Course Title: Mathematics Grade 4 Board Approval Date: 06/16/14 Credit / Hours: NA Course Description: This course focuses on mastery of the PA Core Standards for Mathematics. As students progress through this course they will participate in a systematic study of naming and construction of geometric figures; using numbers and organizing data; multiplication and division; number sentences and algebra; decimals and their uses; big numbers, estimation, and computation; map reference frames and measures of angles; fractions and their uses; chance and probability; perimeter and area; percents; reflections and symmetry; shapes, weight, volume, and capacity; and rates. Learning Activities / Modes of Assessment: Large group instruction Checklists/Teacher Observations Small group work Tests and Quizzes Collaborative Learning - EDM Games (hands-on classroom and online) Instructional Resources: Everyday Mathematics / Common Core State Standards Edition (McGraw Hill, 2012) EM Online (Instructional Resources through Everyday Math) Discovery Education Brain Pop
Course Pacing Guide Course: Mathematics Grade Grade 4 1 Course Unit (Topic) Length of Instruction (Days/Periods) 1. Number Sense 20 days 1. Naming and Construction Geometric Figures 15 days 2. Addition and Subtraction 20 days 2. Using Numbers and Organizing Data 15 days 3. Data and Graphing 15 days 3. Multiplication and Division; Number Sentences and Algebra 17 days 4. Geometry 15 days 4. Decimals and Their Uses 17 days 5. Measurement 20 days 5. Big Numbers, Estimation, and Computation 17 days 6. Fractions 20 days 6. Division; Map Reference Frames; Measures of Angles 18 days 7. Money 20 days 7. Fractions and Their Uses; Chance and Probability 20 days 8. Patterns 20 days 8. Perimeter and Area 13 days 9. Trig/Angles 15 days 9. Percents 13 days 10. Preview: Double Digit Addition with Regrouping 10 days 10. Reflections and Symmetry 12 days 11.3-D Shapes, Weight, Volume, and Capacity 12 days 12.Rates 10 days DAYS TOTAL 179 days
Topic: 01 Naming and Construction Geometric Figures Days: 15 - identify lines, segments, and rays - identify polygons based on their properties using appropriate geometric terms including congruent - identify parallel and perpendicular figures - basic addition and subtraction facts 1.2: geometry, point, line segment, ray, line, endpoint 1.3: angle, vertex, right angle, triangle, quadrangle, quadrilateral, square, rhombus, rectangle, parallelogram, trapezoid, kite 1.4: parallel lines, intersect, parallel line segments, parallel rays, perpendicular line segments 1.5: side, pentagon, polygon, vertex, convex, concave (nonconvex), hexagon, heptagon, octagon, nonagon, n- gon, interior, regular polygon, equilateral triangle, congruent 1.6: compass, circle, center (of a circle), inscribed square 1.7: radius, congruent, concentric circles Mathematics involves more than numbers. Mathematics has a strong link to language and art. - label lines, segments, rays, and angles - name lines, segments, rays, and angles CC.2.3.4.A.1 - Draw lines and angles and identify these in two-dimensional figures. CC.2.3.4.A.2 - Classify two-dimensional figures by properties of their lines and angles.
Topic: 02 Using Numbers and Organizing Data Days: 15 - answer questions by reading a tally chart or graph - read and write whole numbers up to 1,000,000,000 - identify place values up to 1,000,000,000 and the values of digits in those places - 2.2: name-collection box, equivalent name, mathematical expression 2.3: counting number, whole number, digit, place, expanded notation 2.5: guess, estimate, tally chart, landmark, maximum, minimum, range, mode 2.6: line plot, median 2.7: partial-sums method, columnaddition method, algorithm, ballpark estimate 2.8: bar graph 2.9: trade-first method, partial-differences method, subtrahend, minuend Understanding the patterns in the base-ten place-value system is essential to accurate use of numbers and data organization. Landmarks such as maximum, minimum, range, median, and mode are used in organizing data. - provide explainations describing mathematical thought processes in reaching an answer - analyze problems and determine if there are errors in the mathematical processes provided - calculate statistical landmarks for data: maximum, minimum, median, mode, and range - calculate equivalent names for numbers CC.2.4.4.A.2 - Translate information from one type of data display to another. CC.2.1.4.B.1 - Apply place value concepts to show an understanding of multidigit whole numbers.
Topic: 03 Multiplication and Division; Number Sentences and Algebra Days: 15 - know multiplication and division facts - use a map scale - identify prime and composite numbers 3.1:function machine, input, output, rule, "What's My Rule?" 3.2:multiplication facts, factors, products, factor pair, multiples, square numbers, turn-around facts, prime number, composite number 3.3:percent 3.5:dividend, divisor, quotient, remainder, fact family 3.9:number sentence, true number sentence, false number sentence, variable 3.10:parentheses 3.11:open sentence, solve, solution There is a relationship between the operations of multiplication and division. Number stories can be solved using a 4 step process. - solve addition and subtraction number stories - determine whether a number sentence is true or false - solve open sentences - create true number sentences by inserting parentheses CC.2.2.4.A.2 - Develop and/or apply number theory concepts to find factors and multiples. CC.2.2.4.A.4 - Generate and analyze patterns using one rule.
Topic: 04 Decimals and Their Uses Days: 17 - read, write, and represent decimals through thousandths 4.2:ONE, whole, unit, tenth, hundredth 4.3:decimal 4.4:odometer, trip meter, speedometer 4.6:deposit, withdrawal, balance, interest 4.7:thousandth 4.8:centimeter, millimeter, meter, decimeter 4.9:personal measurement reference 4.10:invertebrate The base-ten number system includes decimals. Metric units of length can be converted from one unit to another by moving the decimal right or left depending on the new unit of measure. - compare and order decimals through thousandths - measure to the nearest centimeter CC.2.1.4.B.1 - Apply place value concepts to show an understanding of multidigit whole numbers. CC.2.4.4.A.1 - Solve problems involving measurement and conversions from a larger unit to a smaller unit.
Topic: 05 Big Numbers, Estimation, and Computation Days: 17 - know basic multiplication facts - read and write whole numbers through millions - identify digits and their values 5.1: extended multiplication facts 5.3: estimation, round 5.4: rough estimate 5.5: partial products method, partial product 5.7: lattice method, lattice 5.8: million, billion 5.9: trillion, quadrillion, quintillion, sextillion, powers of 10, exponent, scientific notation 5.10: rounding Basic multiplication facts can be extended to big numbers. The partial-products algorithm and the lattice method for solving multidigit multiplication Large numbers are read using patterns in the base-ten place-value system. - order whole numbers through millions - solve extended multiplication facts - make estimates for addition and multiplication problems - measure line segments to the nearest 1/4 inch and 0.5 centimeter CC.2.1.4.B.1 - Apply place value concepts to show an understanding of multidigit whole numbers. CC.2.2.4.A.4 - Generate and analyze patterns using one rule.
Topic: 06 Division; Map Reference Frames; Measures of Angles Days: 18 - know basic multiplication and division facts 6.1:multiplication and division diagram 6.2:equal-groups notation, quotient, remainder 6.3:dividend, divisor, partial quotient 6.4:mixed number 6.5:rotation, turn, clockwise, degree, right angle 6.6:angle, sides of an angle, vertex, clockwise rotation, counterclockwise rotation, full-circle protractor 6.7:acute angle, obtuse angle, reflex angle, straight angle, half-circle protractor, base line of a protractor 6.8:index of locations, letter-number pair, ordered number pair, map scale 6.9:sphere, North Pole, South Pole, equator, axis, prime meridian, hemisphere, latitude lines, longitude lines, parallels, meridian bar Application of division algorithms. Drawing, measuring, and naming angles using half-circle and full-circle protractors. Location of places on a map using lines of longitude, lines of latitude, and coordinate grids. - solve multiplication and division number stories - interpret a remainder in the context of a division problem - make reasonable estimates for whole number multiplication and division problems - round numbers to a given place - locate points using ordered number pairs - classify angles according to their measure CC.2.3.4.A.1 - Draw lines and angles and identify these in two-dimensional figures. CC.2.4.4.A.6 - Measure angles and use properties of adjacent angles to solve problems.
Topic: 07 Fractions and Their Uses; Chance and Probability Days: 20 - know how to use basic probability terms 7.1:whole, denominator, numerator, "whole" box, mixed number 7.3:equally likely, outcome, event, probability, favorable outcome 7.7:equivalent fractions, equivalent fractions rule 7.11:fair die or spinner, equal chance, expect, equally more or less likely 7.12a:multiple, equation Fractions are parts of a whole. There are equivalent names for fractions. Fractions can be used to identify parts of sets. Fractions are used to name probability results. Results of predicted and actual chance experiments can be compared. - add and subtract fractions and mixed numbers - use ordered number pairs on a coordinate grid - calculate expected probability CC.2.1.4.C.1 - Extend the understanding of fractions to show equivalence and ordering. CC.2.1.4.C.2 - Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. CC.2.1.4.C.3 - Connect decimal notation to fractions, and compare decimal fractions (base 10 denominator, e.g., 19/100). CC.2.4.4.A.4 - Represent and interpret data involving fractions using information provided in a line plot.
Topic: 08 Perimeter and Area Days: 13 - know the formulas to find the areas of rectangles, parallelograms, and triangles 8.1:time-and-motion study, work triangle, perimeter 8.2:rough floor plan, scale drawing, scale 8.3:area, square units 8.5:length, base of a polygon, width, height, formula 8.6:height, perpendicular 8.7:equilateral triangle, isosceles triangle, scalene triangle, right triangle, height of a triangle Area and perimeter are applied to scale drawings. Perimeters are found by adding the total distance around an object. Formulas are used to find the area of rectangles, parallelograms, and triangles. - predict outcomes of experiments - express the probability of an event as a fraction - measure length to the nearest centimeter - describe and use strategies to measure the perimeters of polygons - describe and use strategies to find the areas of polygons. CC.2.3.4.A.1 - Draw lines and angles and identify these in two-dimensional figures. CC.2.4.4.A.1 - Solve problems involving measurement and conversions from a larger unit to a smaller unit.
Topic: 09 Percents Days: 13 - know equivalent decimal and percent names for "easy" fractions 9.1: percent, 100% box 9.3: terminating decimal, repeating decimal 9.4: regular price (list price), discount, percent or fraction of discount, sale price (discounted price) 9.7: urban, rural, life expectancy, rank There is a link among fraction, decimal, and percent names for numbers. Converting between fractions, decimals, and percents. Application of whole number algorithms for multiplication and division to decimals. - find a fraction or percent of a number - rename fractions as decimals and percents - use an estimation strategy to divide decimals by whole numbers - use an estimation strategy to multiply decimals by whole numbers - find the area and perimeter of polygons - insert grouping symbols to make number sentences true CC.2.1.4.B.1 - Apply place value concepts to show an understanding of multidigit whole numbers. CC.2.1.4.C.3 - Connect decimal notation to fractions, and compare decimal fractions (base 10 denominator, e.g., 19/100). CC.2.2.4.A.4 - Generate and analyze patterns using one rule.
Topic: 10 Reflections and Symmetry Days: 12 - name equivalent fractions, decimals, and percents 10.1: transparent mirror, recessed, image, preimage, congruent 10.2: reflection (flip), line of reflection (mirror line) 10.4: line of symmetry, symmetric, rotation (turn) 10.5; frieze pattern, translation (slide), rotation (turn) 10.6: opposite (of a number), credit, debit The basic properties of reflections and their connection with line symmetry. Geometric transformations: reflections, translations, and rotations. Addition involving negative integers. - add signed numbers - add and subtract fractions - make reasonable estimates for multiplication and division problems - measure an angle - locate multiple lines of symmetry in a twodimensional shape - identify and sketch examples of reflections - identify examples of translations and rotations CC.2.3.4.A.1 - Draw lines and angles and identify these in two-dimensional figures. CC.2.3.4.A.2 - Classify two-dimensional figures by properties of their lines and angles. CC.2.3.4.A.3 - Recognize symmetric shapes and draw lines of symmetry.
Topic: 11 3-D Shapes, Weight, Volume and Capacity Days: 12 - describe events using basic probability terms - name formulas to find the volume of a rectangular prism 11.1: gram, ounce 11.2: prism, pyramid, rectangular prism, triangular prism, square pyramid, cylinder, cone, sphere, geometric solid, curved surface, cube, edge, face, flat surface, vertex, congruent, 3- dimensional 11.3: polyhedron, regular polyhedron, triangular pyramid, dodecahedron 11.4: cubic units, volume, dimensions, surface area 11.5: formula 11.6: integer 11.7: capacity, cup, pint, quart, gallon, liter, milliliter There is a relationship between weight and capacity. Identify 3-D shapes when given their properties. How to apply the properties of geometric solids (3-D shapes) to concepts and units of volume. Subtraction of positive and negative integers. - add and subtract signed numbers - multiply and divide whole numbers and decimals - round decimals to the nearest tenth - make reasonable estimates for whole number and decimal multiplication problems; explain how the estimates were obtained - estimate weight with and without tools - describe and use strategies to find the volume of a rectangular prism - describe the relationships among units of weight, length, and capacity - identify, describe, compare, and classify plane and solid figures CC.2.3.4.A.2 - Classify two-dimensional figures by properties of their lines and angles. CC.2.4.4.A.1 - Solve problems involving measurement and conversions from a larger unit to a smaller unit.
Topic: 12 Rates Days: 10 - use a rate table - formulas for finding volumes of rectangular prisms 12.1: rate, per 12.2: rate table, unit rate 12.4: consumer, products, services, comparison shopping, unit price Rates are used frequently in our everyday world. Consumers collect and compare rate data to be informed of where they will receive the "best buy." - find whole-number factors of numbers - compare and order fractions - compare and order integers - add and subtract signed numbers - add and subtract decimals - solve problems involving division - use scaling to model rate situations - analyze and interpret data - find the volumes of rectangular prisms - convert among units of capacity - solve open sentences CC.2.1.4.B.1 - Apply place value concepts to show an understanding of multidigit whole numbers. CC.2.2.4.A.4 - Generate and analyze patterns using one rule. CC.2.4.4.A.1 - Solve problems involving measurement and conversions from a larger unit to a smaller unit.