Rationale for Instructional Guide Organizational Highlights In students will apply the four basic operations to fractions and decimals and also learn how to add and subtract positive and negative numbers. The Number Sense standards 1.2 and 1.5 are therefore critical for students to understand and master. (See page 138 Mathematics Framework for California Public Schools) Fifth graders will also use measuring units to determine length and area and know and use formulas to determine the volume of simple geometric figures. Students will solve problems involving linear functions and be able to write the equation and graph the resulting ordered pairs of integers on a grid. The mathematics program in the fifth grade includes the use of manipulatives. All students should have access to concrete objects and/or manipulatives as it enables student to create models which facilitate their understanding of the mathematical concepts being taught. The Lesson Resources in Harcourt Math are identified in the Instructional Guide for each of the content standards. These resources include the use of manipulatives to introduce lessons, math background for teachers, the Problem of the Day, home-school connection activities, and strategies for English learners. Quarter One Number Sense is the focus of the first quarter of in order to expand and enhance the understanding of whole number, fraction and decimal concepts from fourth grade. This includes estimating and rounding very large and very small numbers, all operations with decimals, and prime factors and exponents. The number of assessed standards in this quarter is purposely low to allow sufficient time to develop these concepts. Quarter Two Building on quarter one, fractions, decimals and percents are the emphasized concepts for this quarter. Students will be able to apply these concepts to representations on a number line and to use them to solve problems using all four operations. The Statistics, Data and Probability standards are included in this quarter to facilitate the application of these fraction and percentage concepts. Graphing of ordered pairs is introduced in this quarter in order to allow sufficient time for practice and review throughout the rest of the year. Quarter Three Students will expand graphing from last quarter to include linear functions in this quarter. Operations with rational numbers are also an area of emphasis. The balance of this quarter is devoted to the measurement and geometry standards with an emphasis on volume, angles, and the use of appropriate tools such as the compass and protractor.
Quarter Four Quarter Four is an opportunity for teachers to review key concepts that their students found difficult. The emphasis here will be dictated by the needs of the students. In addition, students will preview the skills they will encounter during the first part of 6 th grade, with a particular emphasis on ratio, rates and probability.
Mathematics Instructional Guide: Quarter One NUMBER SENSE: WHOLE NUMBERS DECIMALS FRACTIONS Standards: * NS 1.1 Estimate, round, and manipulate very large (e.g. millions) and very small numbers (e.g. thousandths) * NS 1.3 Understand and compute positive integer powers of non-negative integers; compute examples as repeated multiplication. (e.g. 2 4 =16) * NS 1.4 Determine the prime factors of all numbers through 50 and write the numbers as the product of their prime factors b y using exponents to show multiples of a factor(e.g. 24=2x2x2x3=2 3 x 3). * NS 1.5 Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers. * NS 2.1 Add, subtract, multiply and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of the results. * NS 2.2 Demonstrate proficiency with division, including division with positive decimals and long division with multi-digit divisors. AF 1.3 Know and use the distributive property in equations and expressions with variables. MR 1.0-3.0 Embedded NS 1.1 Place Value through Lesson Resources 2A-10B Place Value Lessons from About Teaching NS 1.5 millions; Comparing and Lessons 1.1-1.5 Mathematics, pp 173 182 ordering whole numbers Place value: tenths, hundredths, thousandths; Comparing and ordering decimals Lesson Resources 18A-24B Lessons 2.1-2.4 The Place Value Game from 50 Problem-Solving Lessons (by M. Burns), pp 65-67 NS 1.1 NS 2.1 Rounding whole numbers and decimals; Adding and Subtracting greater whole numbers and decimals Lesson Resources 32A-38B Lessons 3.1-3.4 Lesson Resources 46A-54B Lessons 4.1-4.4 Quarter One, 2003-2004
Mathematics Instructional Guide: Quarter One NUMBER SENSE: WHOLE NUMBERS DECIMALS FRACTIONS NS 1.1 Lesson Resources 144A 152B Multiplication Lessons from About AF 1.3 Lessons 9.1-9.5 Teaching Mathematics, pp 194 203 Estimating products; Multiplication of Greater Numbers; Distributive Property Extending Multiplication Concepts from About Teaching Mathematics, pp 212 215 Lessons for Extending Multiplication Grades 4-5 (by M. Burns) NS 2.1 Decimal Factors and Products Lesson Resources 160A-168B Lessons 10.2, 10.4, 10.5 Decimals on Grids from About Teaching Mathematics, M. Burns pp 240-241 NS 1.1 NS 2.2 MR 3.1 Estimate quotients; 3-digit Dividends 2-digit Divisors Lesson Resources 182A-194B Lessons 11.1-11.4; 11.6 Division Lessons from About Teaching Mathematics, M. Burns pp 204 211 Lesson Resources 202A-210B Lessons 12.2-12.5 Relating Multiplication and Division from About Teaching Mathematics, pp 215 222 NS 2.2 Decimal Division Lesson Resources 220A-222B; 238A- 238B Lessons 13.2-13.3; 14.3 Decimals on Grids from About Teaching Mathematics, M. Burns pp 240-241 Mental Calculation with Decimals from About Teaching Mathematics, pp 241-244 Quarter One, 2003-2004
Mathematics Instructional Guide: Quarter One NUMBER SENSE: WHOLE NUMBERS DECIMALS FRACTIONS NS 2.2 Divisibility; Least Lesson Resources 254A- 256B Common Multiple Lesson 15.1-15.2 NS 1.3 NS 1.4 Factors, Exponents, Prime and Composite Numbers Lesson Resources 264A-272B Lessons 15.5-15.8 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, 2003-2004
Mathematics Instructional Guide: Quarter Two FRACTIONS DECIMALS PERCENTS GRAPHING Standards: * NS 1.2 Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number. * NS 1.5 Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers. * NS 2.3 Solve simple problems including ones arising in concrete situations, involving the addition and subtraction of fractions and mixed numbers (like and unlike denominators of 20 or less) and express answers in the simplest form. * NS 2.4 Understand the concept of multiplication and division of fractions. * NS 2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems. * SDAP 1.1 Know the concepts of mean, median, and mode; compute and compare simple examples to show that they may differ. * SDAP 1.2 Organize and display single-variable data in appropriate graphs and representations (e.g., histogram, circle graphs) and explain which types of graphs are appropriate for various data sets. SDAP 1.3 Use fractions and percentages to compare data sets of different sizes. * SDAP 1.4 Identify ordered pairs of data from a graph and interpret the meaning of the data in terms of the situation depicted by the graph. * SDAP 1.5 Know how to write ordered pairs correctly; for example (x,y). MR 1.0-3.0 Embedded SDAP 1.1 Analyze graphs; Lesson Resources 98A-105B; 108AB SDAP 1.2 Mean, Median, Mode Lessons 7.1-7.3 and 7.5 SDAP 1.2 SDAP 1.3 SDAP 1.4 SDAP 1.5 Organizing Data; Writing and Graphing Ordered Pairs Lesson Resources 122A-130B Lessons 8.3-8.6 Graphing in the Classroom from About Teaching Mathematics, pp 75-78 NS 1.5 Decimals and Fractions Lesson Resources 280A-294B Lessons 16.1-16.5 Lessons for Introducing Fractions, Grades 4-5 by Marilyn Burns Decimals on Grids from About Teaching Mathematics, pp 240-241, Gr 3-5 Quarter Two, 2003-2004
Mathematics Instructional Guide: Quarter Two FRACTIONS DECIMALS PERCENTS GRAPHING NS 1.2 Percents Lesson Resources 316A-324B Introducing Percents from About Teaching Lessons 18.1-18.4 Mathematics, pp 245 246 SDAP 1.3 Comparing Data sets Lesson Resources 332AB Lesson 18.7 NS 2.3 Add and Subtract Fractions and Mixed Numbers; LCD Lesson Resources 344A-374B Lessons 19.1-19.6; 20.1-20.5 Lessons for Introducing Fractions, Grades 4-5 by Marilyn Burns NS 2.4 NS 2.5 Multiplying and Dividing Fractions and Mixed Numbers Lesson Resources 380A-400B Lessons 21.1-21.4; 22.1-22.4 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, 2003-2004
Mathematics Instruction Guide: Quarter Three OPERATIONS WITH RATIONAL NUMBERS ALGEBRA CONCEPTS GEOMETRIC CONCEPTS Standards: * NS 2.1 Add, subtract, multiply and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of the results. * AF 1.1 Use information taken from a graph or equation to answer questions about a problem situation. * AF 1.2 Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution. * AF 1.4 Identify and graph ordered pairs in the four quadrants of the coordinate plane. * AF 1.5 Solve problems involving linear functions with integer values; write the equations; and graph the resulting ordered pairs of integers on a grid. * MG 1.1 Students understand and compute the volumes and areas of simple objects. * MG 1.2 Construct a cube and rectangular box from two-dimensional patterns to compute the surface area for these objects. * MG 1.3 Understand the concept of volume and use the appropriate units in common measuring systems ( ie cubic centimeter [cm 3 ] ) to compute the volume of rectangular solids. MG 1.4 Differentiate between, and use appropriate units of measure for, two- and three-dimensional objects (i.e. find the perimeter, area, and volume). * MG 2.1 Measure, identify and draw angles, perpendicular and parallel lines, rectangles, and triangles, by using appropriate tools (e.g. straightedge, ruler, compass, protractor, drawing software). * MG 2.2 Know that the sum of the angles of any triangle is 180 o and the sum of the angles of any quadrilateral is 360 o and use this information to solve problems. MG 2.3 Visualize and draw two-dimensional views of three-dimensional objects made from rectangular solids. MR 1.0-3.0 Embedded AF 1.1 Expressions and Lesson Resources 68A-78B; 86A-92B Patterns, Functions, and Algebra from AF 1.2 Equations Lessons 5.1-5.4; 6.1-6.4 About Teaching Mathematics, by Marilyn Burns, pp 112 124 NS 2.1 Integers Lesson Resources 416A-428B Lessons 23.1-23.5 AF 1.4 AF 1.5 Graphing on a Coordinate Plane Lesson Resources 438A-448B Lessons 24.1-24.4 MG 2.1 MG 2.2 Lines and Angles; Polygons; Circles Lesson Resources 454A-490B Lessons 25.1-26.5 Quarter Three, 2003-2004
Mathematics Instruction Guide: Quarter Three OPERATIONS WITH RATIONAL NUMBERS ALGEBRA CONCEPTS GEOMETRIC CONCEPTS MG 1.1 Measurement Lesson Resources 504A-516B Lessons 27.1-27.6 MG 1.1 MG 1.4 Perimeter, Area. Circumference Lesson Resources 524A-536B Lessons 28.1-28.6 About Teaching Mathematics, M. Burns, Area on the Geoboard: p. 97-99, p. 283-4 The Banquet Table Problem p. 281 MG 1.1 MG 1.2 MG 1.3 MG 2.3 Surface Area and Volume Lesson Resources 546A-558B Lessons 29.1-29.5 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, 2003-2004
Mathematics Instruction Guide: Quarter Four RATIONAL NUMBERS FRACTIONS PROBABILITY Standards: NS 2.0 Students perform calculations and solve problems involving addition, subtraction, and simple multiplication of fractions and decimals: * NS 2.1 Add, subtract, multiply and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of the results. * NS 2.2 Demonstrate proficiency with division, including division with positive decimals and long division with multi-digit divisors. * NS 2.3 Solve simple problems including ones arising in concrete situations, involving the addition and subtraction of fractions and mixed numbers (like and unlike denominators of 20 or less) and express answers in the simplest form. NS 2.4 Understand the concept of multiplication and division of fractions. * NS 2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems * AF 1.5 Solve problems involving linear functions with integer values; write the equations; and graph the resulting ordered pairs of integers on a grid. * MG 2.1 Measure, identify and draw angles, perpendicular and parallel lines, rectangles, and triangles, by using appropriate tools (e.g. straightedge, ruler, compass, protractor, drawing software). * MG 2.2 Know that the sum of the angles of any triangle is 180 o and the sum of the angles of any quadrilateral is 360 o and use this information to solve problems. * SDAP 1.1 Know the concept of mean, median, and mode; compute and compare simple examples to show that they may differ. * SDAP 1.2 Organize and display single-variable data in appropriate graphs and representations (e.g histogram, circle graphs) and explain which types of graphs are appropriate for various data sets. * SDAP 1.3 Use fractions and percentages to compare data sets of different sizes. MR 1.0-3.0 Embedded NS 1.6 Ratio and Rates Lesson Resources: 302A-308B (See Additional Resources from Quarters (6 th Gr) Lessons 17.1-17.4 One to Three) NS 2.1 All Operations with Decimals, Negative and Positive Integers Lesson Resources: 414 H 428B Lessons 23.1-23.5 NS 2.2 Division Lesson Resources: 182A-242B Quarter Four, 2003-2004
Mathematics Instruction Guide: Quarter Four RATIONAL NUMBERS FRACTIONS PROBABILITY NS 2.3 NS 2.4 NS 2.5 All Operations with Fractions and Mixed Numbers Lesson Resources: 342A-400B AF 1.5 Graphing Ordered Pairs Lesson Resources: 438A-444B MG 2.1 MG 2.2 Identify and Draw Angles; Sums of Angles Lesson Resources: 454A-484B SDAP 1.1 Mean, Median, Mode Lesson Resources: 102A-104B SDAP 1.2 SDAP 1.3 Making a Graph; Comparing Data Sets Lesson Resources: 330A-332B Lessons 18.6-18.7 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, 2003-2004