Rationale For Fourth Grade Instructional Guide

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2 Rationale For Instructional Guide Organizational Highlights All power standards are being assessed. Fourth grade has the most power standards of any grade. There was an attempt made to reduce the number of standards being assessed by only focusing on assessing the power standards. However, in discussions with teachers and coaches, it was felt that there were nonpower standards that also needed to be assessed because they are on the Blueprint for the California Standards Assessment. Also, there was a concern that certain standards needed to be assessed more than one time. For these reasons, the number of assessed standards is high for each quarter in the fourth grade. Recommended lessons from Harcourt Math, are listed for each of the content standards The mathematics program in fourth grade includes the use of manipulatives. All students should have access to concrete objects and/or manipulatives during mathematics. Manipulatives enables the students to create models which facilitate their understanding of the mathematics being taught. Throughout Harcourt Math the publisher includes manipulatives when introducing a lesson. The teacher resource pages of the teacher edition provide a number of activities that involve the use of manipulatives. It is strongly recommended that the teaching suggestions in Reaching All Learners at the beginning of each chapter as well as the Intervention and Extension Resources at the beginning of each lesson be utilized for planning lessons. Lessons listed in Additional Resources by Marilyn Burns and from LUCI also provide activities using manipulatives. It is recommended that the use of manipulatives extend beyond the introduction of a lesson. However, manipulatives should not be used in isolation. It is important that a link be created between the manipulative and the paper and pencil representations. The Problem of the Day should be included as part of the daily routine when teaching mathematics. The Instructional Guide lists the recommended Lesson Resource pages and accompanying lessons for each of the content standards. Harcourt Math also provides various resources such as literature connections, strategies for English Language Learners, the Family Involvement Activities, Activities and Games for Home and School, and Intervention Strategies and Activities.

3 Quarter One This Quarter begins the year with the content standards from Statistics, Data, and Probability. The writers of the 4 th grade instructional guide felt that place value was a difficult concept to begin the school year. Reading and writing thousands and millions numbers with one or more zeros in the middle can be particularly troublesome for students. They felt that the strand of Statistics, Data and Probability is more interactive and would allow teachers to become better acquainted with their children at the beginning of the school year. By learning this skill early in the school year, students are also able to use this knowledge in social studies and science throughout the year. Instruction then proceeds to the more difficult topic of Place Value through the millions. Students will also compare and order numbers which lays foundation for later locating numbers on the number line. Although this key standard includes the concept, decimals to two decimal places, it has been omitted and will be taught in the third assessment period. Addition and subtraction of whole numbers and money is taught and builds on the learning from previous grades. Multiplication and division facts are reviewed before multiplication by one and two digit numbers. Algebra concepts focus on understanding expressions, variables and equals added to equals. The algebra chapter in Harcourt is well developed and is used throughout the year to teach and review fourth grade algebraic concepts. Quarter Two This Quarter begins with reinforcing multiplication facts through number theory. Multiplication lays the foundation for studying division, area and fractions. Factors, and prime numbers provide students with an opportunity to decompose numbers in many ways. Students will be using these factoring skills extensively in the later grades as they study fractions. By inserting this topic at this time provides students an opportunity to take a break from two place multipliers. Students then revisit two place multiplication to reinforce this concept. A review of rounding whole numbers precedes division by a one digit divisor. The concept development for division includes estimation, and finding averages. Algebra concepts continue to weave their way through the year with an exploration of equations, functions and equality. Graphing ordered pairs continue the algebra concept development from the first instructional Quarter. Multiplication concepts are reviewed again in studying area. Perimeter concepts are expanded on from third grade. The development and use of formulas are also introduced. Fractions, both as parts of sets and parts of the whole, as well as comparing and ordering fractions complete this unit of study. Locating fractions and mixed numbers on a number line is a key standard at this grade level. A review of prime factorization is included here in order to support learning equivalent fractions. Addition and subtraction are reviewed and reassessed to provide additional time for mastery.

4 Quarter Three This quarter begins with the content standards relating to decimal concepts. Decimal concepts are related to fractional concepts taught in the second quarter. Negative numbers introduce students to integers for the first time. Ordering decimals, fractions and negative numbers on the number line are key fourth grade standards. Interactive lessons on probability follow. Probability lessons provide an opportunity for students to utilize fractional concepts learned in Quarter two. The focus is on making predictions and determining outcomes. Graphing on the coordinate plane has connections to both geometry and algebra. Students learn that intersecting perpendicular number lines make it possible to locate points anywhere on a plane. It is during this Quarter that students learn to graph algebraic equations as a set of number points on the coordinate grid. The text book resources are thin and will need to be supplemented with additional resources to allow students to practice locating points on a coordinate grid. It is during this quarter that students learn to graph algebraic equations on the coordinate grid. A geometry unit follows, which focuses on the lines, angles, polygons, spatial reasoning, circles, solids and congruency. Hands on activities in geometry are strongly suggested. Problem solving is assessed using all the operations. Prime numbers are reviewed to continue to build automaticity. Quarter Four This Quarter includes the concepts that are necessary to prepare students for the first Quarter of the fifth grade math instructional period. The writers of the fifth grade Instructional Guide requested that certain skills be retaught because many students come to fifth grade needing extensive reteaching in these areas: prime factorization; fractions, mixed numbers, and decimals on a number line. Not only will reteaching these concepts save precious time for fifth grade teachers, this review strengthens the most important new fourth grade skills added to the students basic math understanding. Addition and subtraction of fractions along with measurement skills are included here because they are not key concepts for fourth grade but they are for fifth grade. By teaching them during this period, they address a gap in the grade level standards. In addition to the fifth grade preparation lessons, problem solving is again assessed using all the operations. Student data should be used to determine differentiated concepts for review. Additional resources such as Marilyn Burns material and LUCI investigations can provide a rich experience for students to grasp a deeper understanding of mathematical concepts.

5 Mathematics Instructional Guide: Quarter One DATA ANALYSIS PLACE VALUE ADDITION/SUBTRACTION ALGEBRA MULTIPLICATION Standards: * NS 1.1 Read and write whole numbers in the millions. * NS 1.2 Order and compare whole numbers and decimals to two decimal places. * NS 1.3 Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand. * NS 1.4 Decide when a rounded solution is called for and explain why such a solution may be appropriate. NS 2.1 Estimate and compute the sum or difference of whole numbers and positive decimals to two places. * NS 3.0 Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations. * NS 3.1 Demonstrate an understanding of, and the ability to use, standard algorithms for the addition and subtraction of multidigit numbers. * NS 3.2 Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multidigit number by a two-digit number and for dividing a multidigit number by a one-digit number; use relationships between them to simplify computations and to check results. * NS 3.3 Solve problems involving multiplication of multidigit numbers by two-digit numbers. NS 4.1 Understand that many whole numbers break down in different ways (e.g., 12 = 4 x 3 = 2 x 6 = 2 x 2 x 3). AF 1.0 Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences. AF 1.1 Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g., demonstrate an understanding and the use of the concept of a variable). * AF 1.2 Interpret and evaluate mathematical expressions that now use parentheses. * AF 1.3 Use parentheses to indicate which operation to perform first when writing expressions containing more than two terms and different operations. * AF 2.1 Know and understand that equals added to equals are equal. SDAP 1.0 Students organize, represent, and interpret numerical and categorical data and clearly communicate their findings. SDAP 1.1 Formulate survey questions; systematically collect and represent data on a number line; and coordinate graphs, tables, and charts. * SDAP 1.2 Identify the mode(s) for sets of categorical data and the mode(s), median, and any apparent outliers for numerical data sets. * SDAP 1.3 Interpret one- and two-variable data graphs to answer questions about a situation. MR Embedded Quarter One,

6 Mathematics Instructional Guide: Quarter One DATA ANALYSIS PLACE VALUE ADDITION/SUBTRACTION ALGEBRA MULTIPLICATION SDAP 1.0 SDAP 1.1 SDAP 1.2 Lesson Planning: 82A- 90B Lessons: A Collection of Math Lessons Grades 3-6, Alphabetical Statistics, Pp Collect, organize, summarize, and interpret data: Median, and mode One and two variable graphs GS: Getting to Know You Graphs SDAP 1.0 SDAP 1.1 SDAP 1.3 MR 2.3 Interpret, analyze, and display data One and two variable graphs Lesson Planning 92A-94B, 100A-106B Lesson: , Ideas for Graphs, Pp NS 1.1 MR 2.0 MR 2.3 Place Value through Millions Lesson Planning: 4A-12B Lessons: Place Value Game, P 244 NS 1.1 NS 1.2 Compare and order numbers Lesson Planning: 18A 24B Lessons: NS 1.1 NS 1.3 Rounding numbers Lesson Planning: 26A-26B Lesson: 2.4 COMP5: Estimation Warmup Quarter One,

7 Mathematics Instructional Guide: Quarter One DATA ANALYSIS PLACE VALUE ADDITION/SUBTRACTION ALGEBRA MULTIPLICATION NS 1.4 NS 2.1 NS 3.0 NS 3.1 MR 1.0 MR 2.0 Estimate and compute sums and differences Multidigit numbers Lesson Planning: 34A-48B Lessons: Palindromes, Pp A Collection of Math Lessons, Grades 3-6, Palindromes, Pp AF 1.2 AF 1.3 Expressions Lesson Planning: 54A-58B Lessons: AF 1.0 AF 1.1 Variables Lesson Planning: 60A-60B Lesson: 4.4 Uses of Variables, Pp AF 2.1 Equals added to equals Lesson Planning: 66A-70B Lesson: Quarter One,

8 Mathematics Instructional Guide: Quarter One DATA ANALYSIS PLACE VALUE ADDITION/SUBTRACTION ALGEBRA MULTIPLICATION NS 3.0 NS 4.1 MR 1.1 Strategies for multiplication and division facts Lesson Planning: 140A-148B Lessons: A Collection of Math Lessons, Grades 3-6, Exploring Multiplication with Rectangles, Pp NS 1.3 NS 3.0 NS 3.2 NS 3.3 MR 2.0 Multiplication by onedigit numbers Estimation by rounding Lesson Planning: 186A-200B Lessons: Patterns in Multiples, P. 198 Candy Box Research, P 199 Multiplication Possibilities, P 133 COMP5: Multidigit Strategies for Multiplication and Division NS 1.3 NS 3.2 NS 3.3 MR 1.2 Multiplication by twodigit numbers: Estimation by rounding Lesson Planning: 206A-214B Lessons: How Many Beans? P. 216 COMP5: Strategies, Algorithms COMP5: Estimation Strategies A S S E S S M E N T E N R I C H M E N T / R E T E A C H I N G Quarter One,

9 Mathematics Instructional Guide: Quarter Two NUMBER THEORY MULTIPLICATION DIVISION PERIMETER AND AREA ALGEBRA FRACTIONS Standards: NS 1.3 Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand. NS 1.4 Decide when a rounded solution is called for and explain why such a solution may be appropriate. * NS 1.5 Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain equivalents of fractions. * NS 1.7 Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line. * NS 1.9 Identify on a number line the relative position of positive fractions, positive mixed numbers, and positive decimals to two decimal places. * NS 3.0 Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations. * NS 3.2 Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multidigit number by a two-digit number and for dividing a multidigit number by a one-digit number; use relationships between them to simplify computations and to check results. * NS 3.3 Solve problems involving multiplication of multidigit numbers by two-digit numbers. * NS 3.4 Solve problems involving division of multidigit numbers by one-digit numbers. NS 4.1 Understand that many whole numbers break down in different ways (e.g., 12= 4 x 3= 2 x 6 = 2 x 2x 3). * NS 4.2 Know that numbers such as 2, 3, 5, 7, and 11 do not have any factors except 1 and themselves and that such numbers are called prime numbers. AF 1.0 Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences. AF 1.1 Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g., demonstrate an understanding and the use of the concept of a variable). * AF 1.2 Interpret and evaluate mathematical expressions that now use parentheses. * AF 1.3 Use parentheses to indicate which operation to perform first when writing expressions containing more than two terms and different operations. AF 1.4 Use and interpret formulas (e.g., area = length x width or A = lw) to answer questions about quantities and their relationships. * AF 1.5 Understand that an equation such as y=3x + 5 is a prescription for determining a second number when a first number is given. * AF 2.0 Students know how to manipulate equations. * AF 2.1 Know and understand that equals added to equals are equal. * AF 2.2 Know and understand that equals multiplied by equals are equal. * MG 1.1 Measure the area of rectangular shapes by using appropriate units, such as square centimeter (cm 2 ), square meter (m 2 ), square kilometer (km 2 ), square inch (in 2 ), square yard (yd 2 ), or square mile (mi 2 ). MG 1.2 Recognize that rectangles that have the same area can have different perimeters. MG 1.3 Understand that rectangles that have the same perimeter can have different areas. * MG 1.4 Understand and use formulas to solve problems involving perimeters and areas of rectangles and squares. Use those formulas to find the areas of more complex figures by dividing the figures into basic shapes. MR Embedded Quarter Two,

10 Mathematics Instructional Guide: Quarter Two NUMBER THEORY MULTIPLICATION DIVISION PERIMETER AND AREA ALGEBRA FRACTIONS NS 4.1 Factors and Multiples Lesson Planning: 294A-296B Lessons: Factor Fiddling, P 221 The Factor Game, P202 NS 4.2 Prime and Composite Numbers Lesson Planning: 297A-304B Lessons: A Collection of Math Lessons, Grades 3-6, Exploring Multiplication with Rectangles, Pp NS 3.2 NS 3.3 Multiplication by two-digit numbers: Estimation by rounding Lesson Planning: 220A-230B Lessons: Largest Product, P 219 Through Real World Problems, P Hit the Target, P 217, 221 COMP5: Estimation Strategies NS 1.3 Review - Round whole numbers Refer to Instructional Quarter 1 for additional resources Quarter Two,

11 Mathematics Instructional Guide: Quarter Two NUMBER THEORY MULTIPLICATION DIVISION PERIMETER AND AREA ALGEBRA FRACTIONS NS 1.4 NS 3.0 NS 3.2 NS 3.4 MR 1.0 MR 1.1 MR 3.1 Division by a 1-digit divisor Rounding Estimation Multidigit numbers Lesson Planning: 242A -254B, 260A-272B Lessons: , Leftovers with 20, P A Long Division Activity, P 215 The Doorbell Rings Again, P 211 Remainders of Zero, P 220 Division Stories, P 210 AF 1.4 MG 1.1 MG 1.2 MG 1.3 MG 1.4 Perimeter and Area of Polygons Lesson Planning: 496A-506B Lessons COMP5: Multidigit Strategies for Multiplication/Division Squaring Up, P 54 Area and Perimeter, P 87 The Perimeter Stays the Same, P. 54 AF 1.5 Find a Rule - Functions Lesson Planning: 64A-64B Lesson: 4.5 Patterns, Functions, and Algebra, Pp ALGINTRO: Finding Patterns/Toothpick Staircase Quarter Two,

12 Mathematics Instructional Guide: Quarter Two NUMBER THEORY MULTIPLICATION DIVISION PERIMETER AND AREA ALGEBRA FRACTIONS AF 1.0 Review: Concept of Refer to Instructional Quarter 1 for AF 1.1 Variable additional resources AF 2.1 Review: Equals Added to Equals Refer to Instructional Quarter 1 for additional resources AF 1.2 AF 1.3 AF 2.0 AF 2.2 NS 3.0 NS 1.5 NS 1.7 NS 1.9 NS 4.2 Equations and Variables Equals multiplied by equals Review Addition/Subtraction of Multidigit Numbers Review: Prime Factors Equivalent Fractions Lesson Planning: 158A- 170B Lessons: Refer to Instructional Quarter 1 for resources Lesson Planning: 316A 320B Lessons: ALGINTRO: What s the Problem? Fractions as Parts of Sets, P. 225 Fractions with Two-Color Counters, Pp The Fraction Kit, Pp Building Rectangles, P 234 FRACT1A: Fraction Squares Puzzle FRACT1A: Triangle Puzzle FRACT2: Flower Garden Problem Quarter Two,

13 Mathematics Instructional Guide: Quarter Two NUMBER THEORY MULTIPLICATION DIVISION PERIMETER AND AREA ALGEBRA FRACTIONS NS 1.9 MR 2.3 MR 2.6 Compare and order fractions Number Line Lesson Planning: 324A-330B Lessons: Put in Order, P 231 Closest to 0, 1/2 or 1? P 232 NLB: Fraction Lines A S S E S S M E N T E N R I C H M E N T / R E T E A C H I N G Quarter Two,

14 Los Angeles Unified School District Mathematics Instruction Guide: Quarter Three DECIMALS NEGATIVE NUMBERS PROBABILITY ALGEBRA COORDINATE GRAPHING GEOMETRY Standards: * NS 1.2 Order and compare whole numbers and decimals to two decimal places. * NS 1.6 Write tenths and hundredths in decimal and fraction notations and know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 or 0.50; 7/4= 1 3/4= 1.75) * NS 1.7 Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line. * NS 1.8 Use concepts of negative numbers (e.g., on a number line, in counting, in temperature, in owing ). * NS 1.9 Identify on a number line the relative position of positive fractions, positive mixed numbers, and positive decimals to two decimal places. NS 2.1 Estimate and compute the sum or difference of whole numbers and positive decimals to two places. NS 2.2 Round two-place decimals to one decimal or the nearest whole number and judge the reasonableness of the rounded answer. * NS 3.0 Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations. * NS 4.2 Know that numbers such as 2, 3, 5, 7 and 11 do not have any factors except 1 and themselves and that such numbers are called prime numbers. * AF 1.5 Understand that an equation such as y=3x + 5 is a prescription for determining a second number when a first number is given. * MG 2.0 Students use two-dimensional coordinate grids to represent points and graph lines and simple figures: * MG 2.1 Draw the points corresponding to linear relationships on graph paper (e.g., draw 10 points on the graph of the equation y = 3x and connect them by using a straight line). * MG 2.2 Understand that the length of a horizontal line segment equals the difference of the x-coordinates. * MG 2.3 Understand that the length of a vertical line segment equals the difference of the y-coordinates. MG 3.1 Identify lines that are parallel and perpendicular. MG 3.2 Identify the radius and diameter of a circle. MG 3.3 Identify congruent figures MG 3.4 Identify figures that have bilateral and rotational symmetry MG 3.5 Know the definitions of a right angle, an acute angle, and an obtuse angle. Understand that 90, 180, 270 and 360 are associated, respectively, with 1/4, 1/2, 3/4, and full turns. * MG 3.6 Visualize, describe, and make models of geometric solids (e.g., prisms, pyramids) in terms of the number and shape of faces, edges, and vertices; interpret two-dimensional representations of three-dimensional objects; and draw patterns (of faces) for a solid that, when cut and folded, will make a model of the solid. * MG 3.7 Know the definitions of different triangles (e.g., equilateral, isosceles, scalene) and identify their attributes. * MG 3.8 Know the definition of different quadrilaterals (e.g., rhombus, square, rectangle, parallelogram, trapezoid). * SDAP 2.0 Students make predictions for simple probability situations; SDAP 2.1 Represent all possible outcomes for a simple probability situation in an organized way (e.g., tables, grids, tree diagrams). SDAP 2.2 Express outcomes of experimental probability situations verbally and numerically (e.g., 3 out of 4; 3/4). MR Embedded Quarter Three,

15 Los Angeles Unified School District Mathematics Instruction Guide: Quarter Three DECIMALS NEGATIVE NUMBERS PROBABILITY ALGEBRA COORDINATE GRAPHING GEOMETRY NS 1.6 Relate fractions to Lesson Planning: 358A 364B NS 1.7 decimals Lessons: DEC: Fraction-Decimal Conversions NS 1.2 NS 1.6 NS 1.9 Compare and order decimals and fractions Lesson Planning: 366A 366B, 372A-372B Lessons: 19.4, 19.6 NS 2.2 NS 2.1 NS 2.2 MR 2.1 MR 3.1 NS 1.8 MR 2.3 MR 2.4 SDAP 2.0 SDAP 2.1 SDAP 2.2 MR 1.1 MR 2.6 Round decimals nearest whole number nearest tenth Sums and differences of decimals Estimate and compute Negative Numbers Probability Predictions and outcomes Lesson Planning: 380A-380B Lesson: 20.1 Lesson Planning: 382A 392B Lessons: Lesson Planning: 438A 442B Lessons: Lesson Planning: 556A 562B, 570A 576B Lessons: ; Spinner Experiments, Pp Tiles in the Bag, Pp Fair-Game, P 74 PROB1: Flip and Roll PROB1: Spinners PROB1: Cubes in a Bag Quarter Three,

16 Los Angeles Unified School District Mathematics Instruction Guide: Quarter Three DECIMALS NEGATIVE NUMBERS PROBABILITY ALGEBRA COORDINATE GRAPHING GEOMETRY NS 3.0 Review: Problem solving All operations Refer to Chapters 3, 8, for additional resources MG 2.0 MG 2.1 MG 2.2 MG 2.3 AF 1.5 MG 2.0 MG 2.1 MG 3.1 MG 3.5 MG 3.3 MG 3.4 Coordinate Grids Graph an equation Lines, rays, angles, and line relationships Congruent and similar figures Lesson Planning: 452A-454B Lessons: Lesson Planning: 458A-466B Lessons: Lesson Planning: 478A-482B Lessons: Lesson Planning: 484A-484B Lesson: 25.3 Paper Tearing, P 11 Geoboard Line Segments, P 96 Explorations Using the Geoboard, P 95 Tangram, P 83 MG 3.4 Symmetry Lesson Planning: 488A-490B Lessons: GEO4: Tangram Activities Mirror Cards, P 88 GEO4: Transformations Quarter Three,

17 Los Angeles Unified School District Mathematics Instruction Guide: Quarter Three DECIMALS NEGATIVE NUMBERS PROBABILITY ALGEBRA COORDINATE GRAPHING GEOMETRY MG 3.6 Faces, Edges, and Vertices Lesson Planning: 516A 520B Lessons: MR 2.3 Volume of rectangular prisms Lesson Planning: 522A 524B Lesson: GEO3: Construct Polyhedra Using Nets MG 3.5 MR 2.3 Types of Angles Lesson Planning: 530A-532B Lessons: Angles with Pattern Blocks and Hinged MG 3.2 MR 2.3 Parts of a Circle: radius and diameter Lesson Planning: 534A-536B Lessons: Mirrors, P 91 Round Things, P 56 MG 3.7 MR 2.3 Types of Triangles Lesson Planning: 538A-538B Lesson: 28.5 Sorting Shapes on the Geoboard, p. 96 MG 3.7 MG 3.8 MR 2.3 NS 4.2 Types of Quadrilaterals Review: Prime Numbers Lesson Planning: 540A-544B Lessons: Refer to Quarter 2 for additional resources GEO3: Tangram Activities Sorting Shapes on the Geoboard, p. 96 GEO3: Tangram Activities A S S E S S M E N T E N R I C H M E N T / R E T E A C H I N G Quarter Three,

18 Mathematics Instructional Guide: Quarter Four FRACTIONS MEASUREMENT REVIEW 4 TH GRADE STANDARDS Standards: * NS 1.2 Order and compare whole numbers and decimals to two decimal places. * NS 1.5 Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain equivalents of fractions. NS 1.7 Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line. * NS 1.9 Identify on a number line the relative position of positive fractions, positive mixed numbers, and positive decimals to two decimal places. * NS 3.0 Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations. * NS 4.2 Know that numbers such as 2, 3, 5, 7 and 11 do not have any factors except 1 and themselves and that such numbers are called prime numbers. * AF 1.4 Use and interpret formulas (e.g., area= length x width or A = lw) to answer questions about quantities and their relationships. * AF 1.5 Understand that an equation such as y=3x + 5 is a prescription for determining a second number when a first number is given. * AF 2.0 Students know how to manipulate equations. * MG 2.0 Students use two-dimensional coordinate grids to represent points and graph lines and simple figures: * SDAP 1.2 Identify the mode(s) for sets of categorical data and the mode(s), median, and any apparent outliers for numerical data sets. MR Embedded NS 3.0 Review Problem Solving: All operations Lesson Planning: 288A-288B Lesson: 15.5 Division Stories, P 210 NS 4.2 Review: Prime Factors Refer to Instructional Quarter 2 for additional resources NS 1.2 NS 1.9 Review: Fraction Concepts Mixed Numbers Decimals on a Number line Refer to Chapters 17 and 19 for review; preparation for 5 th grade curriculum Quarter Four,

19 Mathematics Instructional Guide: Quarter Four FRACTIONS MEASUREMENT REVIEW 4 TH GRADE STANDARDS NS 1.5 NS 1.7 MR 2.3 The Fraction Kit, Pp MR 1.0 MR 1.1 MR 1.0 MR 1.1 MR 3.2 Fractions: Introduction: Addition and Subtraction of Fractions Measurement: Customary Units Length Capacity Weight Measurement: Metric Length Capacity Weight Lesson Planning: 338A-352B Lessons: Refer to Instruction Guide Quarter 2 for additional resources Lesson Planning: 404A-414B Lessons: , Lesson Planning: 422A-422B, 428A-430B Lessons: 22.1, FRACT2: Adding and Subtracting Fractions Practice Measuring, P. 52 AF 1.4 Review: Use and interpret formulas Refer to Chapter 26 for review; preparation for 5 th grade curriculum AF 1.5 Review: Functions Refer to Instruction Quarter 2 for additional resources, preparation for 5 th grade curriculum AF 2.0 Review: Manipulate equations Refer to Chapters 4 and 9 for review; preparation for 5 th grade curriculum Quarter Four,

20 Mathematics Instructional Guide: Quarter Four FRACTIONS MEASUREMENT REVIEW 4 TH GRADE STANDARDS MG 2.0 Review: Coordinate Refer to Chapter 24 for review; grids preparation for 5 th grade curriculum SDAP 1.2 Mode, median, outliers Refer to Chapters 5 and 14 for review; preparation for 5 th grade curriculum A S S E S S M E N T E N R I C H M E N T / R E T E A C H I N G Quarter Four,