home » instructional materials » grade 4 » clarifying activities with assessment connections

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.

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

(4.1.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.

Clarifying Activity with Assessment Connections

Students use three different colors of paper to make place-value pocket charts, designating one color for each period. Using number cards, students model numbers that are read aloud to them by placing their cards in the correct place of each period's pocket. For example, for 12,405 students place number cards in the following positions:

Students can continue the activity by working with partners, taking turns with one student reading a number and the other student displaying it.

Assessment Connections

Questioning . . .

Open with . . .

• What is the number in your place-value chart?

Probe further with . . .

• Is this the number read aloud to you?
• How did you decide where to put the number cards on your place-value chart to represent the number?
• What digit is in the thousands place? Tens place? Millions place? Ten thousands place?
• What would happen if I swap the number cards in the thousands place and the tens place? How would the new number compare to the original? Why?
• What is the greatest number you can create by moving the number cards on your place-value chart?
• What is the lowest number you can create by moving the number cards on your place-value chart?
• How would your five-digit number compare to a seven-digit number?
• How would you write the number using words?

Listen for . . .

• Does the student accurately read the numbers using the proper number naming patterns?
• Does the student clearly describe the strategy used to create large numbers?
• Does the student use ideas of place value to explain and justify strategies and responses?

Look for . . .

• Does the student demonstrate an understanding of the number system and place value?
• Does the student use place value and patterns in number relationships to compare numbers?
• 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)?
• Can the student read and compare numbers with the digit 0 in at least one place?
• Can the student write the number using words?

TAKS Connection

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

Additional Clarifying Activity

Students work together to represent two numbers using their place-value pocket charts. They place the pocket charts displaying their numbers one under the other and, beginning with the number in the greatest place, compare each number digit by digit. Students then use words and symbols to record the comparison. For example, they say, "5,292 is less than 5,305" and write "5,292 < 5,305."

(4.1.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 involving tenths and hundredths, including money, using concrete objects and pictorial models.

Clarifying Activity with Assessment Connections

Students are given index cards with three decimals involving tenths and hundredths. Students use base-ten blocks to model, record, read, and compare the decimal numbers, with the 10x10x1 square flat representing one, the 10x1x1 rod representing one tenth, and the 1x1x1 small cube representing one hundredth.

Assessment Connections

Questioning . . .

Open with . . .

• Tell me about the decimals on your index card.

Probe further with . . .

• How do you read the numbers?
• How did you decide which blocks to use to model your numbers?
• Could you use another collection of base-ten blocks to model your number another way? How?
• Which of the models uses the fewest number of pieces? Why?
• Order your decimals from least to greatest.
• How did you decide which decimal is the least?
• How did you decide which decimal is the greatest?
• What is the digit in the units place of the greatest decimal?
• What is the digit in the tenths place of the least decimal?
• What is the digit in the hundredths place of the decimal that was neither the greatest nor the least?

Listen for . . .

• Does the student read the decimals correctly?
• Can the student clearly describe the strategy used to create the models?
• Can the student explain the strategy used to compare and order the decimals?

Look for . . .

• Can the student use base-ten blocks to model decimal numbers involving tenths and hundredths?
• Does the student demonstrate a grasp of the number system and place value for decimals?
• Does the student use place value and number relationship patterns to compare decimal numbers?
• Can the students read, model, and compare decimals when at least one of the digits is 0?
• Can the student identify the values in the different places in a decimal number?

TAKS Connection

• This student expectation is not tested on TAKS. Although this is not directly tested at Grade 4, it is an important foundation for student expectations tested at later grades.

Additional Clarifying Activity

Students use play money (dollars, dimes, and pennies) to model, record, read, and compare decimal numbers.

- Top -

(4.2) Number, operation, and quantitative reasoning. The student describes and compares fractional parts of whole objects or sets of objects.

(4.2.a) Number, operation, and quantitative reasoning. The student describes and compares fractional parts of whole objects or sets of objects. The student is expected to use concrete objects and pictorial models to generate equivalent fractions.

Clarifying Activity with Assessment Connections

Students use Cuisenaire® rods (fraction strips, pattern blocks, or other manipulatives) to build a wall in which 1 is represented by a train of rods. For example, an orange rod plus a red rod might represent 1. Students then use the wall to identify equivalent fractions. For example, if orange + red is 1, then 1 dark green (1/2) = 2 light greens (2/4), and 3 reds (3/6) = 6 whites (6/12).

To keep track of findings, students make a list of the fractions equivalent to 1/2 and describe how each is represented in their walls. Using graph paper, students draw their wall and label the fractions.

Assessment Connections

Questioning . . .

Open with . . .

• If we say that an orange and red rod together in your wall represents one, then do you agree that one dark green rod represents 1/2? Why? Use your wall to identify fractions equivalent to 1/2. How do you know these fractions are equivalent to 1/2?

Probe further with . . .

• What do you notice about the fractions equivalent to 1/2?
• Using your wall, what do you notice about 1/2 and 3/6? 1/3 and 2/6? 2/3 and 4/6?
• What patterns do you notice?
• What are some other names for 1/2? 1/4? 1/3? How do you know?
• How much does an orange rod represent? How do you know?
• How much does a red rod represent? How do you know?

Listen for . . .

• Can the student use mathematical language to describe how he or she generated equivalent fractions? (numerator, denominator, equivalent, factor, equals)
• Is the student using fractions to answer "how much" questions?
• Can the student describe parts of the wall length using fractions?

Look for . . .

• Can the student justify equivalent fractions using concrete models?
• Can the student generate equivalent fractions using a concrete model?
• Can the student write fractions?
• Is the student able to notice patterns in the lists of equivalent fractions?
• Can the student record the wall on grid paper?

TAKS Connection

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

Additional Clarifying Activity

Students use pattern blocks to represent fractions. They answer questions such as, "If we say that 1 yellow hexagon = 1, what fractional part does each of the other pattern blocks represent? Which arrangements of single-color blocks represent 1/2? 1/3? If we say that 2 hexagons = 1, what fractional part does each of the other pattern blocks represent now? Which arrangements of single-color blocks now represent 1/2? 1/3? 1/4? 1/6?" Students record their observations in a table and look for patterns.

(4.2.b) Number, operation, and quantitative reasoning. The student describes and compares fractional parts of whole objects or sets of objects. The student is expected to model fraction quantities greater than one using concrete objects and pictorial models.

Clarifying Activity with Assessment Connections

Students select a concrete model (such as pattern blocks, fraction strips, or Cuisenaire® rods) that can be used to represent fractions. Using their model, they build representations of mixed numbers. For example, when one orange rod represents 1, students show that 5 red rods or 5/5 = 1; 6 red rods or 6/5 = 1 and 1/5; 7 red rods or 7/5 = 1 and 2/5; and so forth.

Assessment Connections

Questioning . . .

Open with . . .

• If one orange rod represents 1, use the red rods to show me 2 and 4/5.

Probe further with . . .

• How many red rods make 1? (5)
• How much of 1 is a red rod? (1/5)
• How many red rods will you need to represent 2 and 4/5? (14) Why?
• How would you write this as a fraction? (14/5)
• Draw a picture to represent 2 and 4/5.

Listen for . . .

• Does the student use appropriate vocabulary?
• Does the student communicate an understanding of the concept of fractions and mixed numbers?

Look for . . .

• Can the students create a concrete model for fraction quantities greater than 1?
• Can the student use symbols to write the fractions? (for example, 3/2)
• Is the student able to demonstrate how to make one whole from a fractional part?
• Can the student draw a representation of the fraction greater than 1?

TAKS Connection

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

Additional Clarifying Activity

Students use concrete models and fraction calculators, such as the TI Math Explorer, to explore mixed numbers by modeling an improper fraction (like 15/12), entering the improper fraction into the calculator, using the Ab/c key to change it to a mixed number, and then using the key to change it back to the improper fraction. Students explore several improper fractions and answer questions such as, "What patterns do you see? How does the fraction you enter into the calculator match your concrete model? How does the calculator display of the mixed number match your concrete model? Can you predict what the calculator display will be when you press the Ab/c key? How do you know?"

(4.2.c) Number, operation, and quantitative reasoning. The student describes and compares fractional parts of whole objects or sets of objects. The student is expected to compare and order fractions using concrete objects and pictorial models.

Clarifying Activity with Assessment Connections

Pairs of students select four cards from a deck of fraction cards. Students order the cards using fraction strips, circles, other manipulatives, or pictorial models.

Assessment Connections

Questioning . . .

Open with . . .

• How did you order your fraction cards?

Probe further with . . .

• Which fraction is least? Greatest? How do you know?
• Do your fraction models match the fraction cards?
• How did you decide to model the fractions this way?
• What did you notice first about your fractions?

Listen for . . .

• Does the student clearly describe his or her strategy?
• Does the student correctly identify the fractions?
• Does the student use appropriate language to talk about the fractions?

Look for . . .

• Can the student order the fractions?
• Can the student model the fractions using concrete or pictorial models?
• How does the student model the fractions?
• Does the student recognize unit fractions (numerator is 1)?

TAKS Connection

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

(4.2.d) Number, operation, and quantitative reasoning. The student describes and compares fractional parts of whole objects or sets of objects. The student is expected to relate decimals to fractions that name tenths and hundredths using concrete objects and pictorial models.

Clarifying Activity with Assessment Connections

Students use base-ten blocks to represent fractions and record them in both fraction and decimal form. For example, if the 10x10x1 block represents 1, then two 10x1x1 rods represent 2/10 or 0.2, and 23 of the small cubes represent 23/100 or 0.23.

Assessment Connections

Questioning . . .

Open with . . .

• Can you represent twenty-five hundredths with your base-ten blocks?

Probe further with . . .

• How did you decide how to build your model?
• What digit is in the tenths place of the decimal? In the hundredths place?
• Could you have chosen a different way to build your model? How could it have been different? How did it need to be the same?
• Can you write a fraction equivalent to this decimal?
• Can you name other fractions that are equivalent?
• How did you find these equivalent factions?
• How do you know they are equivalent?

Listen for . . .

• Can the student identify place value of decimals through hundredths?
• Can the student explain and give reasons for the decimal model he or she built?
• Does the student use appropriate mathematical language to indicate an understanding of place value and equivalence?
• Can the student clearly explain the process used to determine fractions equivalent to the decimal?

Look for . . .

• Can the student represent a decimal number using base-ten blocks?
• Can the student use the base-ten blocks model to relate fractions to decimals that name tenths and hundredths?
• Are the fractions accurately written?

TAKS Connection

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

- Top -

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

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

Clarifying Activity with Assessment Connections

Students use information from a chart to solve problems. For example, Tommy Traveler decided to travel around the United States during his one-week vacation. He kept a chart of his trip but never finished it. Use the information below the chart to complete it for him. (Note that the chart also includes multiplication and division problems.)

Click here for a larger version of this table.

1. On Tuesday, the driving speed was 65. What were the total miles traveled?
2. Tommy traveled 376 miles on Sunday. How many miles did he travel on Saturday and Sunday?
3. On Saturday, Tommy drove for nine hours. How fast did he drive that day?
4. Tommy was so tired on Friday that he could only drive for two hours. How many miles did he travel?
5. If Tommy traveled eight hours on Wednesday, how many more miles did he travel on Wednesday than he did on Sunday?
6. If, during another week, Tommy traveled eight hours a day, how many hours did he travel?

Assessment Connections

Questioning . . .

Open with . . .

• How did you complete the chart?

Probe further with . . .

• Where did you use addition to complete the chart? Why?
• Where did you use subtraction to complete the chart? Why?
• Can you write an addition word problem that can be answered using the information in the chart?
• What addition sentences can you write using the information in the chart?
• Can you write a subtraction word problem that can be answered using the information in the chart?
• What subtraction sentences can you write using the information in the chart?
• How did you decide what operation to use?
• Did you use a strategy or an operation other than addition or subtraction to complete the chart? Where? How? Why?

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 addition?
• Can the student identify real-world problems that can be solved using subtraction?
• Does the student correctly write addition and subtraction sentences?
• Does the student write word problems that are clear and easily interpreted?
• Does the student's written work show understanding of the addition and subtraction algorithms, especially regrouping?
• Does the student multiply or use repeated addition?
• Is the student able to recognize errors in his or her work?
• How does the student self-correct errors?

TAKS Connection

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

(4.3.b) Number, operation, and quantitative reasoning. The student adds and subtracts to solve meaningful problems involving whole numbers and decimals. The student is expected to add and subtract decimals to the hundredths place using concrete objects and pictorial models.

Clarifying Activity with Assessment Connections

Students use information from the newspaper (such as data from the sports page) to write original problems involving addition or subtraction with decimals. Groups trade problems and select a manipulative or draw a picture to solve the problems. Students then describe their solution strategies and how the manipulatives or pictures were helpful in solving the problems.

Assessment Connections

Questioning . . . (before trading problems)

Open with . . .

• Tell me about your problem.

Probe further with . . .

• Does your problem use decimals?
• Does your problem describe a joining, comparing, or separating?
• Can your problem be answered by adding or subtracting decimals?
• How did you decide to create this problem?

Questioning . . . (after trading problems)

Open with . . .

• What is the problem? How did you solve the problem?

Probe further with . . .

• What operation did you use? Why? What do you know about this operation?
• With what number do you start?
• What describes the change?
• What is the resulting number?
• What number sentence can you write to show your problem?
• Can you solve the problem another way?
• How do you know your solution is reasonable?
• How did you use your manipulative or drawing to help you solve the problem?

Listen for . . .

• Does the problem that the student constructs clearly define an action (joining, comparing, separating) involving decimal numbers?
• Is the student able to clearly explain his or her thought process?
• Does the student discuss the reasonableness of his or her solution?
• Does the student use words such as "add" and "subtract"?
• Is the student able to read decimal numbers using mathematical vocabulary such as "five-tenths"?

Look for . . .

• Is the student selecting the necessary information to solve the problem?
• 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?
• Is the student able to recognize errors in his or her work?
• How does the student self-correct errors?

TAKS Connection

Click here for a larger version of the TAKS item.

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

- Top -

(4.4) Number, operation, and quantitative reasoning. . The student multiplies and divides to solve meaningful problems involving whole numbers.

(4.4.a) Number, operation, and quantitative reasoning.. The student multiplies and divides to solve meaningful problems involving whole numbers. The student is expected to model factors and products using arrays and area models.

Clarifying Activity with Assessment Connections

Students use centimeter grid paper to build all arrays (rectangular models) that represent each number 1 through 36 and investigate the number of arrays that result. Below each array, students write number sentences representing the multiplication. For example, the following are arrays for 6, 4, and 3.

Assessment Connections

Questioning . . .

Open with . . .

• Using the arrays you built for 36, what can you tell me about the factors of the numbers 1 through 36?

Probe further with . . .

• Is 4 a factor of 36? How do you know?
• Since 4 is a factor of 36, what is another factor of 36? How do you know?
• Is 7 a factor of 36? How do you know?
• Did you find all of the arrays that can represent 36?
• How did you find the arrays? Did you have a plan?
• How many arrays did you find?
• How many factors of 36 are there?
• How would you find the factors of 35?

Listen for . . .

• Can the student identify factors of a number using an array model?
• Does the student begin to notice factor pairs (such as 4 and 9 are factor pairs of 36)?

Look for . . .

• Can the student create an array to represent a number?
• Can the student find all of the arrays that represent the number?
• Can the student recognize the relationship between factors of a number and size of the array?
• Does the student have an organized strategy for finding the arrays?
• What is the student's strategy for finding the arrays?

TAKS Connection

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

(4.4.b) Number, operation, and quantitative reasoning.. The student multiplies and divides to solve meaningful problems involving whole numbers. The student is expected to represent multiplication and division situations in picture, word, and number form.

Clarifying Activity with Assessment Connections

Students draw or find pictures of rectangular arrays in their world (such as seats in an auditorium or rows of plants in a garden). They use the pictures to write story problems involving multiplication and division and post the problems for others to solve.

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 or dividing whole numbers?
• How can your problem be solved?

Listen for . . .

• Does the student's explanation match his or her written work?
• Does the student use appropriate mathematical language to describe the problem and solution?

Look for . . .

• Can the student identify real-world problems that can be solved using multiplication or division?
• Does the student pose a problem that can be solved by multiplying or dividing whole numbers?
• Does the student pose a problem that is clear and easily interpreted?

Questioning . . . (after trading problems)

Open with . . .

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

Probe further with . . .

• How are you solving the problem? Why?
• What do you know?
• 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 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 or division to solve problems involving whole numbers?
• Does the student select manipulatives or draw pictures to help solve the problem?
• Does the student solve the problem in more than one way?
• Does the student use skip counting, repeated addition, or related multiplication facts to solve the problem?
• Does the number sentence match the student's explanation?
• Does the student recognize any errors in his or her work?
• Is the student able to self-correct?

TAKS Connection

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

(4.4.c) Number, operation, and quantitative reasoning.. The student multiplies and divides to solve meaningful problems involving whole numbers. The student is expected to recall and apply multiplication facts through 12 x 12.

Clarifying Activity with Assessment Connections

Students compute and fill in the multiplication facts on a blank 12 x 12 multiplication chart and describe the patterns they discover. They then select a multiplication fact from the chart and write an original problem for others to solve using that fact.

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 using a multiplication fact from the chart? How?
• Did the patterns you discovered on the chart help you solve the problem?

Listen for . . .

• Does the student use appropriate mathematical language to describe the problem and solution?
• Does the student's explanation match his or her written work?

Look for . . .

• Is the student able to self-correct errors in his or her work?
• Can the student identify real-world problems that can be solved using mathematics?
• 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?

Questioning . . . (after trading problems)

Open with . . .

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

Probe further with . . .

• How are you solving the problem? Why?
• How can you use what you learned from the chart to solve a multiplication problem?
• What number sentence could 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?
• Does the student recall the multiplication fact necessary to solve the problem or use a related fact?
• Does the student select manipulatives or draw pictures 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?
• Is the student able to recognize errors and self-correct his or her work?

TAKS Connection

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

Technology Extension

Ask a student to write the problem using a computer software drawing program. Another student solves the problem using a picture or diagram.

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

Clarifying Activity with Assessment Connections

Students brainstorm situations in which it is necessary to solve problems using multiplication and record the examples on a poster. Students select examples from the poster, write original story problems, and post them for other students to solve.

Assessment Connections

Questioning . . . (before posting 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 two-digit numbers?
• Can your problem be answered by multiplying two-digit numbers? How?
• What kinds of multi-digit problems are easiest to solve? Why?
• What kinds of multi-digit problems are hardest to solve? Why?

Listen for . . .

• Does the student use appropriate mathematical language to describe the problem and solution?
• Does the student's explanation match his or her written work?

Look for . . .

• Does the student include extra information in his or her problem?
• 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 two-digit numbers?
• Does the student pose a problem that is clear and easily interpreted?
• Does the student choose numbers for the problem purposefully?

Questioning . . . (after posting problems)

Open with . . .

• What is 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 two-digit numbers?
• Can the student recall multiplication facts?
• Does the student use number sense to check for reasonableness of the solution?
• Does the student use the standard multiplication algorithm or an alternative algorithm to multiply two-digit 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?
• Is the student able to recognize errors in his or her work?
• Does the student self-correct?

TAKS Connection

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

Additional Clarifying Activity

Students use grid paper or base-ten blocks to form a rectangular model for a multiplication problem such as 21 x 13. They outline an area that is 21 rows of 13 squares and use the model to identify the partial products in the multiplication algorithm.

(4.4.e) Number, operation, and quantitative reasoning.. The student multiplies and divides to solve meaningful problems involving whole numbers. The student is expected to use division to solve problems (no more than one-digit divisors and three-digit dividends without technology).

Clarifying Activity with Assessment Connections

After reading the book, A Remainder of One, by Elinor J. Pinczes, students use beans to represent all of the ways the 25th squadron arranged themselves throughout the story and use division equations (showing quotients and remainders) to record the groupings. Students then try a different number of soldier bugs (such as 36) and use beans or drawings to record the ways the soldier bugs could arrange themselves to march in front of their queen. Students use division equations (showing quotients and remainders) to record the groupings.

Assessment Connections

Questioning . . .

Open with . . .

• What do you notice about your findings?

Probe further with . . .

• How many rows did you make? How many are in each row?
• Are the rows the same length?
• How did you write number sentences to describe the arrangements of the squadron of 36?
• What ways can you arrange the squadron with all rows of equal length? How do you know this? How do you know you have all the ways?
• How many ways can you group with a remainder of 1? Why?

Listen for . . .

• Does the student determine patterns in the number sentences?
• Can the student clearly explain his or her thought process?
• Is the student able to discuss the reasonableness of his or her solution?
• Is the student using words that describe division?

Look for . . .

• Does the student select manipulatives or draw a picture to help solve the problem?
• Does the student try different arrangements?
• Does the student solve the problem in more than one way?
• Does the number sentence match the student's explanation?
• When trying to determine how many ways to group with a remainder of 1, does the student set the remainder aside?
• Does the student notice the relationship between the number sentences and multiplication facts?
• Does the student self-correct when necessary?

TAKS Connection

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

- Top -

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

(4.5.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, hundred, or thousand to approximate reasonable results in problem situations.

Clarifying Activity with Assessment Connections

Students use a spinner labeled 0–9 and spin four times to construct a four-digit number. They then draw a card on which is written "nearest ten," "nearest hundred," or "nearest thousand" and record their rounded number. With a partner students investigate the sum of their own number and their partner's number. They estimate sums, calculate sums (for both rounded and original numbers), and discuss results.

Assessment Connections

Questioning . . .

Open with . . .

• Before you pick a partner and combine numbers, can you tell me something about your sum?

Probe further with . . .

• Can your sum be smaller than 0? Can your sum be larger than 10,000?
• Can your sum be larger than 20,000? How do you know?
• Who would you choose as a partner to get a sum closest to 0? 10,000? 20,000? What strategies did you use to select your partner?
• After picking a partner, estimate the sum of your rounded numbers. How did you estimate this sum?
• Estimate the sum of your original four-digit numbers. How did you estimate this sum?
• Add your rounded and your original numbers. Do your results make sense? Why? How do your estimates and sums compare with one another?

Listen for . . .

• Is the student rounding correctly?
• Does the student notice that the sum cannot be larger than 20,000?
• Is the student able to clearly explain his or her thought process?
• Is the student able to discuss the reasonableness of his or her solution?

Look for . . .

• Is the student rounding before adding?
• Is the student doing mental arithmetic or resorting to paper-and-pencil calculations?
• What strategies does the student use to round and calculate the sum?
• Does the student self-correct when necessary?

TAKS Connection

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

Additional Clarifying Activity

Students use grocery store ads to estimate food bills and discuss the different strategies they used in making the estimates.

(4.5.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 multiplication and division problems.

Clarifying Activity with Assessment Connections

Students select four number cards from a bag containing the digits 1–9. They arrange the number cards to make a two-digit by two-digit multiplication problem and estimate the product. Students then establish a "range of success" (such as "within 10 or 100 of the actual product") and compare their estimates with the actual product to see if they are within the success range. Students can repeat the activity, arranging their cards to make division problems with one-digit divisors.

Assessment Connections

Questioning . . .

Open with . . .

• How close was your estimate to the actual amount?

Probe further with . . .

• What was your estimate?
• What was the actual solution to the problem?
• How does your estimate compare with the actual solution? Are you in the range of success?
• How did you find your estimate? What strategy did you use?
• Could you estimate the solution another way? Why did you decide not to use this method?
• Is your estimate reasonable?
• How did you determine the range of success?
• Do you wish to adjust your range of success before repeating this activity? Why?

Listen for . . .

• Does the student use approximation language?
• Can the student clearly explain his or her rationale for estimating the solution?
• Is the student able to discuss the reasonableness of his or her solution?

Look for . . .

• Can the student estimate the product of two-digit numbers?
• Can the student estimate the quotient of a three-digit number divided by a one-digit number?
• Does the student use a reasonable range of success?
• Does the student appropriately apply the skill of rounding to estimate the solution?
• Is the student's solution within the range of success?
• Can the student determine if the estimate is in the range of success?
• Can the student use a variety of strategies to estimate a product and quotient?
• Can the student determine which strategy will best give an estimate within the range of success?
• Is the student able to self-correct when necessary?

TAKS Connection

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

- Top -

(4.6) Patterns, relationships, and algebraic thinking. The student uses patterns in multiplication and division.

(4.6.a) Patterns, relationships, and algebraic thinking. The student uses patterns in multiplication and division. The student is expected to use patterns and relationships to develop strategies to remember basic multiplication and division facts (such as the patterns in related multiplication and division number sequences (fact families) such as 9 x 9 = 81 and 81 ÷ 9 = 9).

Clarifying Activity with Assessment Connections

On grid paper, students form a rectangular model for a multiplication problem such as 6 x 12, 7 x 12, or 8 x 12. They cover the grid paper with base-ten blocks and are guided into recognizing the pattern of the distributive property of multiplication over addition; for example, 7 x 12 = 7 x (10 + 2) = (7 x 10) + (7 x 2) = 70 + 14 = 84.

Students use this pattern to check 9 x 12. Students then use grid paper (with markers now) to model 7 x 6 =(5+2) x 6, and 3 x 9 = 3 x (10-1)= (3 x 10) - 3. The students extend the pattern to break down a "hard-to-remember" multiplication fact into two more easily remembered multiplication facts.

Each student develops a personal list of "tough" facts to remember and shows ways the facts can be broken down to make them easier to remember.

Assessment Connections

Questioning . . .

Open with . . .

• Tell me about your hard-to-remember multiplication facts and how you might use this pattern to remember them.

Probe further with . . .

• What are some multiplication facts that you don't always recall?
• How can you break this down into facts you do remember?
• How did we break down 7 x 6? Can you extend this approach to break down your hard-to-remember fact? How?
• How did you decide how to break it down? Did you draw a picture? Did you use paper and pencil? Did you do this in your head?
• Are there other ways you could break this down? How?

Listen for . . .

• Can the student explain the strategy used to break down (partition) hard-to-remember facts?
• Does the student check for the reasonableness of the solution?

Look for . . .

• Does the student notice the pattern of the distributive property of multiplication over addition (subtraction)? (Note: Students will not identify with terminology such as distributive property.)
• Can the student apply the pattern of the distributive property of multiplication over addition (subtraction)?
• Can the student use the pattern of the distribution of multiplication over addition (subtraction) to create strategies that can help them figure out hard-to-remember multiplication facts?
• Can the student break down hard-to-remember multiplication facts into two multiplication facts that can be used to find the product of the hard-to-remember one?
• Does the student use mental arithmetic, paper and pencil, or a rectangular model to break down the hard-to-remember facts?
• Does the student apply this method to help remember facts on other occasions?
• Is the student able to self-correct?

TAKS Connection

• This student expectation is not tested on TAKS. Although this is not directly tested at Grade 4, it is an important foundation for student expectations tested at later grades.

Additional Clarifying Activity with Assessment Connections

Students make a set of triangle flash cards depicting fact families, as shown below.

Students draw a card and use the three numbers to write all the multiplication and division number sentences in that fact family.

Assessment Connections

Questioning . . .

Open with . . .

• What do you notice about the number sentences in your fact family?

Probe further with . . .

• How many number sentences are in your fact family? How do you know?
• What pattern do you notice in the number sentences?
• How are your number sentences alike?
• How are your number sentences different?

Listen for . . .

• Is the student identifying patterns in his or her number sentences?
• Is the student using mathematical language when comparing and contrasting number sentences?
• Is the student able to describe the relationships among number sentences in a fact family?

Look for . . .

• Does the student recognize and describe the inverse relationships between the multiplication and division problems in the fact family?
• Does the student accurately record the number sentences for the fact family from the numbers on the flash card?

TAKS Connection

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

Additional Clarifying Activity

Students work in partners. One partner writes a division equation with the quotient missing, e.g. 32 ÷ 4 = ___. The other partner writes the multiplication equation that can be used to solve the given division equation, such as 8 x 4 = 32.

(4.6.b) Patterns, relationships, and algebraic thinking. The student uses patterns in multiplication and division. The student is expected to use patterns to multiply by 10 and 100.

Clarifying Activity with Assessment Connections

Students use a calculator to generate a list of number sentences of products of numbers multiplied by 10 or 100.

4 x 10 = 40
4 x 100 = 400
14 x 10 = 140
14 x 100 = 1400
24 x 10 = 240
24 x 100 = 2400

Assessment Connections

Questioning . . .

Open with . . .

• What patterns do you notice in your number sentences?

Probe further with . . .

• What do you think the product of 123 x 10 is? Why? Use your calculator to check your answer.
• What do you think the product of 123 x 100 is? Why? Use your calculator to check your answer.
• What does the product of a number and 10 look like?
• What does the product of a number and 100 look like?
• How does the product of a number and 100 compare to the original number? How does multiplying by 100 affect the place value of the digits?
• What do you think the product of 123 x 1000 is? Why? Use your calculator to check your answer.

Listen for . . .

• Does the student identify patterns in his or her number sentences?
• Does the student use appropriate mathematical language to discuss his or her number sentences?

Look for . . .

• Does the student recognize and describe patterns to multiply by 10 and 100?
• Does the student use patterns to multiply by 10 and 100?
• Is the student able to use the calculator properly?

TAKS Connection

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

- Top -

(4.7) Patterns, relationships, and algebraic thinking. The student uses organizational structures to analyze and describe patterns and relationships.

(4.7) Patterns, relationships, and algebraic thinking. The student uses organizational structures to analyze and describe patterns and relationships. The student is expected to describe the relationship between two sets of related data such as ordered pairs in a table.

Clarifying Activity with Assessment Connections

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

Students can record the relationship shown in the table as a set of ordered pairs: (0, 0), (1, 12), (2, 24), (3, 36)

Students then use mathematical words and symbols to represent the relationship shown in the table and the ordered pairs:

Assessment Connections

Questioning . . .

Open with . . .

• What can you tell me about the cost of CDs from looking at this table?

Probe further with . . .

• How much does one CD cost?
• How much do two CDs cost?
• Can you use this table to figure out the cost of five CDs? Ten CDs?
• What patterns help you figure out how much the CDs cost?
• What other patterns do you notice?
• Would (6, 72) be a relationship shown in this table? How do you know?

Listen for . . .

• Does the student use mathematical language to represent the relationship in the table?
• Is the student able to explain his or her thought process clearly?
• Is the student able to discuss the reasonableness of his or her solution?

Look for . . .

• Can the student recognize the pattern in the table?
• Can the student extend the pattern and generalize?
• Can the student represent the values in the table with the ordered pairs of numbers?
• Can the student use mathematical symbols to represent the relationship in the table?
• Is the student able to self-correct any errors?

TAKS Connection

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

Additional Clarifying Activity

Collect data and use a computer application to make a graphical representation.

- Top -

(4.8) Geometry and spatial reasoning. The student identifies and describes attributes of geometric figures using formal geometric language.

(4.8.a) Geometry and spatial reasoning. The student identifies and describes attributes of geometric figures using formal geometric language. The student is expected to identify and describe right, acute, and obtuse angles.

Clarifying Activity with Assessment Connections

Students construct an angle maker by joining two cardboard strips with a brass fastener and use it to replicate angles found on real objects, such as the hands on an analog clock at a specific time, the corner of a room, or an open pair of scissors. Students make a chart showing the angles they have found, recording the angles with drawings and classifying them as acute, right, or obtuse.

Assessment Connections

Questioning . . .

Open with . . .

• Which type of angle occurs most often in this room? How do you know?

Probe further with . . .

• Did you find any right angles in the room? Where? Describe your drawings.
• How do you know this is a right angle?
• Did you find any obtuse angles in the room? Where? Describe your drawings.
• How do you know this is an obtuse angle?
• Did you find any acute angles in the room? Where? Describe your drawings.
• How do you know this is an acute angle?

Listen for . . .

• Does the student use mathematical vocabulary ("right," "acute," and "obtuse") to describe angles?
• Can the student describe what it means for angles to be right, acute, or obtuse?

Look for . . .

• Is the student's chart accurate?
• Is the student able to self-correct any errors?
• Can the student correctly draw right, acute, and obtuse angles?
• Does the student recognize the relationship between right, obtuse, and acute angles?
• Does the student recognize that all right angles are the same size?
• Does the student recognize that all acute angles are not the same size?
• Does the student recognize that all obtuse angles are not the same size?
• Can the student create a definition for right, acute, and obtuse angles?

TAKS Connection

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

Additional Clarifying Activity

Students trace a right angle using tracing paper, fold a right angle with waxed paper, or tear off the "square" corner of a piece of paper or cardboard. They compare the right angles to other angles, such as where a brace is fastened onto a desk or the hands of an analog clock at a certain time. Students predict whether the angle they have located has a measure greater than a right angle (obtuse), less than a right angle (acute), or about the same as a right angle, then use their model of a right angle to test their predictions.

(4.8.b) Geometry and spatial reasoning. The student identifies and describes attributes of geometric figures using formal geometric language. The student is expected to identify and describe parallel and intersecting (including perpendicular) lines using concrete objects and pictorial models.

Clarifying Activity with Assessment Connections

Students identify locations in the room where models of parallel lines occur, such as the top and bottom of the door, the opposite edges of their notebook paper, or the opposite edges of the ceiling tiles. They also identify locations where models of perpendicular lines occur, such as the top and side edges of the chalkboard. As a class, students then develop a list of both examples and nonexamples of parallel lines and justify each response.

Assessment Connections

Questioning . . .

Open with . . .

• Tell me about the examples you placed in the "parallel line" category.

Probe further with . . .

• How do you know lines are parallel?
• What do the non-parallel lines have in common?
• Can you re-sort into perpendicular lines vs. non-perpendicular lines?
• How do you know if the lines are perpendicular?
• Can parallel lines also be perpendicular? Why?

Listen for . . .

• Does the student use mathematical vocabulary (such as parallel, perpendicular, intersecting, and right angles) to describe the lines?
• Can the student justify his or her choices?
• Does the student make and test conjectures about parallel and perpendicular lines? Does the student develop logical arguments to justify his or her conclusions?

Look for . . .

• Can the student identify models of parallel and perpendicular lines?
• Does the student understand the relationship between right angles and perpendicular lines?
• Does the student recognize that lines extend?
• Does the student recognize that lines that do not intersect in vision may not be parallel?
• Does the student recognize that lines can intersect but not be perpendicular?
• Can the student create a definition for parallel lines? Perpendicular lines?

TAKS Connection

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

(4.8.c) Geometry and spatial reasoning. The student identifies and describes attributes of geometric figures using formal geometric language. The student is expected to use essential attributes to define two- and three-dimensional geometric figures.

Clarifying Activity with Assessment Connections

Students reach into a mystery box, feel a geometric solid that has been placed inside, and describe the solid to the class one clue at a time, without looking, telling how many faces, edges, and vertices the solid has. The class tries to guess the solid. (Examples of several possible solids can be available for students to look at and choose from as the description is given.)

Assessment Connections

Questioning . . .

Open with . . .

• What information does this clue give you?

Probe further with . . .

• What solids have you eliminated?
• Why did you eliminate those solids?
• What are the similarities and differences between the solids that you did not eliminate?
• What would be a good clue to give next? Why?

Listen for . . .

• Does the student know the name of the geometric solid?
• Does the student use appropriate mathematical vocabulary for critical attributes (such as vertices, edges, and faces)?
• Can the student create a description for three-dimensional solids that includes mathematical language?

Look for . . .

• Does the student know the meaning of vocabulary such as vertices, edges, and faces?
• Can the student use critical attributes to identify geometric solids?
• Can the student identify solids that do not fit a particular definition?

TAKS Connection

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

Additional Clarifying Activity

Students cut a variety of shapes from paper and arrange them onto a page to form a picture. Students then write a descriptive paragraph about their picture, using geometric vocabulary including "vertices," and "edges" or "sides" to describe the shapes used.

- Top -

(4.9) Geometry and spatial reasoning. The student connects transformations to congruence and symmetry.

(4.9.a) Geometry and spatial reasoning. The student connects transformations to congruence and symmetry. The student is expected to demonstrate translations, reflections, and rotations using concrete models.

Clarifying Activity with Assessment Connections

Students use a computer drawing program to create a design exploring translations, reflections, and rotations.

Assessment Connections

Questioning . . .

Open with . . .

• How did you create the design?

Probe further with . . .

• What kinds of transformations did you use to create the design?
• Did you use reflections? Where?
• Did you use translations? Where?
• Did you use rotations? Where?
• What are the differences between a translation, a rotation, and a reflection?
• What would happen if you [turned, flipped, slid] your design?

Listen for . . .

• Does the student use mathematical vocabulary to describe the transformations (such as reflection, translation, rotation, and congruent)?
• Can the student explain the differences between translations, rotations, and reflections?
• Does the student predict and describe the results of translations, rotations, and reflections on two-dimensional shapes when creating the design?
• Can the student describe mental images of a transformation of his or her design?

Look for . . .

• Can the student demonstrate translations, reflections, and rotations using a computer drawing program?
• Does the student visualize and plan the design?

TAKS Connection

• This student expectation is not tested on TAKS. Although this is not directly tested at Grade 4, it is an important foundation for student expectations tested at later grades.

Additional Clarifying Activity

Students create a list of real-world examples of translations (riding on an escalator or in an elevator, pushing a vacuum cleaner back and forth, sliding down a slide), reflections (flipping a pancake or turning over a playing card), and rotations (turning a doorknob, walking in a revolving door, doing cartwheels). Students then go onto the playground to act out some of their examples.

Students create a design using pattern blocks or color tiles and show a translation of that design by creating an identical design to the right, left, above, or below the original.

Students demonstrate reflections by working with a partner and acting out "mirror images" of each other.

Students create shapes on geoboards and record their shapes on dot paper. Students then select a peg on the geoboard to be the center of rotation, place a finger on the peg, and rotate the board one-fourth turn, one-half turn, and three-fourths turn around that peg. Students make a sketch on the dot paper after each rotation and compare it to the shape's original position.

(4.9.b) Geometry and spatial reasoning. The student connects transformations to congruence and symmetry. The student is expected to use translations, reflections, and rotations to verify that two shapes are congruent.

Clarifying Activity with Assessment Connections

Students create two congruent shapes by folding a piece of paper in half and cutting out a shape from the two layers of paper. Working together in pairs, one student lays his or her two shapes on the table, and the other student describes what motions he or she must use (translation, rotation, reflection) to move one shape until it fits exactly on top of the other.

Assessment Connections

Questioning . . .

Open with . . .

• Describe the motions you might use to move one shape until it fits exactly on top of the other.

Probe further with . . .

• How many different transformations did you use?
• Did you use any translations? How?
• Did you use any rotations? How?
• Did you use any reflections? How?
• Is there another way to move one shape until it fits exactly on the other?
• Can you use the same exact transformations in a different order? Why?
• Are there other transformations (motions) that you could use?
• Are the shapes congruent? How do you know?

Listen for . . .

• Does the student use mathematical vocabulary to describe the results of transformations?
• Can the student describe what it means for shapes to be congruent?

Look for . . .

• Can the student demonstrate a transformation or a series of transformations that will verify that two shapes are congruent?
• Can the student predict the outcome of translations, reflections, and rotations?
• Can the student use a different order of transformations to verify congruence?

TAKS Connection

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

(4.9.c) Geometry and spatial reasoning. The student connects transformations to congruence and symmetry. The student is expected to use reflections to verify that a shape has symmetry.

Clarifying Activity with Assessment Connections

Students make a design with pattern blocks and investigate the lines of symmetry in the design by placing mirrors in positions where the reflection replicates the design.

Assessment Connections

Questioning . . .

Open with . . .

• Tell me about your design. Is it symmetric? How do you know?

Probe further with . . .

• Where are the lines of symmetry?
• How did you know you found a line of symmetry?
• How did you use the mirror to find a line of symmetry?
• Did you find more than one line of symmetry?
• How many lines of symmetry does your design have? How do you know?
• If you did not find a line of symmetry, could you change your design so it would have at least one line of symmetry?
• Could you change your design to have more than one line of symmetry?
• Does a reflection verify that a shape has symmetry? Why?

Listen for . . .

• Does the student use mathematical vocabulary to describe symmetry?
• Does the student use the word "reflection" to define symmetry?
• Can the student describe what it means for shapes to have symmetry?

Look for . . .

• Is the design accurate?
• Can the student use reflection to verify that a shape has symmetry?
• Can the student identify lines of symmetry?
• Can the student identify all the lines of symmetry in a shape?
• Does the student self-correct?

TAKS Connection

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

- Top -

(4.10) Geometry and spatial reasoning. The student recognizes the connection between numbers and their properties and points on a line.

(4.10) Geometry and spatial reasoning. The student recognizes the connection between numbers and their properties and points on a line. The student is expected to locate and name points on a number line using whole numbers, fractions such as halves and fourths, and decimals such as tenths.

Clarifying Activity with Assessment Connections

Students work in groups of four. Each student is given a transparency with a number line printed on it. The locations for 0 and 1 are marked, but nothing else. One student records whole numbers on one transparency, one student records halves (0/2, 1/2, 2/2, 3/2, etc.), one student records fourths (0/4, 1/4, 2/4, etc.), and one student records decimals (0.0, 0.1, 0.2, 0.3, 0.4, etc.). The students place their transparencies on top of one another, staggered so that the number lines appear as shown below:

Students compare the number lines and identify equivalent fractions and decimals that name the same points on the number line.

Assessment Connections

Questioning . . .

Open with . . .

• Describe your number line.

Probe further with . . .

• How did you decide where to place the halves?
• How did you decide where to place the fourths?
• How did you decide where to place the decimals?
• What other numbers are equal to 1/2? Equal to 1? Equal to 1.5? Equal to 2?
• What patterns do you notice?

Listen for . . .

• Does the student use mathematical vocabulary such as five-tenths, three-halves, or equals?
• Does the student notice patterns and relationships? (For example, one-fourth is between zero and one-half.)

Look for . . .

• Is the student's number line accurate?
• How does the student determine fractional parts (by folding, measuring, estimating)?
• Does the student use mathematical notation to label points on the number line?
• Is the student able to self-correct errors as the transparencies are placed on top of one another?

TAKS Connection

Click here for a larger version of the TAKS item.

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

- Top -

(4.11) Measurement. The student applies measurement concepts. The student is expected to estimate and measure to solve problems involving length (including perimeter) and area. The student uses measurement tools to measure capacity/volume and weight/mass.

(4.11.a) Measurement. The student applies measurement concepts. The student is expected to estimate and measure to solve problems involving length (including perimeter) and area. The student uses measurement tools to measure capacity/volume and weight/mass. The student is expected to estimate and use measurement tools to determine length (including perimeter), area, capacity and weight/mass using standard units SI (metric) and customary.

Clarifying Activity with Assessment Connections

Students play "The Weight is Right" in which they estimate and measure the weights of everyday objects (an empty tin can, a bag of candy, a bowl of chips, a toy car, a small bean bag animal).

The class is divided into four groups; one student from each group is asked to "come on down" and get a set of measurement cards to be matched with the items. (Cards should be prepared by the teacher prior to the activity and should include weights written in ranges, such as 15–20 ounces. There should be more cards than items.) The groups are asked to confer and estimate the weight of each object. One student acts as the group spokesperson and posts the group's estimate next to the first item.

When all of the estimates are posted for a single item, the groups are asked to discuss and justify different estimates. The object is then weighed and a point is awarded to groups with the correct answers. Allow time for group rethinking and revision before moving on to the next item. Repeat the procedure for each item.

Assessment Connections

Questioning . . .

Open with . . .

• Post your estimates. Why did you choose these estimates?

Probe further with . . .

• Which of the objects do you think is the lightest?
• Does your estimate seem reasonable?
• Which measurement card has the smallest choice for weight?
• Did you use this as an estimate for the lightest object? Why?
• Which of the objects do you think is the heaviest?
• Do your weight estimates make sense based on which object you think is heaviest?
• Do the units for each of your estimates make sense?

Listen for . . .

• Does the student clearly explain his or her thought process?
• Is the student able to discuss the reasonableness of his or her estimate?
• Does the student use units of measurement to describe selections?
• Does the student use language to indicate a comparison of units?
• Is the student able to rethink and revise estimates before moving on to the next item?

Look for . . .

• Does the student solve the problem in more than one way?
• Can the student compare different standard units of measurement?
• Can the student estimate and measure using standard units of weight?

TAKS Connection

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

Additional Clarifying Activity with Assessment Connections

• Students use standard units (milliliters, liters, cups, pints, quarts, gallons) to estimate the capacities of two differently-shaped bowls and use standard measuring tools to measure the capacities of the bowls. Students compare the measurements of the two bowls using the different units and write statements summarizing their observations.

Assessment Connections

Questioning . . .

Open with . . .

• How close were your estimates to the actual measurements?

Probe further with . . .

• What were your estimates?
• Were your estimates reasonable given what you know about the relationship between cups, pints, quarts, and gallons?
• How many cups are in a pint? Quart? Gallon?
• What were the actual measurements?
• Would this container hold more than one liter of water?
• How would you know if this container holds more than one liter?
• How would you know if this container holds less than one liter?
• How can you use what you know about the size of this container to make an estimate about the size of your other container (in liters)?

Listen for . . .

• Does the student clearly explain his or her thought process?
• Is the student able to discuss the reasonableness of his or her solutions?
• Does the student use units of measurement in his or her descriptions?
• Does the student use mathematical language to indicate a comparison of units?

Look for . . .

• Does the student correctly measure the capacity of the container by accurately filling the standard units?
• Does the student recognize and use the relationships between different standard units to develop consistent estimates? If not, is the student guessing?
• Can the student solve the problem in more than one way?
• Can the student compare different standard units of measurement?
• Are the student's estimates reasonable?
• Can the student measure using standard units of capacity?
• Can the student compare estimates and actual measurements?
• Is the student's summary of the observations accurate and understandable?

TAKS Connection

© 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 centimeter paper to draw different rectangles that have perimeters of 36 centimeters. Students use the squares on the grid paper to determine the area of each rectangle drawn. They collect and organize the data, and look for a relationship between the shapes of the rectangles with constant perimeter and their areas. (For example, the closer the rectangle is to a square, the greater the area.)

Assessment Connections

Questioning . . .

Open with . . .

• Tell me what you noticed about the area of rectangles.

Probe further with . . .

• Do all of your rectangles have a perimeter of 36? How do you know?
• What is the area of this rectangle? Why?
• How did you determine which rectangles to draw?
• Do rectangles with the same perimeter always have the same area? How do you know?
• Are there any rectangles with the same perimeter and the same area? How else are they the same?
• What strategy did you use to create rectangles with a perimeter of 36?
• Which rectangle with a perimeter of 36 has the greatest area?
• What do you notice about the changes in the area as the shape of the perimeter changes?
• If you were exploring rectangles with a perimeter of 16, what predictions do you have about their areas? Check your predictions.
• What generalization might be made? (For example, the rectangle with the greatest area for any perimeter is a square.)

Listen for . . .

• Does the student use appropriate units to describe the length of the perimeter (cm) and the area (cm²)?
• Can the student describe the relationship between the shape of the perimeter and the area?
• Is the student able to discuss the reasonableness of his or her solution?

Look for . . .

• Does the student determine the perimeter of the rectangle by counting the centimeter squares or by adding the length of each side?
• Does the student follow a strategy to create the rectangles?
• Can the student identify the characteristics of the shape with the greatest area?
• Can the student make generalizations based on the observations?
• Can students solve problems involving length and area?

TAKS Connection

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

(4.11.b) Measurement. The student applies measurement concepts. The student is expected to estimate and measure to solve problems involving length (including perimeter) and area. The student uses measurement tools to measure capacity/volume and weight/mass. The student is expected to perform simple conversions between different units of length, between different units of capacity, and between different units of weight within the customary measurement system.

(4.11.c) Measurement. The student applies measurement concepts. The student is expected to estimate and measure to solve problems involving length (including perimeter) and area. The student uses measurement tools to measure capacity/volume and weight/mass. The student is expected to use concrete models of standard cubic units to measure volume.

Clarifying Activity with Assessment Connections

Students choose the appropriate cubic unit from centimeter cubes, inch cubes, or student-constructed meter cubes to estimate and then measure the volume of various containers (e.g., a suitcase, a pencil box, the classroom).

Assessment Connections

Questioning . . .

Open with . . .

• Tell me about the capacity of the pencil box.

Probe further with . . .

• What is the volume of the pencil box?
• How would you record the measurement of the volume of the pencil box?
• How did you measure the volume of the pencil box?
• What unit did you use to measure the volume of the pencil box?
• Could you use other units to measure the pencil box?
• What other units might be reasonable to use to measure the volume of the pencil box? Why?
• Would you want to use the same units of measure to measure the classroom? Why?

Listen for . . .

• Does the student use mathematical language while measuring the volume of an object using concrete units?
• Does the student explain the reasonableness of his or her solution?

Look for . . .

• Can the student use concrete models of cubic units to measure volume?
• Can the student identify appropriate units for volume of a pencil box and a room?
• Does the student make choices of units and tools based on the size of the item?
• Does the student use a number and a unit to record the measurement?

(4.11.d) Measurement. The student applies measurement concepts. The student is expected to estimate and measure to solve problems involving length (including perimeter) and area. The student uses measurement tools to measure capacity/volume and weight/mass. The student is expected to estimate volume in cubic units.

Clarifying Activity with Assessment Connections

Students estimate the volume of their mathematics textbook and design a box that would hold only the book. Rounding each dimension of the box to the nearest inch or centimeter, students use linear measurements to estimate the volume of the box in cubic units. Students can use models of cubic units to test their estimates.

Assessment Connections

Questioning . . .

Open with . . .

• Estimate the volume of the box you have constructed to hold your textbook.

Probe further with . . .

• How many cubic centimeters do you think you will need to fill the box? Write your estimate on a piece of paper.
• How did you find your estimate?
• How many cubes do you think you will need to cover the bottom of the box? Write your estimate on a piece of paper.
• Would you like to adjust your estimate for the volume of the box? How? Why?
• Test your estimate. How close was your estimate to the actual volume of the box?
• What are the dimensions of the box in cm? How do you know?
• How are the dimensions of the box related to the volume of the box? Why?

Listen for . . .

• Does the student clearly explain how he or she found the estimate?
• Does the student explain educated strategies and use prior experience to develop an estimate?
• Is the student able to discuss the reasonableness of his or her estimate?
• Can the student explain the relationship between the dimensions of the box and the volume of the box?
• Does the student use appropriate units to describe measures of length, area, and volume?

Look for . . .

• Is the student able to use additional information to evaluate and adjust his or her original estimate?
• Is the student able to estimate the number of cubes that will cover the bottom and number of layers that will fill the box to determine an estimate prior to your questioning?
• Is the student able to estimate the volume in cubic units with increasing accuracy?
• Can the student use concrete models of cubic units to measure volume?
• Does the student use a number and a unit to record the measurements of capacity and area?
• What strategy does the student use to determine the volume of the box? For example, does the student use a measuring stick or does the student use the concrete model to determine the dimensions of the box?

(4.11.e) Measurement. The student applies measurement concepts. The student is expected to estimate and measure to solve problems involving length (including perimeter) and area. The student uses measurement tools to measure capacity/volume and weight/mass. The student is expected to explain the difference between weight and mass.

- Top -

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

(4.12.a) Measurement. The student applies measurement concepts. The student measures time and temperature (in degrees Fahrenheit and Celsius). The student is expected to use a thermometer to measure temperature and changes in temperature.

(4.12.b) Measurement. The student applies measurement concepts. The student measures time and temperature (in degrees Fahrenheit and Celsius). The student is expected to use tools such as a clock with gears or a stopwatch to solve problems involving elapsed time.

- Top -

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

(4.13.a) Probability and statistics. The student solves problems by collecting, organizing, displaying, and interpreting sets of data. The student is expected to use concrete objects or pictures to make generalizations about determining all possible combinations of a given set of data or of objects in a problem situation.

Clarifying Activity with Assessment Connections

• Students discuss and list the possible outcomes of flipping two different coins. (For example: HH, HT, TH, TT or 2 heads, 2 tails, 1 head, 1 tail.)

Assessment Connections

Questioning . . .

Open with . . .

• Tell me about your list of possible outcomes.

Probe further with . . .

• How did you decide the possible outcomes?
• Do you have all possible outcomes? How do you know?
• Is there another way to describe the outcomes of this experiment?
• What patterns do you notice?

Listen for . . .

• Is the student able to clearly express his or her thought process?
• Is the student able to discuss the reasonableness of his or her solution?

Look for . . .

• Can the student find all of the outcomes?
• Does the student include outcomes that do not belong?
• Is the student using a systematic approach to listing all the outcomes?

TAKS Connection

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

Additional Clarifying Activity with Assessment Connections

Students make flipbooks (with each page cut in thirds) showing different parts of sports uniforms. For example, the top third of each page has a different helmet, the middle third has a different type of jersey, and the bottom third has a different type of pants. Students use the flipbooks to show possible combinations, using one of each of the three categories. Students record each combination, organize them into a pattern, and look for a generalization to help determine the total number of combinations.

Assessment Connections

Questioning . . .

Open with . . .

• What information did you need to find the total number of combinations?

Probe further with . . .

• Did you organize the combinations into a pattern? How did you organize?
• How did you record your combinations?
• Is there any pattern in your combinations?
• Is there a way to arrange the combinations to make a pattern?
• What generalizations can you make?

Listen for . . .

• Can the student explain and justify the strategy for finding the total number of combinations?
• Is the student able to discuss the reasonableness of his or her work?

Look for . . .

• How does the student record the combinations?
• Can the student organize the combinations to look for a pattern?
• Does the student notice a pattern and generalize to find the total number of combinations?
• Can the student justify that all possible combinations have been recorded?

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

Clarifying Activity with Assessment Connections

Students display their coin data (collected from flipping two coins in experiment 4.13B) in a bar graph, then generate and answer questions using information from the graph. For example, "How many ways can the coins land? Out of our total number of trials, how many did we get two heads? At least one head?"

Assessment Connections

Questioning . . .

Open with . . .

• Tell me about your graph.

Probe further with . . .

• Does your graph look the same as everyone else's? Why?
• How do they look the same? How are they different?
• How many ways can the coins land?
• Which way does it land most often?
• Out of our total number of trials, how many times did we get two heads? At least one head?
• How does the number of times we get exactly one head compare with the number of times we get exactly two heads? How many more times did we get exactly one head than two heads? Can you explain this?
• If you conducted this experiment again, what would you expect the results to be?

Listen for . . .

• Can the student answer questions about the experiment using information from the graph?
• Can the student interpret the graph?

Look for . . .

• Does the student accurately display the results of the experiment using the bar graph?
• Does the student label the graph?
• Does the student compare outcomes using numbers or the graphs?

TAKS Connection

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

- Top -

(4.14) Underlying processes and mathematical tools. The student applies Grade 4 mathematics to solve problems connected to everyday experiences and activities in and outside of school.

(4.14.a) Underlying processes and mathematical tools. The student applies Grade 4 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 a story, such as The Math Curse, by Jon Scieszka, students interview parents and friends about how they use mathematics in their daily lives. Students either write a paragraph summarizing the interviews or deliver oral reports to the class.

Assessment Connections

Questioning . . .

Open with . . .

• Tell us about how the people you interviewed use mathematics in their daily lives.

Probe further with . . .

• What did you learn?
• Did you find that other people use mathematics on a daily basis in ways similar to your own?
• What is the most common way that people use mathematics in their daily lives?
• Were you surprised at some of the ways that people use mathematics? How so?
• Did the people you interviewed describe mathematics tools that they use?

Listen for . . .

• Does the student use mathematical terms in the report or interview?
• Can the student identify a variety of mathematics used in the real world?

Look for . . .

• Does the student listen to others' ideas?
• Does the student recognize that mathematics is not limited to numbers?

TAKS Connection

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

(4.14.b) Underlying processes and mathematical tools. The student applies Grade 4 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 in groups to write original story problems involving addition, subtraction, multiplication, and division of whole numbers. The groups then trade problems and solve them by representing the problem with manipulatives (by drawing it, acting it out, etc.).

Assessment Connections

Questioning . . .

Open with . . .

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

Probe further with . . .

• How are you solving the problem? What's your plan? Why?
• How is your plan helping you solve the problem?
• What do you know? What information do you need to solve the problem?
• Which operations might be used to solve this problem?
• How did you decide which operations to use?
• How would you describe those operations?
• What number sentence can you write to show how you solved 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 the solution?

Look for . . .

• Can the student identify the information necessary to solve the problem?
• Does the student make and follow a plan to solve the problem?
• Does the student check for reasonableness of the solution?
• Does the student select manipulatives or draw pictures 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 errors?

TAKS Connection

Click here for a larger version of the TAKS item.

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

Additional Clarifying Activity

Students create a mini-book to record their problemsolving procedures. On the first page, they copy the 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.

(4.14.c) Underlying processes and mathematical tools. The student applies Grade 4 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 a problem-solving situation, students try different ways to solve the problem and select an appropriate strategy, such as looking for a pattern. Teachers focus students' thinking onto the type of strategy used by asking questions.

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 which strategy to use?
• Is there another strategy you can use?

Listen for . . .

• Can the student describe the strategy he or she used?
• Does the student discuss important information from the problem in his or her solution?
• Is the student able to discuss a variety of strategies?

Look for . . .

• Can the student identify information important for developing successful strategies?
• Does the student abandon a strategy when it proves not to be useful?
• 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?
• Which strategy is the student most comfortable using to solve the problem?

TAKS Connection

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

(4.14.d) Underlying processes and mathematical tools. The student applies Grade 4 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 concrete models and fraction calculators (such as the TI Math Explorer) to explore mixed numbers; they model an improper fraction (like 15/12), enter the improper fraction into the calculator, use the Ab/c key to change it to a mixed number, and then use the key to change it back to the improper fraction. Students explore several improper fractions and answer questions.

Assessment Connections

Questioning . . .

Open with . . .

• What do you notice as you explore the models and the fraction calculator?

Probe further with . . .

• What pattern do you notice?
• How does the fraction you enter into the calculator match your concrete model?
• How does the calculator's display of the mixed number match your concrete model?
• Can you predict what the calculator display will be when you press the Ab/c key? Why?

Listen for . . .

• Can the student answer questions about improper fractions based on experiences with a calculator and concrete models?

Look for . . .

• Can the student use the fraction calculator accurately?
• Does the student notice the connection between the concrete models and the calculator displays?
• Does the student develop an understanding of mixed numbers and improper fractions?
• Can the student determine the mixed number equivalent of an improper fraction?

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.

- Top -

(4.15) Underlying processes and mathematical tools. The student communicates about Grade 4 mathematics using informal language.

(4.15.a) Underlying processes and mathematical tools. The student communicates about Grade 4 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 use a calculator to generate a list of products when multiplying by 10 or 100. For example,

4 x 10 = 40
4 x 100 = 400
14 x 10 = 140
14 x 100 = 1400
24 x 10 = 240
24 x 100 = 2400

Students discuss the patterns they see and extend the patterns by answering questions such as, "What do you think the product of 123 x 10 is?"

Assessment Connections

Questioning . . .

Open with . . .

• What patterns do you notice?

Probe further with . . .

• What do you think the product of 123 x 10 is? Why? Use your calculator to check your answer.
• What do you think the product of 123 x 100 is? Why? Use your calculator to check your answer.
• What will the product of a number and 10 look like?
• What does the product of a number and 100 look like?
• How does the product of a number and 100 compare to the original number? How does multiplying by 100 affect the place value of the digits?
• What do you think the product of 123 x 1000 is? Why? Use your calculator to check your answer.

Listen for . . .

• Can the student explain his or her observations?
• Is the student able to identify patterns in the number sentences?
• Does the student use appropriate mathematical language to discuss the number sentences?

Look for . . .

• Can the student accurately use a calculator?
• Can the student record observations generated by multiplying by 10 or 100 using a calculator?
• Does the student recognize and describe patterns to multiply by 10 and 100?
• Does the student use patterns to multiply by 10 and 100?

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.

(4.15.b) Underlying processes and mathematical tools. The student communicates about Grade 4 mathematics using informal language. The student is expected to relate informal language to mathematical language and symbols.

Clarifying Activity with Assessment Connections

Students use information from the newspaper to write original problems involving addition or subtraction with decimals. Groups trade problems and select a manipulative or draw a picture to solve the problems. Students then describe their solution strategies and how the manipulatives or pictures were helpful in solving the problems.

Assessment Connections

Questioning . . . (before trading problems)

Open with . . .

• Tell me about your problem.

Probe further with . . .

• Does your problem use decimals?
• Does your problem describe a joining, comparing, or separating situation?
• Can your problem be answered by adding or subtracting decimals?
• How did you decide to create this problem?

Questioning . . . (after trading problems)

Open with . . .

• What is the problem? How did you solve the problem?

Probe further with . . .

• What operation did you use? Why?
• With what number do you start?
• What describes the change?
• What is the resulting number?
• What number sentence can you write to show how you solved your problem?
• Can you solve the problem another way?
• How do you know your solution is reasonable?

Listen for . . .

• Does the student construct a problem that clearly defines an action involving decimal numbers (joining, comparing, separating)?
• Is the student able to clearly explain his or her thought process?
• Is the student able to discuss the reasonableness of his or her solution?
• Does the student use words like "add" and "subtract"?
• Is the student able to read decimal numbers using mathematical vocabulary such as "five-tenths"?

Look for . . .

• Is the student able to self-correct errors?
• Does the student select the information necessary to solve the problem?
• 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?

TAKS Connection

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

- Top -

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

(4.16.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

Each student makes a shape on a geoboard. The teacher sorts the shapes into two groups, "Belongs" and "Doesn't Belong," according to a secret geometric attribute (such as closed shapes vs. shapes that are not closed, shapes with right angles vs. shapes with no right angles, etc.). Students analyze the examples in each group to determine the secret geometric attribute. They then use formal geometric vocabulary to describe the attribute.

Assessment Connections

Questioning . . .

Open with . . .

• What do you notice about the shapes in the "Belongs" and "Doesn't Belong" groups?

Probe further with . . .

• What's my rule? How do you know?
• Are there other attributes that you may have considered?
• What are some attributes that these two shapes have in common?
• Do the others in the group have this attribute?
• Do the members of the "Doesn't Belong" group have this attribute?
• Can you write a description of the members of the "Belongs" group?

Listen for . . .

• Can the student describe a rule?
• Does the student use formal geometric vocabulary to describe the attributes of the shapes?

Look for . . .

• Does the student develop generalizations?
• Can the student identify common attributes of a group?
• Can the student analyze the examples in the groups to determine the defining attribute?

TAKS Connection

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

(4.16.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

After making two groups of shapes labeled "Belongs" and "Doesn't Belong" based on a secret geometric attribute (as in 4.16A), the teacher makes a shape on his or her geoboard. Students determine whether the teacher's shape "Belongs" or "Doesn't Belong" and explain their choices.

Assessment Connections

Questioning . . .

Open with . . .

• Does this shape fit into "Belongs" or "Doesn't Belong"? Why?

Probe further with . . .

• How did you decide whether this shape fits the rule?
• What was a description for the members of the "Belongs" group?
• How do you know this shape fits the description?

Listen for . . .

• Can the student justify and explain his or her solution process?

Look for . . .

• Can the student apply a rule to determine if the shape belongs to a collection?

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.

- Top -