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Arizona Math Standards - 5th Grade

MathScore aligns to the Arizona Math Standards for 5th Grade. The standards appear below along with the MathScore topics that match. If you click on a topic name, you will see sample problems at varying degrees of difficulty that MathScore generated. When students use our program, the difficulty of the problems will automatically adapt based on individual performance, resulting in not only true differentiated instruction, but a challenging game-like experience.

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View the Arizona Math Standards at other levels.

Number Sense and Operations

C1 Number Sense
   1. Make models that represent improper fractions.
   2. Identify symbols, words, or models that represent improper fractions.
   3. Use improper fractions in contextual situations.
   4. Compare two proper fractions or improper fractions with like denominators. (Fraction Comparison )
   5. Order three or more unit fractions, proper or improper fractions with like denominators, or mixed numbers with like denominators.
   6. Compare two whole numbers, fractions, and decimals (e.g., 1/2 to 0.6). (Compare Mixed Values , Compare Mixed Values 2 , Fractions to Decimals , Decimals To Fractions , Positive Number Line )
   7. Order whole numbers, fractions, and decimals.
   8. Determine the equivalency between and among fractions, decimals, and percents in contextual situations. (Percentage Pictures )
   9. Identify all whole number factors and pairs of factors for a number. (Factoring )
   10. Recognize that 1 is neither a prime nor a composite number. (Prime Numbers )
   11. Sort whole numbers (through 50) into sets containing only prime numbers or only composite numbers. (Prime Numbers )
C2 Numerical Operations
   1. Select the grade-level appropriate operation to solve word problems.
   2. Solve word problems using grade-level appropriate operations and numbers. (Arithmetic Word Problems , Unit Cost , Fraction Word Problems )
   3. Multiply whole numbers. (Long Multiplication )
   4. Divide with whole numbers. (Long Division , Long Division with Remainders )
   5. Demonstrate the distributive property of multiplication over addition. (Distributive Property , Basic Distributive Property )
   6. Demonstrate the addition and multiplication properties of equality.
   7. Apply grade-level appropriate properties to assist in computation.
   8. Apply the symbol "[ ]" to represent grouping.
   9. Use grade-level appropriate mathematical terminology.
   10. Simplify fractions to lowest terms. (Basic Fraction Simplification , Fraction Simplification )
   11. Add or subtract proper fractions and mixed numbers with like denominators with regrouping. (Fraction Addition , Fraction Subtraction )
   12. Add or subtract decimals. (Decimal Addition , Decimal Subtraction )
   13. Multiply decimals. (Money Multiplication , Decimal Multiplication )
   14. Divide decimals. (Small Decimal Division , Money Division , Decimal Division )
   15. Simplify numerical expressions using the order of operations with grade- appropriate operations on number sets. (Using Parentheses , Order Of Operations )
C3 Estimation
   1. Solve grade-level appropriate problems using estimation. (Estimated Multiplication , Estimated Division , Estimated Multiply Divide Word Problems )
   2. Use estimation to verify the reasonableness of a calculation (e.g., Is 4.1 x 2.7 about 12?).
   3. Round to estimate quantities. (Rounding Numbers , Rounding Large Numbers , Decimal Rounding to .01 , Decimal Rounding , Estimated Addition , Estimated Subtraction , Money Addition , Money Subtraction )
   4. Estimate and measure for area and perimeter.
   5. Compare estimated measurements between U.S. customary and metric systems (e.g., A yard is about a meter.).

Data Analysis, Probability, and Discrete Mathematics

C1 Data Analysis (Statistics)
   1. Formulate questions to collect data in contextual situations.
   2. Construct a double-bar graph, line plot, frequency table, or three-set Venn diagram with appropriate labels and title from organized data.
   3. Interpret graphical representations and data displays including bar graphs (including double-bar), circle graphs, frequency tables, three-set Venn diagrams, and line graphs that display continuous data. (Bar Graphs , Line Graphs )
   4. Answer questions based on graphical representations, and data displays including bar graphs (including double-bar), circle graphs, frequency tables, three-set Venn diagrams, and line graphs that display continuous data. (Bar Graphs , Line Graphs )
   5. Identify the mode(s) and mean (average) of given data. (Mean, Median, Mode )
   6. Formulate reasonable predictions from a given set of data.
   7. Compare two sets of data related to the same investigation.
   8. Solve contextual problems using graphs, charts, and tables.
C2 Probability
   1. Name the possible outcomes for a probability experiment.
   2. Describe the probability of events as being:
        • certain (represented by 1)
        • impossible, (represented by 0), or
        • neither certain nor impossible (represented by a fraction less than 1). (Probability )
   3. Predict the outcome of a grade-level appropriate probability experiment.
   4. Record the data from performing a grade-level appropriate probability experiment.
   5. Compare the outcome of an experiment to predictions made prior to performing the experiment.
   6. Make predictions from the results of student-generated experiments using objects (e.g., coins, spinners, number cubes).
   7. Compare the results of two repetitions of the same grade-level appropriate probability experiment.
C3 Discrete Mathematics - Systematic Listing and Counting
   1. Find all possible combinations when one item is selected from each of two sets of different items, using a systematic approach. (e.g., shirts: tee shirt, tank top, sweatshirt; pants: shorts, jeans).
C4 Vertex-Edge Graphs
   1. Color maps with the least number of colors so that no common edges share the same color (increased complexity throughout grade levels).

Patterns, Algebra, and Functions

C1 Patterns
   1. Communicate a grade-level appropriate iterative pattern, using symbols or numbers.
   2. Extend a grade-level appropriate iterative pattern. (Patterns: Numbers )
   3. Solve grade-level appropriate iterative pattern problems. (Patterns: Numbers )
C2 Functions and Relationships
   1. Describe the rule used in a simple grade-level appropriate function (e.g., T-chart, input/output model). (Function Tables , Function Tables 2 )
C3 Algebraic Representations
   1. Evaluate expressions involving the four basic operations by substituting given decimals for the variable.
   2. Use variables in contextual situations.
   3. Solve one-step equations with one variable represented by a letter or symbol (e.g., 15 = 45 ÷ n). (Missing Factor , Single Variable Equations )
C4 Analysis of Change
   1. Describe patterns of change:
        • constant rate (speed of movement of the hands on a clock), and
        • increasing or decreasing rate (rate of plant growth).

Geometry and Measurement

C1 Geometric Properties
   1. Recognize regular polygons. (Quadrilateral Types , Polygon Names )
   2. Draw 2-dimensional figures by applying significant properties of each (e.g., Draw a quadrilateral with two sets of parallel sides and four right angles.).
   3. Sketch prisms, pyramids, cones, and cylinders.
   4. Identify the properties of 2- and 3-dimensional geometric figures using appropriate terminology and vocabulary.
   5. Draw points, lines, line segments, rays, and angles with appropriate labels.
   6. Recognize that all pairs of vertical angles are congruent.
   7. Classify triangles as scalene, isosceles, or equilateral. (Triangle Types )
   8. Recognize that a circle is a 360º rotation about a point.
   9. Identify the diameter, radius, and circumference of a circle. (Circle Measurements )
   10. Understand that the sum of the angles of a triangle is 180º (Triangle Angles )
   11. Draw two congruent geometric figures.
   12. Draw two similar geometric figures.
   13. Identify the lines of symmetry in a 2-dimensional shape.
C2 Transformation of Shapes
   1. Demonstrate reflections using geometric figures.
   2. Describe the transformations that created a tessellation.
C3 Coordinate Geometry
   1. Graph points in the first quadrant on a grid using ordered pairs.
C4 Measurement - Units of Measure - Geometric Objects
   1. State an appropriate measure of accuracy for a contextual situation (e.g., What unit of measurement would you use to measure the top of your desk?).
   2. Draw 2-dimensional figures to specifications using the appropriate tools (e.g., Draw a circle with a 2-inch radius.).
   3. Determine relationships including volume (e.g., pints and quarts, milliliters and liters).
   4. Convert measurement units to equivalent units within a given system (U.S. customary and metric) (e.g., 12 inches = 1 foot; 10 decimeters = 1 meter). (Distance Conversion , Time Conversion , Volume Conversion , Weight Conversion , Temperature Conversion )
   5. Solve problems involving the perimeter of convex polygons. (Perimeter )
   6. Determine the area of figures composed of two or more rectangles on a grid. (Perimeter and Area of Composite Figures )
   7. Solve problems involving the area of simple polygons. (Triangle Area , Parallelogram Area )
   8. Describe the change in perimeter or area when one attribute (length, width) of a rectangle is altered. (Area And Volume Proportions )

Structure and Logic

C1 Algorithms and Algorithmic Thinking
   1. Discriminate necessary information from unnecessary information in a given grade-level appropriate word problem.
   2. Design simple algorithms using whole numbers. (Function Tables , Function Tables 2 )
   3. Develop an algorithm or formula to calculate areas of simple polygons.
C2 Logic, Reasoning, Arguments, and Mathematical Proof
   1. Construct if...then statements.
   2. Identify simple valid arguments using if... then statements based on graphic organizers (e.g., 3-set Venn diagrams and pictures).

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