Older Resources. The resources on this page have been aligned with the 2005–06 revised K–12 mathematics TEKS. However, they have not been fully updated with new material.

For fully updated versions of these activities, please consider purchasing Mathematics Standards in the Classroom.

Clarifying Activities with Assessment Connections

Grade 3

(a) Introduction

(1) Within a well-balanced mathematics curriculum, the primary focal points at Grade 3 are multiplying and dividing whole numbers, connecting fraction symbols to fractional quantities, and standardizing language and procedures in geometry and measurement.

(2) Throughout mathematics in Grades 3-5, students build a foundation of basic understandings in number, operation, and quantitative reasoning; patterns, relationships, and algebraic thinking; geometry and spatial reasoning; measurement; and probability and statistics. Students use algorithms for addition, subtraction, multiplication, and division as generalizations connected to concrete experiences; and they concretely develop basic concepts of fractions and decimals. Students use appropriate language and organizational structures such as tables and charts to represent and communicate relationships, make predictions, and solve problems. Students select and use formal language to describe their reasoning as they identify, compare, and classify two- or three-dimensional geometric figures; and they use numbers, standard units, and measurement tools to describe and compare objects, make estimates, and solve application problems. Students organize data, choose an appropriate method to display the data, and interpret the data to make decisions and predictions and solve problems.

(3) Throughout mathematics in Grades 3-5, students develop numerical fluency with conceptual understanding and computational accuracy. Students in Grades 3-5 use knowledge of the base-ten place value system to compose and decompose numbers in order to solve problems requiring precision, estimation, and reasonableness. By the end of Grade 5, students know basic addition, subtraction, multiplication, and division facts and are using them to work flexibly, efficiently, and accurately with numbers during addition, subtraction, multiplication, and division computation.

(4) Problem solving, language and communication, connections within and outside mathematics, and formal and informal reasoning underlie all content areas in mathematics. Throughout mathematics in Grades 3-5, students use these processes together with technology and other mathematical tools such as manipulative materials to develop conceptual understanding and solve meaningful problems as they do mathematics.

(b) Knowledge and skills

(3.1) Number, operation, and quantitative reasoning. The student uses place value to communicate about increasingly large whole numbers in verbal and written form, including money.

(3.1.a) Number, operation, and quantitative reasoning. The student uses place value to communicate about increasingly large whole numbers in verbal and written form, including money. The student is expected to use place value to read, write (in symbols and words), and describe the value of whole numbers through 999,999.

Clarifying Activity with Assessment Connections

Students play a game in which they try to build the largest number possible. Each player draws a game board as shown:

six blanks

Players take turns rolling a ten-sided number polyhedron or spinning a spinner labeled with numbers zero through nine. After each roll or spin, every player writes that number as a digit in one space on his or her game board. Once written, that digit cannot be moved. The winner has the largest number and can read it.

Assessment Connections
Questioning . . .

Open with . . .

  • Do you think you have made the greatest number and will win? Why or why not?

Probe further with . . .

  • What is your number?
  • How can you write your number with words?
  • Who has made the greatest number? What is it? How did you decide this is the greatest number?
  • Who has a 3 in the thousands place?
  • Whose number is closest to your number? How did you decide this is the closest number to yours?
  • Order all the numbers. How did you go about putting these numbers in order?
  • What strategy did you use to make your number?
  • What is the greatest number you can create by moving the digits of your number?
  • What is the lowest number you can create by moving the digits of your number? What strategy would you try the next time you play this game?
Listen for . . .
  • Does the student accurately read the six-digit numbers using patterns to name the numbers? (Caution: Students should use "and" only to indicate a decimal point.)
  • Does the student clearly describe the strategy used to create large numbers?
  • Does the student clearly describe the strategy used to compare and order numbers?
  • Does the student use ideas of place value to explain and justify strategies and responses?
Look for . . .
  • Does the student use place value and patterns in number relationships to compare and order six-digit numbers?
  • Does the student demonstrate an understanding of place value in strategies for the game?
  • Can the student identify the different values of the different places in a number?
  • Does the student recognize the relative values of the places in a number?
  • Can the student write the number in words?
TAKS Connection

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's Released Tests and Interactive Online Tests, Spring 2001 Mathematics TAAS. Reprinted with permission.

(3.1.b) Number, operation, and quantitative reasoning. The student uses place value to communicate about increasingly large whole numbers in verbal and written form, including money. The student is expected to use place value to compare and order whole numbers through 9,999.

Clarifying Activity with Assessment Connections

The teacher posts an unlabeled, classroom-sized number line and distributes a variety of whole numbers (up to four digits) on index cards. Students use place value to justify the placement of each number on the number line.

Assessment Connections
Questioning . . .

Open with . . .

  • How are you going to decide where to place your number on the number line?

Probe further with . . .

  • What is your number?
  • Who has the greatest number we are going to place on the number line? How do you know?
  • Who has the least number we are going to place on the number line? How do you know?
  • Could you decide where your number belongs if there were no other numbers marked on the number line (benchmarks)?
  • Could you decide where your number belongs if ___ were the only number marked on the number line? What are some numbers you think you would need to know on the number line to be able to decide where your number goes?
  • How do you know your number is on this side of ______?
  • How do you know how far away from _________ to place your number?
Listen for . . .
  • Does the student accurately read the numbers using the proper number naming patterns?
  • Does the student clearly describe a reasonable strategy for placing the numbers on the number line?
  • Does the student's strategy and explanations involve place value and benchmarks?
Look for . . .
  • Can the student place numbers on a number line fairly accurately?
  • Does the student demonstrate a good grasp of the number system and place value?
  • Does the student apply useful benchmark numbers to guide in developing the number line and placing the number?
  • Does the student successfully compare and order numbers on the given number line?
  • Does the student use place value and patterns in number relationships to compare, order, and place numbers on the given number line?
TAKS Connection

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's Released Tests and Interactive Online Tests, Spring 2001 Mathematics TAAS. Reprinted with permission.

(3.1.c) Number, operation, and quantitative reasoning. The student uses place value to communicate about increasingly large whole numbers in verbal and written form, including money. The student is expected to determine the value of a collection of coins and bills.

Clarifying Activity with Assessment Connections

Students use play money to model the story, Alexander Who Used to Be Rich Last Sunday, by Judith Viorst. As students are reading the story, they determine and compare the different collections of coins and bills that can be used to represent each amount.

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me about the money Alexander has at this point in the story.

Probe further with . . .

  • How much money does Alexander have left? How did you determine this? Show me how you counted the money.
  • Can you add up the money in a different way to be sure Alexander does have ____ left?
  • What are some other collections of coins and bills Alexander could have that are the same amount as the money here? How did you find these other collections?
  • What is the fewest number of coins or bills you could use to show how much money Alexander has left? How did you decide this?
  • How much money did Alexander have to start?
  • Can you make a collection of money to show me how much has been spent so far? How did you do this?
  • How much money has Alexander spent?
  • Has Alexander spent more money than he has left? How do you know?
Listen for . . .
  • Can the student tell the names and values of the coins?
  • Does the student use appropriate counting procedures and accurately count the money? (25, 30, 40, 50)
  • Does the student demonstrate efficient counting techniques?
Look for . . .
  • Does the student accurately represent the action in the story?
  • Does the student appropriately exchange money for different denominations?
  • What strategy does the student use to find different money collections worth the same amount?
  • Can the student count the collection of money in more than one way?
  • Does the student organize the money to help count?
  • Does the student start with efficient counting techniques?
  • Can the student compare different collections of money? What strategy does the student use to compare the collections? Does the student use direct comparison based on numbers and types of coins in the collection or compare based on sums?
  • Does the student self-monitor and self-correct when counting?
TAKS Connection

Click here for a larger version of the TAKS item.

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's Released Tests and Interactive Online Tests, Spring 2001 Mathematics TAAS. Reprinted with permission.

Additional Clarifying Activity with Assessment Connections

Students set up a store in the classroom and show with play coins and bills the amount of money needed to purchase each item.

Assessment Connections
Questioning . . .

Open with . . .

  • How do you decide if you have enough money to buy what you want?

Probe further with . . .

  • What is the fewest number of coins or bills you could use to buy this item?
  • What are some other collections of coins or bills you could use to buy this item?
  • How much change would you get? What collection of money might your change be?
  • Do you have enough money left to buy something else? What else can you buy with your change?
Listen for . . .
  • Can the student give the names and values of the coins and bills in the collections?
  • Does the student accurately count the money? (25, 30, 40, 50)
  • Does the student demonstrate efficient counting techniques (counting by fives and tens when appropriate)?
  • Does the student check for reasonableness of the results?
Look for . . .
  • Is the student selecting items that are appropriate for the amount of money available?
  • Does the student appropriately exchange money for different denominations?
  • Can the student count a collection of money in more than one way?
  • Does the student organize the money to help in counting?
  • Does the student start with efficient counting techniques?
  • Can the student determine correct change? Does the student count on or subtract the cost from the total to determine the amount of the change?
  • Does the student self-monitor and self-correct?

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(3.2) Number, operation, and quantitative reasoning. The student uses fraction names and symbols (with denominators of 12 or less) to describe fractional parts of whole objects or sets of objects.

(3.2.a) Number, operation, and quantitative reasoning. The student uses fraction names and symbols (with denominators of 12 or less) to describe fractional parts of whole objects or sets of objects. The student is expected to construct concrete models of fractions.

Clarifying Activity with Assessment Connections

After reading a book such as Fractions Are Parts of Things, by J. Richard Dennis, students use a variety of concrete objects (such as two-color counters, coins, pattern blocks, Cuisenaire® rods, color tiles, or linking cubes) to model fractions written on index cards. For example, for 3/4, one student places 4 coins on the table with 3 heads and 1 tail and reports, "Three-fourths of the coins are heads." Another student uses color tiles to build a rectangle that is 3/4 red and 1/4 green.

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me about the model of your fraction.

Probe further with . . .

  • What is your fraction?
  • How did you decide to use this model?
  • How does your model show the numerator and denominator of 3/4?
  • How many heads are in your collection? (3)
  • How much of the collection is heads? (3/4)
  • How much of the collection is not heads? (1/4)
  • In addition to 3/4, what other fraction does this collection model? Why?
  • How can you write the fraction for your model?
  • What are some other ways you could use to model 3/4?
Listen for . . .
  • Does the student use appropriate language to talk about the fraction?
  • Does the student have an understanding of the concept of a fraction describing part of a whole?
Look for . . .
  • Can the student construct a concrete model of a fraction?
  • Does the student notice that there are a variety of models that can be used to represent a particular fraction?
  • Does the student notice that a particular model can represent more than one fraction? (For example, if there are three heads and one tail showing, then the fraction 3/4 is modeled since 3/4 of the coins show heads. Also, this models 1/4, since 1/4 of the coins are not heads but tails.)
  • Is the student able to write the fraction for his or her model?
TAKS Connection
  • This student expectation is not tested on TAKS. Although this is not directly tested at Grade 3, it is an important foundation for student expectations tested at later grades.

(3.2.b) Number, operation, and quantitative reasoning. The student uses fraction names and symbols (with denominators of 12 or less) to describe fractional parts of whole objects or sets of objects. The student is expected to compare fractional parts of whole objects or sets of objects in a problem situation using concrete models.

Clarifying Activity with Assessment Connections

Pairs of students use appropriate concrete objects (such as two-color counters, coins, pattern blocks, Cuisenaire® rods, color tiles, or interlocking cubes) to represent and compare two fractions. For example, each student makes a bar by connecting 15 interlocking cubes to represent one whole. One student breaks her bar into thirds, while another student breaks his bar into fifths to compare 1/3 and 1/5.

Assessment Connections
Questioning . . .

Open with . . .

  • What can you tell me about your fractions?

Probe further with . . .

  • Ask the first student: How many cubes were in your whole bar? (15)
  • How many cubes are in this part of the bar that was broken off? (5)
  • How much of the bar was broken off? (1/3)
  • How would you write this fraction?
  • Ask the other student: How many cubes are in this part of the bar that was broken off? (3)
  • How much of the bar was broken off here? (1/5)
  • How would you write this fraction?
  • Which fraction is greater, 1/3 or 1/5? How do you know?
  • Draw a figure to represent the bar and the pieces that were broken off.
  • How much would you need to add to 1/3 to make a whole? (2/3 or 10/15)
  • Which is greater, 1/3 or the fractional part you needed to add to make a whole?
Listen for . . .
  • Does the student use fractions to answer "how much" questions?
  • Does the student use appropriate vocabulary?
  • Does the student communicate an understanding of the concept of fraction?
  • Can the student communicate how he or she compares fractions?
Look for . . .
  • Can the student create a concrete model for fractional parts of whole objects?
  • Can the student use symbols to write the fractions?
  • Can the student compare fractional parts of whole objects using a concrete model?
  • Is the student able to demonstrate how to make one whole from a fractional part?
  • Can the student draw a representation of the fractions?
TAKS Connection

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's Released Tests and Interactive Online Tests, Spring 2001 Mathematics TAAS. Reprinted with permission.

(3.2.c) Number, operation, and quantitative reasoning. The student uses fraction names and symbols (with denominators of 12 or less) to describe fractional parts of whole objects or sets of objects. The student is expected to use fraction names and symbols to describe fractional parts of whole objects or sets of objects.

Clarifying Activity with Assessment Connections

Students reach into a bag containing blue and green linking cubes. They snap them together into a two-color train (or rectangle) and record the fraction of the train that is blue and the fraction of the train that is green. For example, one student snaps together five cubes, two of which are green.

Assessment Connections
Questioning . . .

Open with . . .

  • What can you tell me about your set of cubes?

Probe further with . . .

  • How many cubes in your train are green? (2)
  • How many cubes are in your whole train? (5)
  • How much of your train is green? (2/5)
  • What part of your train is blue? (3 out of 5 or 3/5)
  • Take your cubes apart and put them together in a different order. Now how much of your train is green? (2/5)
  • What do you notice about the fractions when you changed the order of the cubes?
  • Color a figure (grid strip, sectioned circle, sectioned rectangle, or other sectioned figure) to show the make-up of your train.
  • How would you write a fraction for the green part? blue part?
Listen for . . .
  • Is the student using fractions to answer "how much" questions?
Look for . . .
  • Does the student recognize that the order of the cubes does not affect the fractions?
  • Can the student represent his or her train in another form by coloring in a grid strip, sectioned circle, sectioned rectangle, or other sectioned figure?
TAKS Connection

Click here for a larger version of the TAKS item.

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's TAKS Information Booklets, January 2002. Reprinted with permission.

(3.2.d) Number, operation, and quantitative reasoning. The student uses fraction names and symbols (with denominators of 12 or less) to describe fractional parts of whole objects or sets of objects. The student is expected to construct concrete models of equivalent fractions for fractional parts of whole objects.

Clarifying Activity with Assessment Connections

Pairs of students use a paper model of a rectangle, fold it into equal parts, open it, and mark the folds with a color marker. They refold the rectangle, add additional folds to create smaller equal parts, open the rectangle, identify equivalent fractions, and record their findings. They refold and continue. Eventually they start the process over with a new rectangle and a different set of folds.

For example, a pair of students folds a rectangle in half. They open it and color along the crease. They refold the rectangle into three equal parts, and then open it and identify that 1/2 is equal to 3/6. They record their findings. Then they refold the rectangle, fold it in half again, and find that 1/2 is equal to 6/12. They continue, finding other fractions equivalent to 1/2. After the rectangle is difficult to fold any further, the pair starts over with another paper rectangle to find fractions equivalent to 2/3.

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me about the fractions that you can model using the geometric shape you are folding.

Probe further with . . .

  • What is another fraction name for 1/2? How do you know?
  • How do you know this fraction is equivalent to 1/2?
  • How would you find other fractions equivalent to 1/2?
  • List some of the fractions equivalent to 1/2.
  • What do you notice about the equivalent fractions?
  • What fraction could you model if you fold the shape one more time?
Listen for . . .
  • Does the student use mathematical language to describe how to generate equivalent fractions?
Look for . . .
  • Can the student list equivalent fractions to 1/2?
  • Can the student use folding geometric shapes to generate equivalent fractions?
  • Does the student notice patterns in the list of equivalent fractions?
  • Are the folded parts of the geometric shapes congruent?
TAKS Connection
  • This student expectation is not tested on TAKS. Although this is not directly tested at Grade 3, it is an important foundation for student expectations tested at later grades.

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(3.3) Number, operation, and quantitative reasoning. The student adds and subtracts to solve meaningful problems involving whole numbers.

(3.3.a) Number, operation, and quantitative reasoning. The student adds and subtracts to solve meaningful problems involving whole numbers. The student is expected to model addition and subtraction using pictures, words, and numbers.

Clarifying Activity with Assessment Connections

Given expressions such as 23 + 56 =, students find a solution, and then write original story problems to fit the number sentences. In pairs, students trade their story problems, work each other's problems, and compare solutions to determine accuracy.

Assessment Connections
Questioning . . . (before trading problems)

Open with . . .

  • Tell me about your problem.

Probe further with . . .

  • What did you think about when you were creating your problem?
  • Can your problem be solved with your number sentence?
Listen for . . .
  • Does the student's explanation match the written work?
  • Does the student use words that describe the act of separating or combining?
Look for . . .
  • Can the student identify word problems that can be solved with a given number sentence?
  • Does the student pose a problem that can be solved by the operation described in the number sentence?
  • Does the student pose a problem that is clear and can be easily interpreted by the partner?
Questioning . . . (after trading problems)

Open with . . .

  • What is the question in the problem you're working? Tell me about your thinking.

Probe further with . . .

  • How are you solving the problem? Why?
  • Can you show a picture that may help you solve the problem?
  • Is your solution reasonable?
  • Can you solve the problem another way?
  • What number sentence could you write to show your problem?
Listen for . . .
  • Is the student describing the action in the problem? (joining, separating,comparing)
  • Is the student using words like "add" and "subtract?"
  • Is the student talking about whether the answer is reasonable?
  • Does the student's explanation match the written work?
Look for . . .
  • Can the student identify the information necessary to solve the problem?
  • Can the student use addition or subtraction to solve problems involving whole numbers?
  • Does the student select manipulatives or draw a picture to help solve the problem?
  • Does the student solve the problem in more than one way?
  • Does the number sentence match the student's explanation?
  • Does the student self-monitor and self-correct?
TAKS Connection

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's Released Tests and Interactive Online Tests, Spring 2001 Mathematics TAAS. Reprinted with permission.

(3.3.b) Number, operation, and quantitative reasoning. The student adds and subtracts to solve meaningful problems involving whole numbers. The student is expected to select addition or subtraction and use the operation to solve problems involving whole numbers through 999.

Clarifying Activity with Assessment Connections

Students use information from a baseball card to answer mathematical questions such as, "How old was the baseball player when he had his best slugging record? Did he get more hits his first three years in professional baseball, or in his last three years? How would you figure this out?"

Assessment Connections
Questioning . . .

Open with . . .

  • How did you find the answer to your question?

Probe further with . . .

  • What operation did you use? Why?
  • What number sentence could you write to show your solution?
  • Can you solve the problem another way?
  • Is your solution reasonable?
Listen for . . .
  • Is the student describing the action in the problem? (joining, separating, comparing)
  • Is the student using words like "add" and "subtract?"
  • Is the student talking about whether the answer is reasonable?
Look for . . .
  • Does the number sentence match the student's explanation?
  • Does the student try to solve the problem in more than one way?
  • Does the student select the necessary information from the card to solve the problem?
  • Does the student self-monitor and self-correct?
TAKS Connection

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's Released Tests and Interactive Online Tests, Spring 2001 Mathematics TAAS. Reprinted with permission.

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(3.4) Number, operation, and quantitative reasoning. The student recognizes and solves problems in multiplication and division situations.

(3.4.a) Number, operation, and quantitative reasoning. The student recognizes and solves problems in multiplication and division situations. The student is expected to learn and apply multiplication facts through 12 by 12 using concrete models and objects.

activity under revision

Clarifying Activity with Assessment Connections

Students use rectangular tiles to build all rectangles that represent the numbers 1 through 25 and investigate the rectangles that result.

For example, the rectangles for three are

rectangles

The rectangles for four are

rectangles

The rectangles for six are

rectangles

Assessment Connections
Questioning . . .

Open with . . .

  • What do you notice about your findings?

Probe further with . . .

  • How many different rectangles did you make with 4 tiles?
  • What are the number sentences that go with the arrangements that you made?
  • How many rectangles with an area of 6 did you make?
  • What are the number sentences that go with the arrangements that you made?
  • What do you notice about the collections of number sentences that go with 4 and 6?
  • How do the collections of number sentences for 4 and 6 compare? How are they alike? How are they different?
  • How do the arrangements of 4 and 6 compare?
  • Have you found all of the number sentences that go with 4 and 6? How do you know?
Listen for . . .
  • Does the student describe patterns in their number sentence? (relationship to multiplication facts)
  • Does the student use words that describe multiplication?
Look for . . .
  • Do the student's number sentences match the rectangles?
  • Are all the rectangles represented?
  • Does the student relate the multiplication facts to the rectangles?
TAKS Connection
  • This student expectation is not tested on TAKS. Although this is not directly tested at Grade 3, it is an important foundation for student expectations tested at later grades.

(3.4.b) Number, operation, and quantitative reasoning. The student recognizes and solves problems in multiplication and division situations. The student is expected to solve and record multiplication problems (up to two digits times one digit).

activity under revision

Clarifying Activity with Assessment Connections

Students brainstorm lists of things that come in sixes, sevens, eights, and nines, and record them on a class chart. Students use the information in the class chart to write and illustrate story problems and post them for others to solve. For example: How many legs do six octopi have altogether?

Assessment Connections
Questioning . . .

Open with . . .

  • How many legs will six octopi have?

Probe further with . . .

  • How many legs does one octopus have?
  • How many legs do two octopi have?
  • How many legs do six octopi have?
  • How can you figure this out?
  • How do you know?
Listen for . . .
  • Does the student use language associated with multiplication when explaining how to find the total?
Look for . . .
  • Does the student write a problem that is clear and easily interpreted?
  • Does the student quickly give a correct solution to the problem?
  • Does the student solve the problem by adding groups of eight?
  • Does the student solve the problem by drawing a picture or through direct modeling with concrete materials?
  • Can the student give a clear explanation of the solution method?
  • Does the student self-monitor and self-correct?
  • Is the solution accurate?
TAKS Connection

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's TAKS Information Booklets, January 2002. Reprinted with permission.

activity under revision

Additional Clarifying Activity

Students work with a partner. The first student rolls a number cube and draws the corresponding number of circles. The second student rolls the number cube and draws the corresponding number of objects in each circle. Students then write the multiplication equation that represents the drawing and write, in words, what the equation means. For example, "3 x 2 = 6" means 3 groups of 2 equals 6 total objects.

(3.4.c) Number, operation, and quantitative reasoning. The student recognizes and solves problems in multiplication and division situations. The student is expected to use models to solve division problems and use number sentences to record the solutions.

Clarifying Activity with Assessment Connections

Students work in groups and are provided with a bucket of 24 cubes and some small paper cups. Students use the cubes and cups to answer mathematical questions such as, "How many different ways can you divide this set of cubes into equal groups?" (into one cup, into two cups, into three cups, etc.) Students record their findings with division number sentences. Students might compare their observations to a story such as A Remainder of One, by Elinor J. Pinczes.

Assessment Connections
Questioning . . .

Open with . . .

  • What do you notice about your findings?

Probe further with . . .

  • How many groups did you make?
  • How many are in each group?
  • What if you had 25 cubes? How does it change your groups?
  • How did you use your cubes to write number sentences?
  • How is separating a group into equal groups like multiplication? How is it different? How do you know you have found all of the ways?
  • What kind of real-life situations can you think of in which you would be dividing objects into equal groups?
Listen for . . .
  • Does the student recognize the relationship between multiplication and division?
  • Does the student use words that describe division?
Look for . . .
  • Do the student's number sentences match the groups of cubes?
  • Are all the groups divided into equal parts?
  • Is the solution accurate?
  • Does the student count accurately?
  • Does the student self-monitor and self-correct?
TAKS Connection

Click here for a larger version of the TAKS item.

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's Released Tests and Interactive Online Tests, Spring 2001 Mathematics TAAS. Reprinted with permission.

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(3.5) Number, operation, and quantitative reasoning. The student estimates to determine reasonable results.

(3.5.a) Number, operation, and quantitative reasoning. The student estimates to determine reasonable results. The student is expected to round whole numbers to the nearest ten or hundred to approximate reasonable results in problem situations.

activity under revision

(3.5.b) Number, operation, and quantitative reasoning. The student estimates to determine reasonable results. The student is expected to use strategies including rounding and compatible numbers to estimate solutions to addition and subtraction problems.

activity under revision

Clarifying Activity with Assessment Connections

Students use a restaurant menu to estimate the cost of a meal for four people. They decide whether they can pay with a $20 bill, and, if so, how much change they should expect to get back.

Assessment Connections
Questioning . . .

Open with . . .

  • What could the four people order? Will the total bill be less than $20?

Probe further with . . .

  • What kinds of things did you think about as you checked to see if you had enough money?
  • How did you decide if you had enough?
  • About how much will it cost?
  • How did you estimate the change you should get back?
Listen for . . .
  • Can the student round correctly?
  • Can the student justify why they decided to round each item cost or round the total cost?
  • Does the student clearly explain his or her thought process?
  • Does the student talk about the reasonableness of the estimate?
Look for . . .
  • Can the student use rounding techniques to decide if answers are within the designated range?
  • What strategies does the student use to round and calculate the sum?
  • Does the student round before adding?
  • Does the student use mental arithmetic or resort to paper and pencil calculations?
TAKS Connection

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's TAKS Information Booklets, January 2002. Reprinted with permission.

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(3.6) Patterns, relationships, and algebraic thinking. The student uses patterns to solve problems.

(3.6.a) Patterns, relationships, and algebraic thinking. The student uses patterns to solve problems. The student is expected to identify and extend whole-number and geometric patterns to make predictions and solve problems.

Clarifying Activity with Assessment Connections

Students use counters to build the first three triangular numbers as shown below.

picture of three triangular numbers

Students then use geometric and number patterns to extend to the next three triangular numbers.

Assessment Connections
Questioning . . .

Open with . . .

  • What can you tell me about your triangles?

Probe further with . . .

  • How many counters did you use for each triangle?
  • What happens between the second and third triangle?
  • What patterns do you notice in the triangles?
  • What patterns do you notice in the numbers of counters it takes to make the triangles?
  • How many counters would it take to make the sixth triangle? How do you know?
  • How can you record your information to find patterns or make predictions about how many counters it takes to make bigger triangles?
Listen for . . .
  • Does the student use numbers to describe a rule to extend the pattern?
  • Does the student use the attributes of a triangle to explain the rule?
  • Does the student use logical reasoning to explain predictions about larger triangles?
Look for . . .
  • Does the student arrange the counters correctly (in an equilateral triangle)?
  • Does the student use charts or tables to organize information?
  • Can the student use the rule to extend the pattern and make predictions?
  • Are the predictions accurate?
  • Does the student self-monitor and self-correct?
TAKS Connection

Click here for a larger version of the TAKS item.

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's TAKS Information Booklets, January 2002. Reprinted with permission.

(3.6.b) Patterns, relationships, and algebraic thinking. The student uses patterns to solve problems. The student is expected to identify patterns in multiplication facts using concrete objects, pictorial models, or technology.

Clarifying Activity with Assessment Connections

Students color the multiples of a given number (2, 3, 6, etc.) on a hundreds chart and discuss the pattern that is formed. After doing several sets of multiples, students can compare the patterns that are formed. For example, the multiples of four are "included in" the pattern of the multiples of two.

Assessment Connections
Questioning . . .

Open with . . .

  • What did you notice as you colored the hundreds chart?

Probe further with . . .

  • How did you determine this pattern?
  • What did you notice about multiples of four? Did you need to color any more numbers in your chart? Why do you think this was the case?
  • What did you notice about multiples of five? Were they easy to find? Why?
  • What did you notice about multiples of six? Did you need to color any more numbers in your chart? Why do you think this was the case?
  • Can you make a rule to describe what you have noticed?
  • Will you need to color more numbers to color multiples of ten? Why?
Listen for . . .
  • Can the student identify a rule to describe the patterns?
  • Does the student use appropriate language describing multiplication in explanations?
  • Can the student justify his or her answers?
Look for . . .
  • Does the student accurately color multiples of a given number on the numbers chart?
  • Does the student recognize properties of multiplication?
  • Does the student recognize a pattern?
  • Does the student use the rule to extend the pattern and make predictions?
  • Does the student self-monitor and self-correct?
TAKS Connection

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's TAKS Information Booklets, January 2002. Reprinted with permission.

Additional Clarifying Activity with Assessment Connections

Students place counters (buttons, cubes, beans) on a grid to make arrays to show that three sets of two are equal to two sets of three (3 x 2 = 2 x 3, the commutative property of multiplication).

Assessment Connections
Questioning . . .

Open with . . .

  • What do you notice about your arrays?

Probe further with . . .

  • How are the arrays alike? How are they different?
  • Can you write number sentences that go with your arrays?
  • Can you show that four sets of three is the same as three sets of four?
  • Can you write number sentences that go with your arrays?
  • If 5 x 3 = 15, what do you think 3 x 5 is? Why?
  • Can you use counters to show me that you are correct?
  • If 11 x 12 = 132, what is 12 x 11? How do you know?
  • What have you noticed about multiplication?
Listen for . . .
  • Can the student identify patterns in multiplication facts?
  • Does the student use appropriate language to describe multiplication?
  • Can the student justify his or her answers?
Look for . . .
  • Does the student recognize the commutative property of multiplication?
  • Does the student's number sentence match the array?
  • Are the number sentences accurate?
  • Can the student construct arrays to represent multiplication?

(3.6.c) Patterns, relationships, and algebraic thinking. The student uses patterns to solve problems. The student is expected to identify patterns in related multiplication and division sentences (fact families) such as 2 x 3 = 6, 3 x 2 = 6, 6 2 = 3, 6 3 = 2.

Clarifying Activity with Assessment Connections

Students lay out twelve linking cubes in a six-cube by two-cube array. Students join the cubes to make two rows of six, showing that 12 = 2 x 6. Students then unsnap the cubes and rejoin them into six columns of two to show that 12 = 6 x 2. Students snap all twelve cubes together into a six-inch by two-inch rectangle, then separate the cubes into two groups of six to show that 12 2 = 6. Finally, students snap the twelve cubes back together and separate them into six groups of two to show that 12 6 = 2.

Assessment Connections
Questioning . . .

Open with . . .

  • What are the number sentences that go with the arrangements you made? What do you notice about them?

Probe further with . . .

  • What pattern do you notice in the number sentences? (For example, they all use the same numbers.)
  • How are your number sentences alike?
  • How are your number sentences different?
  • Are these all the number sentences that go with your arrangements? How do you know?
Listen for . . .
  • Is the student identifying patterns in the number sentences?
  • Is the student using the words "multiplication" and "division?"
Look for . . .
  • Does the student recognize the inverse relationship of joining equal groups and separating into equal groups? (Multiplication and division are inverse operations.)
  • Is the student able to record the number sentence that matches each action? (Multiplication is for joining and division for separating.)
  • Are the number sentences accurate?
TAKS Connection

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's Released Tests and Interactive Online Tests, Spring 2001 Mathematics TAAS. Reprinted with permission.

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(3.7) Patterns, relationships, and algebraic thinking. The student uses lists, tables, and charts to express patterns and relationships.

(3.7.a) Patterns, relationships, and algebraic thinking. The student uses lists, tables, and charts to express patterns and relationships. The student is expected to generate a table of paired numbers based on a real-life situation such as insects and legs.

Clarifying Activity with Assessment Connections

Students develop a chart showing the relationship between the number of batches of cookies made to the number of eggs needed for the given recipe: 3 eggs, 1 tsp vanilla, 3c flour, 2c sugar, 1/2c butter, 1/2 bag chocolate chips.

Students should indicate how many eggs they would need for 0, 1, 2, and 3 batches of cookies. Students' tables should look similar to the table below:

table showing relationship between batches of cookies and eggs needed

Assessment Connections
Questioning . . .

Open with . . .

  • Can you make a table that will help figure out how many eggs you need?

Probe further with . . .

  • What are you recording in your table?
  • To make one batch of cookies how many eggs do you need?
  • To make two batches of cookies how many eggs do you need? For three batches? For four batches?
  • How did you find the number of eggs needed to make four batches of cookies?
  • Can you organize this information into a table that tells the number of batches of cookies and gives the number of eggs needed?
  • Tell me about your table. How would I use it?
Listen for . . .
  • Does the student explain what each side of the table represents?
Look for . . .
  • Is the student able to generate the data for a table?
  • Can the student generate a table of paired numbers?
  • Does the student place the data appropriately within the table?
  • Does the student label the table?
TAKS Connection

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's TAKS Information Booklets, January 2002. Reprinted with permission.

(3.7.b) Patterns, relationships, and algebraic thinking. The student uses lists, tables, and charts to express patterns and relationships. The student is expected to identify and describe patterns in a table of related number pairs based on a meaningful problem and extend the table.

activity under revision

Clarifying Activity with Assessment Connections

Students identify the pattern in the pairs of related numbers in the table they made in the activity for 3.7A. For example, if for each batch of cookies you need three eggs, then ten batches of cookies will take thirty eggs.

Assessment Connections
Questioning . . .

Open with . . .

  • How will you decide how many eggs you need to make ten batches of cookies?

Probe further with . . .

  • Do you notice any patterns in the table?
  • What number sentences can you write for each row (each number of batches) of the table that would describe how you figure out how many eggs you need to make that many batches of cookies? (e.g., 2 x 3 = 6)
  • How can you use the number of batches to figure out how many eggs you need? (number of batches x 3 = number of eggs)
  • How many batches could you make with 18 eggs?
  • How do you know?
Listen for . . .
  • Does the student describe patterns between the rows in the table. (For example, each row is three more than the row before.)
  • Does the student describe patterns between the columns? (The number of eggs is three times the number of batches.)
Look for . . .
  • Can the student identify patterns in the table?
  • Can the student extend the table?
  • Does the student use the table to write number sentences and make predictions?
  • Are the number sentences accurate?
  • Does the student self-monitor and self-correct?
TAKS Connection

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's Released Tests and Interactive Online Tests, Spring 2001 Mathematics TAAS. Reprinted with permission.

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(3.8) Geometry and spatial reasoning. The student uses formal geometric vocabulary.

(3.8) Geometry and spatial reasoning. The student uses formal geometric vocabulary. The student is expected to identify, classify, and describe two- and three-dimensional geometric figures by their attributes. The student compares two-dimensional figures, three-dimensional figures, or both by their attributes using formal geometry vocabulary.

activity under revision

Clarifying Activity with Assessment Connections

Given a set of geometric solids such as prisms, cones, cylinders, pyramids, and spheres, students are asked to classify the solids according to their characteristics. For example, the solids could be classified by the number of faces, shape of faces, number of edges, or number of vertices.

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me about your groups of geometric solids.

Probe further with . . .

  • What characteristics do the solids in this group have? How are the solids in this group the same? What do these geometric solids have in common?
  • How do the solids in this group differ from the solids in that group?
  • Can you name the geometric solids in this group?
  • Can you name a real-life object that has the same attributes as this solid?
  • What are some other ways you can use to classify the solids?
  • If you decide to classify by [another attribute] will your groupings change? How?
Listen for . . .
  • Can the student describe the attributes of shapes and solids?
  • Does the student use appropriate mathematical vocabulary for critical attributes? (For example: vertices, angles, corners, sides, and edges.)
  • Can the student name a variety of shapes and solids using formal geometric language?
  • Can the student compare a variety of shapes and solids using formal geometric language?
  • Is the student making and testing conjectures about the geometric properties of a solid?
Look for . . .
  • Can the student determine classifications of geometric solids using a variety of attributes?
  • Does the student accurately classify the geometric solids?
TAKS Connection

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's TAKS Information Booklets, January 2002. Reprinted with permission.

activity under revision

Additional Clarifying Activity

Each student makes a shape on a geoboard with bands. The teacher sorts the shapes into two groups according to a secret geometric attribute, such as closed shapes versus shapes that are not closed, or shapes with right angles versus shapes with no right angles. Students analyze the shapes in each group, use formal geometric vocabulary to write a summarizing statement about each group, and share and discuss their statements.

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(3.9) Geometry and spatial reasoning. The student recognizes congruence and symmetry.

(3.9.a) Geometry and spatial reasoning. The student recognizes congruence and symmetry. The student is expected to identify congruent two-dimensional figures.

activity under revision

Clarifying Activity with Assessment Connections

Students use five square tiles to form pentominoes and record each pentomino shape on inch-grid paper. Students cut out their pentominoes and compare theirs to someone else's to determine which ones are congruent.

Assessment Connections
Questioning . . .

Open with . . .

  • How do you know if two shapes are congruent?

Probe further with . . .

  • How is size important?
  • How is shape important?
Listen for . . .
  • Does the student use corners and edges to describe shapes?
  • Can the student state a definition of congruency? (same size and shape)
  • Is the student using geometry vocabulary to describe congruency? (turn, flip, slide to match shapes)
  • Does the student describe movement using common language and geometric vocabulary (turn, flip, slide, reflect, translate, rotate)?
Look for . . .
  • Does the student reflect, translate, rotate shapes to match them?
  • Can the student identify or create a pair of shapes that are not congruent?
TAKS Connection

Click here for a larger version of the TAKS item.

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's Released Tests and Interactive Online Tests, Spring 2001 Mathematics TAAS. Reprinted with permission.

(3.9.b) Geometry and spatial reasoning. The student recognizes congruence and symmetry. The student is expected to create two-dimensional figures with lines of symmetry using concrete models and technology.

Clarifying Activity with Assessment Connections

Given a work mat with a line drawn across it, students use pattern blocks (or color tiles) to make a design along one side of the line. Students can transfer the design onto triangular grid paper (or square grid paper) or use die-cut pieces to glue the design onto paper. Students find a partner to complete the design on the other side of the line so that the line becomes a line of symmetry for the whole design.

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me your strategy for copying the design on the other side of the line.

Probe further with . . .

  • Where did you start? Why?
  • How do you know if the shape is symmetrical?
  • Where is the line of symmetry for the design?
  • Does your design have other lines of symmetry?
  • If I drew a line here, would the design still be symmetrical?
  • How might you extend this design to make a design with two lines of symmetry?
Listen for . . .
  • Can the student explain a strategy for creating the mirror image?
  • Can the student explain symmetry?
  • Does the student use appropriate language to describe symmetry?
  • Can the student identify both an example and a non-example of symmetry?
Look for . . .
  • Can the student represent a pattern block design on grid paper?
  • Can the student identify the line of symmetry?
  • Can the student create a symmetrical design?
TAKS Connection
  • This student expectation is not tested on TAKS. Although this is not directly tested at Grade 3, it is an important foundation for student expectations tested at later grades.

(3.9.c) Geometry and spatial reasoning. The student recognizes congruence and symmetry. The student is expected to identify lines of symmetry in two-dimensional geometric figures.

activity under revision

Clarifying Activity with Assessment Connections

Students predict the lines of symmetry for a cut-out shape, then fold it or trace it on a transparency and flip it over to verify their predictions. The shapes might include die-cut letters of the alphabet, and students could sort the letters of the alphabet according to how many lines of symmetry each letter has. Or, the shapes could be different types of polygons (triangles, squares, rectangles that are not squares, parallelograms that are not rectangles, circles), and students could sort the shapes according to how many lines of symmetry each polygon has.

Assessment Connections
Questioning . . .

Open with . . .

  • How do you decide where a line of symmetry is?

Probe further with . . .

  • On which shapes is it easiest to find a line of symmetry?
  • Which shapes have more than one line of symmetry?
  • Which shapes have no lines of symmetry?
  • How do you know a shape is symmetrical?
Listen for . . .
  • Does the student use correct vocabulary (match, same, alike, even, congruent) to describe symmetry?
  • Can the student describe how to find a line of symmetry?
  • Can the student predict which shapes will have a line of symmetry?
Look for . . .
  • Can the student fold a symmetrical shape to make the two halves match?
  • Can the student apply this description of symmetry to a new shape?
  • Can the student identify or create a shape that does not have a line of symmetry?
TAKS Connection

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's TAKS Information Booklets, January 2002. Reprinted with permission.

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(3.10) Geometry and spatial reasoning. The student recognizes that a line can be used to represent numbers and fractions and their properties and relationships.

(3.10) Geometry and spatial reasoning. The student recognizes that a line can be used to represent numbers and fractions and their properties and relationships. The student is expected to locate and name points on a number line using whole numbers and fractions, including halves and fourths.

Clarifying Activity with Assessment Connections

Students select a card or paper plate on which a whole number or fraction has been written. Each student chooses a position for their card on an unlabeled, classroom-sized number line made from rope or tape and explains why that position was chosen.

Assessment Connections
Questioning . . .

Open with . . .

  • How are you going to decide where to place your number on the number line?

Probe further with . . .

  • What is your number?
  • Who has the greatest number we are going to place on the number line? How do you know?
  • Who has the least number we are going to place on the number line? How do you know?
  • Could you decide where your number belongs if there were no other numbers marked on the number line (benchmarks)?
  • Could you decide where your number belongs if ___ were the only number marked on the number line? What are some benchmark numbers you think you would need to know on the number line to be able to decide where your number goes?
  • How do you know your number is on this side of ______?
  • How do you know how far away from _________ to place your number?
Listen for . . .
  • Does the student accurately read the numbers?
  • Does the student clearly describe a reasonable strategy used for placing the numbers on the number line?
  • Does the student's strategy and explanations involve number sense and benchmarks?
Look for . . .
  • Can the student place numbers on a number line fairly accurately?
  • Does the student demonstrate a good grasp of the number system?
  • Does the student apply useful benchmark numbers to guide in developing the number line and placing the number?
  • Does the student successfully compare and order numbers on the given number line?
  • Does the student use place value and patterns in number relationships to compare, order, and place decimal numbers on the given number line?
TAKS Connection

Click here for a larger version of the TAKS item.

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's TAKS Information Booklets, January 2002. Reprinted with permission.

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(3.11) Measurement. The student directly compares the attributes of length, area, weight/mass, and capacity, and uses comparative language to solve problems and answer questions. The student selects and uses standard units to describe length, area, capacity/volume, and weight/mass.

(3.11.a) Measurement. The student directly compares the attributes of length, area, weight/mass, and capacity, and uses comparative language to solve problems and answer questions. The student selects and uses standard units to describe length, area, capacity/volume, and weight/mass. The student is expected to use linear measurement tools to estimate and measure lengths using standard units.

Clarifying Activity with Assessment Connections

Students go on a linear measurement scavenger hunt. Students are given a list of target linear measurements in either customary or metric units, e.g. 3 inches, 2 feet, 12 centimeters, 1 meter. While sitting in their seats, students look around the room and find objects whose lengths they estimate are about the same as the target lengths.

Students record their objects in a table like the one below, share what they have recorded, and explain their reasoning. Students then select appropriate measuring tools to actually measure the lengths of the objects, record each length to the nearest whole unit, and compare each actual measurement to the target measurement.

sample table showing chalk as a three-inch object

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me about the results of your measurement scavenger hunt.

Probe further with . . .

  • How did you decide which objects to record with each measurement on the list?
  • How did you decide which measuring tools to use to check your measurements?
  • Why do you think this item should be measured with centimeters instead of meters?
  • Which items could you measure with inches also?
  • How close were the actual lengths of the objects you recorded to the target measurements? How did you determine this?
Listen for . . .
  • Is the student using the language that describes the relative sizes of the units? (For example, inches are smaller than feet, so we use inches to measure smaller things.)
  • Can the student explain and justify the decisions made?
Look for . . .
  • Can the student estimate (with reasonable accuracy) the length of an object in standard units such as inches, feet, yards, centimeters, decimeters, and meters?
  • Does the student base his or her choice of unit and tool on the size of the item?
  • Does the student use the measuring tools correctly?
  • Is the student able to record each length to the nearest whole unit?
  • Is the student using a number and a unit to record the measurement?
  • Can the student compare the actual measurement with his or her target? (For example, twenty-one inches compared with two feet.)
TAKS Connection

Click here for a larger version of the TAKS item.

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's TAKS Information Booklets, January 2002. Reprinted with permission.

(3.11.b) Measurement. The student directly compares the attributes of length, area, weight/mass, and capacity, and uses comparative language to solve problems and answer questions. The student selects and uses standard units to describe length, area, capacity/volume, and weight/mass. The student is expected to use standard units to find the perimeter of a shape.

Clarifying Activity with Assessment Connections

Students go on a scavenger hunt around the school grounds to find objects that have a given perimeter. Students use appropriate measurement tools to verify their choices. Students draw a representation of the chosen objects and label the length of the sides.

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me about the objects you found.

Probe further with . . .

  • What is the perimeter of these objects? How do you know?
  • Can you explain in words what the perimeter is?
  • How did you figure out the perimeter for the object?
  • Is there another way you could have figured it out?
  • What is the shape of the object?
  • How did you decide which measurement tools to use?
  • Could you have chosen a different measuring tool? Why?
  • Can you write a number sentence to represent the perimeter of your object?
Listen for . . .
  • Can the student explain how to measure the perimeter?
  • Does the student talk about the reasonableness of the choices?
  • Does the student use appropriate mathematical vocabulary to describe the perimeter?
  • Does the student describe a strategy used to find objects of a given perimeter?
Look for . . .
  • Does the student select an appropriate measuring tool?
  • Does the student use the measuring tool properly and measure accurately?
  • Does the student understand perimeter?
  • Can the student determine perimeter of a shape?
  • Can the student draw a representation of the objects?
  • Does the student label the length of the sides of the objects including appropriate units (feet, inches, centimeters)?
  • Can the student write a number sentence to represent the perimeter?
  • Does the student find objects of a variety of shapes with a given perimeter, or are the shapes only rectangular?
TAKS Connection

Click here for a larger version of the TAKS item.

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's TAKS Information Booklets, January 2002. Reprinted with permission.

(3.11.c) Measurement. The student directly compares the attributes of length, area, weight/mass, and capacity, and uses comparative language to solve problems and answer questions. The student selects and uses standard units to describe length, area, capacity/volume, and weight/mass. The student is expected to use concrete and pictorial models of square units to determine the area of two-dimensional surfaces.

Clarifying Activity with Assessment Connections

Students use a rubberband to outline a polygon on a geoboard and count the number of square units enclosed by the rubberband to find the area of the polygon.

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me about the area of your shape.

Probe further with . . .

  • What is the area of your shape? How do you know?
  • How did you keep track of your counting?
  • How did you count a square that isn't full? Why?
  • Can you draw your shape on grid paper?
Listen for . . .
  • Does the student use appropriate mathematical language to describe the shape and its area?
  • Can the student clearly explain his or her strategy for finding the area of the shape?
Look for . . .
  • What strategy did the student use in counting the squares (by ones, by rows, etc.)?
  • Does the student count accurately?
  • Does the student understand area?
  • How does the student count incomplete squares?
  • Can the student approximate the area of shapes using a geoboard?
  • Can the student draw the geoboard shape onto grid paper?
TAKS Connection

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's TAKS Information Booklets, January 2002. Reprinted with permission.

(3.11.d) Measurement. The student directly compares the attributes of length, area, weight/mass, and capacity, and uses comparative language to solve problems and answer questions. The student selects and uses standard units to describe length, area, capacity/volume, and weight/mass. The student is expected to identify concrete models that approximate standard units of weight/mass and use them to measure weight/mass.

activity under revision

(3.11.e) Measurement. The student directly compares the attributes of length, area, weight/mass, and capacity, and uses comparative language to solve problems and answer questions. The student selects and uses standard units to describe length, area, capacity/volume, and weight/mass. The student is expected to identify concrete models that approximate standard units for capacity and use them to measure capacity.

activity under revision

(3.11.f) Measurement. The student directly compares the attributes of length, area, weight/mass, and capacity, and uses comparative language to solve problems and answer questions. The student selects and uses standard units to describe length, area, capacity/volume, and weight/mass. The student is expected to use concrete models that approximate cubic units to determine the volume of a given container or other three-dimensional geometric figure.

activity under revision

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(3.12) Measurement. The student reads and writes time and measures temperature in degrees Fahrenheit to solve problems.

(3.12.a) Measurement. The student reads and writes time and measures temperature in degrees Fahrenheit to solve problems. The student is expected to use a thermometer to measure temperature.

activity under revision

Clarifying Activity with Assessment Connections

Students measure the temperatures of iced tea, hot chocolate, and tap water several times over a span of thirty minutes to an hour. Students make a table for each liquid showing its temperature compared to the time, compare the tables, and write summary statements about their observations. Students record the temperatures with numbers and by filling in a picture thermometer.

Assessment Connections
Questioning . . .

Open with . . .

  • What can you tell me about the temperatures you recorded?

Probe further with . . .

  • How did you read the temperature using this thermometer?
  • What is the temperature of the iced tea now? How did you figure it out? Did you skip count? Why?
  • How many tick marks do you see between each number written on the thermometer? How do the tick marks help you read the thermometer? How do you know what numbers the tick marks represent?
Listen for . . .
  • Does the student consistently read the thermometer correctly?
  • How does the student read the thermometer? Does he or she skip count?
  • Can the student explain his or her strategy for reading the thermometer?
Look for . . .
  • Can the student record temperatures correctly?
  • Can the student read the thermometer to measure the temperatures of the liquids?
  • If the student is not reading the thermometer correctly, is he or she misreading the tick marks between each rounded number?
  • Does the student self-correct errors?
  • Can the student fill in a picture thermometer that matches the recorded temperature?
TAKS Connection

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's Released Tests and Interactive Online Tests, Spring 2001 Mathematics TAAS. Reprinted with permission.

(3.12.b) Measurement. The student reads and writes time and measures temperature in degrees Fahrenheit to solve problems. The student is expected to tell and write time shown on analog and digital clocks.

activity under revision

TAKS Connection

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's Released Tests and Interactive Online Tests, Spring 2001 Mathematics TAAS. Reprinted with permission.

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(3.13) Probability and statistics. The student solves problems by collecting, organizing, displaying, and interpreting sets of data.

(3.13.a) Probability and statistics. The student solves problems by collecting, organizing, displaying, and interpreting sets of data. The student is expected to collect, organize, record, and display data in pictographs and bar graphs where each picture or cell might represent more than one piece of data.

Clarifying Activity with Assessment Connections

Students collect information about how many pints of milk the class drinks in a week at school. They make a chart to record the data for each day and use actual milk cartons to create a real graph of each day's milk consumption. They then draw pictures to translate the real graph information to a pictograph. The pictograph is translated into a bar graph where each cell on the graph may represent two or more milk cartons.

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me about your graph.

Probe further with . . .

  • How did you collect the information for your graph?
  • How did you decide how to set up your graph?
  • Which day had the most milk consumption?
  • Which day had the least milk consumption?
  • What does each picture or cell represent?
  • How did you change your data display from a real graph to a pictograph?
  • How did you change your data display from a pictograph to a bar graph?
  • How are your graphs alike? How are they different?
Listen for . . .
  • Does the student accurately interpret the graphs?
  • Does the student's explanations match the written work?
  • Are the student's explanations reasonable?
Look for . . .
  • Can the student accurately collect and record data on milk consumption?
  • Does the student accurately represent the information collected on each of the graphs?
  • Can the student locate information on a graph?
  • Does the student accurately translate the information in one type of graph to an alternative graph form?
  • Does the student accurately label the graphs?
  • Does the student use pictures or cells to represent more than one piece of data?
  • Does the student create scales or keys to explain the data displayed by the pictures or cells?
TAKS Connection

Click here for a larger version of the TAKS item.

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's TAKS Information Booklets, January 2002. Reprinted with permission.

(3.13.b) Probability and statistics. The student solves problems by collecting, organizing, displaying, and interpreting sets of data. The student is expected to interpret information from pictographs and bar graphs.

Clarifying Activity with Assessment Connections

Students generate and answer questions that can be answered using information from a graph they made in the activity for 3.14A.

Assessment Connections
Questioning . . .

Open with . . .

  • How can you use the graph to answer this question?

Probe further with . . .

  • Can you read the answer to the question right from the graph?
  • Do you need more than one part of the graph to answer the question?
Listen for . . .
  • Can the questions the student generates be answered using the information from the graph?
  • Is the student using information in the graph to answer the questions that other students generated?
Look for . . .
  • Can the student generate and answer problemsolving questions from the graph? (For example: How much more milk did the students drink on Monday than on Tuesday?)
  • Does the student use the scales or keys to help interpret the graph?
TAKS Connection

Click here for a larger version of the TAKS item.

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's TAKS Information Booklets, January 2002. Reprinted with permission.

(3.13.c) Probability and statistics. The student solves problems by collecting, organizing, displaying, and interpreting sets of data. The student is expected to use data to describe events as more likely than, less likely than, or equally likely as.

activity under revision

Clarifying Activity with Assessment Connections

Students open bags of M&M's, record the number of each color of candy, and organize the data in a bar graph. Students use the M&M data to determine if they are more likely, less likely, or equally likely to draw a red M&M than a green M&M from a bag without looking and discuss why.

Assessment Connections
Questioning . . .

Open with . . .

  • Can you use your graph to compare the likelihood of drawing a red M&M to the likelihood of drawing a green M&M from your bag without looking? How?

Probe further with . . .

  • Are you more likely, less likely, or equally likely to draw a red M&M than a green M&M from a bag without looking if M&Ms are mixed up? Why?
  • Why should the M&M's be mixed up? What might happen if all of the green M&M's are put in the bag first and all of the reds are put in the bag last and the bag is not mixed? How might that affect the likelihood of drawing a red M&M?
  • Compare your graph with a friend's graph. How are they the same? How are they different? Why are the graphs different?
  • Is your friend more likely, less likely, or equally likely to draw a green M&M as you are? How do you know?
Listen for . . .
  • Can the student explain how the M&M data was used to determine if he or she is more likely, less likely, or equally likely to draw a red M&M than a green M&M?
  • Can the student discuss why the M&M's need to be mixed up before the data can be used to compare the likelihood of drawing a red with the likelihood of drawing a green?
Look for . . .
  • Can the student accurately record the number of each color of candy?
  • Does the student sort the candy into piles, use tally marks, or use another method to count the number of each color?
  • Can the student organize the data in a bar graph?
  • Can the student use the M&M data to determine if it is more likely, less likely, or equally likely to draw a red M&M than a green M&M from a bag?
  • Can the student determine whether a friend is more likely, less likely, or equally likely to draw a green M&M by comparing data from two graphs?
TAKS Connection

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's TAKS Information Booklets, January 2002. Reprinted with permission.

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(3.14) Underlying processes and mathematical tools. The student applies Grade 3 mathematics to solve problems connected to everyday experiences and activities in and outside of school.

(3.14.a) Underlying processes and mathematical tools. The student applies Grade 3 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to identify the mathematics in everyday situations.

Clarifying Activity with Assessment Connections

After reading or hearing a story such as Math Curse, by John Scieszka, students write their own stories about the mathematics they use in a given day.

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me about your story.

Probe further with . . .

  • How did you decide what to write?
  • How do you use mathematics in the story?
  • Are there other ways that you use mathematics?
  • When do you measure?
  • Where do you see patterns?
  • Where do you see graphs?
  • When do you find yourself using division? addition? multiplication? subtraction?
Listen for . . .
  • What mathematical vocabulary does the student use in the story?
  • Can the student identify mathematics in his or her world?
Look for . . .
  • Does the student write a story that is easily read and interpreted?
  • Does the student identify a variety of uses of mathematics in their world including some that are unusual?
  • Can the student solve real-world problems by applying mathematics?
TAKS Connection

Click here for a larger version of the TAKS item.

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's Released Tests and Interactive Online Tests, Spring 2001 Mathematics TAAS. Reprinted with permission.

(3.14.b) Underlying processes and mathematical tools. The student applies Grade 3 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness.

Clarifying Activity with Assessment Connections

Students create a mini-book to record their problem-solving procedures. On the first page, they copy a problem and highlight relevant data. On the second page, they rewrite the problem in their own words. On the third page, they illustrate the problem with a picture, diagram, chart, or table. On the fourth page, students record their solution, using a numerical equation (if appropriate), and write an explanation of why they think their answer is reasonable.

Assessment Connections
Questioning . . .

Open with . . .

  • How did you get your answer?

Probe further with . . .

  • What information from the problem was important?
  • How did you write the problem in your own words?
  • How did your pictures or diagram help you solve the problem?
  • How does your number sentence go with our solution?
  • How does your picture or number sentence compare to someone else's?
  • How do you know your answer is reasonable? Are there other reasonable answers? What are they?
Listen for . . .
  • Does the student's explanation match what he or she wrote?
  • Is the student's explanation logical and reasonable?
  • Does the student use mathematical vocabulary in explanations?
Look for . . .
  • Does the student highlight relevant data?
  • Is the solution accurate?
  • Is the student using a plan to solve the problem?
  • Is the student understanding the problem?
  • Does the student recognize if the answer is reasonable?
TAKS Connection

Click here for a larger version of the TAKS item.

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's TAKS Information Booklets, January 2002. Reprinted with permission.

(3.14.c) Underlying processes and mathematical tools. The student applies Grade 3 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.

Clarifying Activity with Assessment Connections

During each problem-solving situation, students try different ways to solve the problem and select an appropriate strategy, such as looking for a pattern.

Assessment Connections
Questioning . . .

Open with . . .

  • How did you decide what strategy you wanted to use to solve this problem?

Probe further with . . .

  • What did you think about doing to solve the problem?
  • What did you actually do to solve the problem?
  • What information helped you decide what to do?
  • Is there another strategy you might use?
Listen for . . .
  • Is the student able to describe the strategy he or she used?
  • Does the student talk about important information from the problem in his or her solution?
  • Does the student talk about a variety of strategies?
Look for . . .
  • Is the student selecting reasonable and logical strategies to solve the problem?
  • Can the student use this strategy to get the right answer?
  • Can the student compare his or her strategies to others' strategies?
  • Is the student learning from and sharing strategies with others?
  • What strategy does the student use most often with confidence and accuracy?
TAKS Connection

Click here for a larger version of the TAKS item.

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's TAKS Information Booklets, January 2002. Reprinted with permission.

(3.14.d) Underlying processes and mathematical tools. The student applies Grade 3 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to use tools such as real objects, manipulatives, and technology to solve problems.

Clarifying Activity with Assessment Connections

Students use mirrors and a computer drawing program to create figures with symmetry. Students can draw a line segment on a piece of paper to act as the line of symmetry, draw a design on one side of the line, place the mirror on the line, look into the mirror and view the completed symmetrical design. With the software, as students draw a design on one side of an identified line of symmetry, the design is automatically replicated on the other side of the line of symmetry so that the complete picture remains symmetrical.

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me about what you have discovered about symmetry using the mirror and the computer software.

Probe further with . . .

  • What happens when your design touches the line of symmetry? Why?
  • What would happen if, as you are making a design using the computer program, you cross the line of symmetry? Why?
  • Put your drawing "pen" down on one side of the line of symmetry. Where do you predict the computer will begin to draw on the other side of the line of symmetry?
Listen for . . .
  • Can the student answer questions concerning symmetry based on experiences with mirrors and computer software?
Look for . . .
  • Does the student develop an understanding of symmetry using the mirrors and software?
  • Can the student predict how a symmetrical design will be completed?
TAKS Connection
  • This student expectation is not tested on TAKS. This student expectation is important to the development of mathematical understanding but is not testable within the current testing structure.

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(3.15) Underlying processes and mathematical tools. The student communicates about Grade 3 mathematics using informal language.

(3.15.a) Underlying processes and mathematical tools. The student communicates about Grade 3 mathematics using informal language. The student is expected to explain and record observations using objects, words, pictures, numbers, and technology.

Clarifying Activity with Assessment Connections

Students collect information about how many pints of milk the class drinks in a week at school. They make a chart to record the data for each day and use actual milk cartons to create a real graph of each day's milk consumption. They then draw pictures to translate the real graph information to a pictograph. The pictograph is translated into a bar graph (using technology) where each cell on the graph may represent two or more milk cartons. Students write a letter to a person of their choice, describing what they learned.

Assessment Connections
Questioning . . .

Open with . . .

  • What did you write about the number of pints of milk the class drinks in a week at school?

Probe further with . . .

  • What did you write about how you collected the information for your graph?
  • How did you describe which day had the most milk consumption?
  • How did you describe which day had the least milk consumption?
  • How did you display the observations?
  • Which graph do you think is the best way to present information? Why?
Listen for . . .
  • Do the student's explanations match the work he or she did?
Look for . . .
  • Can the student accurately collect and record data on milk consumption?
  • Does the student accurately represent the information collected on each of the graphs?
  • Can the student locate information on a graph?
  • Can the student use technology to create a bar graph?
  • Does the student accurately translate the information in one type of graph to an alternative graph form?
  • Does the student accurately label the graphs?
  • Does the student use pictures or cells to represent more than one piece of data?
  • Does the student create scales or keys to explain the data displayed by the pictures or cells?
TAKS Connection
  • This student expectation is not tested on TAKS. This student expectation is important to the development of mathematical understanding but is not testable within the current testing structure.

(3.15.b) Underlying processes and mathematical tools. The student communicates about Grade 3 mathematics using informal language. The student is expected to relate informal language to mathematical language and symbols.

Clarifying Activity with Assessment Connections

Students use play money to act out the story Alexander Who Used To Be Rich Last Sunday, by Judith Viorst. As they act out each part of the story, students use number and operation symbols to record what has happened to Alexander's money.

Assessment Connections
Questioning . . .

Open with . . .

  • How did you decide which symbols to use in your number sentences?

Probe further with . . .

  • What actions in the story are important in deciding the operation you use? (earned, lost, gave away)
  • What symbols do you use to represent when Alexander lost his money? (+ or -)
  • What does the equal sign mean?
Listen for . . .
  • Is the student explaining the number sentences by using the appropriateinformal language?
Look for . . .
  • Does the number sentence match the action in the story?
  • Can the student use play money to help connect number sentences to the story?
TAKS Connection

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's Released Tests and Interactive Online Tests, Spring 2001 Mathematics TAAS. Reprinted with permission.

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(3.16) Underlying processes and mathematical tools. The student uses logical reasoning.

(3.16.a) Underlying processes and mathematical tools. The student uses logical reasoning. The student is expected to make generalizations from patterns or sets of examples and nonexamples.

Clarifying Activity with Assessment Connections

Students work in small groups. Each group receives a hundreds chart with the first few numbers in a pattern colored in. Each group uses the examples of the numbers colored in on the chart (and the nonexamples of the numbers not colored in) to determine what the pattern is, describe the pattern in words or symbols, and complete the pattern by coloring in the other squares that fit into the pattern.

Assessment Connections
Questioning . . .

Open with . . .

  • What did you notice about the numbers that are colored on the hundreds chart?

Probe further with . . .

  • What is the pattern?
  • Can you write a rule for this pattern in words?
  • Can you write a rule for this pattern using number sentences?
  • Extend the pattern by coloring the other squares that fit into the pattern.
Listen for . . .
  • Can the student identify a rule to describe the patterns?
  • Does the student use appropriate mathematical language in explanations?
  • Can the student justify his or her answers?
Look for . . .
  • Does the student recognize a pattern?
  • Does the student use the rule to extend the pattern and make predictions?
  • Does the student accurately color the numbers chart to extend the pattern?
  • Does the student self-monitor and self-correct?
TAKS Connection

Click here for a larger version of the TAKS item.

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's TAKS Information Booklets, January 2002. Reprinted with permission.

(3.16.b) Underlying processes and mathematical tools. The student uses logical reasoning. The student is expected to justify why an answer is reasonable and explain the solution process.

Clarifying Activity with Assessment Connections

The teacher has a large hundreds chart on which certain squares have been covered with squares made from colored transparencies (so that the numbers can still be seen) in order to make a pattern. Students observe the pattern and try to describe it. They then close their eyes while the teacher changes the pattern by removing, moving, or adding one or more squares. Students open their eyes, try to identify how the pattern has been changed, and use characteristics of the pattern to explain how they know.

Assessment Connections
Questioning . . .

Open with . . .

  • What has changed?

Probe further with . . .

  • How did you find out what changed?
Listen for . . .
  • Can the student justify and explain his or her solution process?
  • Can the student coherently and clearly communicate his or her mathematical thinking?
  • Can the student analyze and evaluate his or her thinking?
  • Does the student use mathematical language to express ideas precisely?
Look for . . .
  • Does the student use various types of reasoning to justify his or her mathematical thinking?
TAKS Connection
  • This student expectation is not tested on TAKS. This student expectation is important to the development of mathematical understanding but is not testable within the current testing structure.

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