Numeration Unit of Study Big Ideas Algebraic Concepts How do I match a story or equation to different symbols? How do I determine a missing symbol in an equation? How does understanding place value help me understand numerals? How do I compare quantities? Numeration Unit of Study September (9 days) E Create or match a story to a given combination of symbols and numbers. Symbols to use: <,>,=, +, -, x, E Identify the missing symbol (=, <, >) that makes a number sentence true. E Match the word name with the appropriate whole number up through 999,999. F Write whole numbers in expanded, standard, and word form through six digits. E Identify place value through 6 digits. E Differentiate between and give examples of even and odd numbers. E Order a set of whole numbers from least to greatest or greatest to least up to 9,999. E Match a symbolic representation of numbers to appropriate whole numbers. For example: base ten blocks: 7 hundreds, 4 tens, and 8 ones E Compare two whole numbers using greater than (>), less than (<), or equal to (=) up through 9,999. - PA EC: M3.D.2.1.1 PA CC EC: M03.B-O.3.1.6 PA EC: M3.D.2.2.2 PA CC EC: M03.B-O.3.1.7 PA EC: M3.A.1.1.1 PA EC: M4.A.1.1.4 PA EC: M3.A.1.1.2 PA CC: 2.1.3.B.1 PA EC: M3.A.1.1.4 PA CC EC: M03.A-T.1.1.4 PA EC: M3.A.1.1.5 PA EC: M3.A.1.1.3
Addition and Subtraction Unit of Study Algebraic Concepts How can I use operations and patterns to solve addition and subtraction problems? What are properties of addition and subtraction? How do I solve addition and subtraction problems? Addition and Subtraction Unit of Study September and October (15 days) E Create or match a story to a given combination of symbols and numbers. Symbols to use: +, - E Choose the number sentence that matches a given story. One operation + and only E Solve two-step equations using order of operations (equation is explicitly stated with no grouping symbols). E Find a missing number that makes a number sentence true. 1-digit and 2-digit numbers using +, - E Identify the missing symbol +, - that makes a number sentence true. F Use concepts of addition to model the commutative, associative, and identify properties of addition. E Solve single-, double-, and triple-digit addition and subtraction problems within 1000, with and without regrouping in vertical and horizontal form and check with the inverse operation. E Estimate sums and differences of quantities E Round two- and three-digit whole numbers to the nearest ten or hundred, respectively. - PA EC: M3.D.2.1.1 PA CC EC: M03.B-O.3.1.6 PA EC : M3.D.2.1.2 PA CC EC : M03.B-O.3.1.4 PA EC : M3.D.2.2.1 PA EC : M3.D.2.2.2 PA CC EC : M03.B-O.3.1.7 PA EC : M3.A.2.1 PA CC: 2.1.3.B.1 PA EC: M3.A.3.1.3 PA EC: M3.A.3.1.1 PA CC EC: M03.A-T.1.1.2 PA EC: M3.A.3.2.1 PA CC: 2.1.3.B.1 PA CC EC: M03.A-T.1.1.1 PA EC: M3.A.3.2.1
How can I solve realworld problems using addition and subtraction? Addition and Subtraction Unit of Study September and October (15 days) E Identify the correct operation(s) to solve one and two step word problem using all four operations and a variety of problem-solving strategies (expressions are not explicitly stated). Limit to problems with whole numbers and having whole number answers Represent these problems using equations with a letter/symbol standing for the unknown quantity. Assess the reasonableness of answers. Limit problems posed with whole numbers and having whole-number answers. - PA EC : M3.A.2.1.3 PA CC EC: MO3.B-O.3.1.1 PA CC EC: MO3.B-O.3.1.2 PA CC EC: MO3.B-O.3.1.3
Money Unit of Study How do I count, compare and make change using a collection of coins and one-dollar bills? Money Unit of Study October (8 days) E Count a collection of bills and coins less than $5.00(penny, nickel, dime, quarter, and dollar). Money may be represented as 15 cents, 15, or $0.15. E -Compare total values of combinations of coins (penny, nickel, dime, quarter and dollar) less than $5.00. E Make change for an amount up to $5.00 with no more than $2.00 change given (penny, nickel, dime, quarter, and dollar). E Add and subtract money given dollars and cents. E Round amounts of money to the nearest dollar. F Recognize place value to the right of the decimal (tenths and hundredths). PA EC: M3.A.1.3.1 PA EC: M3.A.1.3.2 PA CC EC: M03.D-M.1.3.1 PA CC: 2.4.3.A.3 PA EC: M3.A.1.3.3 PA CC EC: M03.D-M.1.3.2 PA CC: 2.4.3.A.3 PA EC: M4.A.2.1.2 PA CC EC: M03.D-M.1.3.3 PA: 2.4.3.A.3 PA CC: 2.1.3.B.1
Multiplication Unit of Study Big Ideas Algebraic Concepts How can I use operations and patterns to solve multiplication problems? What are properties of multiplication? What is multiplication? Multiplication Unit of Study October and November (15 days) E Create or match a story to a given combination of symbols and numbers. Symbols to use: +, -, x,, <,>,= E Solve two-step equations using order of operations (equation is explicitly stated with no grouping symbols). E Find a missing number that makes a number sentence true. Determine the unknown whole number in a multiplication equation relating three whole numbers. E Identify the missing symbol (x, =, <, >) that makes a number sentence true. E Represent multiplication as repeated addition. E Solve multiplication problems using: Arrays (Interpret 35 as the total number of objects in 5 groups, each containing 7 objects and describe a context in which a total number of objects can be expressed as 5x7) Communicative property of multiplication Associative property of multiplication F Distributive property Students need not use formal terms for these properties. E Identify the one and zero property of multiplication. E Multiply one digit whole numbers by two-digit multiples of 10 (from 10-90) using strategies based on place value and properties of operations. (AFTER PSSA) PA EC: M3.D.2.1.1 PA CC EC: M03.B-O.3.1.6 PA CC EC : M03.B-O.3.1.4 PA CC: 2.2.3.A.1 PA EC: M3.D.2.2.1 PA CC EC : M03.B-O.1.2.2 PA CC EC : M03.B-O.3.1.7 PA CC : M3.A.2.1.1 PA CC: 2.2.3.A.1 PA CC: 2.2.3.A.2 PA CC EC : M03.B-O.1.1.1 PA CC EC: M03.B-O.2.1.1 PA CC EC: M03.B-O.2.1.2 PA CC: 2.2.3.A.2 PA CC: 2.1.3.B.1 PA CC EC : M03.A-T.1.1.3
Big Ideas What is multiplication? How can I solve real-world problems using multiplication? Multiplication Unit of Study October and November (15 days) E Know fluently all multiplication products through 144. E Identify the correct operation(s) to solve one and two step word problems using all four operations and a variety of problem-solving strategies. Use arrays to solve multiplication problems Limit to problems with whole numbers and having whole number answers Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental math computation and estimation strategies including rounding. PA CC: 2.2.3.A.3 PA EC: M3.A.3.1.2 PA CC: 2.2.3A.1 PA CC EC: M03.B-O.1.2.1 PA CC EC: M03.B-O.3.1.1 PA CC EC: M03.B-O.3.1.2 PA CC EC: M03.B-O.3.1.3 PA EC: M3.A.2.1.3
Division Unit of Study Algebraic Concepts How can I use operations and patterns to solve division problems? How can I solve realworld problems using division? Division Unit of Study November (11 days) E Create or match a story to a given combination of symbols and numbers. Symbols to use: +, -, x,, <,>,= E Solve two-step equations using order of operations (equation is explicitly stated with no grouping symbols). E Find a missing number that makes a number sentence true. 1-digit and 2-digit numbers using +, -, x, and E Identify the missing symbol that makes a number sentence true. Division limit dividends through 50 and limit divisors and quotients through 10. E Identify the correct operation(s) to solve one and two step word problem using all four operations and a variety of problem-solving strategies. Represent these problems using equations with a letter standing for the unknown quantity. Use division to solve word problems in situations involving equal groups (limit dividends through 50, and limit divisors and quotients through 10) Assess the reasonableness of an answer - PA CC EC: M03.B-O.3.1.6 PA CC EC : M03.B-O.3.1.4 PA CC: 2.2.3.A.1 PA CC EC : M03.B-O.1.2.2 PA CC EC : M03.B-O.3.1.7 PA CC: 2.2.3.A.1 PA CC EC: M03.B-O.1.2.1 PA CC EC: MO3.B-O.3.1.1 PA CC EC: MO3.B-O.3.1.2 PA CC EC: MO3.B-O.3.1.3 What is division? E Solve division problems involving sharing and repeated subtraction. Divide fluently within 100. PA CC: 2.2.3.A.3
What is division? Division Unit of Study November (11 days) F Identify that when dividing, there may be some left over called a remainder. E Identify how multiplication fact families relate to division. Ex: Find 32 8 by solving 8 x? = 32. E Interpret and/or describe whole-number quotients of whole numbers (limit dividends through 50, and limit divisors and quotients through 10). Ex 1: Interpret 48 8 as the number of objects in each share when 48 objects are partitioned equally into 8 share, or as a number of shares when 48 objects are partitioned into equal shared of 8 objects each Ex 2: Describe a context in which a number of shares or a number of groups can be expressed as 48 8. - PA CC: 2.2.3.A.3 PA CC: 2.2.3.A.2 PA CC EC: M03.B-O.2.2.1 PA CC: 2.2.3.A.1 PA CC EC: M03.B-O.1.1.2
Fractions Unit of Study How do you use fractions to represent quantities as part of a whole or part of a set? What are equivalent fractions? Fractions Unit of Study December (12 days) E Write the fraction that corresponds to a drawing or part of a set. Numerator 1-9, denominators 2-10. No equivalent or improper fractions or mixed numbers. E Create a drawing or set that represents a given fraction. Numerator 1-9, denominators 2-10. E - Demonstrate that when a whole or set is partitioned into y equal parts, the fraction 1/y represents 1 part of the whole and/or the fraction x/y represents x equal parts of the whole (limit the denominators to 2, 3, 4, 6, and 8; limit numerators to whole numbers less than the denominator; no simplification necessary). E Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. Example: partition a shape into 4 parts with equal areas. Example: Describe the area of each of 8 equal parts as 1/8 of the area of the shape. E Identify the numerator and the denominator. E Identify benchmark fractions. E Represent fractions on a number line (limit the denominators to 2, 3, 4, 6, and 8; limit numerators to whole numbers less than the denominator; no simplification necessary). E - Understand two fractions as equivalent if they are the same size, or the same point on the number line. E - Recognize and generate simple equivalent fractions (limit the denominators to 1, 2, 3, 4, 6, and 8; limit the numerators to whole numbers less than the denominator) and explain why they are equivalent by using a visual fraction model. Example: ½ = 2/4 and 4/6 = 2/3 PA EC: M3.A.1.2.1 PA EC : M3.A.1.2.2 PA CC: 2.1.3.C.1 PA CC EC : M03.A-F.1.1.1 PA CC: 2.3.3.A.2 PA CC EC: M03.C-G.1.1.3 PA CC: 2.1.3.C.1 PA CC: 2.1.3.C.1 PA CC EC: M03.A-F.1.1.2 PA CC: 2.1.3.C.1 PA: 2.1.3.C.1 PA CC EC: M03.A-F.1.1.3
What are equivalent fractions? How do we compare fractions? Fractions Unit of Study December (12 days) E - Express whole numbers as fractions, and/or generate fractions that are equivalent to whole numbers. Limit the denominators to 1, 2, 3, 4, 6, and 8 Example 1: Express 3 in the form 3=3/1 and recognize that 6/1=6 E - Compare two fractions with the same denominators (limit denominators to 1, 2, 3, 4, 6, and 8) by reasoning about their size. Record the results of the comparison with the symbols <, >, or =. F Compare, recognize and order fractions and mixed numbers. F Add and subtract fractions with like denominators. F Write a fraction and an equivalent decimal for a model showing tenths and hundredths. F Multiply a whole number by a unit fraction. Example: 5 x ¼ = 5/4. PA CC: 2.1.3.C.1 PA CC EC : M03.A-F.1.1.4 PA CC: 2.1.3.C.1 PA CC EC : M03.A-F.1.1.5 PA EC : M4.A.1.2.1 PA EC : M4.A.3.2.2 PA EC : M4.A.1.1.1
Number Patterns Unit of Study Big Ideas Algebraic Concepts How do I recognize, describe, and extend a variety of patterns? Number Patterns Unit of Study January (9 days) E Extend or find a missing element in a pattern of numbers and shapes. Pattern must show 3 repetitions. When multiples are used, limit to 2, 3, and 5. E Identify and describe the rule for a pattern shown. Pattern must show 3 repetitions. When multiples are used, limit to 2, 3, and 5. E Extend tables of ordered pairs for situations involving addition, subtraction, or multiplication. E Identify arithmetic patterns (including patterns in the addition table and multiplication table), and explain them using properties of operations. (For example, 4 times a number is always even.) - PA EC: M3.D.1.1.1 PA EC : M3.D.1.1.2 PA EC : M3.D.1.1.1 PA CC EC: M03.B-O.3.1.5
Time Unit of Study Measurement How do I determine time and calculate elapsed time? Time Unit of Study January (8 days) E Tell, show and write time to the nearest half hour, quarter hour, and minute using a digital and analog clock. E Calculate elapsed time, involving addition and subtraction, of time intervals in minutes. Represent the problem on a number line diagram. (Total elapsed time limited to 60 minutes or less) E Identify times of day and night as a.m. and p.m. F Match and construct analog time to the same time written on a digital clock. F Identify times as quarter past, half past, and quarter to. PA EC: M3.B.1.1.1 PA CC: 2.4.3.A.2 PA CC EC: M03.D-M.1.1.1 PA EC: M3.B.1.1.2 PA CC: 2.4.3.A.2 PA CC EC: M03.D-M.1.1.2 PA EC: M3.B.1.1.3 PA EC: M4.B.1.1.1 PA EC: M4.B.1.1.2
Measurement Unit of Study E Use and read a ruler to measure to the nearest inch, ½, and ¼ as well as centimeter. PA CC: 2.4.3.A.1 PA EC: M3.B.2.1.1 PA CC EC: M03.D-M.1.2.3 Measurement How do you compare, choose, and use measurement? Why is it important to know how to estimate a measurement? How do I solve real-world measurement problems? Measurement Unit of Study February (11 days) E Choose an appropriate unit (length, area, volume and weight) for the attribute being measured. E Compare and order objects according to length, area, or weight. E Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Display the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, and quarters. E Match the object with its approximate measurement (foot, yard, mile). About how tall is a pop can? 5 inches, 5 feet, 5 yards All measurements given must be of the same system. E Estimate and measure length, capacity, and weight in the same system. Volume: capacity: cup, pint, quart, gallon, milliliters, liters Mass: weight: ounce, pound, ton, gram, kilogram F - Length: decimeter, millimeter, centimeter, meters, kilometers E Add, subtract, multiply, or divide to solve one-step word problems involving masses or liquid volumes that are given in the same units. - PA EC : M3.B.1.2.1 PA EC : M3.B.1.2.2 PA CC: 2.4.3.A.4 PA CC EC: M03.D-M.2.1.3 PA EC : M3.B.2.2.1 PA CC: 2.4.3.A.1 PA EC : M4.B.2.2.1 PA CC EC : M03.D-M.1.2.1 PA CC: 2.4.3.A.1 PA CC EC : M03.D-M.1.2.2
Geometry Unit of Study Geometry Why is it important to analyze shapes? Geometry Unit of Study February and March (12 days) E Name, identify, and describe geometric shapes in twodimensions/classify polygons: (circle, triangle, square, quadrilateral, rectangle, pentagon, hexagon, octagon, parallelogram, trapezoid, and rhombus). E Explain that shapes in different categories may share attributes, and that their shared attributes can define a larger category. Ex.1: A rhombus and a rectangle are both quadrilaterals since they both have exactly four sides. Ex.2: A triangle and a pentagon are both polygons since they are both multi-sided plane figures. E Recognize rhombi, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. E Identify the side and vertex in a polygon. F Name, identify, and describe geometric shapes in threedimensions or solid figures (sphere, cube, cylinder, cone, pyramid, rectangular prism). - PA EC: M4.C.1.1.1 PA EC: M3.C.1.1.1 PA CC: 2.3.3.A.1 PA CC EC: M03.C-G.1.1.1 PA CC: 2.3.3.A.1 PA CC EC: M03.C-G.1.1.2 PA EC : M3.C.1.1.1 PA EC : M3.C.1.1.2 F Describe attributes of solids (face, edge, vertex, vertices). PA EC: M3.C.1.1
Geometry What are different types of angles? What are different types of lines? What is symmetry? Geometry Unit of Study February and March (12 days) F Identify: ray, angle, vertex, right angle, perpendicular, acute angle, obtuse angle F Identify and classify different types of triangles: equilateral, isosceles, scalene, right, acute, obtuse F Identify points, lines, line segments, and rays. F Identify parallel, intersecting, and perpendicular lines. E Identify and draw one line of symmetry in a twodimensional figure. E Identify symmetrical two-dimensional shapes. - PA EC: M4.C.1.2 PA EC : M4.C.1.2.1 PA EC: M4.C.1.2.2 PA EC : M3.C.2.1.1 PA EC: M3.C.2.1.2
Perimeter, Area, and Volume Unit of Study Measurement How do I find perimeter, area and volume? Perimeter, Area and Volume Unit of Study March (10 days) E Solve real-world and mathematical problems involving perimeter of polygons including: (Use the same units throughout the problem) Find the perimeter given the side lengths Find the unknown side length Exhibiting rectangles with the same perimeter and different area Exhibiting rectangles with the same area and different perimeters. E Recognize area as an attribute of plane figures and understand concepts of area measurement. E Measure areas by counting unit squares (square cm, square m, square inch, square foot, and non-standard square units). E Multiply side lengths to find areas of rectangles with wholenumber side lengths in the context of solving real-world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. E Relate area to the operations of multiplication and addition. Use area models to represent the distributive property in mathematical reasoning. Recognize area as additive. - PA CC: 2.4.3.A.6 PA CC: M5.B.2.2.1 PA CC EC: M03.D-M.4.1.1 PA CC: 2.4.3.A.6 PA CC: 2.4.3.A.5 PA EC : M5.B.2.2.2 PA CC EC: M03.D-M.3.1.1 PA CC: 2.4.3.A.5 PA CC EC: M03.D-M.3.1.2 PA CC: 2.2.3.A.1 E Find volume of a solid figure. PA CC: M3.B.1.2
Data, Graphs, and Probability Unit of Study Data Analysis and Probability How do I create graphs using data? How do I interpret graphs using data? How do you use a coordinate grid? How do I apply basic concepts of probability? Data, Graphs, and Probability Unit of Study April (15 days) E Graph data or complete a graph given the data. (Complete a scaled pictograph and a scaled bar graph). Grid is provided. Scales limited to 1, 2, 5, 10. E Translate information from one type of display to another. Example: Convert a tall chart to a bar graph. Limit to pictographs, tally charts, bar graphs and tables. E Describe, interpret, and answer questions based on data shown in tables, charts or bar graphs. E Analyze data shown on tables, charts, or bar graphs using the concepts of largest, smallest, most often, least often, middle, how many more, and how many less. F Match and plot the ordered pair on a simple grid. E Display the data by making a line plot where the horizontal scale is marked in appropriate units whole numbers, halves or quarters. F Solve problems involving adding and subtracting using data on a line plot. - PA CC: 2.4.3.A.4 PA EC: M3.E.1.1.1 PA EC: M3.E.1.2.1 PA CC EC: M03.D-M.2.1.1 PA CC: 2.4.3.A.4 PA EC: M3.E.1.2.2 PA CC EC: M03.D-M2.1.4 PA CC: 2.4.3.A.4 PA EC: M3.E.1.1.2 PA CC EC: M03.D-M.2.1.2 PA EC: M4.C.3.1.1 PA CC EC: M03.D-M.2.1.3 PA CC EC: M03.D-M.2.1.4