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By Michael Surran (Students taking a computerized exam) [CC BY-SA 2.0],

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Credit to: Arizona Math Standard for 3rd Grade

Credit to: Arizona Math Computer Based Sample Test for 3rd Grade

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(State Math Exam for Arizona)

Student are expected to learn how to compare two fractions. In doing comparison students are expected to understand the meaning of greater than symbol > , less than symbol < and equal symbol =

Student must remember the rule in comparing two fraction with common denominators, 1/5 and 3/5 the wholes have been divided into the same of equal parts. So the fraction with the larger number numerator has the larger number of equal parts. Therefore the bigger fraction.

To compare two fractions that have the same numerator but different denominators, student must remember the rule. The fraction with bigger number of denominator means it has smaller pieces of equal parts, 2/5 and 2/3 Therefore the smaller fraction.

To compare two fractions with no common numerator and denominator , the rule is to cross multiply the numerator and denominator on both fractions, 1/2 and 2/3 . Next apply the rule of common denominator 3 ⁄ 6 and 4 ⁄ 6

In computer based State examination, student will use the fraction format and insert the correct fraction or select the correct letter

Student must remember the rule in comparing two fraction with common denominators, 1/5 and 3/5 the wholes have been divided into the same of equal parts. So the fraction with the larger number numerator has the larger number of equal parts. Therefore the bigger fraction.

To compare two fractions that have the same numerator but different denominators, student must remember the rule. The fraction with bigger number of denominator means it has smaller pieces of equal parts, 2/5 and 2/3 Therefore the smaller fraction.

To compare two fractions with no common numerator and denominator , the rule is to cross multiply the numerator and denominator on both fractions, 1/2 and 2/3 . Next apply the rule of common denominator 3 ⁄ 6 and 4 ⁄ 6

In computer based State examination, student will use the fraction format and insert the correct fraction or select the correct letter

Students are expected to learn the operation of division. Division is use to classify how many groups of same object. Division is also use to describe equal sharing or fraction. To develop this understanding , students interpret a problem requiring division using picture, objects, words, numbers, and equations. Student should remember the meaning of terminology like quotient, dividend, divisor, and factor.

In computer based State examination, student will select the correct number or correct letter.

In computer based State examination, student will select the correct number or correct letter.

Measurement and Data (MD) Geometric measurement: Student are expected to learn the concept of area and relate area to multiplication and to addition. Measure areas by counting unit squares ( square cm, square m, square in, square ft, and improvised units).

In computer based State examination, student will select the correct number or correct letter.

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In computer based State examination, student will select the correct number or correct letter.

Students are expected to learn that fractional parts must be equal-sized. For example when a whole pizza is cut into equal parts.

Students are given advance concept of vertex-graph for measurement and estimation. Like estimating the shortest distance or shortest travel time while practicing their addition skill.

Students are expected to learn that fractional parts must be equal-sized. Students are expected to learn the concept of number line or benchmarking in order to compare two fractions and be able to determine which is greater meaning closer to 1. A fraction closer to 0 means lesser value.

Students are expected to learn to explain their thinking to others and critique the reasoning of others. They are encourage to ask "how did you get that?" or Why is that true? or Does this make sense?

Student are expected to do addition and subtracton using the place value in base ten.

Student are expected to learn the important concept of estimating for measurement of interval of time, liquid volumes or counts of objects.

Student are expected to learn the important concept that arithmetic operation like multiplication can be model by grouping of shapes or pictures or objects.

Student are expected to learn the important concept that arithmetic operation like subtraction can be model by a blank box. The blank box is use to represent the number that will make the number on both sides of the equal sign the same. The students are slowly learning the concept of equation or equality which is actually doing simple algebraic calculation.

Student are expected to learn the important concept comparing fraction , the concept of in between two fractions (also called the range). The students are slowly learning the concept of evaluation, estimation and learning the usefulness of the number line to explain their reasoning to other.

**12a) additional question: without drawing a benchmark fraction, which is greater between the two fraction 3/6 and 5/6**.

**12b) additional question: without drawing a benchmark fraction, which is greater between the two fraction 3/10 and 3/8**.

Student are expected to learn the important concept of estimating for measurement of interval of time, liquid volumes or counts of objects.

Student are expected to identify common geometric shapes and be able to explain to others the definition or attributes of each shapes. This is slowly preparing them to the concept of measurement of area , perimeter, and circumference. Geometric shapes discussion is a good training for students to practice their reasoning and communication skill explaining why the answer make sense.

Student are expected to learn to discover pattern from series of numbers. Discovering pattern is a good training for students to practice their reasoning and communication skill explaining why the answer make sense. Discovering pattern not only involve numbers it could be hand-writing recognition, voice recognition and facial recognition. Pattern recognition is used in artificial intelligence.

**21a **The relationship can be given by a table, model, or input/output (function) machine.

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