4R & 4A Math Pacing Guides

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1 GRADING PERIOD: 1st Nine Weeks Getting to Know You - Community Building Data a. Collect data, using observations, surveys, measurement, polls, or questionnaires. b. Organize data into a chart or table. 4.5 Multiples a. Determine common multiples and factors (begin) 4.15 Patterns (begin) a. Describe, create and extend numerical patterns using concrete materials, number lines, tables, and words. 4.1 Place Value: Review Prior Knowledge a. Identify and communicate the place value for each digit in whole numbers, through one millions place. b. Read whole numbers through one millions place in standard format, and select the matching number in written format. c. Write whole numbers through the one millions place in standard format when the numbers are presented orally or in written format. d. Identify and use the symbols for greater than, less than, and equal to. e. Compare two whole numbers expressed through the one millions, using symbols >, <, or =. f. Round whole numbers (to one millions place) to the thousand, ten thousand, and hundred-thousand place. Getting to Know You - Community Building 5.15 Data and graphs: Review prior knowledge a. Formulate the question that will guide the data collection. b. Collect data, using observations (e.g., weather), measurement (e.g., shoe sizes), surveys (e.g., hours watching television), or experiments (e.g., plant growth). c. Organize the data into a chart, table, stem-and-leaf plots, and line graphs. 5.3 Prime, Composite, Even and Odd Numbers (ongoing) a. Identify prime numbers less than or equal to 100. b. Identify composite numbers less than or equal to 100. c. Explain orally and in writing why a number is prime or composite. d. Identify which numbers are even or odd. e. Explain and demonstrate with manipulatives, pictorial representations, oral language, or written language why a number is even or odd Number Patterns (begin) Rev plw 1

2 GRADING PERIOD: 1st Nine Weeks (continued) 4.4 Add and Subtract: Review Prior Knowledge a. Estimate whole number sums, differences b. Refine estimates using terms such as closer to, between, and a little more than. c. Determine the sum or difference of two whole numbers, each 999,999 or less, in vertical and horizontal form with or without regrouping, paper and pencil, and calculator. d. Verify the reasonableness of sums and differences using estimation. 5.4 Whole Number Addition and Subtraction Review prior knowledge a. Select appropriate methods and tools (paper and pencil, estimation, mental computation, and calculators) in order to compute with whole numbers. b. Create and solve single-step problems involving addition, subtraction, using practical situations. c. Estimate the sum, and difference of whole number computations. d. Solve multistep problems using two or more operational steps involving addition, subtraction, (sums and differences will not exceed five digits.) 4.3 Decimals a. Represent fractions for halves, fourths, fifths, and tenths as decimals through hundredths, using concrete objects. b. Identify the place value of each digit in the decimal c. Round decimals to the nearest whole number, tenth and hundredth d. Compare and order decimals 5.1 Rounding Decimals Review prior knowledge a. Round decimal numbers to the nearest whole number b. Round decimal numbers to the nearest tenth c. Round decimal numbers to the nearest hundredth. Rev plw 2

3 GRADING PERIOD: 1st Nine Weeks (continued) 4.5 Add and Subtract Decimals a. Add and subtract decimals ( thousandths) b. Solve single-step and multistep problems with adding and subtracting decimals through thousandths Equality and Associative Property for Addition a. Recognize and demonstrate that the equals sign (=) relates equivalent quantities in an equation. b. Write an equation to represent equivalent mathematical relationships (e.g., = 12-5). c. Recognize and demonstrate appropriate use of the equals sign in an equation. d. Investigate and describe the associative property for addition as (6 + 2) + 3= 6 + (2 + 3). 4.4 Multiplication: Review Prior Knowledge a. Estimate whole number products b. Refine estimates by adjusting the final amount, using the terms closer to, between, and a little more than. c. Estimate and find the products of two whole numbers one factor has two digits or fewer and the other factor has three digits or fewer 5.5 Addition and subtraction with Decimals a. Determine an appropriate method of calculating the sum and difference of two decimals through thousandths. b. Estimate to find the number closest to the sum or difference of two numbers expressed as decimals through thousandths. c. Find the sum and difference of two decimals through thousandths. e. Use estimation to check the reasonableness of a sum and difference of decimals. f. Create and solve single-step problems. g. Create and solve multistep problems which incorporate two or more operational steps 5.18 Algebra a. Describe the concept of a variable (boxes, letters, or symbols) as an unknown quantity. b. Write an open sentence with addition, subtraction, multiplication, or division, using a variable to represent a missing number. c. Model one-step linear equations using a variety of concrete materials (colored chips on an equation mat or weights on a balance scale.) d. Create and write word problems to match a given open sentence with a single variable and one operation. 9-week assessment Remediation and Enrichment Rev plw 3

4 GRADING PERIOD: 2 nd Nine Weeks 4.16 Properties for Multiplication b. Write an equation to represent equivalent mathematical relationships (e.g. 4 3 = 2 6). e. Investigate and describe the associative property for multiplication as (3 x 2) x 4 = 3 x (2 x 4) Distribution Property (review Equality and Associative Property) a. Investigate and recognize the distributive property of whole numbers, limited to multiplication over addition using diagrams and manipulatives. b. Investigate and recognize an equation that represents the distributive property, when given several whole number equations, limited to multiplication over addition. 5.7 Order of Operations a. Simplify expressions by using the order of operations in a demonstrated step-by-step approach. b. Find the value of numerical expressions, using the order of operations. c. Given an expression involving more than one operation, describe which operation is completed first, which is second, etc. 5.4 Single and Multistep Problems b. Create and solve single-step and multistep problems involving the operations of addition, subtraction, and multiplication of whole numbers, using practical situations. c. Estimate the sum, difference, and product of whole number computations. Rev plw 4

5 GRADING PERIOD: 2 nd Nine Weeks 4.6 Mass: Review Prior Knowledge a. Determine an appropriate unit of measure for finding mass in metric and U.S. Customary units. b. Measure the mass of objects in both metric and U.S. Customary units c. Record the mass of an object including the appropriate unit of measure (e.g., 24 grams). d. Identify equivalent measures between units in the US Customary system. e. Identify equivalent measures in the metric system. 5.8 Metric Measurement of Mass Review Prior Knowledge l. Identify equivalent measurements within the metric system for mass: grams and kilograms; o. Solve problems involving measurement by selecting an appropriate measuring device and a U.S. Customary or metric unit of measure for weight: ounces, pounds, and tons; mass: grams and kilograms Rev plw 5

6 GRADING PERIOD: 2 nd Nine Weeks (continued) 4.9 Elapsed Time: Review Prior Knowledge a. Determine the elapsed time in hours and minutes within a 12-hour period (times can cross between a.m. and p.m.) given a starting and stopping time. b. Solve practical problems in relation to time that has elapsed. 4.4 Division: with and without Remainders Review Prior Knowledge a. Estimate whole number quotients. b. Refine estimates using terms such as closer to, between, and a little more than. e. Estimate and find the quotient of two whole numbers, given a onedigit divisor and a two- or three-digit dividend. f. Solve single-step and multistep problems using whole number operations. g. Verify the reasonableness of quotients of whole numbers using estimation Number Patterns Describe, create and extend numerical patterns in tables, number lines, concrete materials and words Elapsed Time a. Determine elapsed time in hours and minutes within a 24-hour period when a beginning and an end time are given. b. Determine the end time when a beginning time and an elapsed time are given. c. Determine a beginning time when an elapsed time and an end time are given. 5.5 Multiply and Divide with Decimals Review prior knowledge a. Determine an appropriate method of calculating the product and quotient of two decimals through thousandths. b. Estimate to find the number that is closest to the product of two numbers expressed as decimals through thousandths. c. Find the product of two numbers expressed as decimals through thousandths d. Determine the quotient, given a dividend expressed as a decimal through thousandths and a single-digit divisor. e. Use estimation to check the reasonableness of a quotient. f. Create and solve single-step problems involving division. g. Create and solve multistep problems which incorporate two or more operational steps Multiplication and Division Patterns a. Describe numerical patterns formed by using concrete materials and calculators. b. Describe the relationship found in patterns, using words, tables, and symbols to express the relationship Rev plw 6

7 GRADING PERIOD: 2 nd Nine Weeks (continued) 4.8 Volume U.S.Customary: Review Prior Knowledge a. Determine an appropriate unit of measure (cups, pints, quarts, gallons) to use when measuring liquid volume in U.S. Customary units. b. Estimate the liquid volume of containers in U.S. Customary units of measure to the nearest cup, pint, quart, and gallon. c. 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). d. Identify equivalent measures of volume between units within the U.S. Customary system. 5.8 Measurement Liquid Volume: m. Identify equivalent measurements within the metric system for liquid volume: milliliters, and liters. p. Solve problems involving measurement by selecting an appropriate measuring device and a U.S. Customary or metric unit of measure for liquid volume: cups, pints, quarts, gallons, milliliters, and liters; 4.14 Continue graphing Extra days for flexible time 9-week assessment Remediation and Enrichment Rev plw 7

8 GRADING PERIOD: 3 rd Nine Weeks 4.2 Fractions: Review Prior Knowledge a. Compare and order fractions having denominators of 12 or less, using manipulative models b. Compare and order fractions with like denominators by comparing number of parts (numerators) (e.g., 1 5 < 3 5 ). c. Compare and order fractions with like numerators and unlike denominators by comparing the size of the parts (e.g., 3 9 < 3 5 ). d. Compare and order fractions having unlike denominators of 12 or less by comparing the fractions to benchmarks (e.g., 0, 1 or 1) to 2 determine their relationships to the benchmarks or by finding a common denominator. e. Compare and order mixed numbers having denominators of 12 or less. f. Use the symbols >, <, and = to compare the numerical value of fractions and mixed numbers g. Represent equivalent fractions through twelfths, using region/area models, set models, and measurement models. h. Identify the division statement that represents a fraction ( 3 5 means the same as 3 divided by 5). Rev plw 8

9 GRADING PERIOD: 3 rd Nine Weeks (continued) 4.3 Fraction and Decimal Equivalents e. Relate fractions to decimals, using concrete objects (e.g., 10-by-10 grids, meter sticks, number lines, decimal squares, decimal circles, money [coins]). f. Write the decimal and fraction equivalent for a given model 5.2 Fractions and their Equivalent Decimal Forms a. Represent fractions (halves, fourths, fifths, eighths, tenths, and twelfths) in their equivalent decimal form and vice versa. b. Recognize and name equivalent relationships between decimals and fractions with denominators up to 12. c. Compare and order from least to greatest and greatest to least a given set of no more than five numbers written as decimals, fractions, and mixed numbers with denominators of 12 or less. 4.5 Add and Subtract Fractions: Review Prior Knowledge b. Use least common multiple and/or greatest common factor to find a common denominator for fractions. c. 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 d. 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 e. 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. f. Solve single-step and multistep problems that involve adding and subtracting with fractions and decimals through thousandths. 5.6 Single-Step and Multistep Problems with Fractions a. Solve single-step and multistep practical problems involving addition and subtraction with fractions having like denominators. Denominators in the problems should be limited to 12 or less and answers should be expressed in simplest form. b. Solve single-step and multistep practical problems involving addition and subtraction with fractions having unlike denominators. Denominators in the problems should be limited to 12 or less and answers should be expressed in simplest form. c. Solve single-step and multistep practical problems involving addition and subtraction with mixed numbers having like and unlike denominators, with and without regrouping. Denominators in the problems should be limited to 12 or less, and answers should be expressed in simplest form. d. Use estimation to check the reasonableness of a sum or difference. Rev plw 9

10 GRADING PERIOD: 3 rd Nine Weeks (continued) 4.7 Length: Review Prior Knowledge a. Determine an appropriate unit of measure (e.g., inch, foot, yard, mile, millimeter, centimeter, and meter) to use when measuring length of everyday objects in both metric and U.S. Customary units. b. Estimate the length of everyday objects (e.g., books, windows, tables) in both metric and U.S. Customary units of measure. c. Measure the length of objects in both metric and U.S. Customary units, measuring to the nearest inch ( 1 2, 1 4, 1 8 ), foot, yard, mile, millimeter, centimeter, or meter, and record the length including the appropriate unit of measure (e.g., 24 inches). d. Compare estimates of the length of objects with the actual measurement of the length of objects. e. Identify equivalent measures of length between units within the U.S. Customary measurements and between units within the metric measurements. Rev plw Measurement: Length k. Identify equivalent measurements within the metric system for length: millimeters, centimeters, meters, and kilometers; n. Solve problems involving measurement by selecting an appropriate measuring device and a U.S. Customary or metric units for length: part of an inch ( 1 2, 1 4, 1 8 ), inches, feet, yards, millimeters, centimeters, meters, and kilometers. Perimeter: Review prior knowledge a. Determine the perimeter of a polygon, with or without diagrams, when the lengths of all sides of a polygon that is not a rectangle or a square are given; the length and width of a rectangle are given; or the length of a side of a square is given. Area: Review prior knowledge q. Solve problems by selecting an appropriate measuring device and a U.S. Customary or metric unit of measure for area: square units; c. Estimate and determine the area of a square, with or without diagrams, when the length of a side is given. d. Estimate and determine the area of a rectangle, with or without diagrams, when the length and width are given. e. Estimate and determine the area of a right triangle, with or without diagrams, when the base and the height are given. Perimeter and Area b. Estimate and determine the perimeter of a polygon, and area of a square, rectangle, and right triangle following the parameters listed above, using only whole number measurements given in metric or U.S. Customary units, and record the solution with the appropriate unit of measure (e.g., 24 square inches).

11 GRADING PERIOD: 3 rd Nine Weeks (continued) 4.13 Probability: Review Prior Knowledge a. 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. b. Write the probability of a given simple event as a fraction, where the total number of possible outcomes is 24 or fewer. c. Identify the likelihood of an event occurring and relate it to its fractional representation (e.g., impossible/0; equally likely/ 1 2 ; certain/1). d. 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. e. Represent probability as a point between 0 and 1, inclusively, on a number line. 5.8 Measurement : Volume g. Develop a procedure for finding volume using manipulatives (e.g., cubes). h. Determine volume in standard units. Perimeter/Area/Volume f. Differentiate among the concepts of area, perimeter, and volume. i. Describe practical situations where area, perimeter, and volume are appropriate measures to use, and justify their choices orally or in writing. j. Identify whether the application of the concept of perimeter, area, or volume is appropriate for a given situation. Temperature Review: (Not tested on the 4th grade SOL Test) r. Solve problems involving temperature: Celsius and Fahrenheit units. s-u. Understand that water freezes at 0 C and 32 F, water boils at 100 C and 212 F, and that normal body temperature is about 37 C and 98.6 F Probability: Review prior knowledge a. Construct a sample space, using a tree diagram to identify all possible outcomes of a single event. b. Construct a sample space, using a list or chart to represent all possible outcomes of a single event. c. Predict and determine the probability of an outcome by constructing a sample space. The sample space will have a total of 24 or less possible outcomes. Rev plw 11

12 GRADING PERIOD: 3 rd Nine Weeks (continued) 4.14 Graphing Line Graphs: (continued) d. 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. Line graphs will have no more than 10 identified points along a continuum for continuous data. e. Title or identify the title in a given graph and label or identify the axes. f. Interpret data from simple line graphs by describing the characteristics of the data and the data as a whole. Data points will be limited to 30 and categories to 8. g. Interpret the data to answer the question posed, and compare the answer to the prediction h. 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. 9-week assessments Remediation and Enrichment 5.16 Measures of Center a. Describe and find the mean of a group of numbers representing data from a given context as a measure of center. b. Describe and find the median of a group of numbers representing data from a given context as a measure of center. c. Describe and find the mode of a group of numbers representing data from a given context as a measure of center. d. Describe mean as fair share. e. Describe and find the range of a group of numbers representing data from a given context as a measure of variation. f. Describe the impact on measures of center when a single value of a data set is added, removed, or changed Line Graphs and Stem and Leaf Plots d. Display data in line graphs and stem-and-leaf plots. e. Construct line graphs, labeling the vertical axis with equal whole number, decimal, or fractional increments 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 six identified points along a continuum for continuous data (e.g., the decades: 1950s, 1960s, 1970s, 1980s, 1990s, and 2000s). f. Construct a stem-and-leaf plot to organize and display data, where the stem is listed in ascending order and the leaves are in ascending order, with or without commas between leaves. g. Title the given graph or identify the title. h. Interpret the data in a variety of forms 5.4 Practical Problems for all Four Operation Rev plw 12

13 GRADING PERIOD: 4 th Nine Weeks 4.10 Lines, Rays and Angles: Review Prior Knowledge a. Identify and describe representations of points, lines, line segments, rays, and angles, including endpoints and vertices. b. Understand that lines in a plane can intersect or are parallel. Perpendicularity is a special case of intersection. c. Identify practical situations that illustrate parallel, intersecting, and perpendicular lines Polygons: Review Prior Knowledge a. Define and identify properties of polygons with 10 or fewer sides. b. Identify polygons by name with 10 or fewer sides in multiple orientations (rotations, reflections, and translations of the polygons) Geometry Patterns a. Describe geometric patterns, using tables, symbols, or words. b. Create geometric patterns, using concrete materials, number lines, tables, and words. c. Extend geometric patterns, using concrete materials, number lines, tables, and words Classifying Angles and Triangles a. Classify angles as right, acute, straight, or obtuse. b. Classify triangles as right, acute, or obtuse. c. Classify triangles as equilateral, scalene, or isosceles Measure Angles and triangles: a. Identify the appropriate tools used to measure and draw angles and triangles. b. Measure right, acute, straight, and obtuse angles, using appropriate tools, and identify their measures in degrees. c. Recognize angle measure as additive. The angle measure of the whole is the sum of the angle measures of the parts. d. Solve addition and subtraction problems to find unknown angles measures on a diagram in practical and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure Definitions of Plane Geometric Figures a. Develop a definition for squares b. Develop a definition for rectangles c. Develop a definition for triangles d. Develop a definition for parallelograms e. Develop a definition for rhombi f. Develop a definition for trapezoids g. Investigate and describe the results of combining and subdividing plane figures. Rev plw 13

14 GRADING PERIOD: 4 th Nine Weeks (continued) 4.11 Congruence: Review Prior Knowledge a. Recognize the congruence of plane figures resulting from translations using mirrors, paper folding and tracing. b. Recognize the congruence of plane figures resulting from reflections using mirrors, paper folding and tracing. c. Recognize the congruence of plane figures resulting from rotations, using mirrors, paper folding and tracing Continue Graphing 5.9 Circles a. Identify and describe the diameter, radius, chord, and circumference of a circle. b. Describe the relationship between diameter and radius c. Describe the relationship between diameter and chord d. Describe the relationship between radius and circumference e. Describe the relationship between diameter and circumference. f. Understand that the length of the diameter of a circle is twice the length of the radius Geometric Patterns a. Describe numerical and geometric patterns formed by using concrete materials and calculators. b. Describe the relationship found in patterns, using words, tables, and symbols to express the relationship Graphing (continued) (Review bar, picture and picto- graphs, line plots, and line graphs) Review for SOL Test Rev plw 14