(5.3) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve meaningful problems.
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1 (5.3) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve meaningful problems. (5.3.a) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve meaningful problems. The student is expected to use addition and subtraction to solve problems involving whole numbers and decimals. Clarifying Activity with Students use technology to find statistics from the last Olympics that involve decimals. They create their own problems from this information that require adding or subtracting decimals to solve and share problems with a partner. Questioning... (before trading problems) Tell me about your problem. What did you think about when you were creating your problem? Does your problem use whole numbers? Can your problem be solved by adding or subtracting decimal numbers? Can the student identify real-world problems that can be solved by adding or subtracting decimal numbers? Can the student pose a problem that can be solved by adding or subtracting decimal numbers? Does the student pose a problem that is clear and easily interpreted by a partner? Questioning... (after trading problems) What is the question asked in the problem you're working? Tell me about your thinking.
2 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? Is the student able to discuss the reasonableness of his or her solution? Can the student identify the information necessary to solve the problem? Can the student add or subtract decimals? Does the student select manipulatives or draw a picture to help solve the problem? Does the student solve the problem in more than one way? Does the number sentence match the student's explanation? Can the student self-correct any errors? Texas Education Agency. Excerpted from TEA's TAKS Information Booklets, January Reprinted with permission. (5.3.b) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve meaningful problems. The student is expected to use multiplication to solve problems involving whole numbers (no more than three digits times two digits without technology). Clarifying Activity with Students brainstorm real-world reasons to use multiplication and record them on a chart. They then select an example from the chart, write an original problem for others to solve, and exchange problems.
3 Questioning... (before trading problems) Tell me about your problem. What did you think about when you were creating your problem? Does your problem use whole numbers? Can your problem be answered by multiplying whole numbers? Can the student identify real-world problems that can be solved using multiplication? Does the student pose a problem that can be solved by multiplying whole numbers? Does the student pose a problem that is clear and easily interpreted by his or her partner? Questioning... (after trading problems) What is the question asked in the problem you're working? Tell me about your thinking. 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? Is the student able to discuss the reasonableness of his or her solution? Can the student identify the information necessary to solve the problem? Can the student use multiplication to solve problems involving whole numbers?
4 Does the student select manipulatives or draw a picture to help solve the problem? Does the student solve the problem in more than one way? Does the number sentence match the student's explanation? Can the student self-correct any errors? Texas Education Agency. Excerpted from TEA's Released Tests and Interactive Online Tests, Spring 2001 Mathematics TAAS. Reprinted with permission. (5.3.c) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve meaningful problems. The student is expected to use division to solve problems involving whole numbers (no more than two-digit divisors and three-digit dividends without technology), including interpreting the remainder within a given context. Clarifying Activity with Students use base-ten blocks or drawings to solve division problems such as calculating the fuel efficiency of the family car: "If your family traveled 94 miles and used 4 gallons of gas, how many miles per gallon did the car travel?" Questioning... What is the question asked in the problem you are working? How are you going to solve it? 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?
5 Does the student talk about the reasonableness of his or her solution? Does the student select manipulatives or draw a picture to help solve the problem? Can the student use division to solve problems involving whole numbers? Can the student identify the information necessary to solve the problem? Can the student use base-ten blocks or drawings to model division? Can the student solve the problem in more than one way? Does the number sentence match the student's explanation? Texas Education Agency. Excerpted from TEA's Released Tests and Interactive Online Tests, Spring 2001 Mathematics TAAS. Reprinted with permission. (5.3.d) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve meaningful problems. The student is expected to identify common factors of a set of whole numbers. Clarifying Activity with Students choose two numbers and make a list of all the factors of each one. Students then circle the factors that are common to both lists, and make a list of those common factors. Students identify this list as the set of common factors of the two numbers. Students can use the list to identify the greatest common factor of the two numbers and the prime factors. Questioning... Tell me about the factors of 18 and 24. Which of their factors are prime numbers?
6 Since 3 is a factor of 18, what is another factor of 18? How do you know? (factor pairs) What are the common factors of 18 and 24? What is the greatest common factor? Use a factor tree to identify the prime factors of 18 and 24. Can you find the prime factors using a different factor tree? What is the same and what is different about the factor trees? What connections do you notice between prime factors, common factors, and greatest common factors? If given the prime factors of two numbers, how could you determine the greatest common factor? Does the student use appropriate mathematical language to describe factorization? Can the student identify the prime factorization of a whole number? Can the student identify common factors of two whole numbers? Can the student identify the greatest common factor of two whole numbers? Does the student use factor pairs when determining the factors of a whole number? Does the student notice that the prime factorization of a number is unique? (Fundamental Theorem of Arithmetic) Can the student determine the greatest common factor and give the prime factorizations of two whole numbers? Texas Education Agency. Excerpted from TEA's Released Tests and Interactive Online Tests, Spring 2001 Mathematics TAAS. Reprinted with permission. (5.3.e) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve meaningful problems. The student is expected to model situations using addition and/or subtraction involving fractions with like denominators using concrete objects, pictures, words, and numbers.
7 Clarifying Activity with Students use pattern blocks and work with partners to create and model addition and subtraction problems involving fractions. For example, "Let a yellow hexagon represent a whole pizza. Gary has 2 1/3 pizzas left over from a party. He eats 2/3 of a pizza for lunch. How much pizza is still left?" Questioning... Describe how you solved your fraction problem. How did you use the pattern blocks to model the problem? How did you use pattern blocks to solve the problem? What number sentence can you write to describe the fraction problem? Is your solution reasonable? How do you know? Can the student read fractions? Does the student use words that describe addition and subtraction involving fractions with common denominators? Can the student clearly explain his or her thought process? Is the student able to discuss the reasonableness of his or her solution? Can the student model addition and subtraction problems involving fractions with like denominators using the pattern blocks? Can the student use mathematical symbols to record addition and subtraction problems involving fractions with like denominators?
8 Texas Education Agency. Excerpted from TEA's TAKS Information Booklets, January Reprinted with permission.
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