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 5

(a) Introduction

(1) Within a well-balanced mathematics curriculum, the primary focal points at Grade 5 are comparing and contrasting lengths, areas, and volumes of two- or three-dimensional geometric figures; representing and interpreting data in graphs, charts, and tables; and applying whole number operations in a variety of contexts.

(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

(5.1) Number, operation, and quantitative reasoning. The student uses place value to represent whole numbers and decimals.

(5.1.a) Number, operation, and quantitative reasoning. The student uses place value to represent whole numbers and decimals. The student is expected to use place value to read, write, compare, and order whole numbers through 999,999,999,999.

activity under revision

Clarifying Activity with Assessment Connections

Students play a game in which they try to build the greatest number possible with a given set of digits. Each player draws a game board as shown:

ten blanks

Players take turns rolling a 10-sided number polyhedron or spinning a spinner labeled 0–9. Each player writes the number that comes up in the roll or spin in one space on his or her game board. Once the digit is written, it cannot be moved.

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?
  • Who has made the greatest number? What is it? How do you know this is the greatest number?
  • Whose number is closest to your number? How do you know?
  • Order all the numbers. How did you go about putting these numbers in order from least to greatest?
  • What strategy did you use to try to make your number?
  • What is the greatest number you can create by moving the digits of your number?
  • What is the least number you can create by moving the digits of your number?
  • What strategy would you use the next time you play this game?
  • How would a 9-digit number compare to your 10-digit number? Why?
  • How would you write your number in words?
Listen for . . .
  • Does the student accurately read the 10-digit numbers? Does he or she use the appropriate number naming patterns? (Note: 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 his or her strategies and responses?
Look for . . .
  • Does the student demonstrate a good grasp of the number system and place value?
  • Does the student use place value and patterns in number relationships to compare and order 10-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 (e.g., each place is ten times greater than the place on its right)?
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.

(5.1.b) Number, operation, and quantitative reasoning. The student uses place value to represent whole numbers and decimals. The student is expected to use place value to read, write, compare, and order decimals through the thousandths place.

Clarifying Activity with Assessment Connections

The teacher posts a piece of a blank number line (with 0 on one end and 1 on the other) and distributes a variety of decimals between 0 and 1 written on index cards. Students use the names and values of the decimal numbers to discuss and determine where to place each number on the number line.

Assessment Connections
Questioning . . .

Open with . . .

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

Probe further with . . .

  • What is your number?
  • Who has the greatest number you are going to place on the number line? How do you know?
  • Who has the least number you 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 on the number line (benchmarks)?
  • Could you decide where your number belongs if 0 were the only number marked on the number line? What are some other numbers you would need to know on the number line to decide where your number belongs?
  • How do you know it is on this side of ______?
  • How do you know how far away from _________ to put it?
Listen for . . .
  • Does the student accurately read the decimal value to the thousandths place using the appropriate number naming patterns?
  • Does the student clearly describe his or her strategy for placing the decimals on the number line?
  • Does the student's strategy and explanations involve place value and benchmarks?
Look for . . .
  • Can the student accurately (or with relative accuracy) place decimals on a number line?
  • Does the student demonstrate a good grasp of the number systemand place value?
  • Does the student apply useful benchmark numbers (between 0 and 1) to guide in developing the number line and ordering decimals?
  • Does the student successfully compare and order decimals to the thousandths?
  • Does the student use place value and patterns in number relationships to compare and order decimals to the thousandths?
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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(5.2) Number, operation, and quantitative reasoning. The student uses fractions in problem-solving situations.

(5.2.a) Number, operation, and quantitative reasoning. The student uses fractions in problem-solving situations. The student is expected to generate a fraction equivalent to a given fraction such as 1/2 and 3/6 or 4/12 and 1/3.

Clarifying Activity with Assessment Connections

Students create 8 1/2-inch by 1-inch fraction strips of whole, halves, thirds, fourths, fifths, sixths, eighths, ninths, tenths, and twelfths and label them. They compare the fractions strips to find and record lists of equivalent fractions. For example, 1/2 = 2/4 = 3/6 = 4/8 = 5/10 = 6/12.

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me about your fraction strips and the equivalent fractions you found.

Probe further with . . .

  • How did you create your fraction strip of halves?
  • How did you make your fraction strip of fourths? Did the strategy for making half strips help you make the fraction strip of fourths?
  • How did you make your fractions strip of fifths? Was this more difficult to make than some of the others you made? Why?
  • What do you notice about these equivalent fractions?
  • How do you know they are equivalent?
  • What patterns do you notice when you compare 1/2, 2/4, 3/6, 4/8?
  • What are some other names for 1/2?
  • Can you find a fraction equivalent to 1/2 with 7 as a denominator? How did you decide this? (Note: If the student insists that the numerator be a whole number, the answer is "no." However, if the student allows the numerator to be a mixed number, the answer can be "yes," (3 1/2)/7.)
  • What are some fractions equivalent to 2/3? 6/8? 6/9? How do you know?
  • What are some fractions equivalent to 9/10? How did you find these?
  • What do the numerator and the denominator of a fraction tell you?
  • If we make the denominator larger, what happens to the size of the parts into which the whole is divided?
  • If we make the numerator smaller, what does this mean?
Listen for . . .
  • Can the student use mathematical language to describe how he or she generated equivalent fractions? (For example: numerator, denominator, equivalent, factor, equals.)
  • Can the student explain his or her strategies for creating the fraction strips?
  • Can the student clearly explain his or her strategies for generating equivalent fractions?
  • Does the student demonstrate an understanding of the meaning of numerator and denominator?
Look for . . .
  • Can the student generate equivalent fractions?
  • Did the student make an effort to make the parts of the fraction strips equal in size?
  • Does the student extend and combine the strategies he or she used for making some fraction strips to make others? For example, to make sixths, did he or she make thirds then fold each section in half?
  • Did the student check his or her strips against someone else's for accuracy?
  • Was the student able to see patterns in his or her lists of equivalent fractions?
  • Was the student able to apply the pattern extending the list of equivalent fractions?
  • Was the student able to apply the pattern to find equivalent fractions for fractions such as 9/10 that could not be modeled using the fraction strips he or she created?
  • Does the student notice properties of equivalence such as, "Since 2/3 is equivalent to 6/9 and 8/12, then 6/9 is equivalent to 2/3 and 8/12"?
  • Can the student justify the equivalent fractions using fraction strips?
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.

(5.2.b) Number, operation, and quantitative reasoning. The student uses fractions in problem-solving situations. The student is expected to generate a mixed number equivalent to a given improper fraction or generate an improper fraction equivalent to a given mixed number.

activity under revision

(5.2.c) Number, operation, and quantitative reasoning. The student uses fractions in problem-solving situations. The student is expected to compare two fractional quantities in problem-solving situations using a variety of methods, including common denominators.

Clarifying Activity with Assessment Connections

Students use tiles to build a rectangle that is 1/2 red, 1/3 yellow, and 1/6 blue and record the rectangle on grid paper. Students compare the different amounts of red, yellow, and blue in the rectangle.

Assessment Connections
Questioning . . .

Open with . . .

  • How can you use your rectangle to compare 1/2 and 1/3?

Probe further with . . .

  • How do you know you have made a rectangle that fits the description?
  • How did you figure out how many tiles to use to build your rectangle?
  • Could you have built your rectangle another way?
  • What is the fewest number of tiles you would need to build your rectangle?
  • Could you have used more tiles? How?
  • Can you describe 1/2 and 1/3 using equivalent fractions that make it easier to compare to the amounts in red and yellow?
  • What is it about these equivalent fractions that makes them easy to compare?
  • How does the number of tiles you need relate to the denominators of the fractions 1/2, 1/3, and 1/6? (common denominators)
Listen for . . .
  • Can the student use comparison language and exact equivalence to describe the fraction model in different ways?
  • Does the student clearly describe the strategy used to construct the rectangle?
Look for . . .
  • Can the student represent the fractions 1/2, 1/3, and 1/6 using the concrete model of a rectangle?
  • Does the student follow a plan or use trial and error to figure out how to build the rectangle?
  • Does the student understand how the number of tiles needed is related to common denominators?
  • Can the student identify the red, yellow, and blue parts of the rectangle using equivalent fractions to 1/2, 1/3, and 1/6?
  • Can the student compare fractions using common denominators?
TAKS Connection

assessment item from TEA's released tests

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

(5.2.d) Number, operation, and quantitative reasoning. The student uses fractions in problem-solving situations. The student is expected to use models to relate decimals to fractions that name tenths, hundredths, and thousandths.

Clarifying Activity with Assessment Connections

Students use a thousandths cube to represent a unit, and then use and record decimal numbers and their equivalent fractional representations.

Assessment Connections
Questioning . . .

Open with . . .

  • Can you represent your decimals (e.g., .5, .25, .125) by recording the decimal number and shading an area of this thousandths cube to represent the number? What fraction is equivalent to this number?

Probe further with . . .

  • How did you decide how to shade your area?
  • Could you have chosen a different way to shade the thousandths cube to represent the decimal?
  • How did you find an equivalent fraction?
  • Can you generate other fractions that are equivalent to this decimal? How?
Listen for . . .
  • Can the student explain and give reasons for the thousandths cube model he or she creates?
  • Does the student use appropriate mathematical language to indicate an understanding of place value and equivalence?
  • Can the student clearly explain the process he or she used to determine fractions equivalent to the decimal?
Look for . . .
  • Can the student write the decimal numbers that name tenths, hundredths and thousandths?
  • Can the student represent a decimal number through concrete models?
  • Can the student use models to relate decimals that name tenths, hundredths, and thousandths to fractions?
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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(5.3) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve meaningful problems.

(5.3.a) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve meaningful problems. The student is expected to use addition and subtraction to solve problems involving whole numbers and decimals.

Clarifying Activity with Assessment Connections

Students use technology to find statistics from the last Olympics that involve decimals. They create their own problems from this information that require adding or subtracting decimals to solve and share problems with a partner.

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?
  • Does your problem use whole numbers?
  • Can your problem be solved by adding or subtracting decimal numbers?
Listen for . . .
  • Does the student's explanation match his or her written work?
Look for . . .
  • Can the student identify real-world problems that can be solved by adding or subtracting decimal numbers?
  • Can the student pose a problem that can be solved by adding or subtracting decimal numbers?
  • Does the student pose a problem that is clear and easily interpreted by a partner?
Questioning . . . (after trading problems)

Open with . . .

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

Probe further with . . .

  • How are you solving the problem? Why?
  • What number sentence can you write to show your problem?
  • Can you solve the problem another way?
  • Is your solution reasonable? How do you know?
Listen for . . .
  • Does the student's explanation match his or her written work?
  • Is the student able to discuss the reasonableness of his or her solution?
Look for . . .
  • Can the student identify the information necessary to solve the problem?
  • Can the student add or subtract decimals?
  • 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?
  • Can the student self-correct any errors?
TAKS Connection

assessment item from TEA's released tests

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

(5.3.b) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve meaningful problems. The student is expected to use multiplication to solve problems involving whole numbers (no more than three digits times two digits without technology).

Clarifying Activity with Assessment Connections

Students brainstorm real-world reasons to use multiplication and record them on a chart. They then select an example from the chart, write an original problem for others to solve, and exchange problems.

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?
  • Does your problem use whole numbers?
  • Can your problem be answered by multiplying whole numbers?
Listen for . . .
  • Does the student's explanation match his or her written work?
Look for . . .
  • Can the student identify real-world problems that can be solved using multiplication?
  • Does the student pose a problem that can be solved by multiplying whole numbers?
  • Does the student pose a problem that is clear and easily interpreted by his or her partner?
Questioning . . . (after trading problems)

Open with . . .

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

Probe further with . . .

  • How are you solving the problem? Why?
  • What number sentence can you write to show your problem?
  • Can you solve the problem another way?
  • Is your solution reasonable? How do you know?
Listen for . . .
  • Does the student's explanation match his or her written work?
  • Is the student able to discuss the reasonableness of his or her solution?
Look for . . .
  • Can the student identify the information necessary to solve the problem?
  • Can the student use multiplication 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?
  • Can the student self-correct any errors?
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.

(5.3.c) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve meaningful problems. The student is expected to use division to solve problems involving whole numbers (no more than two-digit divisors and three-digit dividends without technology), including interpreting the remainder within a given context.

activity under revision

Clarifying Activity with Assessment Connections

Students use base-ten blocks or drawings to solve division problems such as calculating the fuel efficiency of the family car: "If your family traveled 94 miles and used 4 gallons of gas, how many miles per gallon did the car travel?"

Assessment Connections
Questioning . . .

Open with . . .

  • What is the question asked in the problem you are working? How are you going to solve it?

Probe further with . . .

  • What number sentence can you write to show your problem?
  • Can you solve the problem another way?
  • Is your solution reasonable? How do you know?
Listen for . . .
  • Does the student's explanation match his or her written work?
  • Does the student talk about the reasonableness of his or her solution?
Look for . . .
  • Does the student select manipulatives or draw a picture to help solve the problem?
  • Can the student use division to solve problems involving whole numbers?
  • Can the student identify the information necessary to solve the problem?
  • Can the student use base-ten blocks or drawings to model division?
  • Can the student solve the problem in more than one way?
  • Does the number sentence match the student's explanation?
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.

(5.3.d) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve meaningful problems. The student is expected to identify common factors of a set of whole numbers.

activity under revision

Clarifying Activity with Assessment Connections

Students choose two numbers and make a list of all the factors of each one. Students then circle the factors that are common to both lists, and make a list of those common factors. Students identify this list as the set of common factors of the two numbers. Students can use the list to identify the greatest common factor of the two numbers and the prime factors.

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me about the factors of 18 and 24. Which of their factors are prime numbers?

Probe further with . . .

  • Since 3 is a factor of 18, what is another factor of 18? How do you know? (factor pairs)
  • What are the common factors of 18 and 24? What is the greatest common factor?
  • Use a factor tree to identify the prime factors of 18 and 24. Can you find the prime factors using a different factor tree? What is the same and what is different about the factor trees?
  • What connections do you notice between prime factors, common factors, and greatest common factors?
  • If given the prime factors of two numbers, how could you determine the greatest common factor?
Listen for . . .
  • Does the student's explanation match his or her written work?
  • Does the student use appropriate mathematical language to describe factorization?
Look for . . .
  • Can the student identify the prime factorization of a whole number?
  • Can the student identify common factors of two whole numbers?
  • Can the student identify the greatest common factor of two whole numbers?
  • Does the student use factor pairs when determining the factors of a whole number?
  • Does the student notice that the prime factorization of a number is unique? (Fundamental Theorem of Arithmetic)
  • Can the student determine the greatest common factor and give the prime factorizations of two whole numbers?
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.

(5.3.e) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve meaningful problems. The student is expected to model situations using addition and/or subtraction involving fractions with like denominators using concrete objects, pictures, words, and numbers.

Clarifying Activity with Assessment Connections

Students use pattern blocks and work with partners to create and model addition and subtraction problems involving fractions. For example, "Let a yellow hexagon represent a whole pizza. Gary has 2 1/3 pizzas left over from a party. He eats 2/3 of a pizza for lunch. How much pizza is still left?"

Assessment Connections
Questioning . . .

Open with . . .

  • Describe how you solved your fraction problem.

Probe further with . . .

  • How did you use the pattern blocks to model the problem?
  • How did you use pattern blocks to solve the problem?
  • What number sentence can you write to describe the fraction problem?
  • Is your solution reasonable? How do you know?
Listen for . . .
  • Can the student read fractions?
  • Does the student use words that describe addition and subtraction involving fractions with common denominators?
  • Can the student clearly explain his or her thought process?
  • Is the student able to discuss the reasonableness of his or her solution?
Look for . . .
  • Can the student model addition and subtraction problems involving fractions with like denominators using the pattern blocks?
  • Can the student use mathematical symbols to record addition and subtraction problems involving fractions with like denominators?
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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(5.4) Number, operation, and quantitative reasoning. The student estimates to determine reasonable results.

(5.4) 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, subtraction, multiplication, and division problems.

Clarifying Activity with Assessment Connections

Students discuss the different strategies for computational estimation involving rounding. For example, 2.43 + 4.79 may be estimated as a little over 7 since 2.43 + 4.79 = (2 + 0.43) + (4 + 0.79), 2 + 4 = 6, and 0.43 + 0.79 is greater than 1; or 2.43 + 4.79 may be estimated as less than 7.50 because 2.43 is a little less than 2.5 and 4.79 is a little less than 5. Another way to estimate 2.43 + 4.79 is to round 2.43 to 2 and 4.79 to 5 so the sum is approximately 7.

Each student selects a strategy that he or she prefers to use and finds another student who prefers a different strategy. The two students compare their results as they do whole number and decimal calculations.

Give each group of two students a menu from a local restaurant.

Assessment Connections
Questioning . . .

Open with . . .

  • If you are hungry and have only $5.00, what would you order?

Probe further with . . .

  • Does this cost less than $5.00? How do you know?
  • What items did you think about as you checked to see if you had enough money?
  • Is there something else you could order with $5.00?
  • Which combination of items would total less than $3.00? How do you know?
  • Which combination of items would total between $4.00 and $5.00? How do you know?
  • Which combination would total more than $5.00?
Listen for . . .
  • Can the student round correctly?
  • Can the student justify why he or she decided to round each item cost or round the total cost?
  • Does the student explain his or her thought process clearly?
  • Does the student talk about the reasonableness of his or her 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 paper-and-pencil calculations?
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.

Additional Clarifying Activity with Assessment Connections

Students use a Texas road map to create problems involving mileage and population that must be solved using estimation. Students trade problems and estimate solutions to one another's problems.

Assessment Connections
Questioning . . . (before trading problems)

Open with . . .

  • Tell me how you used the road map to get your problem.

Probe further with . . .

  • What kind of action (joining, comparing, or separating) does your problem describe?
  • How did you decide to create this problem?
  • Is your problem clear and easily interpreted?
  • How would you solve your problem?
Questioning . . . (after trading problems)

Open with . . .

  • Estimate the solution to the problem your partner posed.

Probe further with . . .

  • How did you get this estimate?
  • What strategy did you use?
  • Can you solve this another way?
  • Is your estimate reasonable? How do you know?
  • How close do you think you are to the exact solution? Within 50 miles?
Listen for . . .
  • Does the student use approximation language?
  • Can the student clearly explain his or her thought process?
  • Is the student able to discuss the reasonableness of his or her solution?
Look for . . .
  • Does the student pose a problem that is clear and easily interpreted by the partner?
  • Does the student select the necessary information to solve the problem?
  • Can the student estimate to solve problems where exact answers are not required?
  • Does the student round to estimate a solution to the problem?
  • Does the student round correctly?
  • Can the student solve the problem in more than one way?
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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(5.5) Number, operation, and quantitative reasoning. The student makes generalizations based on observed patterns and relationships.

(5.5.a) Number, operation, and quantitative reasoning. The student makes generalizations based on observed patterns and relationships. The student is expected to describe the relationship between sets of data in graphic organizers such as lists, tables, charts, and diagrams.

activity under revision

Clarifying Activity with Assessment Connections

Students generate lists of multiples for the numerator and denominator of a given fraction and arrange the list in a chart like the following to show some possible equivalent fractions:

triangle flash card

Assessment Connections
Questioning . . .

Open with . . .

  • What patterns do you notice in the chart?

Probe further with . . .

  • What patterns do you notice in the denominator row?
  • What patterns do you notice in the numerator row?
  • What is the relationship between the numerator row and the denominator row?
  • What is the relationship between 3/4 and 9/12?
  • What are some other names for 3/4?
  • If your numerator is 18, what would be the denominator for a fraction equivalent to 3/4?
Listen for . . .
  • Is the student able to use mathematical words and symbols to describe the pattern in equivalent fractions? For example, "If you multiply the numerator and denominator of a fraction by the same factor (excluding zero), the new fraction is equivalent to the old one."
Look for . . .
  • Can the student use a list to find a pattern?
  • Can the student continue the chart without using a calculator?
  • Does the student use patterns in the numerator and denominator to generate equivalent fractions?
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 with Assessment Connections

Students make a table showing the relationship between the number of CDs bought and the total cost. For example,

table of relationship between CDs bought and cost

Assessment Connections
Questioning . . .

Open with . . .

  • What patterns do you notice?

Probe further with . . .

  • What patterns do you notice in the "Number of CDs" column?
  • What patterns do you notice in the "Total Cost in Dollars" column?
  • What is the total cost of six CDs?
  • How did you find the total cost of six CDs?
  • What is the relationship between the number of CDs and the cost?
Listen for . . .
  • Can the student use mathematical words and symbols to describe the pattern in equivalent fractions?
Look for . . .
  • Can the student find a pattern?
  • Can the student use the pattern to make a generalization and continue the chart?

(5.5.b) Number, operation, and quantitative reasoning. The student makes generalizations based on observed patterns and relationships. The student is expected to identify prime and composite numbers using concrete objects, pictorial models, and patterns in factor pairs.

Clarifying Activity with Assessment Connections

Students use tiles to build all possible rectangular arrays for the numbers 1 through 24. The students then record the arrays by cutting models out of graph paper. (Note: In this activity, a 2 by 8 array and an 8 by 2 array are considered different rectangular arrays).

array of 1 by 6, 6 by 1, 2 by 3, and 3 by 2

Assessment Connections
Questioning . . .

Open with . . .

  • What do you notice about the arrays you've created?

Probe further with . . .

  • Why do you think the number 7 has only two arrays?
  • What other numbers have only two arrays?
  • Why do you think the number 12 has more than two arrays?
  • What other numbers have more than two arrays?
  • Did any number have only one array?
  • How would you know, by looking at the arrays for a number, if that number is prime?
  • How would you know, by looking at the arrays for a number, if that number is composite?
  • Is 1 prime? Why?
  • Is 1 composite? Why?
Listen for . . .
  • Does the student notice that the number 1 is neither prime nor composite (since it is the only number with exactly one array)?
  • Does the student use mathematical language (factor, multiple, prime, composite)?
  • Does the student relate the size of the array to the factors of the number?
Look for . . .
  • Can the student build rectangular arrays of tiles to model a number?
  • Can the student translate the rectangular arrays of tiles into models cut from graph paper?
  • How does the student determine the rectangular arrays of a number? Does he or she use trial and error or demonstrate a plan?
  • Does the student use patterns of factor pairs to find all of the arrays of a number? (For example, if a student creates a 3 by 4 array, does he or she create a 4 by 3 array immediately afterward?)
  • Does the student recognize that numbers with only two arrays areprime numbers?
  • Does the student recognize that numbers with more than two arrays are composite numbers?
  • Can students identify numbers as prime, composite, or neither using the concrete models of rectangular arrays?
TAKS Connection

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's Educators' Guides to TEKS-Based Assessment, 1999–2000. Reprinted with permission.

Additional Clarifying Activity

To identify prime and composite numbers, students use a hundreds chart and color the multiples of each whole number greater than 1. For example, students first color the multiples of 2 that are greater than 2, then the multiples of 3 that are greater than 3, then the multiples of 4 that are greater than 4, etc. The colored numbers are composite numbers, while the numbers greater than 1 left uncolored are prime numbers (an example of the Sieve of Eratosthenes). Students list the prime numbers and discuss their properties (such as having exactly two factors).

Assessment Connections
Questioning . . .

Open with . . .

  • How do you know that the numbers that have been colored are composite?

Probe further with . . .

  • Are you sure that all of the composite numbers have been colored? How do you know?
  • Why are all of the numbers left uncolored prime?
  • Is 17 prime or composite? Why?
  • Is 27 prime or composite? Why?
  • Is 57 prime or composite? Why?
Listen for . . .
  • Does the student use the words "prime" or "composite" to describe a number?
  • Can the student explain why he or she lists a number as prime or composite?
Look for . . .
  • Does the student know that prime numbers have exactly two factors?
  • Can the student identify prime and composite numbers on the hundred chart?
  • Can the student use the Sieve of Eratosthenes to identify prime and composite numbers on the hundreds chart?

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(5.6) Patterns, relationships, and algebraic thinking. The student describes relationships mathematically.

(5.6) Patterns, relationships, and algebraic thinking. The student describes relationships mathematically. The student is expected to select from and use diagrams and equations such as y = 5 + 3 to represent meaningful problem situations.

activity under revision

Clarifying Activity with Assessment Connections

Part 1:

The teacher makes some index cards that fit into three different categories: a real-life situation, a number sentence representing a real-life situation, and a diagram representing a real-life situation. Each student is then supplied with two blank index cards that are large enough for the class to see (once displayed).

Students select one card from any of the three categories and then use the blank cards to create cards for the other two categories (those that are not represented on the index card selected). For example, if the student selects a card that describes a real-life situation, the student writes a number sentence on one blank card and draws a representative diagram on the other. Some of the students present their sets of index cards to the class. The teacher then collects all of the index cards for review.

Part 2:

After the cards created in part one are reviewed, the sets are distributed to students working together in small groups. Each group selects one real-life situation and prepares a short skit to act out the situation. Students return the cards to the teacher, who shuffles and then displays them. As groups of students present skits to the class, the class chooses the card number sentence and diagram that is being acted out.

Assessment Connections
Questioning . . . (part one)

Open with . . .

  • Tell me about your set of cards.

Probe further with . . .

  • How did you decide that this number sentence is appropriate for this real-life situation? Why?
  • How did you decide that this number sentence is appropriate for this diagram? Why?
  • How did you decide that this diagram is appropriate for this real-life situation? Why?
Listen for . . .
  • Does the student justify that the two representations fit the situation?
  • Does the student use appropriate mathematical language to describe the number sentence?
Look for . . .
  • Can the student connect diagrams, number sentences, and descriptions of real-life situations?
  • Are the diagrams, number sentences, and descriptions of real-life situations reasonable?
Questioning . . . (part two)

Open with . . .

  • Tell me about your skit.

Probe further with . . .

  • How do you decide which real-life situation to choose for your skit?

Open with . . .

  • For the audience: Which number sentence and diagram are being acted out?

Probe further with . . .

  • How did you decide that this is the number sentence? Why?
  • Are there other number sentences that may have been appropriate?
  • What made you eliminate the other number sentences?
  • How did you decide that this diagram is appropriate for this real-life situation?
  • What made you eliminate other diagrams?
Listen for . . .
  • Does the student clearly describe and justify the decisions made to find the representations that fit the situation acted out?
  • Does the student use appropriate mathematical language to describe the number sentence?
Look for . . .
  • Can the student act out real-life situations involving arithmetic?
  • Can the student select from and use diagrams and number sentences to represent real-life situations?
  • Can the student apply the process of elimination to determine the number sentence and diagram being acted out?
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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(5.7) Geometry and spatial reasoning. The student generates geometric definitions using critical attributes.

(5.7) Geometry and spatial reasoning. The student generates geometric definitions using critical attributes. The student is expected to identify essential attributes including parallel, perpendicular, and congruent parts of two- and three-dimensional geometric figures.

Clarifying Activity with Assessment Connections

Students use marshmallows or gumdrops and toothpicks to build models of two-dimensional geometric shapes and three-dimensional solids, identifying the critical attributes of each model, such as which pairs of lines are parallel, perpendicular, or congruent. Students then compare models with a partner and describe similarities and differences in shapes and solids.

Assessment Connections
Questioning . . .

Open with . . .

  • What can you tell me about your geometric structures?

Probe further with . . .

  • How are your structures and your partner's structures the same?
  • How do your structures and your partner's structures differ?
  • Are there any parts of your model that are parallel? Where?
  • How do you know the parts are parallel?
  • Are there any parts of your model that are perpendicular? Where?
  • How do you know if parts are perpendicular?
  • Can parallel parts also be perpendicular?
  • Are there any faces or edges of your model that are congruent? Where?
  • How do you know the parts are congruent?
  • How do you know if two shapes are congruent?
  • Can you show me another part of your model that is congruent (parallel, or perpendicular) to this part?
Listen for . . .
  • Does the student use corners, edges, and faces to describe the structures?
  • Does the student use mathematical vocabulary to describe the structures' attributes (such as parallel, perpendicular, right angles, intersecting, or congruent)?
  • Can the student describe what it means for parts to be parallel, perpendicular, and congruent?
Look for . . .
  • Can the student identify models of parallel and perpendicular lines and congruent shapes?
  • Can the student identify parts of the structure that are not parallel, perpendicular, or congruent?
  • Does the student recognize the relationship between right angles and perpendicular lines?
  • Can the student sketch the shape or solid?
  • Can the student predict the effects of a change in the structure?
  • Does the student recognize that congruent shapes are the same size and shape?
  • Does the student recognize that lines extend (and that therefore, lines that do not intersect in vision may not be parallel)?
  • Does the student recognize that lines can intersect but not be perpendicular?
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.

activity under revision

Additional Clarifying Activity with Assessment Connections

Students play "Who Am I" using models of geometric shapes and solids and clue cards that have sets of critical attributes listed on them. As clues are given, students eliminate the models of shapes and solids until only shapes that fit the set of critical attributes remain. For example, the clue cards says, "I am a quadrilateral" followed by, "I have four congruent angles." Students first eliminate all the models that are not quadrilaterals. Then they eliminate all the quadrilaterals that do not have four right angles and are left with all the rectangles (including squares).

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me about the shapes and solids that you eliminated.

Probe further with . . .

  • Why did you eliminate those shapes and solids?
  • What are the similarities and differences between the shapes and solids that you did not eliminate?
  • What might be a next clue? Why?
Listen for . . .
  • Does the student use appropriate mathematical vocabulary for critical attributes (e.g., vertices, angles, corners, side, edges)?
  • Can the student create a description for two-dimensional shapes and three-dimensional solids that includes mathematical language?
Look for . . .
  • Is the student able to demonstrate knowledge relevant to the properties of geometric shapes?
  • Can the student use critical attributes to identify geometric shapes or solids?
  • Can the student identify shapes and solids that do not fit a particular definition?
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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(5.8) Geometry and spatial reasoning. The student models transformations.

(5.8.a) Geometry and spatial reasoning. The student models transformations. The student is expected to sketch the results of translations, rotations, and reflections on a Quadrant I coordinate grid.

activity under revision

Clarifying Activity with Assessment Connections

Students use translations, reflections, and rotations to create tessellations with geometry software, polygon tiles, or paper patterns.

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me about the pattern you created.

Probe further with . . .

  • What basic shape did you use to create your pattern?
  • How did you create your pattern from the basic shape?
  • Did your pattern involve a translation? How do you know?
  • Did your pattern involve a rotation? How do you know?
  • Did your pattern involve a reflection? How do you know?
  • Name a transformation that you did not use? Why?
Listen for . . .
  • Does the student create and describe mental images of the pattern?
  • Can the student describe the transformation used to create the pattern?
  • Does the student use mathematical vocabulary to describe the pattern (e.g., reflection, translation, rotation, congruent)?
Look for . . .
  • Can the student sketch translations, reflections, and rotations of basic shapes to form tessellation patterns?
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.

(5.8.b) Geometry and spatial reasoning. The student models transformations. The student is expected to identify the transformation that generates one figure from the other when given two congruent figures on a Quadrant I coordinate grid.

activity under revision

Clarifying Activity with Assessment Connections

Students analyze examples of tessellations such as fabric and wallpaper designs, bricklaying patterns, works of art, and patterns in nature.

Assessment Connections
Questioning . . .

Open with . . .

  • Which transformations appear in these examples?

Probe further with . . .

  • Can you describe a motion or a series of motions that will show that the two shapes are congruent?
  • Which transformations are examples of reflections? How do you know?
  • Which transformations are examples of translations? How do you know?
  • Which transformations are examples of rotations? How do you know?
  • What are the differences between a translation, a rotation, and a reflection?
Listen for . . .
  • Can the student predict and describe the results of translation, reflection, rotation of two-dimensional shapes?
  • Does the student use mathematical vocabulary to describe the transformations (e.g., reflection, translation, rotation, congruent)?
  • Can the student explain the differences between translation, rotation, and a reflection?
Look for . . .
  • Can the student identify transformations that generate one figure from the other when given congruent figures?
  • Can the student describe a motion or series of motions that will show the two shapes are congruent?
  • Can the student create and describe mental images of objects, patterns, or paths?
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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(5.9) Geometry and spatial reasoning. The student recognizes the connection between ordered pairs of numbers and locations of points on a plane.

(5.9) Geometry and spatial reasoning. The student recognizes the connection between ordered pairs of numbers and locations of points on a plane. The student is expected to locate and name points on a coordinate grid using ordered pairs of whole numbers.

Clarifying Activity with Assessment Connections

Students choose a partner. One partner secretly places a small washer around a peg on a geoboard that is used to represent the first quadrant. The other partner tries to guess where the washer is by naming the ordered pair that identifies the location of the peg on the geoboard grid. The first partner responds with a clue, telling the other what direction they need to go from their guess to find the peg with the washer (for example, the washer is to the left and up from your guess). The second partner continues to guess until he or she finds the location of the washer.

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me how you locate the washer.

Probe further with . . .

  • Describe how you travel from (1,5) to (2,3)?
  • If you are told that the washer is to the left and up from your guess, how will you decide your next guess?
  • What are possible choices for your next guess? Why?
  • If you are told that the washer is down, how will you decide your next guess? Why?
Listen for . . .
  • Can the student specify locations on a coordinate grid using ordered pairs?
  • Can the student give appropriate directional clues as to location on the grid of the washer in relation to each guess?
  • Can the student describe a path between locations? For example, to travel from (1,5) to (2,3) you need to move one peg to the right and two pegs down.
  • Can the student follow appropriate directional clues? For example, if the student is given the clue that the washer is to the right, does the student recognize that the first coordinate of the ordered pair increases but the second coordinate remains the same?
Look for . . .
  • Can the student locate points on a coordinate grid using ordered pairs of numbers?
  • How does the student use clues to inform the next guess?
  • Does the student use a strategy that reduces the number of guesses needed to find the washer?
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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(5.10) Measurement. The student applies measurement concepts involving length (including perimeter), area, capacity/volume, and weight/mass to solve problems.

(5.10.a) Measurement. The student applies measurement concepts involving length (including perimeter), area, capacity/volume, and weight/mass to solve problems. The student is expected to perform simple conversions within the same measurement system (SI (metric) or customary).

Clarifying Activity with Assessment Connections

Students estimate the number of cups needed to fill a gallon milk jug, then use a measuring cup to pour water into the jug. Students use a marker to note the water level in the jug after each cup of water is added. Students use the results to create a table showing the relationship between cups and gallons.

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me about the relationship between cups and gallons.

Probe further with . . .

  • How many cups are in a gallon?
  • What part of a gallon is one cup?
  • How many cups are in two gallons?
  • How many gallons are in 32 cups? How do you know?
  • How many gallons are in 18 cups? How do you know?
  • How many cups are in 10 gallons? How do you know?
Listen for . . .
  • Can the student describe the relationship between cups and gallons?
  • Can the student use fractions to describe the relationship between cups and gallons?
  • Can the student explain how he or she determined the relationship between cups and gallons?
Look for . . .
  • Can the student create a table showing the relationship between cups and gallons?
  • Does the student accurately mark the gallon jug?
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.

(5.10.b) Measurement. The student applies measurement concepts involving length (including perimeter), area, capacity/volume, and weight/mass to solve problems. The student is expected to connect models for perimeter, area, and volume with their respective formulas.

activity under revision

(5.10.c) Measurement. The student applies measurement concepts involving length (including perimeter), area, capacity/volume, and weight/mass to solve problems. The student is expected to select and use appropriate units and formulas to measure length, perimeter, area, and volume.

activity under revision

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(5.11) Measurement. The student applies measurement concepts. The student measures time and temperature (in degrees Fahrenheit and Celsius).

(5.11.a) Measurement. The student applies measurement concepts. The student measures time and temperature (in degrees Fahrenheit and Celsius). The student is expected to solve problems involving changes in temperature.

activity under revision

(5.11.b) Measurement. The student applies measurement concepts. The student measures time and temperature (in degrees Fahrenheit and Celsius). The student is expected to solve problems involving elapsed time.

activity under revision

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(5.12) Probability and statistics. The student describes and predicts the results of a probability experiment.

(5.12.a) Probability and statistics. The student describes and predicts the results of a probability experiment. The student is expected to use fractions to describe the results of an experiment.

Clarifying Activity with Assessment Connections

Students separate into five groups. Each group has a small box that has been secretly filled with ten marbles or colored gumballs (five green, two blue, two red, and one white). A small hole is cut in one corner of the box; the hole is large enough for a marble to slip into it and be seen when the box is tilted, but small enough so that the marble cannot fall out of the box through the hole. Each group does 20 trials of shaking the box, tilting the box, peeking at the marble, and recording the color of the marble. Students use fractions to record the results of their 20 trials; for example, 6/20 of the trials are green.

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me about the results of your experiment.

Probe further with . . .

  • How many green marbles did you see in the 20 trials?
  • In what proportion of the trials did you see blue marbles?
  • What does this indicate about the likelihood of a blue marble reappearing if the trial were performed again?
  • Which color is most likely to appear?
Listen for . . .
  • Can the student clearly explain the results of the experiment?
  • Does the student use appropriate language when answering "how many" and "how much" questions based on the results of the experiment?
  • Does the student use whole numbers to answer "how many" questions?
  • Does the student use fractions to answer "how much" and "what proportion" questions?
Look for . . .
  • Can the student describe and record the results of the experiment using fractions?
TAKS Connection

assessment item from TEA's released tests

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

(5.12.b) Probability and statistics. The student describes and predicts the results of a probability experiment. The student is expected to use experimental results to make predictions.

Clarifying Activity with Assessment Connections

Students in each group use their group's data from the secret box (as described in 5.12A) to make a prediction about what marbles are in the box. The groups combine their data and the class uses all of the data to evaluate and refine their predictions. Students then open their boxes, compare the contents to the predictions they made, and discuss their findings.

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me your predictions about the marbles that are in the box.

Probe further with . . .

  • Based on this experiment, can you tell me how many green marbles are in the box? (No, only "how much" or "what proportion" questions can be predicted unless the total number of marbles was originally known.)
  • What proportion of the marbles do you think are green? Why?
  • What proportion of the marbles do you think are blue? Why?
  • What proportion of the marbles do you think are red? Why?
  • What proportion of the marbles do you think are white? Why?
  • If I told you that the box contained ten marbles, how many marbles do you think are green? Blue? Red? White?
  • If I told you that the box contained 100 marbles, how many marbles do you think are green? Blue? Red? White?
Listen for . . .
  • Can the student clearly discuss the findings of the experiment?
  • Does the student make reasonable predictions?
  • Does the student justify his or her predictions?
Look for . . .
  • Can the student compare the findings of his or her group's data to the class data?
  • Does the student make appropriate predictions about the contents of the box based on the data?
TAKS Connection

assessment item from TEA's released tests

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

(5.12.c) Probability and statistics. The student describes and predicts the results of a probability experiment. The student is expected to list all possible outcomes of a probability experiment such as tossing a coin.

activity under revision

Clarifying Activity with Assessment Connections

Students perform an experiment by flipping two coins 50 times and recording the results in a table. Students then use pairs of numbers to describe the data they collected about flipping the coins. For example: "Twelve out of 50 times in our data the result was two heads. When we combined our data with that of another group, 23 out of 100 times the result was two heads."

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me the results of your experiment.

Probe further with . . .

  • What are the possible outcomes? How do you know?
  • How much of your experiment resulted in both heads? How do you know? How did you keep track of this?
  • When you joined another group, how much of their tosses were both heads?
  • After joining your data, how much were both heads?
  • How much of your 50 tosses had exactly one head?
  • When you joined another group, how did the number that resulted in exactly one head compare to all tosses?
  • After joining your data, what part resulted in exactly one head?
Listen for . . .
  • Is the student using language such as "Twelve out of 50 were both heads?"
Look for . . .
  • Does the student accurately record the results in a reasonable and efficient way?
  • Does the student use pairs of numbers to compare the favorable outcomes with all possible outcomes?

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

(5.13.a) Probability and statistics. The student solves problems by collecting, organizing, displaying, and interpreting sets of data. The student is expected to use tables of related number pairs to make line graphs.

Clarifying Activity with Assessment Connections

Students plant five pinto beans in identical containers of dirt at the same time. Students put 0 teaspoons of fertilizer into the first container, 1 teaspoon into the second container, 2 teaspoons into the third container, 3 teaspoons into the fourth container, and 4 teaspoons into the fifth container. Plants should receive identical amounts of water and sunlight. Students collect the information on daily growth for each container, using number pairs in a table to represent the day and the height of the plant. For example:

table showing height of plant on each day

Students use the number pairs to make a line graph for each container in order to compare the effects of different amounts of fertilizer.

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me about your graphs that show the daily growth of the plants.

Probe further with . . .

  • How did you use the number pairs representing day and height to make the graph?
  • Can you explain what these graphs are telling you?
  • How are the graphs different? Why?
  • What are the effects of the different amounts of fertilizer?
Listen for . . .
  • Can the student use the graphs to explain the effects of the different amounts of fertilizer?
Look for . . .
  • Can the student create line graphs using tables of numbers?
  • Does the student create five graphs (one for each amount of fertilizer)?
  • Does the student label the graphs so they are easy to interpret?
TAKS Connection

assessment item from TEA's released tests

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

(5.13.b) Probability and statistics. The student solves problems by collecting, organizing, displaying, and interpreting sets of data. The student is expected to describe characteristics of data presented in tables and graphs including median, mode, and range.

activity under revision

Clarifying Activity with Assessment Connections

Students spin three different spinners (see below) ten times each and record, on a class line plot, the number of times they land on blue. The results are represented on the graph using a different symbol for each spinner. Students write about the shape and the spread of the data on their line plot.

three spinners

Possible line plot for Spinner 1:

plot for spinner 1

Number of times Spinner 1 landed on blue

Possible line plot for Spinner 2:

plot for spinner 1

Number of times Spinner 2 landed on blue

Possible line plot for Spinner 3:

plot for spinner 1

Number of times Spinner 3 landed on blue

Assessment Connections
Questioning . . .

Open with . . .

  • Describe the data and compare the number of blue landings for the spinners.

Probe further with . . .

  • What do you notice about the shapes of the data from the spinners? How are they the same? How are they different?
  • What is a typical number of blue landings for spinner 1?
  • What is the median number of blue landings for spinner 1? Is this reasonable based on spinner 1? Why?
  • What is the median number of blue landings for spinner 2? Is this reasonable? Why?
  • What is the median number of blue landings for spinner 3? Is this reasonable? Why?
  • What do you notice about the spreads of the data from the spinners?
  • What is the range of the number of blue landings for spinner 1? 2? 3?
  • Is there an outlier? What does it tell you?
Listen for . . .
  • Does the student use appropriate mathematical vocabulary to compare the typical number of blue landings for the three spinners (e.g., median, range, shape, spread, data)?
  • Can the student describe and compare the data?
  • Can the student give a reasonable justification for the shape and spread of the data?
Look for . . .
  • Can the student identify and compare the shape, spread, and typical number of blue landings for the three spinners?
  • Can the student gather, organize, and display his or her data for each spinner?
  • Can the student incorporate his or her data into the class data to create a class line plot?
  • Does the student understand the concept of median?
  • Can the student determine the median?
  • Does the student understand the concept of range?
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.

activity under revision

Additional Clarifying Activity

Students collect and organize data about their resting pulse rates. Students can describe the shape of the data and determine the typical (median) resting pulse rate and range for the class. Students then exercise, take their post-exercise pulse rates, organize and display the data, and find the median and range. Students compare the exercise results with the resting pulse rates.

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me about your pulse rate data.

Probe further with . . .

  • How can you compare the pulse rates?
  • What was the shape of the data for the resting pulse rate?
  • What is a typical (median) resting pulse rate?
  • How did you find the median?
  • What is the spread of the data for the resting pulse rate (e.g., from ____ to ____)?
  • What is the range of the data for the resting pulse rate (e.g., a single number)? Why?
  • What was the shape of the data for the exercised pulse rate?
  • What is a typical (median) exercised pulse rate. Why?
  • What is the spread of the data for the exercised pulse rate (e.g., from ____ to ____)?
  • What is the range of the data for the exercised pulse rate (e.g., a single number)?
  • How did you find the range?
  • What can you infer about the resting pulse rate when compared to the exercised pulse rate? Why?
Listen for . . .
  • Does the student use appropriate mathematical vocabulary to compare post-exercise pulse rate data with resting pulse rate data (e.g., median, range, shape, spread, data)?
  • Can the student describe the data?
Look for . . .
  • Can the student gather, organize, and display pulse rate data?
  • Does the student understand the concept of median?
  • Can the student determine the median?
  • Does the student understand the concept of range?

(5.13.c) Probability and statistics. The student solves problems by collecting, organizing, displaying, and interpreting sets of data. The student is expected to graph a given set of data using an appropriate graphical representation such as a picture or line graph.

Clarifying Activity with Assessment Connections

Students gather data concerning classmates' favorite or least favorite food. They construct a graph they feel will be appropriate in supporting their requests for specific foods to be served in the school cafeteria.

Assessment Connections
Questioning . . .

Open with . . .

  • How did you decide which graphical representation to use to represent the data?

Probe further with . . .

  • Why do you think this graphical representation supports your request?
  • Are there other graphical representations you could use to represent the data?
  • Could you use a bar graph? Why?
  • Could you use a line graph? Why?
  • Could you use a picture graph? Why?
  • Could you use a number line? Why?
Listen for . . .
  • Can the student justify why he or she would or would not use a specific graphical representation?
  • Does the student clearly and effectively explain the results of the survey?
Look for . . .
  • Does the student select an appropriate graphical representation?
  • Can the student graph a given set of data using an appropriate graphical representation?
  • Does the student appropriately label 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 Released Tests and Interactive Online Tests, Spring 2001 Mathematics TAAS. Reprinted with permission.

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(5.14) Underlying processes and mathematical tools. The student applies Grade 5 mathematics to solve problems connected to everyday experiences and activities in and outside of school.

(5.14.a) Underlying processes and mathematical tools. The student applies Grade 5 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

Students are each assigned a topic or concept from the unit being studied (such as fractions). Students interview parents and friends to identify three ways this concept is used in the real world.

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me how the people you interviewed used this concept in the real world.

Probe further with . . .

  • What did you hear that you already knew?
  • What did you learn? (For example, mathematics is used to solve a variety of real-world problems.)
  • Were you surprised at the ways people use this concept? How so?
Listen for . . .
  • Can the student identify mathematics used in the real world?
Look for . . .
  • Does the student identify a variety of uses of mathematics in their world including some that are unusual?
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.

(5.14.b) Underlying processes and mathematical tools. The student applies Grade 5 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 work together in small groups to plan and present a bid for organizing and conducting a party, including games and refreshments.

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me about your party plans.

Probe further with . . .

  • What is your bid for organizing and conducting the party plans?
  • Are all of your expenses included?
  • How many people are you expecting?
  • What refreshments are you planning?
  • What purchases will you need to make? Will this be enough for the people who attend?
  • How much does each cost?
  • What is the total cost?
  • How long is the party?
  • When will it begin?
  • When will it end?
  • What activities do you have planned?
  • How long will these activities last?
  • When will you serve refreshments?
  • Is this reasonable?
Listen for . . .
  • Can the student make a plan?
  • Can the student determine the reasonableness of the plan?
Look for . . .
  • Does the student include all of the expenses?
  • Is the student's arithmetic correct?
  • Does the student's timing seem reasonable?
  • Is the student able to self-correct errors?
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.

(5.14.c) Underlying processes and mathematical tools. The student applies Grade 5 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 problemsolving 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 . . .
  • Can the student describe the strategy he or she used?
  • Is the student able to use important information from the problem in his or her solution?
  • Is the student able to discuss a variety of strategies?
Look for . . .
  • Does the student select 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 and sharing strategies with others?
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.

(5.14.d) Underlying processes and mathematical tools. The student applies Grade 5 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 tiles to build all possible rectangular arrays for the numbers 1 through 24 and record their arrays by cutting models of the arrays from graph paper. (Note: In this activity, a 2 by 8 array and an 8 by 2 array are considered different rectangular arrays.) Students sort and classify numbers according to their rectangular arrays, e.g., numbers that have exactly two arrays (prime numbers), numbers that have more than two arrays (composite numbers), and the number that has exactly one array (1, the multiplicative identity element).

arrays of 1 by 6, 6 by 1, 2 by 3, and 3 by 2

Assessment Connections
Questioning . . .

Open with . . .

  • Describe how you classified the numbers from 1 to 24 as prime or composite.

Probe further with . . .

  • What is a prime number? What is a composite number?
  • How did building rectangular arrays help you identify prime and composite numbers?
  • How can you determine the factors of numbers using rectangular arrays?
  • How might you have used a calculator to determine if a number is prime or composite?
Listen for . . .
  • Does the student use appropriate vocabulary to clearly describe the methods used to classify numbers using rectangular arrays?
Look for . . .
  • Can the student use tools such as real objects, manipulatives, and technology to solve problems?
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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(5.15) Underlying processes and mathematical tools. The student communicates about Grade 5 mathematics using informal language.

(5.15.a) Underlying processes and mathematical tools. The student communicates about Grade 5 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 plant five pinto beans in identical containers of dirt at the same time. Students put 0 teaspoons of fertilizer into the first container, 1 teaspoon into the second container, 2 teaspoons into the third container, 3 teaspoons into the fourth container, and 4 teaspoons into the fifth container. Plants should receive identical amounts of water and sunlight. Students collect the information on daily growth for each container, using number pairs in a table to represent the day and the height of the plant. For example:

table showing height of plant on each day

Students use the number pairs to make a line graph for each container in order to compare the effects of different amounts of fertilizer.

Assessment Connections
Questioning . . .

Open with . . .

  • Tell me about your graphs that show the daily growth of the plants.

Probe further with . . .

  • How did you use the number pairs representing day and height to make the graph?
  • Can you explain what these graphs are telling you?
  • What are the effects of the different amounts of fertilizer?
Listen for . . .
  • Can the student explain the observations using words, graphs, and numbers?
  • Can the student explain the effects of the different amounts of fertilizer using the graphs?
Look for . . .
  • Can the student accurately measure the fertilizer to put into the containers?
  • Can the student measure the height of the plant?
  • Can the student record observations in a table?
  • Can the student create line graphs using tables of numbers?
  • Does the student create five graphs (one for each amount of fertilizer)?
  • Does the student label the graphs so they are easy to interpret?
  • Is the student able to self-correct errors?
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.

(5.15.b) Underlying processes and mathematical tools. The student communicates about Grade 5 mathematics using informal language. The student is expected to relate informal language to mathematical language and symbols.

Clarifying Activity with Assessment Connections

Students select an index card that has a description of a real-life situation written on it. For the real-life situation, students write an appropriate number sentence and draw a diagram, if possible.

Assessment Connections
Questioning . . .

Open with . . .

  • How did you create your number sentences?

Probe further with . . .

  • How did you decide which symbols to use in your number sentences?
  • What actions in the situation are important in creating your number sentences?
Listen for . . .
  • Does the student explain his or her number sentence by using appropriate informal language?
Look for . . .
  • Does the number sentence match the action in the situation?
  • Is the student able to self-correct errors?
TAKS Connection

assessment item from TEA's released tests

© Texas Education Agency. Excerpted from TEA's Educators' Guides to TEKS-Based Assessment, 1999–2000. Reprinted with permission.

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

(5.16.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 build towers of cubes to represent the factors of numbers on a hundreds chart. Students place a different colored cube on the multiples of each number, 2 through 9. For example, red cubes will be placed on multiples of 2, green cubes on multiples of 3, blue cubes on multiples of 4, and so forth.

Numbers that are multiples of more than one of these factors will have towers made up of different colors. For example, 4 will have a tower made up of a red cube and a blue cube. Students observe and describe the patterns of that form. Then students carefully remove the towers, place them in a bag or box, randomly draw a tower from the bag or box, and try to determine where that tower should be placed on the hundreds chart.

Assessment Connections
Questioning . . .

Open with . . .

  • What do you notice about the towers?

Probe further with . . .

  • What patterns have you noticed?
  • If a tower has a blue cube, what other cube(s) would it contain? How do you know?
  • Where might this tower be placed on the hundreds chart? Why?
  • Is there another appropriate place for this tower on the hundreds chart? Why?
Listen for . . .
  • Is the student able to describe the pattern he or she notices?
  • Is the student able to justify his or her thinking?
Look for . . .
  • Is the student able to recognize a pattern in the towers?
  • Can the student make generalizations from the patterns?
  • Can the student use generalizations and patterns to match the towers to numbers on a hundreds chart?
TAKS Connection

assessment item from TEA's released tests

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

(5.16.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

Students should consistently justify their answers in problemsolving situations and explain how they arrived at a solution. The following is an example: Students brainstorm real-world reasons to use multiplication and record them on a chart. They then select an example from the chart, write an original problem for others to solve, and exchange problems.

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?
  • Does your problem use whole numbers?
  • Can your problem be answered by multiplying whole numbers?
Listen for . . .
  • Does the student's explanation match his or her written work?
Look for . . .
  • Can the student identify real-world problems that can be solved usingmultiplication?
  • Does the student pose a problem that can be solved by multiplying whole numbers?
  • Does the student pose a problem that is clear and easily interpreted by his or her partner?
Questioning . . . (after trading problems)

Open with . . .

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

Probe further with . . .

  • How are you solving the problem? Why?
  • What number sentence can you write to show your problem?
  • Can you solve the problem another way?
  • Is your solution reasonable? How do you know?
Listen for . . .
  • Does the student's explanation match his or her written work?
  • Is the student able to discuss the reasonableness of his or her solution?
Look for . . .
  • Can the student identify the information necessary to solve the problem?
  • Can the student use multiplication 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?
  • Can the student self-correct any errors?
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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