Data Analysis. Harbor Creek School District. Major Understanding. Essential Questions. Timeframe Skills Assessment Standards

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1 Data Analysis Data Analysis How do you collect, organize and display data? Data Analysis Aug./September (12 days) E-Translate information from one type to display to another. Table Chart Bar Graph and/or Pictograph F-Display and interpret data shown in tallies, tables, charts, pictographs, bar graphs, and line graphs, and use a title, appropriate scale, and labels. A grid will be provided to display data on bar graphs or line graphs. E- Make a line plot to display a data set of measurements in fractions of a unit (e.g., intervals, of ½, ¼, ⅛). E-Solve problems involving addition and subtraction of fractions by using information presented in line plots (line plots must be labeled with common denominators, such as 1/4, 2/4, 3/4). For example: From a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collections PA CC: EC: M04.D-M MO5.D-M PA CC EC: M04.D-M PA CC:2.4.4.A.4 PA CC: A.4 PA CC EC: M04.D-M.2.1.1

2 Measurement Measurement identify time? solve problems involving length, weight (mass), liquid volume, and time? Measurement March (15 days) E - Identify time (analog and digital) as the amount of minutes before and after the hour. Ex #1: 2:50 is the same as 10 minutes before 3:00 Ex #2: Quarter past six is the same as 6:15 E Know relative sizes of measurement units within one system of units including standard units. (A table of equivalencies should be provided). in, ft, yd, mi c, pt, qt, gal km, m, cm kg, g lb, oz l, ml Second, minute, hour, day, week, month, year Ex #1: Know that 1 kg is 1,000 times as heavy as 1g. Ex #2: Express the length of a 4-ft snake as 48 inches. E Use all four operations to solve word problems involving distances, intervals of time (such as elapsed time), liquid volumes, masses of objects, money, including problems that require expressing measurements given in a larger unit in terms of a smaller unit. PA CC: A.1 PA EC: M4.B PA EC CC: M04.D-M PA CC: A.1 PA EC: M5.B CC: 4.MD.1 PA CC EC: M04.D-M PA CC: A.1 CC: 4.MD.2 PA CC EC: M04.D-M.1.1.2

3 How do you write numbers in standard, expanded and word form? How do we compare numbers? apply place value concepts? Numeration Numeration September/Oct. (10 days) F- Match the standard form to the word form of decimal numbers. Through the hundredths place *(After PSSA) E- Read and write whole numbers in expanded, standard and word form through 1,000,000. E- Use <,>, and = symbols to compare numbers through 1,000,000. Order numbers through 1,000,000 Students should compare and order within this standard. E - Compare two decimals to hundredths. Record the results of comparisons with the symbols <,>, and =, and justify the conclusions. E- Round multi-digit whole numbers (through 1,000,000) to any place. E- Demonstrate an understanding that in a multi-digit whole number (through 1,000,000), a digit in one place represents ten times what it represents in the place to its right. Example: Recognize that in the number 770, the 7 in the hundreds place is ten times the 7 in the tens place. F- Read & write decimals to hundredths using base ten numerals, word form, expanded form. ex.: (1.87 = *(After PSSA) PA CC EC: M5.A PA CC EC: M04.A-T PA CC: B.1 PA CC EC: M04.A-T PA CC EC: M4.A PA CC EC: M04.A-F PA CC: C.3 PA CC EC: M04.A-T PA CC:2.14.B.1 PA CC EC: M04.A-T PA CC: B.1 PA EC: MOS.A-T.1.1.3

4 Addition & Subtraction of Whole Numbers solve addition and subtraction problems? How does estimating help me with addition and subtraction? Addition and Subtraction of Whole Numbers October (8 days) E Add and subtract multi-digit whole numbers using the standard algorithm: Limit to two-step problems Limit sums and subtrahends up to including 1,000,000 Subtract across zeros E- Solve one step and multistep word problems posed with whole numbers and having whole-number answers using addition and subtraction. Use a variety of strategies to solve word problems. Represent these problems using equations with a letter standing for an unknown quantity. E- Estimate the answer to addition and subtraction problems using whole numbers through 6 digits. PA CC EC: M04.A-T PA CC: B.2 PA CC ED: M04.B PA CC: A.1 PA CC EC: M04.A-T PA CC:2.1.4.B.2 01/06/2017 Math

5 solve real-world problems? apply number theory concepts to multiplication? round and estimate? Multiplication & Division Meanings & Facts Multiplication & Division Meanings and Facts October/Nov. (10 days) E- Solve one step and multistep word problems posed with whole numbers and having whole-number answers using multiplication using a variety of different strategies. Represent these problems using equations with a letter standing for an unknown quantity. E- Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison. Example: Know that 3 4 can be used to represent that Student A has 4 objects and Student B has 3 times as many objects not just 3 more objects. E-Solve basic multiplication problems using the properties of multiplication. E- Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations. Example 1: Interpret 35 = 5 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Example 2: Know that the statement 24 is 3 times as many as 8 can be represented by the equation 24 = 3 8 or 24 = 8 3. PA CC EC: M04.B PA CC: A.1 PA CC: EC: M04.B PA CC: A.1 PA CC:M04.A.T PA CC EC:A.T PA CC: B.2 PA CC:2.2.4.A.1 PA CC EC: M04.B

6 Number and round and estimate? apply number theory concepts to division? Multiplication & Division Meanings and facts Oct./November (10 days) E- Estimate the answer to multiplication problems using whole numbers through 6 digits. E- Solve basic division problems using a variety of strategies. Draw models Fact Families (multiplication and division) Properties of Division (0 and 1 rules) PA CC EC: M04.A.T PA CC: B.2 PA CC EC:MO4.A.T PA CC EC: MO4.A.T.2.1.3

7 Multiplying Larger Numbers apply number theory to multiplication problems? solve real-world problems? Multiplying Larger Numbers November (14 days) E-Multiply a whole number of up to four digits by a one-digit whole number. E- Multiply two two-digit numbers, using strategies based on place value and the properties of operations, Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Multiples of 10 and 100 Mental Math E- Solve one step and multistep word problems posed with whole numbers and having whole-number answers using multiplication using a variety of different strategies. Represent these problems using equations with a letter standing for an unknown quantity E-Estimate the answer to multiplication problems using whole numbers through 6 digits. (no more than 2 digits x 1 digit, excluding powers of ten) PA CC EC: M04.A.T PA CC:2.1.4.B.2 PA CC: A.1 PA CC EC: M04.B PA CC EC: M04.A.T.2.1.4

8 Dividing Larger Numbers apply number theory to division problems? solve realworld problems? apply number theory concepts to division? Dividing Larger Numbers Unit of November/Dec. (10 days) E- Divide up to four digit dividends by one-digit divisors with answer written as whole-number quotients and remainder if applicable. Use a variety of different strategies such as: Use basic facts Patterns of zero E- Solve one step and multistep word problems posed with whole numbers and having whole-number answers using division using a variety of different strategies. Represent these problems using equations with a letter standing for an unknown quantity. E- Find, list, and identify all factor pairs in the range of any given number. Recognize that a whole number is a multiple of each of its factors. E- Determine whether a given whole number in the interval 1 through 100 is a multiple of a given one-digit number. E- Determine if it is prime or composite PA CC EC: M04.A.T PA CC: A.1 PA CC EC: M04.B PA CC EC: M04.B

9 Patterns, Expressions, and Equations Algebraic Concepts generate and identify features of patterns? apply simple function rules? determine a missing number or symbol? Patterns, Expressions & Equations December (8 days) E- Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Example 1: Given the rule add 3 and the starting number 1, generate terms in the resulting sequence and observe that the terms alternate between odd and even numbers. Example 2: Given the rule increase the number of sides by 1 and starting with a triangle, observe that the tops of the shapes alternate between a side and a vertex. E- Determine the missing elements in a function table. Functions may use +, -, or x Whole numbers and money should be used. E- Determine the rule for a function given a table. Functions may use +,-, or x for whole numbers. E- Identify the missing symbol that makes a number sentence true. +,-,x,,<,>,= For division: single digit divisor only Properties of equality PA CC: A.4 PA CC EC: M04.B PA CC: A.4 PA CC EC M04.B.O PA CC: A.4 PA CC EC: M04.B PA CC: A.2 PA CC EC :M04.B

10 Area and Perimeter Measurement calculate area and perimeter? Area and Perimeter January (3 days) F- Calculate area and perimeter of regular polygons (after PSSA). E Apply area and perimeter formulas for rectangles in the real world and mathematical problems. Ex: Find the width of a rectangular room given the area of the flooring and the length. (The formulas will be provided). PA CC: A.1 CC: 4.MD.3 PA CC EC: M04.D- M.1.1.3

11 Geometry Geometry analyze characteristics and properties of geometric shapes? identify and draw different types of lines? How do shapes move? Geometry January (15 days) E - Identify, classify, and compare two-dimensional figures (circle, triangle, square, parallelogram, trapezoid, rhombus, rectangle, pentagon, hexagon, and octagon). F Identify and classify three-dimensional figures (cube, sphere, rectangular prism, and pyramid). (After PSSA). E Recognize and identify right triangles. E Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. E Identify and draw points, lines, line segments, and rays. E Identify and draw parallel and perpendicular lines. Identify these lines in two-dimensional figures. E Recognize a line of symmetry for a two-dimensional figure such that the figure can be folded along the line into mirroring parts. Identify line-symmetric figures and draw lines of symmetry (up to two lines of symmetry). PA EC: M4.C CC: 4.G.1 CC: 4.G.2 PA EC: M4.C PA CC: A.2 PA EC: M5.C CC: 4.G.2 PA CC EC: M04.C-G PA CC: A.2 CC: 4.G.2 PA CC EC: M04.C-G PA CC: A.1 PA EC: M4.C CC: 4.G.1 PA CC EC: M04.C-G PA CC: A.1 PA EC: M4.C CC: 4.G.1 PA CC EC: M04.C-G PA CC EC: M04.C-G.1.1.3

12 Geometry Geometry plot on a coordinate grid? What are angles? Geometry January (15 days) F Match and plot the ordered pair with the appropriate point (or object) on a simple grid. (After PSSA). E Identify, draw, and measure angles in whole number degrees. Use a protractor to measure the angles. E With the aid of a protractor, sketch angles of specified measure. E Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems (angles must be adjacent and non-overlapping). E Identify and draw angles: right, acute, and obtuse. Identify these angles in two-dimensions. PA CC: A.3 PA EC: M4.C CC: 4.G.3 PA CC EC: M04.C-G PA CC: A.6 CC: 4.MD.6 PA CC EC: M04.D-M PA CC: A.6 CC: 4.MD.6 PA CC EC: M04.D-M PA CC: A.6 CC: 4.MD.7 PA CC EC: M04.D-M PA CC: A.1 CC: 4.G.1 PA CC EC: M04.C-G.1.1.1

13 Fractions What are equivalent fractions? E Recognize and generate equivalent fractions. PA CC EC: M04.A-F PA CC: C.1 CC: 4.NF.1 How do you compare fractions? write fractions as decimals and decimals as fractions? Fractions February (20 days) E Compare two fractions with different numerators and different denominators (denominators limited to 2,3,4,5,6,8,10,12, and 100). Record the results of comparisons with the symbols <,> and =, and justify the conclusions. E Write fractions as decimal notations ad decimal notations as fractions. Ex: Rewrite 0.62 as 62/100. PA CC: C.1 CC: 4.NF.2 PA CC EC: M04.A-F PA CC: C.3 CC: 4.NF.6 PA CC EC: M04.A-F.3.1.2

14 E Multiply a whole number by a unit fraction. (Denominators limited to 2,3,4,5,6,8,10,12 and 100; final answers do not need to be reduced or written as a mixed number). Ex: 5 x (1/4) = 5/4 PA CC: C.2 PA CC EC: M04.A-F CC: 4.NF.4 multiply fractions? add and subtract fractions? Fractions February (20 days) E - Multiply a whole number by a non-unit fraction. (Denominators limited to 2,3,4,5,6,8,10,12 and 100; final answers do not need to be reduced or written as a mixed number). E Solve word problems involving multiplication of a fraction by a whole number (Denominators limited to 2,3,4,5,6,8,10,12 and 100). E Add and subtract fractions with a common denominator (Denominators limited to 2,3,4,5,6,8,10,12 and 100; answers do not need to be reduced; no improper fractions as the final answer). E Decompose a fraction or a mixed number into sums of fractions with the same denominator (Denominators limited to 2,3,4,5,6,8,10,12 and 100), recording the decomposition by an equation. Justify decompositions (for example, by using a visual fraction model). Ex #1: 3/8=1/8+1/8+1/8 OR 3/8=2/8+1/8 PA CC: C.2 PA CC EC: M04.A-F CC: 4.NF.4 PA CC: C.2 PA CC EC: M04.A-F CC: 4.NF.4 PA CC: C.2 PA CC EC: M04.A-F CC: 4.NF.3 PA EC: M4.A PA CC: C.2 PA CC EC: M04.A-F Ex #2: 2 1/12=1+1+1/12 OR 2 1/12=12/12+12/12+1/12 E Add and subtract mixed numbers with a common denominator (Denominators limited to 2,3,4,5,6,8,10,12 and 100; no regrouping with subtraction; fractions do not need to be reduced; no improper fractions as the final answer). PA CC: C.2 PA CC EC: M04.A-F.2.1.3

15 add and subtract fractions? Fractions February (20 days) E Solve word problems involving addition and subtraction of fractions referring to the same whole or set and having like denominators (Denominators limited to 2,3,4,5,6,8,10,12 and 100). E Add two fractions with respective denominators 10 and 100. Ex: Express 3/10 as 30/100, and add 3/10 + 4/100 = 30/ /100 = 34/100 F Divide fractions unit fractions by whole numbers and whole numbers by unit fractions (after PSSA). F Simplify fractions and write as mixed numbers (after PSSA). PA CC: C.2 PA CC EC: M04.A-F PA CC: C.3 PA CC EC: M04.A-F CC: 4.NF.5