Big Ideas. Objects can be transferred in an infinite number of ways. Transformations can be described and analyzed mathematically.

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1 Big Ideas Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms. Objects can be transferred in an infinite number of ways. Transformations can be described and analyzed mathematically. Some questions can be answered by collecting, representing, and analyzing data, and the question to be answered determines the data to be collected, how best to collect it, and how best to represent it. Numerical measures describe the center and spread of numerical data. The likelihood of an event occurring can be described numerically and used to make predictions. Numerical quantities and calculations can be estimated by using numbers that are close to the actual values, but are easier to compute with. Some attributes of objects are measurable e.g., length, mass, capacity, and can be quantified. Measures can be estimated by using known referents.

2 Patterns exhibit relationships that can be extended, described, and generalized. Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations. There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities. 2- and 3-Dimensional objects can be described, classified, and analyzed by their attributes, and their location can be described quantitatively. Spatial reasoning and visualization are ways to orient thinking about the physical world.

3 Standard Area 2.1 Numbers, Number Systems, and Number Relationships A Apply number patterns to count and compare values of whole numbers, fractions, and decimals B Use number theory concepts and models to represent or rename whole numbers, fractions, and decimals C Use models to represent the concept of an integer, fraction, decimal, or percent D Apply place value concepts to order and compare 5.NBT.1 Understand the place value system. Compare whole numbers through 9 digits using the words more, less, equal, least, most, greater than, less than, or the symbols >, < =. (M5.A.1.3.1) Compare and/or order decimals through the hundredths (limit to 4 numbers). (M5.A.1.3.2) Compare proper fractions through sixteenths with like and unlike denominators. (M5.A.1.3.3) *Using the appropriate symbol >, <, or =. Compare and/or order decimals through the thousandths using the appropriate symbol >, <, or =. Match the standard form to the word form of decimal numbers through hundredths. (M5.A.1.2.1) *and thousandths Use appropriate sign to indicate the relationship between decimals (greater than or less than). Use or develop regions and/or sets to model fractions and mixed numbers through hundredths (may include reducing the fractions). (M5.A ) Represent decimals through the thousandths using grids. Recognize common equivalents for percents, fractions, and decimals (e.g.10%, 25%, 50%, 75%, and 100%. Locate/identify integers on a number line (greater than or equal to -20). (M5.A.1.4.1) Identify negative temperatures on a thermometer (through -20 degrees C). (M5.A.1.4.2) Convert between common fractions, decimals and percents. Use expanded notation to represent whole number (less than 10,000,000) or decimals (through hundredths). (M5.A.1.1.1) *and thousandths

4 decimals and to express whole numbers and decimals in expanded notation E Develop and apply number theory concepts (e.g., primes, factors, multiples, composites) to represent numbers in various ways F Understand the concepts of multiplication and division and use the inverse relationships between multiplication and division, to determine unknown quantities in equations. Identify the place value of a digit (millions through hundredths). (M5.A.1.2.2) Understand basic exponential notation using powers of 10. Define/list/identify prime and composite numbers less than or equal to 100. (M5.A.1.6.1) Define/list/identify factors and/or multiples of a given whole number less than or equal to 50. (M5.A.1.6.2) *or to 100. Define 0 and 1 as neither prime nor composite. Define and identify Greatest Common Factor (GCF) and Least Common Multiple (LCM) when listing factors and multiples. Write an equation to solve problems involving multiplication and division of whole numbers. Use multiplication to solve a division problem and relate to fact families, such as: 36 divided by = 4 is the same as 4 x = 36 or vice versa. Standard Area 2.2 Computation and Estimation B Multiply and divide single-and double-digit numbers; add and subtract fractions and mixed numbers; add, subtract, multiply and divide decimals. 5.NBT.2 Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NF.1 Use equivalent fractions as a strategy to add and subtract fractions. Solve problems involving +, -, x, of whole numbers (multipliers up to 2 digits, divisors or one digit) and decimals including money (answers through hundredths; no divisors with decimals). (M5.A.2.1.1) Solve problems involving + and of fractions through sixteenths for like and unlike denominators for unlike denominators, the LCD must be one of the given denominators). (M5.A.2.1.2) Use +, -, x, to compute without a calculator (multipliers up to 2-digits, 1-digit divisors or multiples of10; whole numbers through thousands and decimals through hundredths; no divisors with decimals). (M )

5 Use mental math to complete +.-, x, of whole numbers, benchmark decimals to hundredths, fractions (1/2, ¼, 1/10, ). Demonstrate fluency in using the following U.S. Algorithms: 3-Digit and 4-Digit Multiplication (Whole Numbers) 4-Digit by 1-Digit Division (Whole Numbers) 4-Digit by 2-Digit Division (using multiples of 10) Addition and Subtraction of fractions through sixteenths (like or unlike denominators, LCD is one denominator) Use the mathematical terms: addend, sum, factor, product, difference, remainder, divisor, dividend and quotient when performing the operation. Represent and interpret the remainder as a whole number remainder, a fraction. 5.NF.2 Apply and extend previous understanding of multiplication and division to multiply and divide fractions. Use models to demonstrate x of fractions using denominators up to D Estimate results from calculations with basic operations of whole numbers and decimals and check the reasonableness of those estimates. Use estimation to solve problems involving whole numbers and/or decimals (up to 2-digit multipliers, 1-digit divisors or multiples of 10; whole numbers through thousands and decimals through hundredths; no divisors with decimals). (M5.A.3.1.2) Round whole numbers through millions and decimals through hundredths. (M5.A.3.1.1) Standard Area 2.3 Measurement and Estimation A Use concrete objects to demonstrate the meaning of measurement quantities (e.g., Determine the appropriate unit of measure in both customary (standard) and metric units (perimeter, area, weight or capacity/volume).

6 perimeter, area, weight, capacity) B Select and use appropriate instruments and units for measuring quantities to a specified level of accuracy C Calculate perimeter and area, and sums and differences of measurements D Perform basic conversions within a system. 5.MD.1 Convert like measurement units within a given measurement system. Select the appropriate unit both customary (standard) and metric for measuring weight (mass), capacity, length, perimeter, and area. (M5.B.1.1.1) Use a ruler to measure to the nearest 1/8 of an inch or cm. (M5.B.2.1.1) Measure degrees in an angle up to 180 degrees with a protractor. Find the perimeter of a figure drawn and labeled (same units throughout). (5.B.2.2.1) Determine the perimeter and area of quadrilaterals and regular polygons using drawings or representations to develop a formula. Calculate elapsed time to determine and/or compare elapsed time to the minute within AM or PM. Convert using linear measurements, capacity, and weight (mass) within the same systems to the unit immediately above or below the given unit (using only the following units and including a conversion chart or hint: mm, cm, km, ml, L, g, kg, cup, pint, quart, gallon, in., ft., yd., oz., lb.) (M5.B.1.2.1) F Estimate and verify measurements of length, perimeter, area, volume, capacity, temperature, time, weight, and angles. 5.MD.3 Geometric measurement: Understand concepts of volume and relate volume to multiplication and to addition. Estimate which polygon (shown on a grid) has a greater perimeter or area (compare perimeter to perimeter OR area to area). (M5.B.1.3.1) Estimate the area of an irregular figure shown on a grid. (M5.B ) *including diagonals and curved with regrouping. Use tiles and cubes to develop a formula that can be applied in similar situations. Add and subtract linear measurements, (ft. and in.) and units of time (hr. and min.) without having to regroup with subtraction (answer in simplest form). (M5.B.1.2.2) Solve problems involving weight, time, temperature, length and capacity (limited to 3 digits; same units throughout). (M5.B.2.2.3) Use concrete objects to demonstrate the meaning of volume by adding total units which fit into a 3-D figure. Develop strategies that demonstrate volume formulas.

7 2.4.5.A Use models, number facts, properties and relationships to draw conclusions and explain reasons for conclusions B Use if... then statements to express conditional relationships. Standard Area 2.4 Mathematical Reasoning and Connections Use models, words, properties, etc. to explain the validity of mathematical conclusions. Explanations may include the use of distributive, communitative, associative, and identity properties. Use an if/then statement to support related data (e.g., if 5 x 4 = 20 then, 50 x 4 = 200). Standard Area 2.5 Mathematical Problem Solving and Communication A Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense, and explain how the problem was solved in grade appropriate contexts. Choose the correct operations to solve a problem (no more than 2 operations). (M5.A.2.1.3) *and choose the appropriate strategy.

8 2.5.5.B Use appropriate mathematical terms, vocabulary, language, symbols, and graphs to explain clearly and logically solutions to problems. Choose and explain the mathematical tools (graphs, vocabulary, and symbols, etc.) necessary to solve a problem through written and spoken language. (See attached PSSA Assessment Anchor Glossary.) Standard Area 2.6 Statistics and Data Analysis A Gather data from surveys and observations from sources outside the classroom or home B Use pictures, tallies, tables, charts, bar graphs, line graphs, diagrams, and graphs to organize display, and analyze data C Calculate mean and range, identify the median and the mode of a set of data, and use these quantities to describe the data D Compare data using multiple categories displayed in a graph. 5.MD.2 Represent and interpret data. Collect authentic data from classroom or home and organize it into a useful form for analyzing. Display and/or interpret data shown in tables, charts, pictographs, bar graphs, and line graphs using a title, appropriate scale, and labels. A grid will be provided to display data on bar graphs and line graphs. (M5.E.1.1.1) Construct a properly labeled graph including title, axis labels, and key. Compare information between graphs and tables. Determine the mean/average (answer is a whole number), median (answer is a whole number or average of two numbers), and range of data (up to 10 numbers). (M5.E.2.1.1) Identify the mode in a set of data (up to 10 numbers). (M5.E.2.1.2) Use a graph with multiple categories to interpret and compare data.

9 2.6.5.E Determine the reasonableness of a statement based on a comparison to data displayed in a graph and summarized by numerical measures. Use a graph to determine reasonableness of statement(s) by summarizing numerical findings. Standard Area 2.7 Probability and Predictions A Predict and calculate the likelihood of simple events B Predict and determine why some outcomes of a particular event are certain, more likely, less likely, equally likely, or impossible C Express probabilities as fractions and/or decimals D List all possible combinations and arrangements of outcomes of an experiment (e.g., tree diagrams, matrices) E Compare predictions based on theoretical probability Determine the probability of an outcome. Predict or determine whether some outcomes are certain, more likely, less likely, equally likely, or impossible (information could be represented by pictographs, bar graphs, charts, tables and/or spinners). (M5.E ) Determine the probability of an outcome (example: coin toss, roll of # cube) and express as a fraction without reduction. (M5.E.3.1.2) Determine the probability of an outcome and express as a decimal. Use an organized format to list all possible combinations or outcomes of an experiment. Use the likelihood of an event and the actual event to compare the actual results to the predicted results.

10 and experimental results. Standard Area 2.8 Algebra and Functions A Use the concept of equality to demonstrate understanding of the distributive property B Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) and explain the method of solution C Recognize, describe, extend, create, replicate, and form a rule for a variety of patterns, sequences, and relationships verbally, numerically, symbolically, and graphically D Determine a functional rule from a table or graph E Use concrete objects and combinations of symbols and numbers to create expressions, 5.OA.2 Analyze patterns and relationships. 5.OA.1 Write and interpret numerical expressions. Demonstrate understanding by applying the distributive property to order of operations problems. Solve for a missing number (blank, question mark, or variable) in an equation involving a single operation with whole numbers only. (M5.D.2.1.1) Solve number equations using strategies that demonstrate the commutative and associative properties. Extend or find a missing element in a numerical or simple geometric patter ( +, -, x, and of whole numbers.) Pattern must show 3 repetitions. (M5.D.1.1.1) Create or replicate a numerical or geometric pattern showing 3 repetitions of that pattern ( +, -, x, division of whole numbers may be used). (M5.D.1.1.2) Form a rule based on a given pattern, or illustrate a pattern based on a given rule ( +, -, x, division of whole numbers). Pattern must show 3 repetitions. (M5.D.1.2.1) Match a realistic situation to an equation, expression, inequality, table and graph (variable must be isolated). (M5.D )

11 equations, and inequalities that model mathematical situations F Describe data represented in equations, inequalities, tables, or graphs and/or create a story that matches that data. Use graphs and charts to create a story problem. Use a given equation/inequality to create a story problem. Standard Area 2.9 Geometry A Identify, describe, and define 1-2-, and 3-dimensional shapes and their related parts, and classify and compare 2- and 3- dimensional shapes on the basis of their properties B Predict and describe the result of a translation (slide), rotation (turn), or reflection (flip) of a 2-dimensional shape. 5.G.2 Classify 2-dimensional figures into categories based on their properties. Identify and/or classify cubes, rectangular prisms, and pyramids using faces, vertices, and edges. (M5.C.1.1.1) Identify and/or describe properties of all types of quadrilaterals (parallelogram, rectangle, rhombus, square, trapezoid). (M5.C.1.1.2) Identify, draw and/or label points, lines, line segments, and rays. (M5.C.1.2.1) Identify the number of lines of symmetry and/or draw all lines of symmetry in a two-dimensional polygon. (M5.C.2.1.2) Draw or identify a translation (slide), reflection (flip), and rotation (turn) of two-dimensional shape. (M5.C.2.1.1)

12 2.9.5.C Identify location of points with fractional or decimal coordinates on a number line or on a 2-dimensional coordinate system. 5.G.1 Graph points on the coordinate plane to solve real-world and mathematical problems. Plot, locate and identify points in Quadrant I, on the x and y axis, using a sale of 1, 2, 5, or 10 on a 100 by 100 grid. Points will not be in-between lines. Standard Area 2.10 Trigonometry A Identify and compare parts of right triangles, including right angles, acute angles, hypotenuses, and legs. Label and identify types of triangle as determined by angle measurement and length of sides. Use mathematical vocabulary to further describe right triangles (i.e. leg, hypotenuse, etc.). Use a protractor to measure the angles of a right triangle to the nearest 5 degrees. Standard Area 2.11 Concepts of Calculus A Make comparisons of numbers (e.g., more, less, same, Determine relationships using >, <, =,,, and.

13 least, most, greater than, less than) B Describe the relationship between rates of change and another variable (e.g., time, temperature) C Estimate areas and volumes of shapes and solids as the sums of areas of tiles and volumes of cubes. Use more than one measurement to determine the pattern/connection between the two measurements - such as time and temperature. (The temperature dropped two degrees in one hour, four degrees in two hours. If this pattern continues, what would the projected temperature be in ten hours?) Use tiles and cubes to estimate the area and volume of 2-dimensional and 3- dimensional objects. Use tiles and cubes to develop a formula that can be applied in similar situations.