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## Arizona Math Standards - 3rd Grade

MathScore aligns to the Arizona Math Standards for 3rd 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 (through six-digit numbers).
2. Identify six-digit whole numbers in or out of order.
3. Write whole numbers through six-digits in or out of order.
4. State whole numbers, through six-digits, with correct place value, by using models, illustrations, symbols, or expanded notation (e.g., 53,941 = 50,000 + 3,000 + 900 + 40 +1).
5. Construct models to represent place value concepts for the one's, ten's, and hundred's places.
6. Apply expanded notation to model place value through 9,999 (e.g., 5,378 = 5,000 + 300 + 70 + 8). (Place Value )
7. Sort whole numbers into sets containing only odd numbers or only even numbers. (Odd or Even )
8. Compare two whole numbers, through six-digits. (Number Comparison )
9. Order three or more whole numbers through six-digit numbers (least to greatest, or greatest to least). (Order Numbers )
10. Make models that represent proper fractions (halves, thirds, fourths, eighths, and tenths).
11. Identify symbols, words, or models that represent proper fractions (halves, thirds, fourths, eighths and tenths). (Fraction Pictures )
12. Use proper fractions in contextual situations.
13. Compare two proper fractions with like denominators. (Fraction Comparison )
14. Order three or more proper fractions with like denominators (halves, thirds, fourths, eighths, and tenths).
15. Count amounts of money through \$20.00 using pictures or actual bills and coins. (Making Change 2 , Counting Money )
16. Use decimals through hundredths in contextual situations. (Counting Money )
17. Compare two decimals, through hundredths, using models, illustrations, or symbols. (Compare Decimals )
18. Order three or more decimals, through hundredths, using models, illustrations, or symbols. (Decimal Place Value , Order Decimals )
19. Determine the equivalency among decimals, fractions, and percents (e.g., half-dollar = 50¢ = 50% and 1/4 = 0.25 = 25%). (Fractions to Decimals , Decimals To Fractions , Compare Mixed Values , Positive Number Line , Percentages )
20. Identify whole-number factors and/or pairs of factors for a given whole number through 24. (Factoring )
21. Determine multiples of a given whole number with products through 24 (skip counting). (Skip Counting )
C2 Numerical Operations
1. Demonstrate the process of subtraction using manipulatives through three-digit whole numbers.
3. Subtract two three-digit whole numbers. (Long Subtraction , Long Subtraction to 1000 )
5. Select the grade-level appropriate operation to solve word problems.
6. Solve word problems using grade-level appropriate operations and numbers. (Arithmetic Word Problems , Basic Word Problems 2 )
7. Demonstrate the process of multiplication as repeatedly adding the same number, counting by multiples, combining equal sets, and making arrays. (Understanding Multiplication )
8. Demonstrate the process of division with one-digit divisors (separating elements of a set into smaller equal sets, sharing equally, or repeatedly subtracting the same number). (Understanding Division )
9. Demonstrate families of equations for multiplication and division through 9s. (Inverse Equations 2 )
10. State multiplication and division facts through 9s. (Fast Multiplication , Fast Multiplication Reverse , Multiplication Facts Strategies , Fast Division )
11. Demonstrate the commutative and identity properties of multiplication. (Commutative Property 2 )
12. Identify multiplication and division as inverse operations. (Inverse Equations 2 )
13. Apply grade-level appropriate properties to assist in computation.
14. Apply the symbols: ×, ÷, /, *, %, and the grouping symbols ( ) and ",".
15. Use grade-level appropriate mathematical terminology.
16. Add or subtract fractions with like denominators (halves, thirds, fourths, eighths, and tenths) appropriate to grade level. (Basic Fraction Addition , Basic Fraction Subtraction )
17. Apply addition and subtraction in contextual situations, through \$20.00. (Money Addition , Money Subtraction , Making Change )
C3 Estimation
1. Solve grade-level appropriate problems using estimation.
2. Estimate length and weight using U.S. customary units.
3. Record estimated and actual linear measurements for real-life objects (e.g., length of fingernail; height of desk). (Requires outside materials )
4. Compare estimations of appropriate measures to the actual measures. (Estimated Addition , Estimated Subtraction )
5. Evaluate the reasonableness of estimated measures.

## Data Analysis, Probability, and Discrete Mathematics

C1 Data Analysis (Statistics)
1. Formulate questions to collect data in contextual situations.
2. Construct a horizontal bar, vertical bar, pictograph, or tally chart with appropriate labels and title from organized data.
3. Interpret data found in line plots, pictographs, and single-bar graphs (horizontal and vertical). (Tally and Pictographs , Bar Graphs , Line Graphs )
4. Answer questions based on data found in line plots, pictographs, and single-bar graphs (horizontal and vertical). (Tally and Pictographs , Bar Graphs , Line Graphs )
5. Formulate questions based on graphs, charts, and tables to solve problems.
6. Solve problems using graphs, charts and tables. (Tally and Pictographs , Bar Graphs , Line Graphs )
C2 Probability
1. Name the possible outcomes for a probability experiment.
2. Make predictions about the probability of events being more likely, less likely, equally likely or unlikely.
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. Compare the results of two repetitions of the same grade-level appropriate probability experiment.
C3 Discrete Mathematics - Systematic Listing and Counting
1. Make a diagram to represent the number of combinations available when 1 item is selected from each of 3 sets of 2 items (e.g., 2 different shirts, 2 different hats, 2 different belts).
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. (Patterns: Shapes )
2. Extend a grade-level appropriate repetitive pattern (e.g., 5, 10, 15, 20, . . . rule: add five or count by five's). (Patterns: Numbers )
3. Solve grade-level appropriate pattern problems.
C2 Functions and Relationships
1. Describe the rule used in a simple grade-level appropriate function (e.g., T-chart, input/output model, and frames and arrows). (Function Tables , Function Tables 2 )
C3 Algebraic Representations
1. Use variables in contextual situations.
2. Solve equations with one variable using missing addends to sums of 18 (e.g., ? + 9 = 18, 9 + ? = 18); and using minuend through 18 (e.g., 18 - ? = 9, 18 - 9 = ?). (Missing Term )
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., increases in allowance as you get older). (Line Graphs )

## Geometry and Measurement

C1 Geometric Properties
1. Build geometric figures with other common shapes (e.g., tangrams, pattern blocks, geoboards).
2. Name concrete objects and pictures of 3-dimensional solids (cones, spheres, and cubes).
3. Describe relationships between 2-dimensional and 3-dimensional objects (squares/cubes, circles/spheres, triangles/cones).
4. Recognize similar shapes. (Congruent And Similar Triangles )
5. Identify a line of symmetry in a 2-dimensional shape.
C2 Transformation of Shapes
1. Recognize same shape in different positions (turn/rotation).
C3 Coordinate Geometry
1. Identify points in the first quadrant of a grid using ordered pairs.
C4 Measurement - Units of Measure - Geometric Objects
1. Select the appropriate measure of accuracy:
• length - cetimeters, meters, kilometers,
• capacity/volume - liters, and
• mass/weight - grams.
2. Tell time with one-minute precision (analog). (Telling Time )
3. Determine the passage of time across months (units of days, weeks, months) using a calendar.
4. Measure a given object using the appropriate unit of measure:
• length - centimeters, millimeters, meters, kilometers,
• capacity/volume - liters, and
• mass/weight - grams.
5. Record temperatures to the nearest degree in degrees Fahrenheit and degrees Celsius as shown on a thermometer.
6. Compare units of measure to determine more or less relationships for:
• length - inches to feet; centimeters to meters
• time - minutes to hours; hours to days; days to weeks; months to years, and
• money - pennies, nickels, dimes, quarters, and dollars.
7. Determine relationships for:
• volume - cups and gallons
• weight - ounces and pounds
• money - extend to amounts greater than one dollar.
8. Compare the length of two objects using U.S. customary or metric units.
9. Determine the perimeter using a rectangular array.
10. Represent area using a rectangular array.

## Structure and Logic

C1 Algorithms and Algorithmic Thinking
1. Discriminate necessary information from unnecessary information in a given grade-level appropriate word problem.
C2 Logic, Reasoning, Arguments, and Mathematical Proof
1. Draw conclusions based on existing information (e.g., All students in Ms. Dean's 1st grade class are less than 7 years old. Rafael is in Ms. Dean's class. Conclusion: Rafael is less than 7 years old.).