve problems and/or make sense of phenomena? • Draw line segments and identify parallel line segments • Identify, describe, construct, and model plane and solid figures: circles,

triangles, squares, rectangles, hexagons, trapezoids, rhombuses, spheres, cylinders, prisms, pyramids, cones, and cubes – both 2D and 3D shapes

• Combine shapes to make a new shape • Cover a region, without gaps or overlaps, using a single shape, or

multiple shapes • Describe attributes of and sorting 2-D and 3-D shapes • Identify names and attributes and construct 2-D (square, rectangle,

circle, triangle) and 3-D shapes (cube, rectangular prism, sphere, cone, cylinder, and pyramid) designs

• Identify, classify, and describe vertex, edge, face, and side • Recognize, describe, extend, and create designs and patterns with

geometric objects of different shapes and colors • Give and follow directions for getting from one point to another point

on a map or grid • Describe and identify objects and designs that have mirror symmetry • Construct 2-D and 3-D symmetrical designs with mirror symmetry • Reflect a shape across a line of symmetry • Explore symmetry by folding and cutting paper patterns

Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Chips Popsicle Sticks Games White boards Singapore Math Marbles Other manipulatives Abacus Geoboard Attribute Blocks Meter Stick Ruler Centimeter Cube

Formative Assessments Math Message Mental Math Math Boxes Use of White Boards Individual Profile of Progress Questions & Answers Think, Pair, Share Home Links Math Journals Math Masters Math Minutes On-line Math Facts Games Teach Observation Problem of the Day Summative Assessments Unit Assessments Teacher Prepared Assessments Additional Assessments Open Ended Questions – Scored Using Rubric Multiple Choice questions Creative Story Writing What’s My Rule


Everyday Math, 2007

Objectives/Goals

Materials


• Identify lines of symmetry • Orient shapes so that a line of symmetry aligns with a mirror (utilize

computer software, if available) • Determine what makes a design symmetrical • Congruence (i.e., same size and shape) • Create and complete two-dimensional symmetric shapes or 4.2.2. B,C Transforming Shapes / Coordinate Geometry Essential Question What situations can be analyzed using transformations and symmetries? • Use simple shapes to make designs, patterns, and pictures • Combine and subdivide simple shapes to make other shapes • Give and follow directions for getting from one point to another on a

map or grid 4.2.2. D, E Units of Measurement/ Measuring Geometric Objects Essential Question How can measurements be used to solve problems? • Develop skills involving length, weight, and angles • Estimate length with and without tools • Measure length to the nearest foot, yard, centimeter, meter, inch and

centimeter • Use standard and non-standard tools to measure and estimate weight in

grams, kilograms, and pounds • Develop skills involving area, perimeter, volume, and capacity • Count unit squares to find the area of rectangles • Identify and label partial units • Develop skills involving units and systems of measurement • Describe the relationship between days in a week and hours in a day • Develop skills involving money, temperature, and time

Thermometer Paper Clock Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models

Frames & Arrows


Everyday Math, 2007

Objectives/Goals

Materials


• Make exchanges between coins and bills • Read temperatures on both Fahrenheit and Celsius scales • Tell and write time in digital notation • Associate times with daily events • Use a timeline to determine duration • Directly compare and order objects according to measurable

attributes (length, weight, capacity, time, temperature) • Select and use appropriate standard and non-standard units of

measure and standard measurement tools to solve real-life problems length-(inch, foot, yard, centimeter meter), weight-(pound, gram, kilogram) capacity-(pint, quarter, liter) time-(second, minute, hour, day, week, month, year) temperature-(degrees Celsius, degrees Fahrenheit)

• Estimate measures • Define biggest in different ways • Directly measure the area and perimeter of simple two-dimensional

shapes


Everyday Math, 2007

Objectives/Goals

Materials


Standard 4.3 Patterns and Algebra

All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic

concepts and processes.

4.3.2. A Patterns Essential Questions How can change be best represented mathematically? How can patterns, relations, and functions be used as tools to best describe and help explain real-life situations? • Develop skills involving patterns and functions • Extend, describe, and create numeric patterns • Describe rules for patterns • Use words and symbols to describe and write rules for functions

involving addition and subtraction • Use those rules to solve problems • Recognize, describe, create, and extend a repeating pattern • Identify number patterns on the 100 chart using multiples of 2, 5, and

10 • Use algebraic notation and solve number sentences • Read, write, and explain expressions and number sentences using

greater than and less than symbols • Solve number sentences involving addition and subtraction • Develop skills involving the properties of arithmetic operations • Describe the Commutative and Associative properties of addition and

apply them to mental arithmetic problems • Define even and odd numbers • Determine and describe the number sequence associated with one of

the elements in an AB, ABC, ABCD, or AABBC repeating pattern (e.g., 2,4.6,8,…; 3,6,9,…; 1,4,7,…)

Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Chips Popsicle Sticks Games White boards Singapore Math Marbles Other manipulatives Abacus Geoboard Attribute Blocks Meter Stick Ruler Centimeter Cube

Formative Assessments Math Message Mental Math Math Boxes Use of White Boards Individual Profile of Progress Questions & Answers Think, Pair, Share Home Links Math Journals Math Masters Math Minutes On-line Math Facts Games Teach Observation Problem of the Day Summative Assessments Unit Assessments Teacher Prepared Assessments Additional Assessments Open Ended Questions – Scored Using Rubric Multiple Choice questions Creative Story Writing


Everyday Math, 2007

Objectives/Goals

Materials


4.3.2. B Functions & Relationships Essential Question How are patterns of change related to the behavior of functions? • Connect numbers in a table to the situation they represent • Use conventional language for a table and its parts; rows, columns • Describe what is the same about situations that look different but can

be represented by the same table • Describe how the two numbers in the row of a table are connected to

the situation the table represents • Use information in a table to determine the relationship between two

quantities • Find the missing addends to make different totals • Organize data in table to uncover a rule • Used concrete and pictorial models of function machines to explore the

basic concept of a function 4.3.2. C,D Modeling/Procedures Essential Questions How can we use mathematical models to describe physical relationships? How can we use physical models to clarify mathematical relationships? • Find the missing addend to make a total of 10 • Solve problems with an unknown change • Collect and record data from a survey • Order, represent, and describe a set of numerical data • Represent data on a line plot • Recognize and describe changes over time (e.g., temperature, height) • Understand and apply the following properties of addition: Commutative (e.g., 5+3 = 3+5) Zero as the identity element (e.g., 7 + 0= 7) Associative (e.g., 7 + 3 + 2 can be found by first adding either 7 + 3 or 3 + 2)

Thermometer Paper Clock Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models


Everyday Math, 2007

Objectives/Goals

Materials



All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to


4.4.2. A Data Analysis Essential Question How can the collection, organization, and display of data be used to answer questions? • Select and create appropriate graphical representations of collected or

given data and analyze and interpret data in order to apply the basic concepts of probability

• Group data into categories based on similar attributes • Sort data in different ways • Compare two sets of data • Develop a hypothesis based on a set of data • Make a plan for collecting data • Make predictions about data to be collected • Collect and record data from a survey • Select and create appropriate graphical representations for data • Generate, collect and organize data or use given data to create bar and

line graphs, tally charts, and tables • Data generated from chance devices, such as spinners and dice • Use a Venn diagram, pictures, tally chart, pictograph, and bar graph to

represent and display sorted set of data • Use graphs to answer simple questions and draw conclusions • Find the maximum, minimum, mode, and median of a data set

Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Chips Popsicle Sticks Games White boards Singapore Math Marbles Other manipulatives Abacus Geoboard Attribute Blocks Meter Stick Ruler Centimeter


Everyday Math, 2007

Objectives/Goals

Materials


4.4.2. B Probability Essential Question How can experimental and theoretical probabilities be used to make predictions or draw conclusions? • Understand and apply the basic concepts of probability • Describe events using terms such as likely, possible, unlikely, and

impossible • Describe and develop strategies to predict the probability of specific

outcomes • Explain the choice of language. 4.4.2. C,D Discrete Mathematics - Systematic Listing and Counting/ Vertex-Edge Graphs and Algorithms Essential Questions How can visual tools such as networks (vertex- edge graphs) be used to answer questions? How can algorithmic thinking be used to solve problems? • Develop skills involving systemic listing and counting • Generate all possibilities in simple counting situations such as all

outfits for two shirts and 3 pants • Sort and classify object according to attributes using Venn Diagrams

Cube Thermometer Paper Clock Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models


Everyday Math, 2007

Objectives/Goals

Materials


Standard 4.5 Mathematical Processes

All students will use mathematical processes of problem solving, communication, connections, reasoning, representations, and technology to

solve problems and communicate mathematical ideas.

4.5. A Problem Solving • Learn mathematics through problem solving, inquiry, and discovery • Solve problems:


• Select and apply a variety of appropriate problem-solving strategies

(e.g., “try a simpler problem” or “make a diagram”) to solve problems • Pose problems of various types and levels of difficulty 4.5. B Communication • Clarify and express mathematical thinking through reading, writing,

discussion, listening, and questioning. • Use communication to organize and clarify mathematical thinking • Communicate mathematical thinking coherently and clearly to peers,

teachers, and others, both orally and in writing • Analyze and evaluate the mathematical thinking and strategies of

others 4.5. C Connections • Recognize and apply the concept that mathematics is used in a variety

of concepts outside mathematics; understand that mathematical ideas build on one another to produce a coherent whole


Everyday Math, 2007

Objectives/Goals

Materials


4.5. D Reasoning

• Use reasoning to support their mathematical conclusions and problem

solutions; evaluate examples of mathematical reasoning and determine if they are valid.

• Use reasoning to support their mathematical conclusions and problem solutions

• Select and use various types of reasoning and methods of proof • Rely on reasoning, rather than answer keys, teachers, or peers, to check

the correctness of their problem solutions 4.5. E Representations • Create and use representations to organize, record, and communicate

mathematical ideas: o Concrete representations (e.g., base-ten blocks or algebra tiles) o Pictorial representations (e.g., diagrams, charts, or tables) o Symbolic representations (e.g., a formula) o Graphical representations (e.g., a line graph)

• Use representations to model and interpret physical, social, and mathematical phenomena

4.5 F Technology • Use technology to gather, analyze, and communicate mathematical



validate solutions) • Use computer-based laboratory technology for mathematical applications

in the sciences



Everyday Math, 2007

Objectives/Goals

Materials



Everyday Math, 2007

Objectives/Goals

Materials Assessment/Evaluation

Standard 4.1 Number and Numerical Operations All students will develop number sense and will perform standard numerical operations

and estimations on all types of numbers in a variety of ways. Big Idea: Numeric reasoning involves fluency and facility with numbers. 4.1.3.A Number Sense Essential Questions How do mathematical ideas interconnect and build on one another? How can we compare and contrast numbers? How can counting, measuring or labeling help to make sense of the world around us? • Understand the meanings, uses, and representation of numbers • Recognize and represent the place value of each digit in 2- and 3- digit numbers • Use equivalencies among pennies, dimes, and dollars • Find different combinations of 100s, 10s, and 1s for a number and recognizing

their equivalence (i.e. 1 hundred, 3 tens, and 7 ones equals 1 hundred, 2 tens, and 17 ones, or 13 tens and 7 ones)

• Use real-life experiences, physical materials, and technology to construct meanings for numbers

• Read, write, and sequence whole numbers through hundred thousands and decimals through hundredths

• Represent the structure of 3-digit numbers as being composed of 100s, 10s, and 1s • Use the value of each place to make a 2- and 3-digit numbers closest to 100 • Identify place value in conjunction with expanded notation and the use of base 10

blocks • Identify whether a number is odd or even • Comparing/Ordering numbers • Understand the various uses of numbers (counting, measuring and labeling) • Read, write, and model fractions using denominators or 2,3,4,5,6,8 and 10. Solve

Singapore math Math facts LCD Projector Document Camera Overhead AppleWorks KidPix Reference Books Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Pattern Blocks Pocket Charts Place Value Cubes Chips

Formative Assessments Math Message Mental Math Math Boxes Use of White Boards Individual Profile of Progress Questions & Answers Think, Pair, Share Home Links Math Journals Math Masters Math Minutes On-line Math Facts Games Teacher Observation Problem of the Day Drawings and Diagrams Portfolio assessments Summative Assessments Unit Assessments Teacher Prepared Assessments Additional Assessments Open Ended Questions – Scored Using 1-4 Rubric


Everyday Math, 2007

Objectives/Goals


problems involving fractional parts of a region or a collection; describe strategies used. Locate fractions on a number line. Use fraction notation to record equivalencies (e.g., 3/6=1/2, ! = 2/4)

• Use mixed numbers to represent quantities greater than 1 • Identify equivalent fractions and decimals for values involving halves and fourths

(e.g., ! = 0.5, " = 0.25, 4.1.3.B Numerical Operations Essential Questions What makes a computational strategy both effective and efficient? How do operations affect numbers? How do mathematical representations reflect the needs of society across cultures? • To develop the meaning of the four basic arithmetic operations by modeling and

discussing a large variety of problems with: • Addition and subtraction: joining, separating, comparing • Solve addition problems with 2-digit numbers by using strategies that involve

breaking numbers apart by place or adding one number in parts • Solve addition problems with 2-digit numbers that involve more than 10 ones in

the ones place and explaining the effect on the sum • Solve addition problems with 2- and 3-digit numbers (up to 400) by breaking

numbers apart and recombining them • Represent addition strategies • Add and subtract multiples of 100 • Solve subtraction problems with 2- and 3-digit numbers (up to 300) using

strategies that involve either subtracting one number in parts, adding up, or subtracting back

• Solve subtraction problems that involve finding a missing part • Visualize and represent the action of a subtraction problem that involves finding a

missing part • Understand comparison as the difference between two numbers

Popsicle Sticks Games White boards Marbles Other manipulatives Geoboard Meter Stick Centimeter Stick Ruler Centimeter Cube Thermometer Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models Templates Compass Protractor Maps Mirrors Tape Measure Measuring Cups Tangrams Spinners Clothing Graph Paper

Multiple Choice Questions Creative Story Writing Math Journals Venn Diagram Timed Multiplication Quizzes Venn Diagram


Everyday Math, 2007

Objectives/Goals


• Solve subtraction story problems that involve comparison • Visualize and represent the action of comparison problems • Multiplication: repeated addition, area/array • Division: repeated subtraction, sharing • Find the multiples of the numbers 2, 3, 4, 5, 6, and 10 by skip counting • Describe and compare characteristics of the multiples of a number • Understand that doubling (or halving) one factor in a multiplication expression

doubles (or halves) the product • Use arrays to model situations • Use arrays to find factors of 2-digit numbers up to 50 • Understand division as the splitting of a quantity into equal groups • Use the inverse relationship between multiplication and division to solve problems • Use multiplication combinations to solve division problems • Use arrays to identify characteristics of numbers, including prime and square

numbers • Demonstrate automaticity with all addition, subtraction, multiplication, and

division in facts up to 10 and fact extensions such as 80 +70, or 80x7 • Construct, use and explain procedures for performing calculations with paper- and-

pencil, mental math and calculator • Solve problems involving the computation with whole numbers • Addition of 3-digit numbers • Subtraction of 3-digit numbers • Multiplication of 2-digit number by 1-digit number • Count and perform simple operations with money in all four basic operations

including cents • Find combinations of coins that equal $1.00 • Check reasonableness of results 4.1.3.C Estimation Essential Question How can we decide when to use an exact answer and when to use an estimate?

Deck of Cards Calculator


Everyday Math, 2007

Objectives/Goals


• Judge without counting whether a set of objects has less than, more than, or the

same number of objects as a reference set • Round numbers and use mental math for estimating both quantities and the results

of computation • Recognize if an answer is appropriate using estimation • Distinguish when to use estimation or an exact answer in problem solving • Check for the reasonableness of results of computation


Everyday Math, 2007

Objectives/Goals



All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.

Big Idea Geometry: Spatial sense and geometric relationships are a means to solve problems and make sense of a variety of phenomena. Big Idea Measurement: Measurement is a tool to quantify a variety of phenomena. 4.2.3.A Geometric Properties Essential Questions How can spatial relationships be described by use of geometric language? How do geometric relationships help to solve problems and/or make sense of phenomena? • Identify and describe spatial relationships of two or more objects in space • Determine the geometric moves needed (slides, flips, turns) to prove or disprove

congruence between two shapes • Explain direction, orientation and perspectives as to where an object is in relation

to another • Ability to compare and contrast relative shapes and sizes • Identify a shape when it is partially shaded from view • Use the properties of standard 3- and 2-dimensional shapes to identify, classify and

describe • Explain vertices, faces, edges, angles, base, and sides • Describe components and properties of 3D-figures: spheres, cylinders, rectangular

prisms, pyramids, cones and cubes • Describe components and properties of 2D-figures: squares, rectangle, circle,

triangle, quadrilateral, pentagon, hexagon and octagon • Explain the relationship between 2D and 3D figures (squares are rectangles and

cubes are rectangular prisms) • Identify congruence and locate multiple lines of symmetry in a 2D figure • Compare the sizes of angles

LCD Projector Document Camera Overhead AppleWorks Reference Books Templates Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Pattern Blocks Pocket Charts Place Value Cubes Chips Popsicle Sticks Games White boards Marbles Other manipulatives

Formative Assessments Math Message Mental Math Math Boxes Use of White Boards Individual Profile of Progress Questions & Answers Think, Pair, Share Home Links Math Journals Math Masters Math Minutes On-line Math Facts Games Teach Observation Problem of the Day Drawings and Diagrams Portfolio assessments Summative Assessments Unit Assessments Teacher Prepared Assessments


Everyday Math, 2007

Objectives/Goals


• Design patterns that make nets for triangular pyramids • Communicate about special relationships • Decompose images of 3-D shapes and then recombining them to make a given

structure 4.2.3.B Transforming shapes Essential Question What situations can be analyzed using transformations and symmetries? • Geometric transformations (slide, flip and turn) • Investigate and apply transformation to environment in nature and art 4.2.3.C Coordinate Geometry Essential Question How can we best represent and verify geometric/algebraic relationships? • Locate and name points in the first quadrant on a coordinate grid 4.2.3.D Units of Measurement Essential Questions How can measurement be used to solve problems? • Estimate length with and without tools • Use U. S. standard and metric units to accurately measure length • Measure to nearest ! and 1/4 inch and to ! and 1/4 centimeter • Describe and compute perimeter and area of polygons • Choose the correct measurement unit to use depending on what object is being

measured (weight-ounces, lbs) (capacity- fluid ounce, cup, gallon, milliliter) • Measure time between minutes in an hour, hours in a day and days in a week, • Tell and show time to nearest minute (be able to compute elapsed time) • Read and interpret positive and negative temperatures on a thermometer and on a

line graph

Geoboard Meter Stick Centimeter Stick Ruler Centimeter Cube Thermometer Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models Templates Compass Protractor Maps Mirrors Tape Measure Measuring Cups Tangrams Spinners Clothing Graph Paper Deck of Cards LCD Projector Document Camera

Additional Assessments Open Ended Questions – Scored Using 1-4 Rubric Multiple Choice Questions Creative Story Writing Math Journals Venn Diagram Timed Multiplication Quizzes Venn Diagram


Everyday Math, 2007

Objectives/Goals


• Associate temperatures with particular activities or clothing 4.2.3.E Measuring Geometric Objects Essential Question How can measurements be used to solve problems? • Understand perimeter as the measure around the outside edges of a 2-dimensional

figure • Find the perimeter using standard units • Create different shapes with the same perimeter • Find the perimeter of an irregular shape • Understand that area is measured in square units • Understand that when measuring area, the space being measured must be

completely covered with no gaps or overlaps • Use squares and triangles to make shapes with an area of four square units • Examine the relationship between the area of squares and triangles • Understand that shapes with the same area can look different • Find the area of partially covered rectangles • Find the area of an irregular shape • Design a shape for a given area • Find area by counting or calculating whole and partial square units • Determine the number of cubes that will fit in the box made by a given pattern • Design patterns for boxes that will hold a given number of cubes • See that the cubes filling a rectangular prism can be decomposed into congruent

layers

Overhead AppleWorks KidPix Reference Books


Everyday Math, 2007

Objectives/Goals



All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.

Big Idea: Algebra provides language through which we communicate the patterns in mathematics. 4.3.3. A Patterns Essential Questions How can change be best represented mathematically? How can patterns, relations, and functions be used as tools to best describe and help explain real-life situations? • To recognize, describe, extend and create patterns • Using words and number sentences • Show that a pattern can grow or shrink as a result of repeatedly suing adding,

subtracting, multiplication or division • Use concrete models to explore the basic concept of a function (input/output boxes,

T-charts) • To use algebraic notation to represent and analyze situations and structures • Read, write and explain number sentences using the symbols +, -, x, = , division

and greater than or less than symbols • Recognize that numeric expressions can have different values depending on the

order in which operations are carried out; understand that grouping symbols can be used to affect the order in which operations are carried out

• Construct and solve simple open sentences, solving for n • Understand and apply the properties of operations and numbers: commutative • Identity element for multiplication and the zero property

Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Pattern Blocks Pocket Charts Place Value Cubes Chips Popsicle Sticks Games White boards Marbles Other manipulatives Abacus Geoboard Meter Stick Centimeter Stick Ruler Centimeter Cube Thermometer Clock Face

Formative Assessments Math Message Mental Math Math Boxes Use of White Boards Individual Profile of Progress Questions & Answers Think, Pair, Share Home Links Math Journals Math Masters Math Minutes On-line Math Facts Games Teach Observation Problem of the Day Drawings and Diagrams Portfolio assessments Summative Assessments Unit Assessments Teacher Prepared Assessments


Everyday Math, 2007

Objectives/Goals


4.3.3 B Functions & Relationships Essential Question How are patterns of change related to the behavior of functions? • Use tables to represent the relationship between two quantities in a situation with a

constant rate of change • Interpret numbers in a table in terms of the situation they represent • Compare situations by describing differences in the tables that represent them

4.3.3. C Modeling Essential Questions How can we use mathematical models to describe physical relationships? How can we use physical models to clarify mathematical relationships? • Describe the overall shape of a line graph-increasing, decreasing, staying the same • Find the difference between values on a line graph, including the difference

between a positive and negative value • Associate a story with its corresponding graph • Plot points on a graph to represent a situation in which one quantity is changing in

relation to another • Identify points on a graph with corresponding values in a table and interpreting the

numerical information in terms of the situation the graph represents • Compare situations by describing differences in their graphs • Describe the relationship between two quantities in a situation with a constant rate

of change, taking into account a beginning amount and a constant increase • Create a representation for a situation with a constant rate of change • Compare different representations that show the same situation • Make rules that relate one variable to the other in situations with a constant rate of

change Connect the steps of a general method or rule to the parts of the situation they represent

Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models Templates Compass Protractor Maps Mirrors Tape Measure Measuring Cups Tangrams Spinners Clothing Graph Paper Deck of Cards

Additional Assessments Open Ended Questions – Scored Using 1-4 Rubric Multiple Choice Questions Creative Story Writing Math Journals Venn Diagram Timed Multiplication Quizzes Venn Diagram


Everyday Math, 2007

Objectives/Goals


4.3.3 D. Procedures Essential Question What makes an algebraic algorithm both effective and efficient? • Understand and apply the properties of operations and numbers: commutative (e.g.

3x7=7x3), identity element for multiplication (e.g. 1x8=8), any number multiplied by 0 is 0

• Understand and use the concepts of equals, less than, and greater than to describe relations between numbers (=,<,>)


Everyday Math, 2007

Objectives/Goals


Standard 4.4 Data Analysis, Probability and Discrete Mathematics

All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations,

solve problems, and analyze and draw appropriate inferences from data. Big Idea Data Analysis: Reading, understanding, interpreting, and communicating data are critical in modeling a variety of real-world situations, drawing appropriate inferences, making informed decisions, and justifying those decisions. Big Idea Probability: Probability quantifies the likelihood that something will happen and enables us to make predictions and informed decisions. Big Idea Discrete Mathematics: Discrete mathematics consists of tools and strategies for representing, organizing, and interpreting non-continuous data. 4.4.3 A. Data Analysis Essential Questions How can the collection, organization, interpretation, and display of data be used to answer questions? How can probabilities be used to make predictions? • To collect, organize and display data in response to surveys taken • Read, interpret, construct, analyze, draw inferences from displays of data

(pictographs, bar graphs, and tables) • Use everyday events and chance devises (dice, coins, unevenly divided spinners) to

explore concepts of probability • Describe events using very likely, unlikely, impossible, certain and evenly likely to

happen • Predict probabilities in a variety of situations (ex. What color block will be chosen

form the bag depending on a given reference group) • Use everyday events and chance devises (dice, coins, unevenly divided spinners) to

explore concepts of probability • Predict probabilities in a variety of situations (ex. What color block will be chosen

form the bag depending on a given reference group)

Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Pattern Blocks Pocket Charts Place Value Cubes Chips Popsicle Sticks Games White boards Marbles Other manipulatives Abacus Geoboard Meter Stick Centimeter Stick Ruler Centimeter Cube Thermometer Clock Face

Formative Assessments Math Message Mental Math Math Boxes Use of White Boards Individual Profile of Progress Questions & Answers Think, Pair, Share Home Links Math Journals Math Masters Math Minutes On-line Math Facts Games Teach Observation Problem of the Day Drawings and Diagrams


Everyday Math, 2007

Objectives/Goals


• Determine the number of combinations that can be made using a specified group of

items (represent all possibilities for a simple counting situation in an organized way)

• Using organized lists, charts and tree diagrams • Find the smallest colors needed to color a map or graph • Which path to take to get to get to a specified number 4.4.3 B. Probability Essential Question How can experimental and theoretical probabilities be used to make predictions or draw conclusions? • Use everyday events and chance devices, such as dice, coins, and unevenly divided

spinners, to explore concepts of probability (likely, unlikely, impossible, certain, more likely, less likely, equally likely)

4.4.3 C. Discrete Mathematics - Systematic Listing and Counting Essential Questions How can attributes be used to classify data/objects? What is the best way to solve this? What counting strategy works best here? 4.4.3 D. Discrete Mathematics - Vertex-Edge Graphs and Algorithms Essential Question How can visual tools such as networks (vertex- edge graphs) be used to answer questions? (4.5E1; 4.5E3)** How can algorithmic thinking be used to solve problems? • Follow, devise, and describe practical sets of directions (e.g. to add two 2-digit

numbers)

Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models Templates Compass Protractor Maps Mirrors Tape Measure Measuring Cups Tangrams Spinners Clothing Graph Paper Deck of Cards

Portfolio assessments Summative Assessments Unit Assessments Teacher Prepared Assessments Additional Assessments Open Ended Questions – Scored Using 1-4 Rubric Multiple Choice Questions Creative Story Writing Math Journals Venn Diagram Timed Multiplication Quizzes Venn Diagram


Everyday Math, 2007

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All students will use mathematical processes of problem solving, communication, connections, reasoning, representations, and technology to solve problems and

communicate mathematical ideas. 4.5.A Problem Solving • Is able to adapt appropriate problem solving techniques in order to find a solution • Monitor and reflect on the mathematical process of problem solving 4.5. B Communication • Organize and consolidate their mathematical thinking through communication • Express their strategies in written and verbal form • Use communication to organize and clarify mathematical thinking • Communicate mathematical thinking coherently and clearly to peers, teachers, and

others, both orally and in writing 4.5. C Connections • Seeing relationships between different topics and connecting math to their daily

lives 4.5. D Reasoning • Reasoning enables a student to make use of all other mathematical skills in

evaluating situations, selecting strategies, drawing logical conclusions and recognizing how a solution can be applied

Everyday Math Games • Flash Card Voc. Math • Baseball Multiplication • War • 24 • Hangman Rounding • Symmetry Drawings • Tic Tax Toe • Measure It • Fresh Baked Fractions • Find the Area • Take a Survey • Soccer Shoot Out • Football Problem Solving • Basketball Order of Operations • Number Line Help • Around the World (Engineer)


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4.5. E Representations • Use concrete representations, manipulatives, graphs, charts and symbols to

represent mathematical concepts and problem situations 4.5. F Technology • Use technology to gather, analyze, and communicate mathematical information • Use computer software to make and verify conjectures about geometric objects • Use calculators as problem-solving tools (e.g., to explore patterns, to validate

solutions) • Use computer-based laboratory technology for mathematical applications in the

sciences


ROOSEVELT SCHOOL DISTRICT Mathematics Curriculum – Grade 4

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Materials


Standard 4.1 Number and Numerical Operations

All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety of

ways. Big Idea: Numeric reasoning involves fluency and facility with numbers. 4.1.3.A Number Sense Essential Questions How do mathematical ideas interconnect and build on one another? How can we compare and contrast numbers? How can counting, measuring or labeling help to make sense of the world around us? • Through the use of manipulatives, real-life experiences, and technology

students will be able to: • Read and write whole numbers to billions • Identify commonly used fractions (with denominators of 2,3,4,5,8,10,12

and 16) as part of a whole, subset and location on a number line • Read and write decimals to hundredths • Magnitude of the uses of numbers ( ex. ordering, labeling and for

location) • Demonstrate the understanding of place value concepts • Compare and order numbers • Explore negative numbers as an extension to the number line • Use concrete and pictorial representations of equivalent forms of the

same number 4.1.3.B Numerical Operations Essential Questions What makes a computational strategy effective and efficient? How do operations affect numbers? How do mathematical representations reflect the needs of society?

Singapore Math Math facts LCD Projector Document Camera Overhead AppleWorks Reference Books Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Pattern Blocks Pocket Charts Place Value Cubes Chips Popsicle Sticks Games

Formative Assessments Math Message Mental Math Math Boxes Use of White Boards Individual Profile of Progress Questions & Answers Think, Pair, Share Home Links Math Journals Math Masters Math Minutes On-line Math Facts Games Teacher Observation Problem of the Day Drawings and Diagrams Portfolio assessments Summative Assessments Unit Assessments Teacher Prepared Assessments Additional Assessments Open Ended Questions – Scored Using 1-4 Rubric Multiple Choice Questions


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• Develop, apply and explore the basic four arithmetic operations • Addition and subtraction: joining, separating, comparing • Multiplication: repeated addition and arrays • Division: repeated subtraction, sharing • Construct, use and explain procedures for calculating equations with:

pencil-paper, mental math and calculator to solve problems involving the multiplication of multidigit whole numbers by 2-digit whole numbers and the division of multidigit whole numbers by 1-digit whole numbers

• Construct and use procedures for performing decimal addition and subtraction

• Use concrete models to explore addition and subtraction with fractions • Understand and explain the inverse relationships between

addition/subtraction and multiplication/division • Check the reasonableness of results of computations using estimations

and explain how the estimates were obtained • Recognize when an estimate is appropriate 4.1.3.C Estimation Essential Question How can we decide when to use an exact answer and when to use an estimate? • Judge without counting whether a set of objects has less than, more

than, or the same number of objects as a reference set • Round numbers and use mental math for estimating both quantities and

the results of computation • Recognize if an answer is appropriate using estimation • Distinguish when to use estimation or an exact answer in problem

solving • Check for the reasonableness of results of computation

White boards Marbles Other manipulatives Geoboard Meter Stick Centimeter Stick Ruler Centimeter Cube Thermometer Deck of Cards Calculator Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models Templates Compass Protractor Maps Mirrors Tape Measure Measuring Cups Tangrams Spinners Clothing Graph Paper

Creative Story Writing Math Journals Venn Diagram Timed Multiplication Quizzes Venn Diagram


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All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze

phenomena. Big Idea Geometry: Spatial sense and geometric relationships are a means to solve problems and make sense of a variety of phenomena. Big Idea Measurement: Measurement is a tool to quantify a variety of phenomena. 4.2.3.A Geometric Properties Essential Questions How can spatial relationships be described by careful use of geometric language? How do geometric relationships help us to solve problems and/or make sense of phenomena?

Geometric Properties • Identify and describe 2-D and 3-D shapes in reference to size, shape

and classification • Describe Vertex, edge, face, side angle • Congruence • Lines of symmetry • Understand and apply concepts involving lines, angles and circles

(point, line, line segment, endpoint, parallel, perpendicular, types of angles, diameter, radius and center point)

• Use shapes to cover a shaded area • Describe and use transformations of flips, slide and turn • Distinguish between area and perimeter and compute both with

manipulatives and paper-pencil techniques • Read and locate coordinates on a coordinate grid (first quadrant) • Use coordinates to follow directions on a map from one location to

another.

LCD Projector Document Camera Overhead AppleWorks Reference Books Templates Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Templates Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Pattern Blocks Pocket Charts Place Value Cubes Chips Popsicle Sticks Games White boards Marbles Other manipulatives Geoboard Meter Stick Centimeter Stick

Formative Assessments Math Message Mental Math Math Boxes Use of White Boards Individual Profile of Progress Questions & Answers Think, Pair, Share Home Links Math Journals Math Masters Math Minutes On-line Math Facts Games Teach Observation Problem of the Day Drawings and Diagrams Portfolio assessments Summative Assessments Unit Assessments Teacher Prepared Assessments Additional Assessments Open Ended Questions – Scored Using 1-4 Rubric Multiple Choice Questions Creative Story Writing


Everyday Math, 2007

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4.2.3.B Transforming shapes Essential Question What situations can be analyzed using transformations and symmetries? • Geometric transformations (slide, flip and turn) • Investigate and apply transformation to environment in nature and art 4.2.3.C Coordinate Geometry Essential Question How can we best represent and verify geometric/algebraic relationships? • Locate and name points in the first quadrant on a coordinate grid 4.2.3.D Units of Measurement Essential Questions How can measurement be used to solve problems? • Estimate length with and without tools • Use U. S. standard and metric units to accurately measure length • Measure to nearest ! and 1/4 inch and to ! and 1/4 centimeter • Describe and compute perimeter and area of polygons • Choose the correct measurement unit to use depending on what object

is being measured (weight-ounces, lbs) (capacity- fluid ounce, cup, gallon, milliliter)

• Measure time between minutes in an hour, hours in a day and days in a week,

• Tell and show time to nearest minute (be able to compute elapsed time) • Read and interpret positive and negative temperatures on a thermometer

and on a line graph • Associate temperatures with particular activities or clothing

Ruler Centimeter Cube Thermometer Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models Templates Compass Protractor Maps Mirrors Tape Measure Measuring Cups Tangrams Spinners Clothing Graph Paper

Math Journals Venn Diagram Timed Multiplication Quizzes Venn Diagram


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4.2.3.E Measuring Geometric Objects Essential Question How can measurements be used to solve problems? • Understand perimeter as the measure around the outside edges of a 2-

dimensional figure • Find the perimeter using standard units • Create different shapes with the same perimeter • Find the perimeter of an irregular shape • Understand that area is measured in square units • Understand that when measuring area, the space being measured must

be completely covered with no gaps or overlaps • Use squares and triangles to make shapes with an area of four square

units • Examine the relationship between the area of squares and triangles • Understand that shapes with the same area can look different • Find the area of partially covered rectangles • Find the area of an irregular shape • Design a shape for a given area • Find area by counting or calculating whole and partial square units • Determine the number of cubes that will fit in the box made by a given

pattern • Design patterns for boxes that will hold a given number of cubes • See that the cubes filling a rectangular prism can be decomposed into

congruent layers


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concepts and processes. Big Idea: Algebra provides language through which we communicate the patterns in mathematics. 4.3.3. A Patterns Essential Questions How can change be best represented mathematically? How can patterns, relations, and functions be used as tools to best describe and help explain real-life situations? • Sequences that stop or continue indefinitely • Patterns that shrink or grow as a result of a mathematical operations • Sequences that are extended in more than one way (eg. Add,1, then 2,

etc.) 4.3.3 B Functions & Relationships Essential Question How are patterns of change related to the behavior of functions? • Using pictorial models to explore: input/output, function machines

(combining function machines) T-charts, reverse function machine 4.3.3. C Modeling Essential Questions How can we use mathematical models to describe physical relationships? How can we use physical models to clarify mathematical relationships?

LCD Projector Document Camera Overhead AppleWorks KidPix Reference Books Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Pattern Blocks Pocket Charts Place Value Cubes Chips Popsicle Sticks Games White boards Marbles Other manipulatives Abacus Geoboard

Formative Assessments Math Message Mental Math Math Boxes Use of White Boards Individual Profile of Progress Questions & Answers Think, Pair, Share Home Links Math Journals Math Masters Math Minutes On-line Math Facts Games Teach Observation Problem of the Day Drawings and Diagrams Portfolio assessments Summative Assessments Unit Assessments Teacher Prepared Assessments Additional Assessments


Everyday Math, 2007

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Materials


• Recognizing change in quantities over a period of time in graphs, and

how one change in quantity can produce a corresponding change in another

• Construct and solve simple open sentences involving any operation • (eg. N = 15 x2) 4.3.3 D. Procedures Essential Question What makes an algebraic algorithm both effective and efficient? • Understand, name and apply the properties of operations and numbers • Commutative • Identity element • Associative • Division by zero is undefined • Anything times zero is zero • Understand and use the concepts of equals, less than and greater than in

number sentences. Evaluate the numeric expression to see if it is true; insert symbols to make a number sentence true.

Meter Stick Centimeter Stick Ruler Centimeter Cube Thermometer Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models Templates Compass Protractor Maps Mirrors Tape Measure Measuring Cups Tangrams Spinners Clothing Graph Paper LCD Projector

Open Ended Questions – Scored Using 1-4 Rubric Multiple Choice Questions Creative Story Writing Math Journals Venn Diagram Timed Multiplication Quizzes Venn Diagram


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Big Idea Data Analysis: Reading, understanding, interpreting, and communicating data are critical in modeling a variety of real-world situations, drawing appropriate inferences, making informed decisions, and justifying those decisions. Big Idea Probability: Probability quantifies the likelihood that something will happen and enables us to make predictions and informed decisions. Big Idea Discrete Mathematics: Discrete mathematics consists of tools and strategies for representing, organizing, and interpreting non-continuous data. 4.4.3 A. Data Analysis Essential Questions How can the collection, organization, interpretation, and display of data be used to answer questions? How can probabilities be used to make predictions? • Collect, generate, organize and display data in response to a collection • Read, interpret, construct, analyze and draw inferences from displays of

data using • tables, pictographs, bar graphs, line graphs, line plots • benchmark assessments: mean, median, mode 4.4.3 B. Probability Essential Question How can experimental and theoretical probabilities be used to make predictions or draw conclusions?

Document Camera Overhead AppleWorks KidPix Reference Books Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Pattern Blocks Pocket Charts Place Value Cubes Chips Popsicle Sticks Games White boards Marbles Other manipulatives Abacus Geoboard Meter Stick Centimeter Stick



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• Using dice, spinners, and other chance devices (even when the device is

unevenly divided), the students will be able to say if the outcome is: likely, unlikely, certain, impossible, improbable, fair or unfair

• Say if an event is dependent or independent based on a previous outcome

• Express the probability of an event as a fraction • Predict and summarize outcomes to use them in predicting future

events. 4.4.3 C. Discrete Mathematics - Systematic Listing and Counting Essential Questions How can attributes be used to classify data/objects? What is the best way to solve this? What counting strategy works best here? • Represent and classify data according to shape, color and its

relationship in a Venn diagram or in ABC order • Represent all possibilities for a simple counting situation in an

organized way (through lists, charts and tree diagrams) • Explore vertex-edge graphs and tree diagrams • Path circuits (path that ends at its starting point) • Find the smallest number of colors needed to color a map or graph 4.4.3 D. Discrete Mathematics - Vertex-Edge Graphs and Algorithms Essential Question How can visual tools such as networks (vertex- edge graphs) be used to answer questions? (4.5E1; 4.5E3)** How can algorithmic thinking be used to solve problems?

Ruler Centimeter Cube Thermometer Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models Templates Compass Protractor Maps Mirrors Tape Measure Measuring Cups Tangrams Spinners Clothing Graph Paper LCD Projector Document Camera



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solve problems and communicate mathematical ideas. 4.5.A Problem Solving • Open-ended problems • Problems with multiple solutions • Explaining appropriate problem solving techniques (eg. Making a

problem simpler) 4.5. B Communication • Write and discuss mathematical thinking and the use of their strategies

to others 4.5. C Connections • Recognize that mathematics is used in a variety of context outside of

mathematics 4.5. D Reasoning • Rely on reasoning to infer if the solution, or method of solving an

equation makes math sense • Make mathematical conjectures • Select and use various types of reasoning and methods of proof 4.5. E Representations • Create representations in: concrete form, pictures, symbolic (formulas)

and graphical representations

Overhead AppleWorks KidPix Reference Books Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Pattern Blocks Pocket Charts Place Value Cubes Chips Popsicle Sticks Games White boards Marbles Other manipulatives Abacus Geoboard Meter Stick Centimeter Stick



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4.5. F Technology • Use technology to gather, analyze, and communicate mathematical



validate solutions) • Use computer-based laboratory technology for mathematical applications

in the sciences

Ruler Centimeter Cube Thermometer Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models Templates Compass Protractor Maps Mirrors Tape Measure Measuring Cups Tangrams Spinners Clothing Graph Paper



Everyday Math, 2007

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Materials

Assessment/ Evaluation

Standard 4.1 Number and Numerical Operations All students will develop number sense and will perform

Standard numerical operations and estimations on all Types of numbers in a variety of ways.

BIG IDEA: Numeric reasoning involves fluency and facility with numbers. 4.1.5.A Number Sense Essential Questions How do mathematical ideas interconnect and build on one another to produce a whole? How can we compare and contrast numbers? How can counting, measuring, or labeling help to make sense of the world around us? • Understand the meanings, uses, and representations of numbers • Read and write whole numbers and decimals; identify places in such

numbers and the values of the digits in those places; use expanded notation to represent whole numbers and decimals.

• Solve problems involving percents and discounts, describe and explain strategies used; identify the unit whole in situations involving fractions.

• Identify prime and composite numbers; factors of numbers; and prime factorization

• Use numerical expressions involving one or more of the basic arithmetic operations, grouping symbols, and exponents to give equivalent names for whole numbers and convert between exponential and repeated –factor notations.

• Use numerical expressions to find and represent equivalent names for fractions, decimals, and percent; convert fractions to mixed numbers and simplest form.

LCD Projector Document Camera Overhead AppleWorks KidPix Reference Books Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Pattern Blocks Pocket Charts Place Value Cubes Chips Popsicle Sticks Games White boards

Formative Assessments Math Message Mental Math Math Boxes Use of White Boards Individual Profile of Progress Questions & Answers Think, Pair, Share Home Links Math Journals Math Masters Math Minutes On-line Math Facts Games Teach Observation Problem of the Day Drawings and Diagrams Portfolio assessments Summative Assessments Unit Assessments Teacher Prepared Assessments Additional Assessments Open Ended Questions – Scored Using 1-4 Rubric Multiple Choice Questions


Everyday Math, 2007

Objectives/Goals

Materials


• Compare and order whole numbers up to 1,000,000,000 and decimals through the thousandths; order integers between –100 and 0

• Interpret everyday uses of fractions, decimals and percents • Identify fraction and percent equivalents through reasoning about

representations and known equivalents and relationships • Order fractions and justify their order through reasoning about fraction

equivalence and relationships • Use equivalencies to place fractions on a set of number lines • Compare fractions on a number line • Interpret the meaning of the numerator and the denominator of a

fraction • Use equivalent fractions and percents to solve problems • Compare fractional parts of different sized wholes • Order mixed numbers and fractions greater than 1 • Identify everyday uses of fractions and decimals 4.1.5.B Numerical Operations Essential Questions What makes a computational strategy both effective and efficient? How do operations affect numbers? How do mathematical representations reflect needs of society across cultures? • Understand the meanings of operations in order to estimate and

compute accurately • Make sense of remainders in terms of problem context • Use mental arithmetic, paper and pencil algorithms, and calculators to

solve problems involving the addition and subtraction of whole numbers, decimals, and signed numbers; describe the strategies used and explain how they work.

• Demonstrate automaticity with multiplication facts and proficiency

Marbles Other manipulatives Abacus Geoboard Meter Stick Centimeter Stick Ruler Centimeter Cube Thermometer Percen Chart Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models Templates Compass Protractor Maps Mirrors Tape Measure Measuring Cups Tangrams Spinners Clothing Graph Paper Deck of Cards

Creative Story Writing Math Journals Venn Diagram Timed Multiplication Quizzes Venn Diagram Battleship Game Around the World Bingo


Everyday Math, 2007

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Materials


with division facts and extensions • Use mental arithmetic, pencil and paper algorithms, and calculators to

solve problems involving the multiplication of whole numbers and decimals and the division of multi-digit whole numbers and decimals by whole numbers; express remainders as whole numbers and fractions, and describe the strategies used and explain how they work

• Interpret and solve multi-step problems • Identify, describe, and compare subtraction strategies by focusing on

how each strategy starts • Add fractions by using a rotation model • Add and subtract fractions through reasoning about fraction

equivalents and relationships • Add and subtract fractions by using a number line • Find combinations of fractions with sums between 0 and 2 • Solve 2 digit by 2 digit multiplication problems • Find fractional parts of a whole or a group • Find a percentage of a group 4.1.5.C Estimation Essential Question How can we decide when to use an exact answer and when to use an estimate? • Estimate the product of 2 numbers including 2, 3 and 4 digit

multiplication and division problems • Estimate solutions to 3, 4 and 5 digit addition and subtraction

problems • Estimate solutions to addition and subtraction problems with fractions

and mixed numbers • Break apart, reorder or change numbers mentally to determine a

reasonable estimate • Estimate sums of decimal numbers


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All students will develop spatial sense and the ability to use Geometric properties, relationships, and measurement to

model, describe and analyze phenomena

BIG IDEA Geometry: Spatial sense and geometric relationships are a means to solve problems and make sense of a variety of phenomena. BIG IDEA Measurement: Measurement is a tool to quantify a variety of phenomena. 4.2.5.A Geometric Properties Essential Questions How can spatial relationships be described by careful use of geometric language? How do geometric relationships help in solving problems and/or make sense of phenomena? • Investigate the characteristics and properties of two and three

dimensional shapes and understand the systems and processes of measurement.

• Identify, describe, compare, name, and draw right, acute, obtuse, straight, and reflex angles; determine angle measures in vertical and supplementary angles and the sums of angle measures in triangles and quadrangles

• Identify attributes of polygons • Use attributes to describe and compare quadrilaterals, including

parallelograms, rectangles, rhombuses, and squares • Find the perimeter and the area of a rectangle • Decompose 3-D shapes and then recombining them to make a given

building • Determine the number of cubes that will fit into the box made by a


Formative Assessments Math Message Mental Math Math Boxes Use of White Boards Individual Profile of Progress Questions & Answers Think, Pair, Share Home Links Math Journals Math Masters Math Minutes On-line Math Facts Games Teacher Observation Problem of the Day Drawings and Diagrams Portfolio assessments Summative Assessments Unit Assessments Teacher Prepared Assessments Additional Assessments Open Ended Questions – Scored Using 1-4 Rubric Multiple Choice Questions Creative Story Writing Math Journals Venn Diagram Timed Multiplication Quizzes


Everyday Math, 2007

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Materials


given pattern • Develop a strategy for determining the volume of rectangular prisms • Design patterns for boxes that hold a given number of cubes • Consider how the dimensions of a box change when the volume is

changed (doubled, halved, or tripled) • Understand and apply concepts involving lines and angles • Notation for line, ray, angle, line segment • Properties of parallel, perpendicular, and intersecting lines 4.2.5.B Transforming Shapes Essential Question What situations can be analyzed using transformations and symmetries? • Describe, compare, and classify plane and solid figures using

appropriate geometric terms; identify congruent figures and describe their properties

4.2.5.C Coordinate Geometry Essential Question How can geometric/algebraic relationships best by represented and verified? • Identify, describe, and sketch examples of reflections, translations, and

rotations • Plot points on a coordinate grid to represent a situation in which one

quantity is changing in relation to another • Identify points on a graph with corresponding values in a table and

interpreting the numerical information in terms of the situation the graph represents

• Describe the relative steepness of graphs or parts of graphs in terms of

Meter Stick Centimeter Stick Ruler Centimeter Cube Thermometer Percent Chart Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models Templates Compass Protractor Maps Mirrors Tape Measure Measuring Cups Tangrams Spinners Clothing Graph Paper Deck of Cards

Venn Diagram Battleship Game Around the World Bingo


Everyday Math, 2007

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Materials


different rates of change • Create geometric shapes with specified properties in the first quadrant

on a coordinate grid 4.2.5.D Units of Measurement Essential Question How can measurements be used to solve problems? • Estimate length with and without tools; measure length with tools to

the nearest 1/8 inch and millimeter; estimate the measure of angles with and without tools; use tools to draw angles for given measures.

• Use ordered pairs of numbers to name, locate, and plot points in all four quadrants of a coordinate grid.

4.2.5.E Measuring Geometric Objects Essential Questions How can measurements be used to solve problems? • Describe the relationship among the U.S. customary units of length;

metric units of length; and U.S. customary units • Convert measurement units with a system • Describe and use strategies to find the perimeter of polygons and the

area of circles • Use appropriate formulas to calculate the area, volume, and capacity of

rectangles, triangles, and prisms • Define pi as the ratio of a circle’s circumference to its diameter


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concepts and processes.

BIG IDEA: Algebra provides language through which we communicate the patterns in mathematics.4.3.5.A Patterns Essential Questions How can change be best represented mathematically? How can patterns, relations, and functions be used as tools to best describe and help explain real-life situations? Understand patterns and functions and to use algebraic notation to represent and analyze situations and structures • Extend, describe, and create numeric patterns; describe rules for

patterns and use them to solve problems; write rules for functions involving the four basic operations; represent functions using words, symbols, tables, and graphs and use those to solve problems.

4.3.5.B Functions and Relationships Essential Question How are patterns of change related to the behavior of functions? • Determine whether sentences are true or false; solve open number

sentences and explain solutions; use a letter variable to write an open sentence to model a number story.


Formative Assessments Math Message Mental Math Math Boxes Use of White Boards Individual Profile of Progress Questions & Answers Think, Pair, Share Home Links Math Journals Math Masters Math Minutes On-line Math Facts Games Teach Observation Problem of the Day Drawings and Diagrams Portfolio assessments Summative Assessments Unit Assessments Teacher Prepared Assessments Additional Assessments Open Ended Questions – Scored Using 1-4 Rubric Multiple Choice Questions Creative Story Writing Math Journals Venn Diagram Timed Multiplication Quizzes Venn Diagram


Everyday Math, 2007

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4.3.5.C Modeling Essential Questions How are mathematical models used to describe physical relationships? How are physical models used to clarify mathematical relationships? • Evaluate numeric expressions containing grouping symbols; insert

grouping symbols, and nested grouping symbols to make number sentences true; describe and use the precedence of multiplication and division over addition and subtraction.

4.3.5.D Procedures Essential Question What makes an algebraic algorithm both effective and efficient? • Describe and apply properties of arithmetic

Meter Stick Centimeter Stick Ruler Centimeter Cube Thermometer Percen Chart Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models Templates Compass Protractor Maps Mirrors Tape Measure Measuring Cups Tangrams Spinners Clothing Graph Paper Deck of Cards

Battleship Game Around the World Bingo


Everyday Math, 2007

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BIG IDEA Data Analysis: Reading, understanding, interpreting, and communicating data are critical in modeling a variety of real-world situations, drawing appropriate inferences, making informed decisions, and justifying those decisions. BIG IDEA Probability: Probability quantifies the likelihood that something will happen and enables us to make predictions and informed decisions. BIG IDEA Discrete Mathematics consists of tools and strategies for representing, organizing, and interpreting non-continuous data. 4.4.5.A Data Anlysis Essential Question How can the collection, organization, interpretation, and display of data be used to answer questions? • Select and create appropriate graphical representations of collected or

given data and analyze and interpret data in order to apply the basic concepts of probability.

• Collect and organize data and use given data to create bar, line, and circle graphs with reasonable titles, labels, keys, and intervals.

LCD Projector Document Camera Overhead AppleWorks KidPix Reference Books Everyday Math Games Number line Coins, bills Pattern Blocks Cards Calculators Dice Dominoes Balance Fact Triangles Base 10 Blocks Attribute Blocks Unifix Cubes Fraction Bar Pattern Blocks Pocket Charts Place Value Cubes Chips Popsicle Sticks Games White boards Marbles Other manipulatives Abacus Geoboard Meter Stick

Formative Assessments Math Message Mental Math Math Boxes Use of White Boards Individual Profile of Progress Questions & Answers Think, Pair, Share Home Links Math Journals Math Masters Math Minutes On-line Math Facts Games Teach Observation Problem of the Day Drawings and Diagrams Portfolio assessments Summative Assessments Unit Assessments Teacher Prepared Assessments Additional Assessments Open Ended Questions – Scored Using 1-4 Rubric Multiple Choice Questions Creative Story Writing Math Journals Venn Diagram Timed Multiplication Quizzes


Everyday Math, 2007

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4.4.5.B Probability Essential Question How can experimental and theoretical probabilities be used to make predictions or draw conclusions? • Use maximum, minimum, range, median, mode, and mean and graphs

to ask and answer questions, draw conclusions, and make predictions. 4.4.5.C Discrete Mathematics – Systematic Listing and Counting Essential Questions How can attributes be used to classify data/objects? What is the best way to solve this? What counting strategy works best here? • Describe events using certain, very likely, likely, 50/50, less likely,

impossible, and other basic probability terms to compare events and explain the choice of language.

4.4.5.D Discrete Mathematics – Vertex-Edge Graphs and Algorithms Essential Questions How can visual tools such as networks (vertex-edge graphs) be used to answer questions? How can algorithmic thinking be used to solve problems? • Predict the outcomes of experiments, test the predictions using

manipulative, and summarize the results; compare predictions based on theoretical probability with the experimental results; use summaries and comparisons to predict future events; express the probability of an event as a fraction, decimal, or percent.

Centimeter Stick Ruler Centimeter Cube Thermometer Percen Chart Clock Face Calendar Balance, Scale Weights Pattern Blocks 2D/3D Models Templates Compass Protractor Maps Mirrors Tape Measure Measuring Cups Tangrams Spinners Clothing Graph Paper Deck of Cards

Venn Diagram Battleship Game Around the World Bingo


Everyday Math, 2007

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solve problems and communicate mathematical ideas.

While no additional big ideas, essential questions, or enduring understandings are listed for this standard, the mathematical processes are imbedded in the content-specific ideas, questions, and understandings delineated for the first four standards. References to the relevant processes can be found above. 4.5.A Problem Solving Use mathematical processes of problems solving, communication, connections, reasoning, representations, and technology to solve problems and communicate mathematical ideas • Use inquiry and discovery to solve problems • Use a variety of problem solving techniques to solve open-ended,

multiple solution, and non-routine problems 4.5.B Communication • Clarify and express mathematical thinking through reading, writing,

discussion, listening, and questioning. 4.5.C Connections • Recognize and apply the concept that mathematics is used in a variety

of concepts outside mathematics; understand that mathematical ideas build on one another to produce a coherent whole


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4.5.D Reasoning • Use reasoning to support their mathematical conclusions and problem

solutions; evaluate examples of mathematical reasoning and determine if they are valid.

4.5.E Representations • Create and use representations to organize, record, and communicate

mathematical ideas; select apply, and translate among mathematical representations to solve problems

4.5.F Technology • Use technology to gather, analyze, and communicate mathematical



validate solutions) • Use computer-based laboratory technology for mathematical


LCD Projector Document Camera Overhead AppleWorks KidPix Internet On-line Games


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Standard 4.1 Number and Numerical Operations All students will develop number sense and will perform

Standard numerical operations and estimations on all types Of numbers in a variety of ways.

BIG IDEA: Numeric reasoning involves fluency and facility with numbers. 4.1.6.A Number Sense Essential Questions How do mathematical ideas interconnect and build on one another? How can we compare and contrast numbers? How can counting, measuring, or labeling help to make sense of the world around us? Understand the meanings, uses, and representations of numbers Number Sense • To use real-life experiences to constrauct meaning for numbers • Develop skills involving place value and notation • Read and write whole numbers and decimals • Recognize the decimal nature of United States currency • Identify places in such numbers and the values of the digits in

those places • Use expanded notation, number and word notation, exponential

notation, and scientific notation to represent whole numbers and decimals

• Develop meanings and uses of fractions • Solve problems involving percents and discounts • Identify the unit whole in situations involving fractions, decimals,

and percents

Fraction bar Pie chart Numberline

Formative Assessments Math Message Mental Math Math Boxes Use of White Boards Individual Profile of Progress Questions & Answers Think, Pair, Share Homelinks Summative Assessments Unit Assessments Teacher Prepared Assessments Open Ended Questions


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• Develop Number Theory • Use GFC’s, LCM’s, and divisibility rules to manipulate fractions • Find equivalent names for whole numbers as well as fractions,

decimals, and percents. • Apply the order of operations to numerical expressions to give

names for rational numbers • Find equivalent fractions and fractions in simplest form by

applying multiplication and division rules and concepts from number theory

• Convert between fractions, mixed numbers, decimals, and percents • Compare and order numbers • Choose and apply strategies for comparing and ordering rational

numbers • Explain those choices and strategies 4.1.6.B Numerical Operations Essential Questions What makes a computational strategy both effective and efficient? How do operations affect numbers? How do mathematical representations reflect the needs of society across cultures? • Recognize the appropriate use of arithmetic operations in problem

solving • Use mental arithmetic, paper and pencil algorithms, and

calculators to solve problems involving the addition and subtraction or whole numbers, decimals, and signed numbers

• Describe the strategies used and explain how they work • Develop procedures for multiplication and division • Use mental arithmetic, paper and pencil algorithms, and

calculators to solve problems involving the multiplication and

• Develop models for the operations • Use ratios and scaling to model size

changes and to solve size-change problem • Represent ratios as fractions, percents,

and decimals • Model and solve problems involving part

to whole and part to part ratios • Model rate and ratio number stories with

proportions


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division of whole numbers, decimals, and signed numbers • Describe the strategies used and explain how they work • Develop procedures for addition, subtraction, multiplication, and

division of fractions • Use mental arithmetic, paper and pencil algorithms, and

calculators to solve problems involving the addition, subtraction, multiplication, and division of fractions and mixed numbers

• Describe the strategies used and explain how they work 4.1.6.C Estimation Essential Question How can we decide when to use an exact answer and when to use an estimate? Develop the skills necessary to make computational estimates • Make reasonable estimates for whole number, decimal, fraction

and mixed number problems • Make reasonable estimates for addition, subtraction,

multiplication, and division problems • Explain how the estimates were obtained

Standard 4.2 Geometry and Measurement All students will develop spatial sense and the ability to use Geometric properties, relationships, and measurement to

Model, describe and analyze phenomena.

BIG IDEA Geometry: Spatial sense and geometric relationships are a means to solve problems and make sense of a variety of phenomena. 4.2.6.A Geometry Properties

• Use and explain cross multiplication and other strategies to solve proportions


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Essential Questions How can spatial relationships be described by careful use of geometric language? How do geometric relationships help us to solve problems and/or make sense of phenomena? This includes identifying, describing and classifying standard geometric object, describing and comparing properties of geometric objects, making conjectures concerning them, and using reasoning and proof to verify or refute conjectures and theorems. Also included here are such concepts as symmetry, congruence, and similarity. 4.2.6.B Transforming Shapes Essential Question What situations can be analyzed using transformations and symmetries? Develop skills involving lines and angles • Identify, describe, classify, name and draw notations for lines,

rays, and line segments • Identify and use the properties of parallel, perpendicular, and

intersecting lines • Identify, describe, classify, name, and draw angles • Determine angle measures by applying properties of orientations

of angles and sums of angle measures in triangles and quadrangles Develop skills involving plane and solid figures • Identify and describe similar and congruent figures and describe

their properties • Construct a figure that is congruent to another figure using a

Attribute blocks 3D Models 2D Models Ruler, protractor, compass Geometry dictionary Calculator Atrribute blocks

Flat pattern that folds into a 3D shape


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compass and straightedge • Identify, describe, compare and classify polygons and circles 4/2/6/C Coordinate Geometry Essential Question How can we best represent and verify geometric/algebraic relationships? Develop skills involving transformations and symmetry • Identify, describe, and sketch reflections, translations and rotations • Recognize, identify and describe geometric relationships and

properties as they exist in nature and real world settings. • Create shapes with specified properties in the 1st quadrant in a

coordinate grid. 4.2.6.D Units of Measurement Essential Question How can measurements be used to solve problems? Develop skills involving length, weight, and angles • Estimate length with and without tools • Measure length to the nearest 1/16 inch and millimeter • Estimate the measure of angles with and without tools • Use tools to draw angles with given measures • Use a scale to find a distance on a map • Convert measurement units within a system • Know equivalents between standard and metric systems. Develop skills involving area, perimeter, volume, and capacity, circumference and surface area


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• Use a protractor to measure angles • Solve area, perimeter, and volume problems for various polygons • Recognize that shapes with same perimeter do not necessarily have

same area 4.2.6.E Measuring Geometric Objects Essential Question How can measurements be used to solve problems? Use coordinate systems • Use ordered pairs of numbers • Name, locate, and plot points in all four quadrants of a coordinate

grid

Standard 4.3 Patterns and Algebra All students will represent and analyze relationships among Variable quantities and solve problems involving patterns,

Functions, and algebraic concepts and processes.

BIG IDEA: Algebra provides language through which we communicate the patterns in mathematics. 4.3.6.A Patterns Essential Questions How can change be best represented mathematically? How can patterns, relations, and functions be used as tools to best describe and help explain real-life situations? Understand patterns and functions and to use algebraic notation to represent and analyze situations and structures


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Develop skills involving patterns and functions • Extend, describe, and create numeric patterns, functions and

relationships • Describe rules for patterns and use them to solve problems • Represent modeling patterns and rules using algebraic notation • Represent functions using words, algebraic notation, tables, and

graphs • Translate from one representation to another and use

representations to solve problems involving functions 4.3.6.B Functions and Relationships Essential Question How are patterns of change related to the behavior of functions? Use algebraic notation and solve number sentences • Determine whether equalities and inequalities are true or false • Solve open number sentences and explain the solutions • Use trial and error and equivalent strategies to solve linear

equations in one unknown • Describe and apply the conventional order of operations • Understand and apply the distributive and commutative properties 4.3.6.C Modeling Essential Questions How can we use mathematical models to clarify mathematical relationships? Model patterns, relations, and linear functions • Draw graphs representing changes over time


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• Draw graphs and models representing rates of change 4.3.6.D Procedures Essential Question What makes an algebraic algorithm both effective and efficient?


BIG IDEA Data Analysis: Reading, understanding, interpreting, and communicating data are critical in modeling a variety of real-world situations, drawing appropriate inferences, making informed decisions, and justifying those decisions. BIG IDEA Probability: Probability quantifies the likelihood that something will happen and enables us tomake predictions and informed decisions. BIG IDEA Discrete Mathematics: Discrete mathematics consists of tools and strategies for representing, organizing, and interpreting non-continuous data. 4.4.6.A Data Analysis Essential Question How can the collection, organization, interpretation, and display of data be used to answer questions? Select and create appropriate graphical representations of collected or given data and analyze and interpret data in order to apply the basic concepts of probability. Select and create appropriate graphical representations for data • Collect and organize data or use given data to create bar, line,


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circle, and symbolism and leaf graphs with reasonable titles, labels, keys, and intervals.

Analyze Data • Use the maximum, minimum, range, median, mode, and mean of

graphs to ask and answer questions • Draw conclusions and make predictions based on landmarks • Compare and contrast the median and mean of a data set 4.4.6.B Probability Essential Question How can experimental and theoretical probabilities be used to make predictions or draw conclusions? Understand and apply the basic concepts of probability • Recognize and understand the connections among the concepts of

independent outcomes, picking at random, and fairness • Use tree diagrams and other counting strategies to identify all

possible outcomes for a situation • Predict the results of an experiment, test the prediction and

summarize the findings • Compare predictions based on theoretical probability with

experimental results • Calculate probabilities and express them as fractions, decimals,

and percents • Explain how simple size affects results • Use results to predict future events 4.4.6.C Discrete Mathematics – Systematic Listing and Counting Essential Questions


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How can attributes be used to classify data/objects? What is the best way to solve this? What counting strategy works best here? Systematic listing and counting • Solve counting problems and justify that all possibilities have been

found without duplication • Organize information into lists, charts, tree diagrams, and tables • List possible combinations of elements • Describe math • Devise strategies for winning simple games • Analyze and use vertex-edge graphs to find solutions to problems 4.4.6.D Discrete Mathematics – Vertex-Edge Graphs and Algorithms Essential Questions How can visual tools such as networks (vertex-edge graphs) be used to answer questions? How can algorithmic thinking be used to solve problems?


While no additional BIG IDEAS, essential questions, or enduring understanding are listed for this standard, the mathematical processes are imbedded in the content-specific ideas, questions, and understandings delineated for the first four standards. References to the relevant processes can be found above. 4.5.A Problem Solving • Use mathematical processes of problems solving, communication,

connections, reasoning, representations, and technology to solve


McGraw-Hill, 2007

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problems and communicate mathematical ideas • Use inquiry and discovery to solve problems • Use a variety of problem solving techniques to solve open-ended,

multiple solution, and non-routine problems 4.5.B Communication • Clarify and express mathematical thinking through reading,

writing, discussion, listening, and questioning. 4.5.C Connections • Recognize and apply the concept that mathematics is used in a

variety of concepts outside mathematics; understand that mathematical ideas build on one another to produce a coherent whole

4.5.D Reasoning • Use reasoning to support their mathematical conclusions and

problem solutions; evaluate examples of mathematical reasoning and determine if they are valid.

4.5.E Representations • Create and use representations to organize, record, and

communicate mathematical ideas; select apply, and translate among mathematical representations to solve problems

4.5.F Technology • Use computers and calculators to gather, analyze, and

communicate mathematical information. • Use connections among mathematical themes to explain concepts • Recognize that math is used in a variety of contexts outside of

math


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