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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.

(2.1) Number, operation, and quantitative reasoning. The student understands how place value is used to represent whole numbers.

(2.1.a) Number, operation, and quantitative reasoning. The student understands how place value is used to represent whole numbers. The student is expected to use concrete models of hundreds, tens, and ones to represent a given whole number (up to 999) in various ways.

(2.1.b) Number, operation, and quantitative reasoning. The student understands how place value is used to represent whole numbers. The student is expected to use place value to read, write, and describe the value of whole numbers to 999.

(2.1.c) Number, operation, and quantitative reasoning. The student understands how place value is used to represent whole numbers. The student is expected to use place value to compare and order whole numbers to 999 and record the comparisons using numbers and symbols (<, =, >).

Clarifying Activity with Assessment Connections

Each student cuts two numbers from a newspaper or magazine and gives them to a partner. The partner uses the >, <, = symbols to compare the two numbers.

For example, the students may compare one hundred forty-three (143) to ninety-six (96). (Caution: students should only use the word "and" to indicate a decimal point when reading numbers. It is important to model this now, so that later when the students begin to encounter decimals, it will not cause problems.)

Each pair of students then compare the four numbers they jointly have and write them in their math journals from greatest to least.

Assessment Connections

Questioning . . .

Open with . . .

• Tell me about your numbers.

Probe further with . . .

• What are your numbers? (For example, one hundred forty-three and ninety-six.)
• Can you show the value of your numbers using blocks?
• What number is the greater? How do you know?
• What number is the least? How did you decide this?
• Paste the two numbers in your mathematics journal and use a number symbol (>, <, = ) to compare the two numbers. Why did you write this symbol? (For example, 143 > 96.)
• Is there another number sentence that you can write comparing 143 and 96? (For example, 96 < 143.)
• If you add 10 to each of your numbers, how would the new numbers compare? How do you know? What are the new numbers?

When pairs of students join to compare and write all of the numbers in order in their journals ask . . .

• How would you order the four numbers of your team from greatest to least? How did you decide this order? (For example, 231, 143, 132, 96.)
• Is there another way of ordering the numbers? (We could have ordered them from least to greatest.)

Listen for . . .

• Can the student accurately read the numbers?
• Does the student clearly describe the strategy used to compare and order numbers?

Look for . . .

• What numbers have been cut from the newspaper? Are the numbers single digit, two-digit, or three-digit numbers?
• Can the student compare a three-digit number with a two-digit number?
• What strategy does the student use to compare and order the numbers?
• Does the student use place value and patterns in number relationship to compare and order the numbers?
• Can the student record the comparison of the numbers using appropriate symbols (>, <, =)?
• How does the student compare numbers that have been increased by 10?
• How does the student determine the new numbers? Does she use concrete models, count on, use mental arithmetic, pencil and paper to find the new numbers, or another method?
• Can the student self-monitor and correct errors if necessary?

Future TEKS Connection

• Grade 3 TEKS Connection 3.1A, B

Additional Clarifying Activity

Students cut out numbers from newspapers or magazines and order them from greatest to least and least to greatest using a number line or hundreds chart.

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(2.2) Number, operation, and quantitative reasoning. The student describes how fractions are used to name parts of whole objects or sets of objects.

(2.2.a) Number, operation, and quantitative reasoning. The student describes how fractions are used to name parts of whole objects or sets of objects. The student is expected to use concrete models to represent and name fractional parts of a whole object (with denominators of 12 or less).

Clarifying Activity with Assessment Connections

Students reach into a bag containing blue and green linking cubes. They snap them together into a two-color train (or rectangle). The student names the fractional parts of the train that is green.

For example, the student snaps together 5 cubes, two of which are green.

Assessment Connections

Questioning . . .

Open with . . .

• What can you tell me about the green cubes in your train?

Probe further with . . .

• How many cubes in your train are green? (2)
• How many cubes are in your whole train? (5)
• How much of your train is green? (2/5) How do you know?
• What part of your train is blue? (3 out of 5 or 3/5) Why?
• Take your cubes apart and put them together in a different order. Now how much of your train is blue? (3 out of 5 or 3/5) What do you notice? (The order of the cubes does not affect how much was blue).

Listen for . . .

• Is the student naming fractional parts of a whole to answer "how much" questions?
• Does the student use appropriate language to talk about the fractions?
• Does the student have an understanding of the concept of a fraction describing part of a whole?

Look for . . .

• Does the student recognize that the order of the cubes does not affect how much was blue?
• Does the student know that parts must be equal size?

Future TEKS Connection

• Grade 3 TEKS Connection 3.2

Additional Clarifying Activity

Students fold or cut paper shapes (rectangle, square, triangle, circle) to show fractional parts. Students name and describe each fraction.

(2.2.b) Number, operation, and quantitative reasoning. The student describes how fractions are used to name parts of whole objects or sets of objects. The student is expected to use concrete models to represent and name fractional parts of a set of objects (with denominators of 12 or less).

Clarifying Activity with Assessment Connections

Students spill a set of eight two-colored counters and identify the fractional part that is red and the fractional part that is yellow. Students use fraction words to name and describe each part of the set. For example, "Three-eighths of the set of counters is red and five-eighths is yellow."

Assessment Connections

Questioning . . .

Open with . . .

• What can you tell me about your counters?

Probe further with . . .

• How many counters are in your set are red?
• How many counters are in your whole set?
• How much of the set is yellow?
• What part of the set is red?
• Can you name a fraction to describe the part of the set that is yellow? Red?

Listen for . . .

• Does the student use appropriate fraction names?

Look for . . .

• Does the student understand the difference between how many and how much? (How many is a number? How much is comparison between part/whole?)

Future TEKS Connection

• Grade 3 TEKS Connection 3.2

(2.2.c) Number, operation, and quantitative reasoning. The student describes how fractions are used to name parts of whole objects or sets of objects. The student is expected to use concrete models to determine if a fractional part of a whole or closer to 0, ½, or 1.

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

(2.3.a) Number, operation, and quantitative reasoning. The student adds and subtracts whole numbers to solve problems. The student is expected to recall and apply basic addition and subtraction facts (to 18).

Clarifying Activity with Assessment Connections

Students are given cards with a number sentence involving a basic addition fact. They make up a story that can be solved with that number sentence to share with a partner. Stories might be related to a book read by the class, a unit in social studies or science, or a field trip. Students take turns sharing and solving the stories. Each student writes the number sentence that solves the story in his or her mathematics journal. The two partners compare to check if the number sentence on the card matches the one in the journal.

Assessment Connections

Before sharing problems:

Questioning . . .

Open with . . .

• Tell me about your story.

Probe further with . . .

• How did you decide to make-up this story?
• What did you think about when you were creating your story?
• Can your story be solved with the number sentence you were given?

Listen for . . .

• Does the student use words that describe the act of joining?
• Can the student tell a story that is clear and easily interpreted by his partner?

Look for . . .

• Can the student identify story problems that can be solved by the basic fact in the number sentence?
• Does the student pose a problem that can be solved by the basic fact in the number sentence?
• If the story problem is unclear, can the student self-correct it so that it is understandable?

Future TEKS Connection

• Grade 3 TEKS Connection 3.2

After trading problems:

Assessment Connections

Questioning . . .

Open with . . .

• What is the question asked in the story your partner has told you? Tell me about your thinking.

Probe further with . . .

• How are you solving the story problem? Why?
• What do you know?
• Can you show a picture that may help you solve the problem?
• Is your solution reasonable?
• Can you solve the problem another way?
• What number sentence could you write to show your problem?

Listen for . . .

• Is the student describing the action in the problem? (joining)
• Is the student using words such as "add"?
• Is the student talking about whether the answer is reasonable?
• Does the student's explanation match the number sentence?
• Does the student talk about the reasonableness of the solution?

Look for . . .

• Can the student identify the information necessary to solve the problem?
• Can the student use addition to solve problems involving whole numbers?
• How is the student solving the problem? Does the student select manipulatives or draw a picture to help solve the problem? Does the student "recall" addition facts?
• 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 self-monitor and correct any errors if necessary?

Future TEKS Connection

• Grade 3 TEKS Connection 3.3

(2.3.b) Number, operation, and quantitative reasoning. The student adds and subtracts whole numbers to solve problems. The student is expected to model addition and subtraction of two-digit numbers with objects, pictures, words, and numbers.

(2.3.c) Number, operation, and quantitative reasoning. The student adds and subtracts whole numbers to solve problems. The student is expected to select addition or subtraction to solve problems using two-digit numbers, whether or not regrouping is necessary.

Clarifying Activity with Assessment Connections

Students solve problems related to the classroom store by choosing addition or subtraction. For example, "How much money would you need to buy the ball for 21 cents and the bat for 69 cents? Would you have any change if you started with 99 cents?"

Assessment Connections

Questioning . . .

Open with . . .

• Tell me about the purchase that you would like to make from the classroom store.

Probe further with . . .

• Do you have enough money for this purchase? If not, how much more do you need? How do you know?
• How much money do you need to make this purchase? What is the total cost? How did you figure this out?
• Can you write a number sentence that describes how you determined the total cost of your purchase?
• How much money do you have?
• How much change would you get back (or would you need)? How did you figure this out?
• What collection of money do you have for the purchase? What collection of money might you get for change (or more do you need)? Could your change be different? How?
• Write a number sentence that describes how you determined how much you get in change (or more you need)?

Listen for . . .

• Can the student verbalize the strategies he or she used?
• Can the student determine the value of a collection of coins?
• Can the student compare and determine the difference between amounts of money?

Look for . . .

• What strategies does the student use solve the problems? Does he or she draw pictures, use number sense, use mental math, or use a standard algorithm to solve the problem?
• Does the problem require regrouping?
• Can the student use more than one strategy to get at the solution?
• Does the student self-monitor and self-correct?
• Does the student choose the correct operation?
• Can the student write a number sentence to describe the operation?

Future TEKS Connection

• Grade 3 TEKS Connection 3.1C, D; 3.3

(2.3.d) Number, operation, and quantitative reasoning. The student adds and subtracts whole numbers to solve problems. The student is expected to determine the value of a collection of coins up to one dollar.

Clarifying Activity with Assessment Connections

Students work in small groups with real coins or models of coins. They select a film canister containing a collection of coins and determine the number of coins in the canister and the value of the collection. They then find all other coin collections worth the same as the collection in the canister. Students record each collection by naming the number of coins of each kind in the collection. For example, the canister may have contained seven dimes and eight pennies so the students show all the different ways to make 78¢.

Assessment Connections

Questioning . . .

Open with . . .

• Tell me about your coin collections.

Probe further with . . .

• What is the value of each collection? How did you figure this out?
• What is this collection worth? Are you sure this is worth 78 cents? How do you know?
• How many coins are in this collection?
• Did you find all collections worth 78¢?
• Are there other collections of coins worth 78¢? How do you know?
• What do you notice about the collections of 78¢?
• How many pennies are in each of your collections? What do you notice? Why do you think this happens?
• Can you have a collection worth 78¢ that contains exactly 4 pennies? Why? (78¢ is 75¢ + 3¢, so each collection must have at least 3 pennies and then must have either 8, 13,18, 23, 28,îto 78 pennies).
• How many quarters can a collection of 78¢ have? Can it have 3 quarters? Why? Can it have 4 quarters? Why?

Listen for . . .

• Does the student know the value of each coin?
• Does the student self-monitor and self-correct when counting value of coins?
• Does the student name the coins accurately?
• How does the student determine the value of a collection of coins? Does the student count by ones? Does the student use an efficient strategy to keep track and find the value of a collection of coins? Does the student use grouping to count more efficiently? When does the student add the value of pennies into the value of the collection?
• How comfortable and accurate was the student when finding the value of the collection?
• What counting strategy does the student use to determine the value of coins?

Look for . . .

• Does the student show all of the different ways to make the value of each coin?
• Can the student record the coin combinations accurately?
• Does the student use a ¢ symbol to record the value of the coins?
• Does the student demonstrate a strategy for organizing and finding all of the collections?

Future TEKS Connection

• Grade 3 TEKS Connection 3.1C, D

(2.3.e) Number, operation, and quantitative reasoning. The student adds and subtracts whole numbers to solve problems. The student is expected to describe how the cent symbol, dollar symbol, and the decimal point are used to name the value of a collection of coins.

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(2.4) Number, operation, and quantitative reasoning. The student models multiplication and division.

(2.4.a) Number, operation, and quantitative reasoning. The student models multiplication and division. The student is expected to model, create, and describe multiplication situations in which equivalent sets of concrete objects are joined.

Clarifying Activity with Assessment Connections

In their math journals using words, pictures, or numbers, students generate stories and questions about a scene in the classroom that has the same number of students in each group or table. Students determine the number of groups and the number of children in each group. For example, "If we set up 3 tables for centers with 5 chairs at each one, that would be 15 chairs in all."

Assessment Connections

Questioning . . .

Open with . . .

• Tell me about the number of children in your story.

Probe further with . . .

• How many groups are in the classroom?
• Does each group have the same number of children?
• How many children are in each group?
• How many children in total are in the classroom? How did you figure this out?
• How many chairs will there be if we set up 4 tables for centers with 5 chairs each? How did you figure this out?
• Can you figure this out another way?
• How do you know your answer is correct?

Listen for . . .

• How does the student solve the problems? Does the student count by ones, skip count, add, or use another efficient method to determine the total?
• Can the student create and describe clearly multiplication situations?

Look for . . .

• Can the student model situations?
• Can the student represent action of a multiplication story using words, pictures, or numbers?
• What strategy does the student use to solve the problem? Does the student use manipulatives to model the situation? Does the student draw pictures? Does the student use numbers and addition to model the problem? Does the student guess and check?
• What strategy does the student use for checking if the solution is correct?
• Does the student self-monitor and self-correct?

Future TEKS Connection

• Grade 3 TEKS Connection 3.4A, B

(2.4.b) Number, operation, and quantitative reasoning. The student models multiplication and division. The student is expected to model, create, and describe division situations in which a set of concrete objects is separated into equivalent sets.

Clarifying Activity with Assessment Connections

In small groups, students find all of the ways that they can separate 20 students into groups that are the same size. They record their thinking and their findings in their math journal using words, pictures, or numbers. The students are provided with manipulatives, for example a bucket of 20 cubes and 20 small paper cups, to help solve the problem.

Assessment Connections

Questioning . . .

Open with . . .

• How can we group 20 students so there are the same number of students in each group?

Probe further with . . .

• How many groups could you make? How many were in each group? How did you figure this out? (I made four groups with five in each group and five groups with four in each group)
• Is there another strategy that you might have used to figure this out?
• Could you separate 20 children into three groups of the same number of children? How do you know?
• Did you find all of the ways to separate the 20 students so there are the same number of students in each group? Are there other ways to distribute the children evenly into groups? How do you know?
• What if you added another student to the class? How would it change your grouping?

Listen for . . .

• Does the student's work match his or her explanation?
• Does the student appropriate vocabulary to clearly describe his or her strategies?

Look for . . .

• Does the student make equal groups with his or her cubes?
• How does the student represent his or her work in his or her journal? Does the student use words, show a visual representation, or use numbers to describe his or her work?
• What strategy does the student use to solve the problem? Does the student demonstrate an organized plan to solve the problem or guess and check?
• What strategy does the student use for checking if the solution is correct?

Future TEKS Connection

• Grade 3 TEKS Connection 3.4C

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(2.5) Patterns, relationships, and algebraic thinking. The student uses patterns in numbers and operations.

(2.5.a) Patterns, relationships, and algebraic thinking. The student uses patterns in numbers and operations. The student is expected to find patterns in numbers such as in a 100s chart.

Clarifying Activity with Assessment Connections

Students fill in the numbers on a blank hundreds chart and discuss the patterns they see (and may be used as they filled it in). For example, the tens digits increase by one as you go down the chart, but the ones digits stay the same.

Assessment Connections

Questioning . . .

Open with . . .

• Look at the hundreds chart. Do you notice any number patterns?

Probe further with . . .

• Touch the 11. Move your finger down the column.
• What do you notice? (The ten's place changes; one's place doesn't.)
• What stays the same? What changes? How does it change?
• Touch the 30. Move your finger across the row.
• What pattern do you see? (The ten's place stays the same; the one's place increases by one.)
• What stays the same? What changes? How does it change?
• How can you use the patterns you notice to help you fill in the hundreds chart quicker the next time you need to complete it?
• If you wanted to create a "more than 100" chart by adding another row, what would the entries in that row be? Why?

Listen for . . .

• Can the student identify and verbalize number patterns found in the hundreds chart?
• Does the student describe number patterns using appropriate vocabulary such as tens-place, ones-place, increase by one, increase by ten, or stay the same?

Look for . . .

• Does the student accurately fill in the hundreds chart?
• Does the student notice the vertical or horizontal number pattern?
• Can the student extend the pattern?

Future TEKS Connection

• Grade 3 TEKS Connection 3.6A

(2.5.b) Patterns, relationships, and algebraic thinking. The student uses patterns in numbers and operations. The student is expected to use patterns in place value to compare and order whole numbers through 999.

Clarifying Activity with Assessment Connections

In pairs, students spin a spinner to create two three-digit numbers. They select one of the numbers, then use a calculator to add (or subtract) 1, 10, or 100 successively to transform this number into the other number created. They record each step by writing the change (what they added or subtracted) and the result. For example, if the numbers created were 158 and 261 the record may be starting with 158.

Assessment Connections

Questioning . . .

Open with . . .

• What patterns in place value do you notice from your records?

Probe further with . . .

• What do you notice about your records? Are the new numbers in order? How do the numbers compare? (Notice that the answer is going to depend on the strategy the student uses.) Can you use a strategy so that the numbers are in order and each new number is greater than the one before? How?
• What happens when you add (subtract) 1? 10? 100?
• What are your numbers? How do they compare? How do you know?
• How would you use patterns you noticed here to help compare and order numbers?
• Which is greater, 345 or 354? Why? 583 or 385? Why? 185 or 183? Why?
• In the number 354, what does the 5 represent?

Listen for . . .

• Does the student accurately read the 3 digit numbers using the patterns in naming of numbers? (Caution: students should only use "and" to indicate a decimal point.)
• Can the student describe patterns in place value to compare and order numbers? (For example, 583 is greater than 385. I looked at the first digits. Five is greater than 3. Or, 185 is greater than 183. I looked at the first digits and they were both 1. I looked at the next digits. They were both 8. So I compared the last digit and 5 is greater than 3.)
• Does the student clearly describe the strategy used to compare and order numbers?
• Does the student use ideas of place value to explain and justify strategies and responses?

Look for . . .

• Can the student use a calculator accurately?
• Does the student notice patterns in place value?
• Does the student use place value and patterns in number relationship to compare and order 3-digit numbers?
• Can the student identify the different values of the different places in a number?

Future TEKS Connection

• Grade 3 TEKS Connection 3.1A, B

(2.5.c) Patterns, relationships, and algebraic thinking. The student uses patterns in numbers and operations. The student is expected to use patterns and relationships to develop strategies to remember basic addition and subtraction facts. Determine patterns in related addition and subtraction number sentences (including fact families) such as 8 + 9 = 17, 9 + 8 = 17, 17 - 8 = 9, and 17 - 9 = 8.

Clarifying Activity with Assessment Connections

Students form models for basic addition such as 6 + 5, 5+6, 8+3, 3+8, 7+6, 6+7. They notice patterns such as 6+5=5+6, 3+8=8+3, and 7+6=6+7(Teachers may recall that this is called the commutative property). They also use concrete models or hundreds charts to notice that 5+6=5+(5+1)=10+1=11; 8+3=8+(2+1)=10+1=11; and 6+7= 6+(4+3)=10+3=13 or 6+7=6+(6+1)=12+1=13 (doubles plus 1). (Teachers may recall that this is called the associative property.) The students extend the pattern to break down a "hard-to-remember" addition fact into more easily remembered 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" addition facts and how you plan to remember them.

Probe further with . . .

• What are some addition facts that you don't always recall right now?
• How can you break this down into facts you do remember?
• Why did you decide to break it down like this? 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 for you to remember? How?

Listen for . . .

• Can the student clearly explain the strategy used to break down (partition) hard to remember facts?
• What strategies are the students using (for example doubles plus 1 or grouping into 10)?
• Does the student check for reasonableness of the solution?

Look for . . .

• Does the student self-correct or self-monitor?
• Does the student notice the pattern of the commutative property of addition?
• Can the student apply the pattern of the commutative property?
• Can the student use the pattern of the associative property addition to create strategies that can help them figure out hard to recall addition facts?
• Can the student separate a number into two convenient parts?
• Does the student use mental arithmetic, paper and pencil, or a concrete model to break down the "touch facts"?
• Does the student apply this method to help remember facts on other occasions?

Future TEKS Connection

• Grade 3 TEKS Connection 3.3A, B; 3.5B; 3.6A, B, C

Additional Clarifying Activity with Assessment Connections

Students work in pairs to make trains from linking cubes, e.g. 8 red cubes and 6 blue cubes. They take turns writing and modeling number sentences from the fact family that can be modeled with their cubes. One student writes an addition sentence about the train (8 + 6 = 14) and the partner models the action of the number sentence using the linking cubes. The partner writes while the student models the subtraction sentence (14 - 8 = 6). The student then models another subtraction sentence (14 - 6 = 8) for the partner to write, and the partner models another addition sentence (6 + 8 = 14) for the student to write.

Assessment Connections

Questioning . . .

Open with . . .

• Tell me about what you are doing.

Probe further with . . .

• The group of number sentences that you have created is called a fact family. Why do you think it is called a fact family?
• What do you notice about the fact family?
• What are the number sentences in the fact family that you can model with your cube collection?
• What do you notice in the number sentences? (For example, they all use the same numbers.)
• How are your number sentences alike?
• How are your number sentences different?
• Are these all the number sentences that go with your collection? How do you know?
• How might you use fact families to help you learn your addition and subtraction facts?

Listen for . . .

• Can the student identify patterns in numbers and operations?
• Can the student clearly explain his or her reasoning using appropriate vocabulary?

Look for . . .

• Does the student recognize the relationship of joining groups and separating groups?
• When given the model of an action, can the student find a number sentence to describe the action?
• Can the student model the action of a number sentence with a train (addition and subtraction)?
• Are the fact families accurate?
• Does the student self-correct?

Future TEKS Connection

• Grade 3 TEKS Connection 3.3A, B; 3.5B; 3.6A, B, C

Additional Clarifying Activity

Students sort a set of basic addition fact cards (with no sums shown) according to a given strategy, e.g. sums that are doubles, sums that are doubles plus one, and other sums. Students use the appropriate strategy to find each sum. Students then can re-sort the cards according to another strategy, such as counting on one or counting on two, and use the new strategy to find the sums.

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(2.6) Patterns, relationships, and algebraic thinking. The student uses patterns to describe relationships and make predictions.

(2.6.a) Patterns, relationships, and algebraic thinking. The student uses patterns to describe relationships and make predictions. The student is expected to generate a list of paired numbers based on a real-life situation such as number of tricycles related to number of wheels.

Clarifying Activity with Assessment Connections

Students determine the number of pencils you can buy with one dime, two dimes, and three dimes if one dime buys three pencils. Students use a chart like the one below to record the data they have collected.

Assessment Connections

Questioning . . .

Open with . . .

• Tell me about the table you created and how I could use it.

Probe further with . . .

• What did you record in your table? (The number of dimes and number of pencils that can be bought with the dimes)
• How many pencils can be bought with no dimes? How do you know?
• How many pencils can be bought with one dime?
• How many pencils can be bought with two dimes? Three dimes? How did you figure this out?
• What pattern do you notice in the table?
• How many pencils can be bought with four dimes? How do you know?

Listen for . . .

• Does the student explain what the table represents and how to use it?

Look for . . .

• Is the student able to generate the data for a table?
• Does the student notice a pattern and use it?
• Does the student write the data in the appropriate place and label the table?

Future TEKS Connection

• Grade 3 TEKS Connection 3.7A

(2.6.b) Patterns, relationships, and algebraic thinking. The student uses patterns to describe relationships and make predictions. The student is expected to identify patterns in a list of related number pairs based on a real-life situation and extend the list.

(2.6.c) Patterns, relationships, and algebraic thinking. The student uses patterns to describe relationships and make predictions. The student is expected to identify, describe, and extend repeating and additive patterns to make predictions and solve problems.

Clarifying Activity with Assessment Connections

Students identify and extend the pattern from the list in the chart in 2.6A showing a given number of dimes and the corresponding number of pencils that can be bought to answer the question, "How many pencils can you buy with 4 dimes?"

Assessment Connections

Questioning . . .

Open with . . .

• How did you decide how many pencils you could buy?

Probe further with . . .

• How did you decide how many pencils you could buy with 4 quarters?
• How did you use the table to figure out how many pencils you could buy? Why?
• How many pencils could you buy with 6 dimes? How do you know?

Listen for . . .

• Can the student clearly and accurately explain the table?
• Can the student identify and explain the pattern in each column?
• Can the student identify and explain the pattern between the rows?
• Can the student identify and explain the relationship between the number of dimes and the number of pencils?
• Can the student extend the pattern to determine how many pencils can be purchased with more dimes?

Look for . . .

• Does the student use the pattern in the table to find a solution to the problem?
• Does the student correctly extend the table?

Future TEKS Connection

• Grade 3 TEKS Connection 3.7B

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(2.7) Geometry and spatial reasoning. The student uses attributes to identify two- and three-dimensional geometric figures. The student compares and contrasts two- and three-dimensional geometric figures or both.

(2.7.a) Geometry and spatial reasoning. The student uses attributes to identify two- and three-dimensional geometric figures. The student compares and contrasts two- and three-dimensional geometric figures or both. The student is expected to describe attributes (the number of vertices, faces, edges, sides) of two- and three-dimensional geometric figures such as circles, polygons, spheres, cones, cylinders, prisms, and pyramids, etc.

Clarifying Activity with Assessment Connections

With a partner, students take turns feeling inside a pillowcase filled with models of shapes or solids to select an object, and then describe the object without looking to the partner who draws the object from the description in her math journal. Together, the team then tries to identify the shape or solid. They remove the object from the pillowcase to check their identification.

Assessment Connections

Questioning . . .

Open with . . .

• Tell me about the shape (solid) that you found in the pillowcase?

Probe further with . . .

• How does it feel?
• How many sides (faces) does it have?
• How many corners does it have?
• How sharp are the corners?
• What do you think it is?
• How did you decide the name for this shape or solid?
• What clues did you give your partner to help her draw the shape (solid)?
• How is the shape (solid) that your partner drew the same as the shape (solid) from the pillowcase? How is it different?

Listen for . . .

• Can the student describe shapes and solids?
• Is the student using informal and formal geometric vocabulary appropriately?
• Can the student explain reasons for the identification of shapes (solids)?

Look for . . .

• Do the pictures in the journal reflect the shape and solid attributes that the student described?
• Does the student self-correct?

Future TEKS Connection

• Grade 3 TEKS Connection 3.8; 3.9A, B, C

(2.7.b) Geometry and spatial reasoning. The student uses attributes to identify two- and three-dimensional geometric figures. The student compares and contrasts two- and three-dimensional geometric figures or both. The student is expected to use attributes to describe how 2 two-dimensional figures or 2 three-dimensional geometric figures are alike or different.

Clarifying Activity with Assessment Connections

Each student chooses a shape (or a solids). With a partner, the students use attributes to compare their shapes (or solids). They discuss how the shapes are alike and different then use words and pictures to describe this in their journals. For example, the pair may have a cone and a square pyramid. They may compare a cone and a pyramid by "Both are solids with a flat base and a point at the top. One will roll, but the other one won't."

Assessment Connections

Questioning . . .

Open with . . .

• Tell me about your shapes (solids).

Probe further with . . .

• What are the names of the geometric shape (solids) that you chose?
• What attribute are you using to compare them?
• How are they the same? What do these have in common?
• How do they differ?
• Tell me about your journal entry.
• Can you name a real life object that has the same attributes as these?

Listen for . . .

• Can the student describe the attributes of shapes and solids?
• Does the student use appropriate mathematical vocabulary for critical attributes? (For example, vertices, angles, corners, sides, and edges.)
• Can the student name a variety of shapes and solids using formal geometric language?
• Can the student compare a shapes and solids using formal geometric language?

Look for . . .

• Can the student create pictorial representations of shapes and solids?
• Does the student accurately describe the geometric shapes and solids?

Future TEKS Connection

• Grade 3 TEKS Connection 3.8; 3.9A, B, C

Additional Clarifying Activity

Students use Venn diagrams to compare and contrast the attributes of two shapes or two solids.

(2.7.c) Geometry and spatial reasoning. The student uses attributes to identify two- and three-dimensional geometric figures. The student compares and contrasts two- and three-dimensional geometric figures or both. The student is expected to cut two-dimensional geometric figures apart and identify the new geometric figures formed.

Clarifying Activity with Assessment Connections

After reading the story Grandfather Tang's Story, by Ann Tompert, students fold and cut a square into tangram pieces and identify the shapes made.

Link: Constructing Your Own Set of Tangrams

Assessment Connections

Questioning . . .

Open with . . .

• Tell me about the shapes that you have created from cutting apart other shapes for Tangram pieces.

Probe further with . . .

• What kinds of shapes did you create from folding and cutting a triangle?
• How did you create a triangle shapes? Were there other ways that you cut a triangle?

Listen for . . .

• Can the student identify the new shapes made from cutting geometric shapes apart?

Look for . . .

• Did the students notice that two triangles could be formed from symmetric cuts of squares and rectangles?

Future TEKS Connection

• Grade 3 TEKS Connection 3.8; 3.9A, B, C

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(2.8) Geometry and spatial reasoning. The student recognizes that a line can be used to represent a set of numbers and its properties.

(2.8) Geometry and spatial reasoning. The student recognizes that a line can be used to represent a set of numbers and its properties. The student is expected to use whole numbers to locate and name points on a number line.

Clarifying Activity with Assessment Connections

Students place Velcro®-ed number cards on the appropriate places of a Velcro® strip number line and discuss how they know which numbers to place in which order. For example, the number cards might display the numbers 6, 18, and 21.

Assessment Connections

Questioning . . .

Open with . . .

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

Probe further with . . .

• What are the numbers?
• Could the student decide where 6 belongs if there were no other numbers marked on the number line (benchmarks)? How? (I could locate it only if I decide that the number line begins at 0 or 1 and each dot was one unit).
• Could the student decide where 6 belongs if 5 was the only number marked on the number line? What are some benchmark numbers you might want on the number line to help you decide where your numbers goes? (If you don't want to locate them all, perhaps 10 and 20.) Why?
• How do you know that 18 is on this side of 10?
• How do you know how far away from 10 to place 18?
• Is there another strategy you could have used to locate 18? How?
• What number would be located here on the number line?
• Can the student draw a picture of our Velcro® strip number line with the numbers on it in your math journal?

Listen for . . .

• Does the student accurately read the numbers?
• Can the student name numbers on a number line accurately?
• Does the student clearly describe a reasonable strategy used for placing the numbers on the number line?
• Do the student's strategy and explanations involve benchmarks?

Look for . . .

• Can the student locate numbers on a number line accurately?
• Does the student demonstrate number sense? (For example, 18 is eight places to the right of 10 and 2 places to the left of 20.)
• Does the student compare numbers and use this to determine where a number is located on a number line? (For example, 6 is one more than 5 so 6 is one unit to the right 5 on the number line.)
• Can the student record the Velcro® strip number line with a pictorial number line?

Future TEKS Connection

• Grade 3 TEKS Connection 3.1B; 3.10

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(2.9) Measurement. The student directly compares the attributes of length, area, weight/mass, and capacity, and uses comparative language to solve problems and answer questions. The student selects and uses nonstandard units to describe length, area, capacity, and weight/mass. The student recognizes and uses models that approximate standard units (from both SI, also known as metric, and customary systems) of length, weight/mass, capacity, and time.

(2.9.a) Measurement. The student directly compares the attributes of length, area, weight/mass, and capacity, and uses comparative language to solve problems and answer questions. The student selects and uses nonstandard units to describe length, area, capacity, and weight/mass. The student recognizes and uses models that approximate standard units (from both SI, also known as metric, and customary systems) of length, weight/mass, capacity, and time. The student is expected to identify concrete models that approximate standard units of length and use them to measure length.

Clarifying Activity with Assessment Connections

Students use models of approximate standard units (for example, decimeter craft sticks, centimeter cubes, inch tiles, or meter strings) and work in pairs to measure objects. For example, the students use craft sticks to measure the length of books.

Assessment Connections

Questioning . . .

Open with . . .

• How did you measure the length of your book?

Probe further with . . .

• How many craft sticks did you use to get your answer?
• Did your craft stick train end exactly with the end of your book?
• If not, how did you decide to report the total number of sticks to measure the book?

Listen for . . .

• Does the student's work match his or her explanation?
• Does the student use mathematical vocabulary to explain his or her answer?
• Does the student use a number and a unit to report the measurement?
• Is the student's explanation logical and reasonable?

Look for . . .

• Do the sticks begin at the start of the book?
• Does the student line up the sticks end to end?
• Does the student report the length to the nearest whole unit?

Future TEKS Connection

• Grade 3 TEKS Connection 3.11

(2.9.b) Measurement. The student directly compares the attributes of length, area, weight/mass, and capacity, and uses comparative language to solve problems and answer questions. The student selects and uses nonstandard units to describe length, area, capacity, and weight/mass. The student recognizes and uses models that approximate standard units (from both SI, also known as metric, and customary systems) of length, weight/mass, capacity, and time. The student is expected to select a non-standard unit of measure such as square tiles to determine the area of a two-dimensional surface.

(2.9.c) Measurement. The student directly compares the attributes of length, area, weight/mass, and capacity, and uses comparative language to solve problems and answer questions. The student selects and uses nonstandard units to describe length, area, capacity, and weight/mass. The student recognizes and uses models that approximate standard units (from both SI, also known as metric, and customary systems) of length, weight/mass, capacity, and time. The student is expected to select a non-standard unit of measure such as a bathroom cup or a jar to determine the capacity of a given container.

Clarifying Activity with Assessment Connections

Students are given a concrete model that approximates a particular standard unit. The students find other objects that approximate that same measure. For example, after filling a one-cup measuring cup with rice, students select from a variety of containers the ones that hold about one-cup. Students check their predictions.

Assessment Connections

Questioning . . .

Open with . . .

• How did you decide which containers hold about one cup?

Probe further with . . .

• How do you know you have one cup of rice? (I filled it to the line without going over.)
• How did you choose the containers that you predicted would hold about one cup?
• How did you find out whether a container holds more than, less than, or approximately one cup?
• How can you use the rice to determine if the container holds approximately one cup?
• What does it mean if the rice overflows and does not all fit in the container? Does the container hold more than, less than, or approximately one-cup?
• What would happen if instead of rice, I had one-cup of water? Which containers would hold approximately one-cup of water? Why? How do you know?

Listen for . . .

• Can the student determine and explain whether a container holds more than, less than, or approximately one-cup? (For example, does the student know if the rice is spilling over the container, the container holds less than one-cup?)
• Are the student's justifications reasonable?

Look for . . .

• Does the student randomly pick containers or does the student use a systematic approach to deciding which containers hold approximately one cup?
• Does the student fill the one-cup container with rice to the line without overfilling?
• Does the student independently use the rice to check predictions?
• Does the student demonstrate conservation of measurement? (That is, a cup is a cup.)
• Does the student check his or her prediction?

Future TEKS Connection

• Grade 3 TEKS Connection 3.11

(2.9.d) Measurement. The student directly compares the attributes of length, area, weight/mass, and capacity, and uses comparative language to solve problems and answer questions. The student selects and uses nonstandard units to describe length, area, capacity, and weight/mass. The student recognizes and uses models that approximate standard units (from both SI, also known as metric, and customary systems) of length, weight/mass, capacity, and time. The student is expected to select a non-standard unit of measure such as beans or marbles to determine the weight/mass a given object.

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(2.10) Measurement. The student uses standard tools to estimate and measure time and temperature (in degrees Fahrenheit).

(2.10.a) Measurement. The student uses standard tools to estimate and measure time and temperature (in degrees Fahrenheit). The student is expected to read a thermometer to gather data.

Clarifying Activity with Assessment Connections

Students read several different thermometers and record the temperatures measured on each for ten school days to look for weather patterns. For example, the students use a digital thermometer that is marked with tens and tick marks of 5 units.

Assessment Connections

Questioning . . .

Open with . . .

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

Probe further with . . .

• How did you read the temperature using this thermometer?
• What is the temperature now? How did you figure it out? Did you skip count to figure this out? Why did you skip count by fives (two)? How did you know that each tick mark was five (two)?
• How do the temperatures you have read using the different thermometers compare? Are they about the same? How do they differ? Why do you think this happened?
• Did you read each thermometer using the same methods? How were the methods different? Why? Which were similar? How were the methods similar?
• Looking at the data you recorded, which day was the hottest/ coolest? How do you know?
• What did you notice about the weather outside and the temperatures you recorded on these 10 days?
• During the summer after school is out, if we read the thermometers, do you think the numbers would be higher or lower? Why?

Listen for . . .

• Can the student read a variety of thermometers correctly?
• Does the student consistently read the thermometers correctly?
• How does the student read the thermometer? Does she skip count?
• Can the student explain the observations?
• Can the student relate mathematical language and informal language to describe temperature (the higher the numbers on the thermometer, the hotter it is outside)?

Look for . . .

• Can the student record observations?
• If the student is not reading the thermometer correctly, are they misreading the tick marks between each rounded number?
• Can the student self-correct errors when reading various thermometers?

Future TEKS Connection

• Grade 3 TEKS Connection 3.12B

(2.10.b) Measurement. The student uses standard tools to estimate and measure time and temperature (in degrees Fahrenheit). The student is expected to read and write times shown on analog and digital clocks using five-minute increments.

Clarifying Activity with Assessment Connections

Students construct a double clock with a traditional face on one side and a digital readout on the other. As students read or listen to a story involving time, they place the hands in position on the traditional side and show the correct time on the digital side, then read the time shown.

Example: Read Pigs on a Blanket Fun with Math by Amy Axelrod once. After you have read the book to the class, revisit this last page of the book for this math activity.

Assessment Connections

Questioning . . .

Open with . . .

• How do you use a clock to describe time?

Probe further with . . .

• What time did the pigs decide to go to the beach?
• What time did the beach close?
• Does the beach close before 3:00 or after 3:00?
• If the traditional clock says (picture), what time is it? Is there another way to describe this time? How would that look on the digital clock? What is happening in the story at this time? Is this before or after the beach closes?
• If the digital clock says 2:55, how would that look on the traditional clock?

Listen for . . .

• Is the student able to describe the time in a variety of ways on both the traditional and digital clock? (For example: 10:15 is also a quarter past 10. and 10:45 is a quarter to 11?)

Look for . . .

• Can the student relate the time displayed on digital and analogue clocks?

Future TEKS Connection

• Grade 3 TEKS Connection 3.12A

(2.10.c) Measurement. The student uses standard tools to estimate and measure time and temperature (in degrees Fahrenheit). The student is expected to describe activities that take approximately one second, one minute, and one hour.

Clarifying Activity with Assessment Connections

In a classroom that has a digital clock, an analogue clock, and timers for minutes and hours, the students set the timer for one second, one minute, and one hour and discuss what they did in the time that elapsed. They then describe activities that take approximately one second, one minute, and one hour.

Assessment Connections

Questioning . . .

Open with . . .

• What you can do in approximately one second? one minute? one hour?

Probe further with . . .

• Can you hold your breath for one second? one minute? one hour?
• Can you finish reading your book in one second? one minute? one hour?
• What do you think we will be doing in one minute from now? Why?
• How do you think the clocks will look in one minute? Set the timer to check your prediction? Were you accurate?
• What do you think we will be doing in one hour from now? Why?
• How do you think the clocks will look in one hour? Set the timer to check your prediction? Were you accurate?

Listen for . . .

• Can the student describe activities that take approximately one second, one minute, and one hour?
• Are the student's activities and explanations reasonable?

Look for . . .

• Can the student describe how the clocks will look after one minute and one hour?

Future TEKS Connection

• Grade 3 TEKS Connection 3.13

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(2.11) Probability and statistics. The student organizes data to make it useful for interpreting information.

(2.11.a) Probability and statistics. The student organizes data to make it useful for interpreting information. The student is expected to construct picture graphs and bar-type graphs.

Clarifying Activity with Assessment Connections

Students use sticky notes to draw pictures of ways they came to school today (e.g. walk, bike, car, bus). Students create a graph using the sticky notes with one picture representing one student's way to come to school. Using the transportation graphs, students answer questions such as "What can we tell about today's weather by looking at the ways students came to school?", and "How many more people rode the bus than walked today?"

Assessment Connections

Questioning . . .

Open with . . .

• Tell me about your graph.

Probe further with . . .

• How did you organize the information for your graph?
• How did you decide how to set up your graphs?
• Which way had most students come to school today?
• Which way had the least number of students come?
• What does each picture represent?
• Can you create a bar type graph in your math journal that shows the same information?
• How did you change your data display from the pictograph to a bar graph?
• How are your graphs alike? How are they different?
• Did more students come to school by bus or did more come by car? How many more? How do you know? How did you use the graph to answer this question?
• Can you generate other questions that can be answered using the graph that we made?
• How can you use the graph to answer this question? Can you read the answer to the question right from the graph? Do you need more than one part of the graph to answer the question?
• What can we tell about today's weather by looking at the ways students came to school? Why? Would you expect the graph to look differently if the weather was different? How? Why?

Listen for . . .

• Does the student accurately interpret the graphs?
• Do the student's explanations match the written work?
• Is the student talking about the information in the graph?
• Are the student's explanations reasonable?

Look for . . .

• Can the student accurately collect, organize, and display data?
• Can the student locate information on a graph?
• Does the student accurately translate the information in a pictograph to a bar graph form?
• Does the student label the graphs?
• Can the student generate and answer problem-solving questions from the graph?

Future TEKS Connection

• Grade 3 TEKS Connection 3.14A, B

(2.11.b) Probability and statistics. The student organizes data to make it useful for interpreting information. The student is expected to draw conclusions and answer questions based on picture graphs and bar-type graphs.

Clarifying Activity with Assessment Connections

See the Clarifying Activity with Assessment Connections for 2.6B.

Additional Clarifying Activity

Using the transportation graphs in 2.11A, students answer questions such as "What can we tell about today's weather by looking at the ways students came to school?", and "How many more people rode the bus than walked today?"

(2.11.c) Probability and statistics. The student organizes data to make it useful for interpreting information. The student is expected to use data to describe events as more likely or less likely such as drawing a certain color crayon from a bag of seven red crayons and three green crayons.

Clarifying Activity with Assessment Connections

Pairs of students draw from a bag containing 6 red beads and 3 black beads, recording the color and putting the bead back each time. They then organize their data and compare their data with other pairs of students to make predictions about the likelihood of drawing a red or a black bead. For example, "I think I am more likely to draw a red bead than a black bead."

Assessment Connections

Questioning . . .

Open with . . .

• Are you more likely (less likely) to draw a red bead or a black bead from the bag? Why?

Probe further with . . .

• How did you collect and organize your data?
• How does your data compare with data from pairs of other students?
• Without looking, would you predict that there are more red beads or more black beads in your bag? Why?
• Is it important that you shake the bag to mix up the beads before you draw to use the data to compare how much of the bag was red beads? Why?
• How is the likeliness of drawing a red bead related to the number of red beads in the bag?

Listen for . . .

• Can the student explain how the data was used to determine if an event was more likely or less likely?
• Can the student discuss why the beads need to be mixed up before the data can be used to compare the likeliness of drawing a red with the proportion of red beads in the bag?

Look for . . .

• Can the student accurately record the number of beads of each color drawn?
• How does the student collect the data? Does the student use tally marks or another method to count the number of each color?
• Does the student keep checks of his or her work? That is, does he or she keep track of the number of red drawn, black drawn, and total drawn. Does he or she self-monitor and self-correct?
• Does the student organize the data into a graph?
• Can the student use the data to determine if an event is more likely or less likely?

Future TEKS Connection

• Grade 3 TEKS Connection 3.14C

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(2.12) Underlying processes and mathematical tools. The student applies Grade 2 mathematics to solve problems connected to everyday experiences and activities in and outside of school.

(2.12.a) Underlying processes and mathematical tools. The student applies Grade 2 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to identify the mathematics in everyday situations.

Clarifying Activity with Assessment Connections

Students describe how the teacher can determine the number of stickers to order based upon the number of students in the class if every student gets three stickers.

Assessment Connections

Questioning . . .

Open with . . .

• How can I figure out how many stickers to order if I want to give each student in our class three stickers?

Probe further with . . .

• How can mathematics help me figure this out? What should I do first? What do I need to know?
• Can you tell me about another everyday situation where you used mathematics? When have you measured? Classified? Found yourself counting, adding, or subtracting?

Listen for . . .

• Can the students identify mathematics needed to solve this everyday problem?
• Can the student identify mathematics in other everyday situations?
• Does the student identify a variety of uses of mathematics in their world including some that are unusual?

Future TEKS Connection

• Grade 3 TEKS Connection 3.15A

(2.12.b) Underlying processes and mathematical tools. The student applies Grade 2 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to solve problems with guidance that incorporates the processes of understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness.

(2.12.c) Underlying processes and mathematical tools. The student applies Grade 2 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, or acting it out in order to solve a problem.

Clarifying Activity with Assessment Connections

Students work in small groups to solve the problem, "How many school buses are needed to take four second-grade classes on a field trip?" Students state and discuss the problem in order to understand it, brainstorm ways to solve the problem, choose a strategy for solving the problem, carry out the plan to determine how many buses are needed, and discuss their solution to determine if it seems reasonable or not.

Assessment Connections

Questioning . . .

Open with . . .

• How did you figure this out?

Probe further with . . .

• What did you think about doing to solve the problem?
• What did you do first?
• What was your strategy? How did you decide what strategy you wanted to use to solve this problem? Did your plan work?
• What other strategies did you think about using to solve the problem? What did you actually do to solve the problem?
• Why did you decide to do that instead of something else?
• What information helped you decide what to do?
• Did you use pictures or manipulatives to help you solve the problem? How did the pictures or manipulatives help you? How does your picture compare to someone else's? How did you organize your work? Did you use a table? Did you notice any patterns?
• How do you know your answer is reasonable? Are there other reasonable answers?
• Is there another way you could have solved the problem?

Listen for . . .

• Is the student able to describe the strategy they used?
• Can the student identify important information from the problem?
• Is the student talking about a variety of strategies?
• Does the student's explanation match work?
• Is the student's explanation logical and reasonable?
• Does the student use mathematical vocabulary in explanations?

Look for . . .

• Is the student using a plan to solve the problem?
• Is the student selecting reasonable and logical strategies to solve the problem?
• Does the student understand the problem?
• Can the student carry out the plan?
• Can the student use this strategy to get the right answer?
• Does the student recognize if the answer is reasonable?
• Can the student compare their strategies to others' strategies?
• Is the student learning and sharing strategies from others?
• What strategy does the student seem to be using most often with accuracy?

Future TEKS Connection

• Grade 3 TEKS Connection 3.15B, C

Additional Clarifying Activity

During each problem-solving situation, such as the bus problem in 2.12B, students try different ways to solve the problem and select an appropriate strategy, such as drawing a picture. Teachers focus students' thinking onto the type of strategy used, by asking questions such as, "What did you think about doing to solve the problem? What did you actually do to solve the problem? Why did you decide to do that instead of something else?"

(2.12.d) Underlying processes and mathematical tools. The student applies Grade 2 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

See the Clarifying Activity with Assessment Connections for 2.13A.

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(2.13) Underlying processes and mathematical tools. The student communicates about Grade 2 mathematics using informal language.

(2.13.a) Underlying processes and mathematical tools. The student communicates about Grade 2 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 calculators, play money, and newspaper ads to develop a strategy to determine how many candy bars can be purchased with one dollar. Students record the strategies used in solving the problem. For example, using repeated subtraction on the calculator to count how many "29 cents" it takes to reach or go over one dollar, the students might record starting with 100 on the calculator to represent $1.00 and subtract 29 for each candy bar purchased.

"I can buy three candy bars, because 100 - 29 = 71, 71 - 29 = 42, and 42 - 29 = 13. I don't have enough money left for another candy bar."

Assessment Connections

Questioning . . .

Open with . . .

• How did you figure this out?

Probe further with . . .

• What did you think about doing to solve the problem?
• What did you do first?
• What was your strategy? How did you decide what strategy you wanted to use to solve this problem? Did your plan work?
• What other strategies did you think about using to solve the problem? What did you actually do to solve the problem?
• Why did you decide to do that instead of something else?
• What information helped you decide what to do?
• Did you use pictures or manipulatives to help you solve the problem? How did the pictures or manipulatives help you? How does your picture compare to someone else's? How did you organize your work? Did you use a table? Did you notice any patterns?
• How do you know your answer is reasonable? Are there other reasonable answers?
• Is there another way you could have solved the problem?

Listen for . . .

• Is the student able to describe the strategy they used?
• Can the student identify important information from the problem?
• Is the student talking about a variety of strategies?
• Does the student's explanation match work?
• Is the student's explanation logical and reasonable?
• Does the student use mathematical vocabulary in explanations?

Look for . . .

• Is the student using a plan to solve the problem?
• Is the student selecting reasonable and logical strategies to solve the problem?
• Does the student understand the problem?
• Can the student carry out the plan?
• Can the student use this strategy to get the right answer?
• Does the student recognize if the answer is reasonable?
• Can the student compare their strategies to others' strategies?
• Is the student learning and sharing strategies from others?
• What strategy does the student seem to be using most often with accuracy?

Future TEKS Connection

• Grade 3 TEKS Connection 3.15B, C

(2.13.b) Underlying processes and mathematical tools. The student communicates about Grade 2 mathematics using informal language. The student is expected to relate informal language to mathematical language and symbols.

Clarifying Activity with Assessment Connections

Students are given cards with a number sentence involving basic addition fact. They make up a story that can be solved with that number sentence to share with a partner. Stories might be related to a book read by the class, a unit in social studies or science, or a field trip. Students take turns sharing and solving the stories. Each student writes the number sentence that solves the story in his or her mathematics journal. The two partners compare to check if the number sentence on the card matches the one in the journal.

Assessment Connections

Before trading problems:

Questioning . . .

Open with . . .

• Tell me about your story.

Probe further with . . .

• How did you decide to make-up this story?
• What did you think about when you were creating your problem?
• Can your story be solved with the number sentence you were given?

Listen for . . .

• Does the student use words that describe the act of joining?
• Can the student tell a story that is clear and easily interpreted by his or her partner?

Look for . . .

• Can the student identify story problems that can be solved by the basic fact in the number sentence?
• Does the student pose a problem that can be solved by the basic fact in the number sentence?

After trading problems:

Questioning . . .

Open with . . .

• What is the question asked in the story your partner has told you? Tell me about your thinking.

Probe further with . . .

• How are you solving the story problem? Why?
• What do you know?
• Can you show a picture that may help you solve the problem?
• Is your solution reasonable?
• Can you solve the problem another way?
• What number sentence could you write to show your problem?

Listen for . . .

• Is the student explaining this number sentence by using the appropriate informal language?
• Is the student describing the action in the problem? (joining)
• Is the student using words such as add?
• Is the student talking about whether the answer is reasonable?
• Does the student's explanation match the number sentence?
• Does the student talk about the reasonableness of the solution?

Look for . . .

• Can the student identify the information necessary to solve the problem?
• Can the student use addition to solve problems involving whole numbers?
• How is the student solving the problem? Does the student select manipulatives or draw a picture to help solve the problem? Does the student "recall" addition facts?
• Does the student solve the problem in more than one way?
• Does the number sentence match the student's explanation?
• Does the number sentence match the action in the story?

Future TEKS Connection

• Grade 3 TEKS Connection 3.16B

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

(2.14) Underlying processes and mathematical tools. The student uses logical reasoning. The student is expected to justify his or her thinking using objects, words, pictures, numbers, and technology.

Clarifying Activity with Assessment Connections

After solving the bus problem in 2.12B, two groups of students who chose different strategies to solve the problem use words, objects, pictures, numbers, or technology to explain their strategies to each other.

Assessment Connections

Before trading problems:

Questioning . . .

Open with . . .

• How did you figure this out?

Probe further with . . .

• What did you think about doing to solve the problem?
• What did you do first?
• What was your strategy? How did you decide what strategy you wanted to use to solve this problem? Did your plan work?
• What other strategies did you think about using to solve the problem? What did you actually do to solve the problem?
• Why did you decide to do that instead of something else?
• What information helped you decide what to do?
• Did you use pictures or manipulatives to help you solve the problem? How did the pictures or manipulatives help you? How does your picture compare to someone else's? How did you organize your work? Did you use a table? Did you notice any patterns?
• How do you know your answer is reasonable? Are there other reasonable answers?
• Is there another way you could have solved the problem?

Listen for . . .

• Is the student able to describe the strategy they used?
• Can the student identify important information in the problem?
• Is the student talking about a variety of strategies?
• Does the student's explanation match the work?
• Is the student's explanation logical and reasonable?
• Does the student use mathematical vocabulary in explanations?

Look for . . .

• Is the student using a plan to solve the problem?
• Is the student selecting reasonable and logical strategies to solve the problem?
• Does the student understand the problem?
• Can the student carry out the plan?
• Can the student use this strategy to get the right answer?
• Does the student recognize if the answer is reasonable?
• Can the student compare their strategies to others' strategies?
• Is the student learning and sharing strategies from others?

Future TEKS Connection

• Grade 3 TEKS Connection 3.17B

Additional Clarifying Activity

Given three different spinners, students identify which one they would choose to play a certain game and explain why they made that choice.

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