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Arizona Math Standards - 4th Grade

MathScore aligns to the Arizona Math Standards for 4th 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.

View the Arizona Math Standards at other levels.

Number Sense and Operations

C1 Number Sense
1. Read whole numbers in contextual situations.
2. Identify whole numbers in or out of order.
3. Write whole numbers in or out of order.
4. State place values for whole numbers (e.g., In the number 203,495 what is the value of the 2?). (Place Value )
5. Construct models to represent place value concepts for the one's, ten's, hundred's, and thousand's places.
6. Apply expanded notation to model place value (e.g., 203,495 = 200,000 + 3,000 + 400 + 90 + 5). (Place Value )
7. Compare two whole numbers. (Number Comparison )
8. Order three or more whole numbers. (Order Numbers , Order Large Numbers )
9. Make models that represent mixed numbers.
10. Identify symbols, words, or models that represent mixed numbers.
11. Use mixed numbers in contextual situations. (Fraction Word Problems )
12. Compare two unit fractions (e.g., 1/2 to 1/5) or proper or mixed numbers with like denominators. (Fraction Comparison )
13. Order three or more unit fractions or proper or improper fractions with like denominators.
14. Use decimals in contextual situations.
15. Compare two decimals. (Compare Decimals )
16. Order three or more decimals. (Decimal Place Value , Order Decimals )
17. Determine the equivalency among decimals, fractions, and percents (e.g., 49/100 = 0.49 = 49%). (Fractions to Decimals , Decimals To Fractions , Compare Mixed Values , Positive Number Line , Percentages )
18. Identify all whole number factors and pairs of factors for a given whole number through 144. (Factoring )
19. Determine multiples of a given whole number with products through 144. (Fast Multiplication , Fast Multiplication Reverse , Multiplication Facts Strategies )
C2 Numerical Operations
2. Subtract whole numbers. (Long Subtraction )
3. Select the grade-level appropriate operation to solve word problems.
4. Solve word problems using grade-level appropriate operations and numbers. (Arithmetic Word Problems , Basic Word Problems 2 , Word Problems With Remainders )
5. Multiply multi-digit numbers by two-digit numbers. (Multiplication By One Digit , Long Multiplication )
6. Divide with one-digit divisors. (Long Division By One Digit , Division with Remainders )
7. State multiplication and division facts through 12s. (Fast Multiplication , Fast Multiplication Reverse , Multiplication Facts Strategies , Fast Division )
8. Demonstrate the associative property of multiplication. (Associative Property 2 )
9. Apply grade-level appropriate properties to assist in computation.
10. Apply the symbol: • and ( ) for multiplication, and ≤, ≥ .
11. Use grade-level appropriate mathematical terminology.
12. Add or subtract fractions with like denominators, no regrouping. (Basic Fraction Addition , Basic Fraction Subtraction )
13. 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.
2. Use estimation to verify the reasonableness of a calculation (e.g., Is 3284 x 343 = 1200 reasonable?).
3. Estimate length and weight using both U.S. customary and metric units.
4. Estimate and measure for distance.

Data Analysis, Probability, and Discrete Mathematics

C1 Data Analysis (Statistics)
1. Formulate questions to collect data in contextual situations.
2. Construct a single-bar graph, line graph or two-set Venn diagram with appropriate labels and title from organized data.
3. Interpret graphical representations and data displays including single-bar graphs, circle graphs, two-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 single-bar graphs, circle graphs, two-set Venn diagrams, and line graphs that display continuous data. (Bar Graphs , Line Graphs )
5. Identify the mode(s) of given data.
6. Formulate predictions from a given set of data.
7. Solve contextual problems using graphs, charts, and tables. (Bar Graphs , Line Graphs )
C2 Probability
1. Name the possible outcomes for a probability experiment.
2. Describe the probability of events as being more likely, less likely, equally likely, unlikely, certain, impossible, fair or unfair.
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 containing up to three objects (e.g., How many outfits can be made with 3 pants and 2 tee shirts?).
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. Create grade-level appropriate iterative patterns.
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 whole numbers for the variable. (Variable Substitution )
2. Use variables in contextual situations.
3. Solve one-step equations with one variable represented by a letter or symbol using multiplication of whole numbers (e.g., 12 = n x 4). (Missing Factor )
C4 Analysis of Change
1. Identify the change in a variable over time (e.g., an object gets taller, colder, heavier). (Line Graphs )
2. Make simple predictions based on a variable (e.g., increase homework time as you progress through the grades). (Line Graphs )

Geometry and Measurement

C1 Geometric Properties
1. Identify the properties of 2-dimensional figures using appropriate terminology.
2. Identify models or illustrations of prisms, pyramids, cones, cylinders, and spheres.
3. Draw points, lines, line segments (open or closed endpoints), rays, or angles.
4. Classify angles (e.g., right, acute, obtuse, straight).
5. Classify triangles as right, acute, or obtuse. (Triangle Types )
6. Identify congruent geometric shapes. (Congruent And Similar Triangles )
7. Identify similar shapes. (Congruent And Similar Triangles )
8. Draw a 2-dimensional shape that has line symmetry.
C2 Transformation of Shapes
1. Demonstrate translation using geometric figures.
2. Identify a tessellation.
C3 Coordinate Geometry
1. Name the coordinates of a point plotted in the first quadrant.
C4 Measurement - Units of Measure - Geometric Objects
1. Identify the appropriate measure of accuracy for the area of an object (e.g., sq. feet or sq. miles).
2. Compute elapsed time using a clock (e.g., hours and minutes since or until...) or a calendar (e.g., days, weeks, years since or until...). (Time Intervals )
3. Select an appropriate tool to use in a particular measurement situation.
4. Approximate measurements to the appropriate degree of accuracy.
5. Compare units of measure to determine more or less relationships including:
• length - yards and miles; meters and kilometers
• weight - pounds and tons; grams and kilograms.
6. State equivalent relationships (e.g., 3 teaspoons = 1 tablespoon, 16 cups = 1 gallon, 2000 pounds = 1 ton.
7. Compare the weight of two objects using both U.S. customary and metric units.
8. Determine the perimeter of simple polygons (e.g., square, rectangle, triangle). (Perimeter )
9. Determine the area of squares and rectangles. (Compare Rectangle Area and Perimeter )
10. Differentiate between perimeter and area of quadrilaterals. (Compare Rectangle Area and Perimeter )

Structure and Logic

C1 Algorithms and Algorithmic Thinking
1. Discriminate necessary information from unnecessary information in a given grade-level appropriate word problem.
2. Develop an algorithm to calculate the perimeter of simple polygons.
C2 Logic, Reasoning, Arguments, and Mathematical Proof
1. Draw a conclusion from a Venn diagram.
2. Identify simple valid arguments using if...then statements based on graphic organizers (e.g., 2-set Venn diagrams and pictures).