GRADE 4 MATHEMATICS CURRICULUM GUIDE

Transcription

1 GRADE 4 MATHEMATICS CURRICULUM GUIDE Loudoun County Public Schools Complete scope, sequence, pacing and resources are available on the LCPS Intranet.

2 INTRODUCTION TO LOUDOUN COUNTY S MATHEMATICS CURRICULUM GUIDE This CURRICULUM GUIDE is a merger of the Virginia Standards of Learning (SOL) and the Mathematics Achievement Standards for Loudoun County Public Schools. The CURRICULUM GUIDE includes excerpts from documents published by the Virginia Department of Education. Other statements, such as suggestions on the incorporation of technology and essential questions, represent the professional consensus of Loudoun s teachers concerning the implementation of these standards. In many instances the local expectations for achievement exceed state requirements. The GUIDE is the lead document for planning, assessment and curriculum work. It is a summarized reference to the entire program that remains relatively unchanged over several student generations. Other documents, called RESOURCES, are updated more frequently. These are published separately but teachers can combine them with the GUIDE for ease in lesson planning. Mathematics Internet Safety Procedures 1. Teachers should review all Internet sites and links prior to using it in the classroom. During this review, teachers need to ensure the appropriateness of the content on the site, checking for broken links, and paying attention to any inappropriate pop-ups or solicitation of information. 2. Teachers should circulate throughout the classroom while students are on the internet checking to make sure the students are on the appropriate site and are not minimizing other inappropriate sites. Teachers should periodically check and update any web addresses that they have on their LCPS web pages. 3. Teachers should assure that the use of websites correlate with the objectives of lesson and provide students with the appropriate challenge. 4. Teachers should assure that the use of websites correlate with the objectives of the lesson and provide students with the appropriate challenge.

3 Grade 4 Mathematics Nine Weeks Overview 1 st Quarter 2 nd Quarter 3 rd Quarter 4 th Quarter Place value 4.1 Add and subtract whole numbers Functions 4.15 Equality a, b, d Multiplication and division of whole numbers 4.4 Probability 4.13 Graphing 4.14 Fractions Decimals c 4.5 a, b, d 4.2 Measurement Geometry Elapsed time 4.9

4 Grade 4 Quarter 1 Number of Days Topics, Essential Questions, and Essential Understandings (Students should be able to answer essential questions.) REQUIRED Critical Thinking Lessons Standard(s) of Learning Essential Knowledge and Skills Additional Instructional Resources ESS: VDOE Enhanced Scope and Sequence 25 days Working with Whole Numbers 4.1 Essential Questions Demonstrate and explain the relationship between each place in a number. Demonstrate and explain how the place value system can be used to name and compare large numbers. Compare and contrast the appropriateness of using estimation and finding the exact value. 4.1 Essential Understandings Understand the relationships in the place value system in which the value of each place is ten times the value of the place to its right. Use the patterns in the place value system to read and write numbers. Understand that reading place value correctly is essential when comparing numbers. Understand that rounding gives a close number to use when exact numbers are not needed for the situation at hand. Develop strategies for rounding. INV: Mathematical Thinking at Grade 4 Investigation 1: How Many Hundreds, Sessions 1 4 Investigation 3: Using Number Patterns, Sessions 1-5 INV: Landmarks in the Thousands Investigation 1: Working with 100, Sessions 1 3 Investigation 2: Exploring Multiples of 100, Sessions 1 5 Investigation 3: How Much is 1000, Sessions 1 5 Investigation 4: Making a 10,000 Chart, Sessions 1-3 SOL 4.1 The student will a) identify orally and in writing the place value for each digit in a whole number expressed through millions; b) compare two whole numbers expressed through millions using symbols (>, <, or =); and c) round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. 4.1 Essential Knowledge and Skills Identify and communicate, both orally and in written form, the placed value for each digit in whole numbers expressed through the one millions place. Read whole numbers through the one millions place that are presented in standard format, and select the matching number in written format. Write whole numbers through the one millions place in standard format when the numbers are presented orally or in written format. Identify and use the symbols for greater than, less than, and equal to. Compare two whole numbers expressed through the one millions, using symbols >, <, or =. Round whole numbers expressed through ESS: Location, Location, Location Estimation Game Modeling Addition and Subtraction Multiplying and Trading Balance Beams Weighty Problems

5 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 4.4 Essential Questions Demonstrate and explain finding a sum, a difference. Demonstrate and explain inverse operations. 4.4 Essential Understandings Develop and use strategies to estimate whole number sums and differences and to judge the reasonableness of such results. Understand that addition and subtraction are inverse operations. Understand how to solve single-step and multistep problems using whole number operations. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 4.15 Essential Questions Create and justify numerical patterns using words, tables, graphs, and/or symbols. Analyze and extend numerical patterns using various methods Essential Understandings Understand that patterns and functions can be represented in many ways and described using words, tables, graphs, and symbols. the one millions place to the nearest thousand, ten thousand, and hundredthousand place. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 4.4 The student will a) estimate sums, differences, ; b) add, subtract, and multiply whole numbers; d) solve single-step and multistep addition, subtractions, problems with whole numbers. 4.4 Essential Knowledge and Skills Estimate whole number sums, differences. Refine estimates by adjusting the final amount, using terms such as closer to, between, and a little more than. Determine the sum or difference of two whole numbers, each 999,999 or less, in vertical and horizontal form with or without regrouping, using paper and pencil, and using a calculator. Solve single-step and multistep problems using whole number operations. Verify the reasonableness of sums, differences of whole numbers using estimation. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 4.15 The student will recognize, create, and extend numerical and geometric patterns Essential Knowledge and Skills Describe geometric and numerical patterns, using tables, symbols, or words. Create geometric and numerical patterns, using concrete materials, number lines, tables, and words. Extend geometric and numerical patterns, using concrete materials, number lines, tables, and words. ~~~~~~~~~~~~~~~~~~~~ Grade 4 ESS: This Fruit is a Mass! Kiddy Pool Grade 5 ESS: Measurement Mania Smart Measurement Site wikispaces.com/ ~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 4.16 The student will ~~~~~~~~~~~~~~~~~~ Exploration of a Balance

6 20 days 4.16 Essential Questions What is an equation? Demonstrate and explain the associative property. How are the associative properties for addition and multiplication alike? Demonstrate and explain the commutative property. How are the commutative properties for addition and multiplication alike? Compare and contrast the associative properties for addition and multiplication Essential Understandings Understand that mathematical relationships can be expressed using equations. Understand that quantities on both sides of an equation must be equal. Understand that the associative property for addition means you can change the groupings of three or more addends without changing the sum. Understand that the associative property for multiplication means you can change the groupings of three or more factors without changing the product. a) recognize and demonstrate the meaning of equality in an equation; and b) investigate and describe the associative property for addition and multiplication Essential Knowledge and Skills Recognize and demonstrate that the equals sign (=) relates equivalent quantities in an equation. Write an equation to represent equivalent mathematical relationships (e.g., 4 3 = 2 6). Recognize and demonstrate appropriate use of the equals sign in an equation. Investigate and describe the associative property for addition as (6 + 2) + 3= 6 + (2 + 3). Investigate and describe the associative property for multiplication as (3 x 2) x 4 = 3 x (2 x 4). (Lesson 2) 3 days Enrichment, Assessment, and Remediation

7 Grade 4 Quarter 2 Number of Days 20 days Topics, Essential Questions, and Essential Understandings (Students should be able to answer essential questions.) Working with Whole Numbers 4.4 Essential Questions There are many methods for determining a product. What are the criteria considered when choosing a strategy? What are inverse relationships? What does it mean to divide? What does multiplication mean? What effect does multiplication have on a number? What does the divisor represent in a real life application? Dividend? Quotient? How are each of these represented using the three division models? What is the similarity between multiplication and addition? What is the similarity between division and subtraction? 4.4 Essential Understandings All students should: Develop and use strategies to estimate whole number sums and REQUIRED Critical Thinking Lessons Packages and Groups Investigation 2: Double Digit Multiplication, Sessions 1 3 Investigation 3: Multiplication and Division Choices, Sessions 1-10 Standards of Learning Essential Knowledge and Skills SOL 4.4 The student will a) estimate products, and quotients of whole numbers; b) multiply whole numbers; c) divide whole numbers, finding quotients with and without remainders; and d) solve single-step and multistep multiplication problems with whole numbers. 4.4 Essential Knowledge and Skills Estimate whole number products, and quotients. Refine estimates by adjusting the final amount, using terms such as closer to, between, and a little more than. Estimate and find the products of two whole numbers. Estimate and find the quotient of two whole numbers. Solve single-step and multipstep problems using whole number operations. Verify the reasonableness of sums, Additional Instructional Resources ESS: VDOE Enhanced Scope and Sequence Lessons ESS: ginia.gov/testing/s ol/standards_docs/ mathematics/index.shtml Page 1

8 Grade 4 Quarter 2 differences and to judge the reasonableness of such results. Understand that addition and subtraction are inverse operations. Understand that division is the operation of making equal groups or equal shares. When the original amount and the number of shares are known, divide to find the size of each share. When the original amount and the size of each share are known, divide to find the number of shares. Understand that multiplication and division are inverse operations. Understand various representations of division and the terms used in division are dividend, divisor, and quotient. differences, products, and quotients of whole numbers using estimation. dividend divisor = quotient 5 days divisor quotient dividend Understand how to solve single-step and multistep problems using whole number operations. Outcomes and Data 4.13 Essential Questions Between what 2 numbers do probability values lie? Why? Explain how the outcome of a simple SOL 4.13 The student will a) predict the likelihood of an outcome of a simple event; and b) represent probability as a number between 0 and 1, inclusive. Page 2

9 Grade 4 Quarter 2 event relates to the numbers of 0 and 1. Identify the likelihood of an event occurring and relate it to its rational representation. Provide a real life example of something that has a probability of ½ and others in between. Represent the probability of an event as a common fraction Essential Understandings Understand and apply basic concepts of probability. Describe events as likely or unlikely and discuss the degree of likelihood, using the terms certain, likely, equally likely, unlikely, and impossible. Predict the likelihood of an outcome of a simple event and test the prediction. Understand that the measure of the probability of an event can be represented by a number between 0 and 1, inclusive Essential Knowledge and Skills Model and determine all possible outcomes of a given simple event where there are no more than 24 possible outcomes, using a variety of manipulatives, such as coins, number cubes, and spinners. Write the probability of a given simple event as a fraction, where the total number of possible outcomes is 24 or fewer. Identify the likelihood of an event occurring and relate it to its fractional representation (e.g., impossible/0; equally likely/ 1 2 ; certain/1). Determine the outcome of an event that is least likely to occur (less than half) or most likely to occur (greater than half) when the number of possible outcomes is 24 or less. Represent probability as a point between 0 and 1, inclusively, on a number line. 10 days 4.14 Essential Questions Collect, organize, display, and interpret data from a variety of graphs. Compare and contrast line, bar, picture, circle graphs, and line plots Essential Understandings Understand the difference between representing categorical data and representing numerical data. Understand that line graphs show INV: The Shape of Data Investigation 1: Introduction to Data Analysis, Sessions 1 3 Investigation 2: Landmarks in the Data, Sessions 1 7 SOL 4.14 The student will collect, organize, display, and interpret data from a variety of graphs Essential Knowledge and Skills Collect data, using, for example, observations, measurement, surveys, scientific experiments, polls, or questionnaires. Organize data into a chart or table. Construct and display data in bar ESS inia.gov/testing/sol/s tandards_docs/math ematics/index.shtml Lucky Sums? Looking for a Pet! How Certain Are You? Sandwich Data Page 3

10 Grade 4 Quarter 2 change over time (numerical data). Understand that bar graphs should be used to compare counts of different categories (categorical data). Understand how data displayed in bar and line graphs can be interpreted so that informed decisions can be made. Understand that the title and labels of the graph provide the foundation for interpreting the data. graphs, labeling one axis with equal whole number increments of 1 or more (numerical data) (e.g., 2, 5, 10, or 100) and the other axis with categories related to the title of the graph (categorical data) (e.g., swimming, fishing, boating, and water skiing as the categories of Favorite Summer Sports ). Construct and display data in line graphs, labeling the vertical axis with equal whole number increments of 1 or more and the horizontal axis with continuous data commonly related to time (e.g., hours, days, months, years, and age). Line graphs will have no more than 10 identified points along a continuum for continuous data. For example, growth charts showing age versus height place age on the horizontal axis (e.g., 1 month, 2 months, 3 months, and 4 months). Title or identify the title in a given graph and label or identify the axes. Interpret data from simple line and bar graphs by describing the characteristics of the data and the data as a whole (e.g., the category with the greatest/least, categories with the same number of responses, similarities and differences, the total number). Data points will be limited to 30 and categories to 8. Interpret the data to answer the question posed, and compare the answer to the prediction (e.g., The Say, Here! Spinning Colors Page 4

11 Grade 4 Quarter 2 summer sport preferred by most is swimming, which is what I predicted before collecting the data. ). Write at least one sentence to describe the analysis and interpretation of the data, identifying parts of the data that have special characteristics, including categories with the greatest, the least, or the same. 6 days Assessment, Enrichment, and Remediation Page 5

12 Grade 4 Quarter 3 Number of Days 22 days Topics, Essential Questions, and Essential Understandings (Students should be able to answer essential questions.) Working with Rational Numbers Fractions 4.5 a, b, d Essential Questions Compare and contrast whole number operations with fraction operations. Explain why least common multiples and least common denominators are used when computing the sums and differences of fractions. Give an example of a practical problem using fractions. Give an example of a practical problem using decimals. 4.5 a, b, d Essential Understandings Understand and use common multiples and common factors for simplifying fractions. Develop and use strategies to estimate addition and subtraction involving fractions. Use visual models to add and subtract with fractions and decimals. REQUIRED Critical Thinking Lessons INV: Different Shapes, Equal Pieces Investigation 3: Ordering Fractions, Sessions 1 9 INV: Three Out of Four Like Spaghetti Investigation 1: Using Fractions to Describe Data, Sessions 1 4 Standards of Learning Essential Knowledge and Skills SOL 4.5 a, b, d The student will a) determine common multiples and factors, including least common multiple and greatest common factor; b) add and subtract fractions having like and unlike denominators that are limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fractions, using common multiples and factors; 4.5 a, b, d Essential Knowledge and Skills Find common multiples and common factors of numbers. Determine the least common multiple and greatest common factor of numbers. Use least common multiple and/or greatest common factor to find a common denominator for fractions. Add and subtract with fractions having like denominators whose denominators are limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fraction using common multiples and factors. Add and subtract with fractions having Additional Instructional Resources ESS: VDOE Enhanced Scope and Sequence Lessons ESS ginia.gov/testing/s ol/standards_docs/ mathematics/index.shtml Fraction Grids Register Tape Fractions Circle Fractions Fraction Strips Egg Carton Fractions Pattern Block Fractions Build the Whole Pattern Block Fraction Game Comparing Fractions Which is Closer? Fraction Strip Addition Fraction Riddles Fraction Bar Kit Page 1

13 Grade 4 Quarter 3 Page 2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 4.2 a, b, c Essential Questions Demonstrate and explain patterns within equivalent fractions. Given more than one fraction, how do you determine which fraction is smallest? Identify the division statement that represents a fraction. Explain the strategy of using landmark ¼, ½, ¾ help you in comparing and ordering fractions. Explain how a fraction can represent a relationship as well as a division operation. Justify how a fractional number describes part of a set. Explain how to determine a fraction is in simplest form. Demonstrate and explain that multiple representations of unlike denominators whose denominators are limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fraction using common multiples and factors. Solve problems that involve adding and subtracting with fractions having like and unlike denominators whose denominators are limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fraction using common multiples and factors. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 4.2 a, b, c The student will a) compare and order fractions and mixed numbers; b) represent equivalent fractions; and c) identify the division statement that represents a fraction. 4.2 Essential Knowledge and Skills Compare and order fractions having denominators of 12 or less, using manipulative models and drawings, such as region/area models. Compare and order fractions with like denominators by comparing number of parts (numerators) (e.g., 1 5 < 3 5 ). Compare and order fractions with like numerators and unlike denominators by comparing the size of the parts INV: Different Shapes, Equal Pieces Investigation 1: Parts of Squares: Halves, Fourths, and Eighths, Sessions 1 5 Investigation 2: Parts of Rectangles: Thirds, Sixths, and Twelfths, Sessions 1 4

14 Grade 4 Quarter 3 answers are equivalent. (For example, ½ and 2/4 are the same.) Explain equivalent fractions through multiple representations. 4.2 a, b, c Essential Understandings Two fractions are equivalent (represent the same number) when both fractions correspond to the same point on the number line. Recognize and generate equivalent fractions with denominators of 2, 3, 4, and 6 (e.g., ½ =2/4, 4/6=2/3), and explain the reasoning. Fractions apply to situations where a whole is decomposed into equal parts; use fractions to describe parts of wholes. For example, to show 1/3 of a length, decompose the length into 3 equal parts and show one of the parts Develop an understanding of fractions as parts of unit wholes, as parts of a collection, and as locations on a number line. (e.g., 3 9 < 3 5 ). Compare and order fractions having unlike denominators of 12 or less by comparing the fractions to benchmarks (e.g., 0, 1 2 or 1) to determine their relationships to the benchmarks or by finding a common denominator. Compare and order mixed numbers having denominators of 12 or less. Use the symbols >, <, and = to compare the numerical value of fractions and mixed numbers having denominators of 12 or less. Represent equivalent fractions through twelfths, using region/area models, set models, and measurement models. Identify the division statement that 3 represents a fraction (e.g., 5 means the same as 3 divided by 5). Understand that a mixed number is a fraction that has two parts: a whole number and a proper fraction. The mixed number is the sum of these two parts. Use models, benchmarks, and equivalent forms to judge the size of fractions. Page 3

15 Grade 4 Quarter 3 Recognize that a whole divided into nine equal parts has smaller parts than if the whole had been divided into five equal parts. Recognize and generate equivalent forms of commonly used fractions and decimals. Understand the division statement that represents a fraction. Understand that the more parts the whole is divided into, the smaller the parts (e.g., ~~~~~~~~ 22 days 1 5 < 1 3 ). ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Decimals 4.3 a, b, c, d Essential Questions Prove how a fraction and a decimal can represent the same value. Explain the difference between reading a number with a decimal compared to reading a number without a decimal. Describe the differences between saying, reading, and/or writing one hundred and one hundredths? (also do tens vs. tenths... and thousands vs. thousandths) Explain how the place value system is used to name and compare decimal numbers smaller than 1. Justify how the magnitude of a base-10 model represents decimals. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 4.3 The student will a) read, write, represent, and identify decimals expressed through thousandths; b) round decimals to the nearest whole number, tenth, and hundredth; c) compare and order decimals; and d) given a model, write the decimal and fraction equivalents. 4.3 Essential Knowledge and Skills Investigate the ten-to-one place value relationship for decimals through thousandths, using Base-10 manipulatives (e.g., place value mats/charts, decimal squares, Base-10 blocks, money). Represent and identify decimals ~~~~~~~~~~~~~~~~ ESS ginia.gov/testing/s ol/standards_docs/ mathematics/index.shtml Comparing Decimals Rounding Decimals Decimal Rings Reading and Writing Decimals Page 4

16 Grade 4 Quarter 3 Demonstrate and prove fraction and decimal equivalents. Compare and prove decimal values using >, <. =. Explain when it would be appropriate to round a number to a whole number, tenths, or hundredths. 4.3 a, b, c, d Essential Understandings Understand the place value structure of decimals and use this structure to read, write, and compare decimals. Understand that decimal numbers can be rounded to an estimate when exact numbers are not needed for the situation at hand. Understand that decimals are rounded in a way that is similar to the way whole numbers are rounded. Understand that decimals and fractions represent the same relationship; however, they are presented in two different formats. Understand that models are used to show decimal and fraction equivalents. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 4.5 c Essential Questions Compare and contrast adding and subtracting fractions and decimals. Compare and contrast whole number operations with decimal operations. 4.5 c Essential Understandings Develop and use strategies to estimate expressed through thousandths, using Base-10 manipulatives, pictorial representations, and numerical symbols (e.g., relate the appropriate drawing to 0.05). Identify and communicate, both orally and in written form, the position and value of a decimal through thousandths. For example, in 0.385, the 8 is in the hundredths place and has a value of Read and write decimals expressed through thousandths, using Base-10 manipulatives, drawings, and numerical symbols. Round decimals to the nearest whole number, tenth, and hundredth. Compare decimals, using the symbols >, <, =. Order a set of decimals from least to greatest or greatest to least. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 4.5 c The student will c) add and subtract with decimals; and. 4.5 c Essential Knowledge and Skills Find common multiples and common factors of numbers. Determine the least common multiple and greatest common factor of Page 5

17 Grade 4 Quarter 3 addition and subtraction involving fractions. Use visual models to add and subtract with decimals. numbers. Use least common multiple and/or greatest common factor to find a common denominator for fractions. Add and subtract with fractions having like denominators whose denominators are limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fraction using common multiples and factors. Add and subtract with fractions having unlike denominators whose denominators are limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fraction using common multiples and factors. Solve problems that involve adding and subtracting with fractions having like and unlike denominators whose denominators are limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fraction using common multiples and factors.. 4 days Enrichment, Assessment, and Remediation Page 6

18 Grade 4 Quarter 4 Number of Days Topics, Essential Questions, and Essential Understandings (Students should be able to answer essential questions.) REQUIRED Critical Thinking Lessons Standard(s) of Learning Essential Knowledge and Skills Additional Instructional Resources ESS: VDOE Enhanced Scope and Sequence 15 days Measurement 4.7 Essential Questions Length/Distance Give a real life example of what you would measure in inches, feet, yards, miles, millimeters, centimeters, meters, and kilometers. Why are there two different units of measurement? What is an appropriate tool to measure in inches, feet, yards, millimeters, centimeters, meters, and kilometers? 4.7 Essential Understandings All students should: Use benchmarks to estimate and measure length. Understand how to convert units of length between the U.S. Customary and metric systems, using ballpark comparisons. Understand the relationship between U.S. Customary units and the relationship between metric units. Measurement Benchmarks (from 5 th grade Investigations) Investigation 1: Measures of Length and Distance, Sessions 1 6 Investigation 2: Measures of Weight and Liquid Volume, Sessions 1-6 SOL 4.7 The student will a) estimate and measure length, and describe the result in both metric and U.S. Customary units; and b) identify equivalent measurements between units within the U.S. Customary system (inches and feet; feet and yards; inches and yards; yards and miles) and between units within the metric system (millimeters and centimeters; centimeters and meters; and millimeters and meters). 4.7 Essential Knowledge and Skills Determine an appropriate unit of measure (e.g., inch, foot, yard, mile, millimeter, centimeter, and meter) to use when measuring everyday objects in both metric and U.S. Customary units. Estimate the length of everyday objects (e.g., books, windows, tables) in both metric and U.S. Customary units of measure. Measure the length of objects in both metric and U.S. Customary units, measuring to the nearest inch ( 1 2, 1 4, 1 8 ), g/lessondetail.aspx?id=l1 84 How Long? How Tall? How Wide? How Deep? g/lessondetail.aspx?id=l6 35 foot, yard, mile, millimeter, centimeter, or meter, and record the length including the appropriate unit of measure (e.g., 24 inches).

19 Grade 4 Quarter 4 Compare estimates of the length of objects with the actual measurement of the length of objects. Identify equivalent measures of length between units within the U.S. Customary measurements and between units within the metric measurements. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 4.6 Essential Questions Weight/Mass What is the difference between weight and mass? Give a real life example of what you would measure in ounces, pounds, tons, grams, and kilograms. 4.6 Essential Understandings Use benchmarks to estimate and measure weight/mass. Identify equivalent measures between units within the U.S. Customary and between units within the metric measurements. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 4.8 Essential Questions Liquid Volume ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 4.6 The student will a) estimate and measure weight/mass and describe the results in U.S. Customary and metric units as appropriate; and b) identify equivalent measurements between units within the U.S. Customary system (ounces, pounds, and tons) and between units within the metric system (grams and kilograms). 4.6 Essential Knowledge and Skills Determine an appropriate unit of measure (e.g., ounce, pound, ton, gram, kilogram) to use when measuring everyday objects in both metric and U.S. Customary units. Measure objects in both metric and U.S. Customary units (e.g., ounce, pound, ton, gram, or kilogram) to the nearest appropriate measure, using a variety of measuring instruments. Record the mass of an object including the appropriate unit of measure (e.g., 24 grams). ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 4.8 The student will a) estimate and measure liquid volume and describe the results in U.S. Customary units;

20 Grade 4 Quarter 4 Give a real life example of what you would measure in cups, pints, quarts, and gallons. 4.8 Essential Understandings All students should: Use benchmarks to estimate and measure volume. Identify equivalent measurements between units within the U.S. Customary system. and b) identify equivalent measurements between units within the U.S. Customary system (cups, pints, quarts, and gallons). 4.8 Essential Knowledge and Skills The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Determine an appropriate unit of measure (cups, pints, quarts, gallons) to use when measuring liquid volume in U.S. Customary units. Estimate the liquid volume of containers in U.S. Customary units of measure to the nearest cup, pint, quart, and gallon. Measure the liquid volume of everyday objects in U.S. Customary units, including cups, pints, quarts, and gallons, and record the volume including the appropriate unit of measure (e.g., 24 gallons). Identify equivalent measures of volume between units within the U.S. Customary system. 20 days Geometry Plane Figures 4.10 Essential Questions Compare and contrast a line, line segment, angle and ray. Create and identify a line, line segment, angle, and ray. What is the relationship between a line segment and an angle? Explain the relationship between a ray and an angle. SOL 4.10 The student will a) identify and describe representations of points, lines, line segments, rays, and angles, including endpoints and vertices; and b) identify representations of lines that illustrate intersection, parallelism, perpendicularity 4.10 Essential Knowledge and Skills Grade 4 ESS Lessons: Simple Pictures Geometry Review Geometric Figures Congruent Figures Coordinate Points Toothpick, Door and Staircase Patterns Investigations: Mathematical Thinking in

21 Grade 4 Quarter 4 Identify and justify real life examples of parallel lines. Identify and justify real life examples perpendicular lines. Compare and contrast characteristics of intersecting lines and perpendicular lines Essential Understandings Understand that points, lines, line segments, rays, and angles, including endpoints and vertices are fundamental components of noncircular geometric figures. Understand that the shortest distance between two points on a flat surface is a line segment. Understand that lines in a plane either intersect or are parallel. Perpendicularity is a special case of intersection. Identify practical situations that illustrate parallel, intersecting, and perpendicular lines. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 4.11 Essential Questions Compare and contrast geometric transformations. Demonstrate and explain congruency of a plane figure after a reflection, translation, and/or rotation. Demonstrate and justify various strategies for rotation, reflection, and translation of an image. What are real life models of reflection, translation, and rotation? Prove the image of a plane figure is congruent to the original image after a transformation. Explain what understandings are important when determining if two figures are congruent. Identify and describe representations of points, lines, line segments, rays, and angles, including endpoints and vertices. Understand that lines in a plane can intersect or are parallel. Perpendicularity is a special case of intersection. Identify practical situations that illustrate parallel, intersecting, and perpendicular lines. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 4.11 The student will a) investigate congruence of plane figures after geometric transformations, such as reflection, translation, and rotation, using mirrors, paper folding, and tracing; and b) recognize the images of figures resulting from geometric transformations, such as translation, reflection, and rotation Essential Knowledge and Skills Recognize the congruence of plane figures resulting from geometric transformations such as translation, reflection, and rotation, using mirrors, paper folding and tracing. Grade 4 Investigation 4: Making Geometric Patterns, Sessions 1 6

22 Grade 4 Quarter 4 5 days 4.11 Essential Understandings Understand the meaning of the term congruent. Understand how to identify congruent figures. Understand that the orientation of figures does not affect congruency or noncongruency. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 4.12 Essential Questions What is a polygon? Create and identify polygons with ten or fewer sides Essential Understandings Identify polygons with 10 or fewer sides in everyday situations. Identify polygons with 10 or fewer sides in multiple orientations (rotations, reflections, and translations of the polygons) Elapsed Time 4.9 Essential Questions What is elapsed time? How do you determine elapsed time? Determine elapsed time given between 2 given hours and additional minutes. Given a beginning and ending time of an event, use at least two different strategies to calculate elapsed time. Provided an ending time and an elapsed time, determine the start time of the event. 4.9 Essential Understandings Understand the counting on strategy for determining elapsed time in hour and minute ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 4.12 The student will a) define polygon; and b) identify polygons with ten or fewer sides Essential Knowledge and Skills Define and identify properties of polygons with 10 or fewer sides. Identify polygons by name with 10 or fewer sides in multiple orientations (rotations, reflections, and translations of the polygons) SOL 4.9 The student will determine elapsed time in hours and minutes within a 12-hour period. Essential Knowledge and Skills The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Determine the elapsed time in hours and minutes within a 12-hour period (times can cross between a.m. and p.m.). Solve practical problems in relation to time that has elapsed

23 Grade 4 Quarter 4 increments over a 12-hour period from a.m. to a.m. or p.m. to p.m. 3 days Enrichment, Assessment, and Remediation