The likelihood of an event occurring can be described numerically and used to make predictions.

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1 Big Ideas Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms. 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. The likelihood of an event occurring can be described numerically and used to make predictions. The same number sentence (e.g., 12 4 = 8) can be associated with different concrete or real-world situations AND different number sentences can be associated with the same concrete or real-world situation. 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. 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. Standard Area 2.1 Numbers, Number Systems, and Number Relationships A Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals. 4.OA.3 Generate and analyze patterns. 4.NF.2 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Compare and/or order whole numbers through 6 digits and amounts of money to $100. (M4.A.1.2.2) Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < through six digits. Locate/identify fractions or decimals on a number line (decimals and fractions through the hundredths-do not mix fractions and decimals). (M4.A.1.2.1) - *fractions through twelfths. Compare fractions and decimals using greater than (>), less than (<), and equal to (=). Compare two fractions with different numerators and different denominators by using strategies such as comparing to a benchmark fraction (1/2), using a visual model, or creating common denominators.

3 2.1.4.B Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols. 4.NF.1 Extend understanding of fraction equivalents and ordering. 4.NF.3 Understand decimal notation for fractions, and compare decimal fractions. Match the standard number form to the word form of decimal numbers through the hundredths place. (M4.A.1.1.3) Write the fractional decimal including mixed numbers, which corresponds to a drawing or set-no simplification. (M4.A.1.1.1) Create a drawing or set that represents a given fraction or decimal, including mixed numbers through the tenths place. (M4.A.1.1.2) Explain why a fraction is equivalent to another fraction using pictures, manipulatives or words C Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number. Demonstrate fractional parts using drawings, diagrams, or models (e.g., using number lines, manipulatives, and simple drawings). Use drawings, diagrams, and models to represent fractions as division of a whole number by a whole number D Apply place value concepts and base-ten numeration to order and compare larger whole numbers. 4.NBT.1 Generalize place value understanding for multi-digit whole numbers. 4.NBT.2 Use place value understanding and properties of operations to perform multi-digit arithmetic. Write * whole numbers in expanded, standard, and /or word form through 6 digits. (M4.A.1.1.4) *(and read) Order a set of whole numbers from least to greatest or greatest to least up through 6 digits E Apply factors and multiples to represent larger numbers in various ways F Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve 4.OA.2 Gain familiarity with factors and multiples. Find/list/identify all factors through 10 of any given number. (M4.A.1.3.1) Identify factors of numbers to 100. Find/list/identify multiples of a number, where the multiples do not exceed 100. (M4.A.1.3.2) Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-50 is prime or composite. Solve problems involving all operations with whole numbers and/or explain the solution (limit to two-step problems, e.g., multiply then add, single digit multipliers and divisors). (M4.A.2.1.1) Solve problems involving addition and subtraction with decimals through the hundredths, or money to the cent and/or explain the solutions. Limit to two-step problems. (M4.A.2.1.2)

4 problems, including word problems and equations. Demonstrate the inverse relationship between addition and subtraction and multiplication and division using fact families. Standard Area 2.2 Computation and Estimation A Develop fluency in the use of basic facts for the four operations B Multiply single-and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals D Estimate sums and differences, products, and quotients, and conclude the reasonableness of those estimates. 4.OA.1 Use the four operations with the whole numbers to solve problems. Solve problems involving multiplication facts through 12 x 12. Solve problems involving division facts through 9 x 9. Solve addition or subtraction problems involving decimals through hundredths (decimal numbers must have the same number of places). (M4.A.3.2.1) Solve addition or subtraction problems with fractions with like denominators (denominators to 10-no simplifying necessary). (M4.A.3.2.2) Demonstrate fluency in using the following U.S. algorithms: 2-, 3-, & 4-digit x 1-digit Multiplication with regrouping 2-digit x 2-digit Multiplication with regrouping 2-digit & 3-digit x 1-digit Division Addition & Subtraction of decimals (through hundredths) Multiply & Divide decimals by 1-digit whole number (through hundredths) Addition & Subtraction of fractions (with like denominators of 10 or less) Round whole numbers to the nearest ten, hundred, thousand, ten-thousand, or hundred-thousand. (M4.A.3.1.1) Round amounts of money to the nearest dollar. (M4.A.3.1.2) Estimate the answer to addition, subtraction, and multiplication problems using whole numbers through six digits (for multiplication, no more than 2 digits times 1 digit excluding powers of 10). (M4.A.3.1.3)

5 Standard Area 2.3 Measurement and Estimation A Use concrete objects to demonstrate an understanding of measurement quantities (e.g., length, weight, temperature) B Select and use appropriate tools and units for measuring quantities (e.g., length, time, weight, temperature) C Calculate elapsed time; use concept of elapsed time to determine start time/end time D Perform basic conversions within the same system to the unit immediately above or below the given unit. 4.MD.1 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Match/construct time (a picture of a clock), to the same time written in digital. (M4.B.1.1.1) Know relative sizes of measurement units within one system of units, including km, m, cm, kg, g, lb, oz, l, ml, hr, min, sec. Use or read a ruler to measure to the nearest ¼ inch or centimeter. (M4.B.2.1.1) Select and use appropriate tools for measuring time, weight, temperature and capacity. Calculate the elapsed time to the minute in a given situation, limited to two adjacent hours. (M4.B.1.1.3) Determine the beginning or ending time, given the elapsed time, limited to two adjacent hours. (M4.B.1.1.4) Use a table to convert feet/mile, inches/foot, feet/yard, inches/yard, ounces, cups, pints, and quarts to other designated units; milliliters/liters, grams/kilograms, meters/centimeters F Estimate and verify measurements of length, perimeter, area, weight, capacity, temperature, and time. Make reasonable estimates of weights, lengths, and capacities of familiar objects (measurements in the same system). (M4.B.2.2.1) Apply the area and perimeter formulas for rectangles to real world and mathematical problems. Recognize that polygons with the same area can have a different perimeter and polygons with the same perimeter can have a difference area. Continue to develop estimation and measurement skills for liquid volume to the nearest half gallon, gallon, and liter; temperature to the nearest degree in Fahrenheit

6 aand Celsium; and time to the nearest minute A Use models, number facts, and properties to make conjectures, draw conclusions and explain reasons for conclusions B Recognize and use precise language to describe connections between mathematical ideas. Standard Area 2.4 Mathematical Reasoning and Connections Use models, words, properties, etc to explain the validity of mathematical conclusions. (Show and explain conclusions.) Use appropriate language when describing relationships between mathematical ideas A Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether a answer makes sense, and explain how the problem was solved in grade appropriate contexts. Standard Area 2.5 Mathematical Problem Solving and Communication Choose an appropriate strategy and correct operation to solve a problem with 1 or 2 steps/operations.

7 2.5.4.B Use appropriate mathematical vocabulary, graphs, and symbols when explaining how to solve a problem. 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 within the classroom or homes B Organize and display data using tables, pictures, tallies, bar graphs, line graphs, or pictographs. 4.MD.2 Represent and interpret data. Collect and organize data in tables properly labeled with title and headings. Graph data or complete a graph given the data (bar graph, line plot, or pictograph, grid is provided). (M4.E.1.2.1) Translate information from one type of display to another (table, chart, bar graph, line plot, or pictograph). (M4.E.1.2.2) C Describe and calculate the mean and use this quantity to describe the data. Recognize and calculate the range, median, mode, and mean of a set of data D Analyze data shown in tables, charts, diagrams, and graphs; compare the data from two categories displayed in a graph and compare representations of a set of data in different graphs. Describe, interpret, and/or answer questions based on data shown in tables, charts, bar graphs, line plots, and pictographs. (M4.E.1.1.1)

8 2.6.4.E Determine the reasonableness of a statement based on a comparison to data displayed in a graph. Determine reasonableness of conclusions drawn based on data in a graph A Determine the chance of an event occurring by performing simulation with concrete devices (e.g., dice, spinner) B Determine whether different outcomes of the same event are equally likely or not equally likely C Express probabilities as fractions D List or graph the possible results of an experiment E Describe possible reasons for the difference between predicted and actual outcomes. Standard Area 2.7 Probability and Predictions Make a prediction based on data or chance (data may be shown in tables, charts, line graphs, bar graphs, line plots, and pictographs). (M4.E.3.1.1) Describe, interpret and/or answer questions based on data or chance. Determine the probability of events recurring (by studying past data). Identify an event as certain, more likely, less likely, equally likely, or impossible. Show fraction equivalencies for events based on the likelihood line with zero being impossible, certain being one, and maybe being one-half (1/2). Describe possible outcomes for events that can be predicted with more than six trials using data from an experiment. Recognize the variable(s) that created the difference between prediction and outcome (by formulating questions about data and/or collecting, organizing, analyzing and displaying data).

9 Standard Area 2.8 Algebra and Functions A Use the concept of equality and concrete objects to demonstrate understanding of commutative, associative, and identity properties B Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole number or unit fraction and explain the method of solution C Recognize, describe, extend, create, replicate, and make generalizations for a variety of patterns, sequences, and relationships verbally and numerically D Use words, tables, and graphs to represent and analyze functions E Use concrete objects and combinations of symbols and numbers to create expressions, equations, and inequalities that 4.OA.3 Generate and analyze patterns. Extend or find a missing element in a numerical or geometric pattern (+, -, or x may be used; whole numbers). (M4.D.1.1.1) Solve equations using multiplication and addition properties (identity, associative, and commutative), using concrete objects to demonstrate equality between the two number expressions (e.g., using cubes on a balance). Correlate story situations with expressions or equations (may use numbers and one operation +, -, or x; no variables). (M4.D.2.1.1) Solve for a missing number in an equation (using estimation, guess & check, etc.). (M4.D.2.2.1) Identify the missing symbol (+, -, x,, <, >, =) that makes a number sentence true. (M4.D.2.2.2) Identify/describe the rule for a numerical or geometric pattern shown (+, -, or x may be used; patterns must be whole numbers). (M4.D.1.1.2) Create or replicate a numerical or geometric pattern showing 3 repetitions (+, -, or x may be used; whole numbers or money). (M4.D.1.1.3) Determine the missing elements in a function table (functions may use +, -, or x and whole numbers). (M4.D.1.2.1) Determine the rule for a function given a table (functions may use +, -, or x and whole numbers). (M4.D.1.2.2) Create or match a story problem to an equation.

10 model mathematical situations F Describe data represented in equations, inequalities, tables, or graphs and/or create a story that matches that data. Correlate story situations with expressions or equations (may use numbers and one operation +, -, or x). (M4.D.2.1.1) Standard Area 2.9 Geometry A Identify, describe, and define 1-,2-, and 3-dimensional shapes and their related parts; compare 2-dimensional shapes; compare 3-dimensional shapes B Identify and draw figures with one or more lines of symmetry C Identify on a 2- dimensional coordinate system the location of points with whole number coordinates; plot in a twodimensional coordinate system a point represented by an ordered pair of whole numbers. 4.G.1 Draw and identify lines and angles and classify shapes by properties of their lines and angles. Identify, classify, and/or compare two-dimensional figures (circle, triangle, square, parallelogram, trapezoid, rhombus, rectangle, pentagon, hexagon, and octagon). (M4.C.1.1.1) Identify or classify three-dimensional figures (cube, sphere, rectangular prism, and pyramid). (M4.C.1.1.2) Identify points, lines, line segments, and rays. (M ) Identify parallel and perpendicular lines. (M4.C.1.2.2) Identify or create figures that have one, two, or no lines of symmetry. (M4.C.2.1.1) Recognize mirror/rotational symmetry. Match or plot the ordered pair with the appropriate point (or object) on a simple grid. (M4.C.3.1.1)

11 Standard Area 2.10 Trigonometry A Identify right angles in geometric figures. 4.MD.3 Geometric measurement: understand concepts of angle and measure angles. Recognize the differences in angle measurements, i.e. acute, obtuse, right. Standard Area 2.11 Concepts of Calculus A Make comparisons of whole numbers and of unit fractions (e.g., more, less, same, least, most, greater than, less than). Compare whole numbers, up through 6 digits, and fractions using <, >, or = (may use number lines or manipulatives).