MATH 392 - Exam #2
Invented strategies are: A. the basis for mental computation and estimation. B. digit-oriented rather than number-oriented. C. generally slower than standard algorithms. D. "right-handed" rather than "left-handed" (students start on the right).
A
Making ten, known facts, derive unknown facts and double and one more group are examples of what effective basic fact teaching strategy? A. Explicit reasoning B. Story problems C. Quick images D. Adding zero
A
Strategies for building a good lesson around a context problem include all of the following for student with the exception of which one? A. Use only paper and pencil to solve B. Discussion about multiple methods for solving C. Use physical materials and drawings to solve D. Focus on few problems to solve
A
Use 10 is a different strategy than Making 10. It does not require decomposition or recomposing a number. Identify the equation below that shows Use 10. A. 9 + 6 = student thinks 10 + 6 is 16 and 9 is one less so the answer is 15 B. 9 + 6= students doubles 6 to get twelve and then adds the 3 left over from 9 to make 15 C. 9 + 6 = students takes 1 one six to make 9 at 10 and then adds 10 + 5 =15 D. 9 + 6= student knows that 8 + 6 is fourteen so they add one more to make 15
A
What are compatible pairs in addition? A. Numbers that easily combine to equal benchmark numbers B. Numbers that add or subtract without regrouping C. Numbers that are even D. Numbers that have the same number of digits
A
What type of problem structure does this phrase describe "the first factor represents the number of rows and the second factor represents the equal number found in each row"? A. Array B. Comparison C. Combination D. Area
A
When adding 10 on a hundreds chart, the most efficient strategy that demonstrates place value understanding is to: A. move down one row directly below the number. B. move to the right 10 spaces. C. move to the left 10 spaces. D. move up one row directly above the number.
A
Which of the following is a common model to support invented strategies? A. Open number line B. Sentence strip C. Hundreds chart D. Geoboard
A
Which of the following statements about standard algorithms is true? A. Teachers should spend a significant amount of time with invented strategies before introducing a standard algorithm. B. Standard algorithms are the only method for adding and subtracting multidigit numbers. C. Most countries use the same standard algorithms in mathematics. D. Standard algorithms should be taught without the use of models (such as completely on a symbolic level).
A
Which reasoning strategy below would require students to know their addition facts to effectively use it for subtraction facts? A. "Think-addition" and "missing addend." B. Take from 10 C. Five as an anchor D. Down under 10
A
Why are teaching students about the structure of word problems important? A. The structures help students focus on sense making and the development of the meaning of the operations. B. The structures help students develop a key word strategy. C. The structures will be on the end-of-year test. D. The structures help students memorize their basic facts.
A
How are addition and subtraction related? Explain. A. Addition and subtraction are the operations that create the natural numbers. Without these two operations, it is not possible to identify the numbers that make up the set of whole numbers. B. Addition and subtraction are inverses of each other; that is, they "undo" each other. That is, if the number 8 had the number 3 added to it, followed by the subtraction of the number 3, the addition and subtraction operations would cancel each other out. C. Addition and subtraction are the only two operations that can be performed for all natural and whole numbers, without any restrictions. D. Addition and subtraction are the only two operations that can be performed on the number line.
B
John claims that he can get the same answer to the problem below by adding up (begin with 1+6) or by adding down (begin with 8+6). He wants to know why and if this works all the time. How do you respond? 8 6 + 1 A. It does not always work. While the commutative property holds, the associative property does not hold for all values. B. It does work all of the time. This is because 8,6, and 1 are whole numbers, so the commutative and associative properties hold and allow the three numbers to be added regardless of their order. C. It does not always work. While the associative property holds, the commutative property does not hold for all values. D. It does work all of the time. Neither the commutative or associative properties hold for all values.
B
Three of these statements are examples of effective formative assessment of basic facts. Identify the one that is often given as the reason given to use timed tests of basic facts. A. Know which facts students do and don't know B. Easier to implement C. More insights into which reasoning strategies are used D. Integrates assessment into instruction
B
To find 9+14, a student says she thinks of 9+14 as 9+(1+13)=(9+1)+13=10+13=23. What property or properties is she using? A. First she used the commutative property to separate 14 into 1+13. Then she used the associative property to get the 9 and 1 together. Next, she added the 9 and 1. Finally she added 10 and 13. B. First she separated 14 into 1+13. Then she used the associative property to get the 9 and 1 together. Next, she added the 9 and 1. Finally she added 10 and 13. C. First she separated 14 into 1+13 with the identity property of addition. Then she used the associative property to get the 9 and 1 together. Next, she added the 9 and 1. Finally she added 10 and 13. D. First she separated 14 into 1+13. Then she used the commutative property to get the 9 and 1 together. Next, she added the 9 and 1. Finally she added 10 and 13.
B
To support knowledge about the commutative property teachers should do what to help the students' focus on the relationship? A. Use terms like "flip flop" and "ring around the Rosie" B. Pair problems with same addends but in different orders C. Help students identify combinations of ten D. Have students just reverse the piles of manipulatives on the part-part-whole mat
B
Which of the following equations illustrates the distributive property of multiplication over addition? Question content area bottom Part 1 A. 2(5+3) = 5+2×3 B. 2(5+3) = 2×5+2×3 C. 2(5+3) = (2+5)×(2+3) D. 2(5+3) = 2×5+3
B
Which of the following is not a strategy for supporting students' learning of basic facts? A. Explicit strategy instruction B. Drill C. Memorization D. Guided invention
B
Which of the following statements would not be evidence of about teaching the basic facts effectively? A. Fluency includes being able to select appropriate strategies and answer problems quickly and correctly. B. Memorizing facts is important to mastering the facts. C. Story problems can help students develop fluency with the basic facts. D. It is important to explicitly teach students strategies for solving basic fact problems.
B
Which problem structure is related to the subtraction situation "how many more?" A. Start unknown B. Comparison C. Part-part-whole D. Take away
B
Effective basic fact remediation requires three phases of intervention. Identify the statement below that would not be a part of an intervention. A. Determining student's level of number sense and reasoning B. Identification of student fact knowledge C. Providing more fact drill and worksheets D. Explicitly teaching reasoning strategies
C
How are addition and subtraction related? Explain. A. Addition and subtraction are the only two operations that can be performed on the number line. B. Addition and subtraction are the only two operations that can be performed for all natural and whole numbers, without any restrictions. C. Addition and subtraction are inverses of each other; that is, they "undo" each other. That is, if the number 8 had the number 3 added to it, followed by the subtraction of the number 3, the addition and subtraction operations would cancel each other out. D. Addition and subtraction are the operations that create the natural numbers. Without these two operations, it is not possible to identify the numbers that make up the set of whole numbers.
C
Sue claims the following is true by the distributive property, where a and b are whole numbers. 9(ab)=(9a)(9b) Is her claim true or false? A. Her claim is false; consider the example where a=1 and b=0. B. Her claim is true; consider the example when a=1 and b=2. C. Her claim is false; consider the example when a=1 and b=2. D. Her claim is true; consider the example where a=1 and b=0.
C
The following statements are true about the benefits of invented strategies except: A. students develop number sense. B. are faster than the standard algorithm. C. more teaching is required. D. basis for mental computation and estimation.
C
Think addition to solve a subtraction story would be effective for three of these problems. Which of the following would not be efficient? A. Lynn had some pencils and she decided to sharpen 32 of them, she has 63 of sharpened and not sharpened altogether. How many are not sharpened? B. Lynn gave some of her pencil collection to the teacher for use as extra pencils. She counted 52 pencils before giving them away. Now she has 43, how many did she give to the teacher? C. Lynn had a collection of 52 pencil and she gave 6 of them to her best friend. How many pencils does she have now? D. Lynn had a collection of 52 pencils. She traded for more pencil with a friend and now she has 63. How many did she obtain in her trade?
C
What is the best way to help students see the equal sign as a relational symbol? A. Tell students it is just like an addition or subtraction symbol. B. Say it is like a calculator—you see it and it and it gives you the answer. C. Use the language "is the same as" when you read an equal sign. D. Call it "the answer is" symbol.
C
What is the main reason for teaching addition and subtraction at the same time? A. Problem structures B. Subtraction as think addition C. Reinforce their inverse relationship D. Use of models
C
What method below would students be able to infuse reasoning strategies, select appropriate strategies and become more efficient in finding the answer? A. Fact drills B. Time fact tests C. Playing games D. Fact worksheets
C
Which of the following open number sentences represents partition division? A. × 6 = 18 B. 3 × 6 = 18 C. 3 × = 18 D. 3 + 6 = 9
C
Which of the following student explanations uses the Making 10 strategy to solve 8 + 9? A. I added 8 + 8 + 1 to get 17. B. I see that the number 8 is two away from 10 and 9 is one away from 10, so the answer is three away from 20: 17. C. I took 9 + 1 and added on 7 to get 17. D. I knew that 8 + 10 was 18, and then I took one off to get 17.
C
Equal group problems involve three quantities. Which of the following would not be a part of equal group problem? A. Number of groups B. Size of each group C. Total of all groups D. Difference between groups
D
Explain how the distributive property of multiplication over addition would be helpful to mentally perform the following computation. 11•26+11•74 A. After switching the order of the terms, 26 can be written as 20+6. It is easier to multiply by 20 than to multiply by 26. B. After switching the order of the terms, the first two terms make a product of 10. It is easier to multiply by 10. C. After factoring out 26, the product has a remainder of 0. It is easier to divide with a remainder of 0. D. After factoring out 11, the other factor sums to 100. It is easier to multiply by 100.
D
For problems that involve joining (adding) or separating (subtracting) quantities, which of the following terms would not describe one of the quantities in the problem? A. Change B. Result C. Product D. Start
D
Identify the problem structure that one group is a particular multiple of the other. A. Part-part-whole problems B. Area problems C. Combination problems D. Comparison problems
D
Identify the reasoning strategy that is used in high performing countries that takes advantage of students' knowledge of combinations that make ten. A. Five as an anchor B. Down under 10 C. "Think-addition" and "missing addend." D. Take from 10
D
The authors recommend strategies to guide students' problem solving skills. Identify the one that is often used by teachers and students but not always an effective approach. A. Think about the answer before solving B. Use a model, diagram, or materials C. Work a simpler problem D. Look for key words
D
Three statements below support students in their development of fluency with basic facts. Identify the statement that does not support basic fact fluency. A. The goal is not just quick recall, but also flexibility and use of strategies. B. Timed tests are not effective and there are better ways to assess students' progress in learning basic facts. C. Games and activities are effective ways to practice strategies and work toward mastery. D. Calculators can interfere with learning the basic facts and they should not be used until after the facts have been mastered.
D
To find 9+6, a student says she thinks of 9+6 as 9+(1+5)=(9+1)+5=10+5=15. What property or properties is she using? A. First she separated 6 into 1+5. Then she used the commutative property to get the 9 and 1 together. Next, she added the 9 and 1. Finally she added 10 and 5. B. First she used the commutative property to separate 6 into 1+5. Then she used the associative property to get the 9 and 1 together. Next, she added the 9 and 1. Finally she added 10 and 5. C. First she separated 6 into 1+5 with the identity property of addition. Then she used the associative property to get the 9 and 1 together. Next, she added the 9 and 1. Finally she added 10 and 5. D. First she separated 6 into 1+5. Then she used the associative property to get the 9 and 1 together. Next, she added the 9 and 1. Finally she added 10 and 5.
D
When presenting addition problems, which of the following would you use last? A. 39 + 23 = B. 645 + 354 = C. 43 + 32 = D. 356 + 127 =
D
When subtracting 10 on a hundreds chart, the most efficient strategy that demonstrates place value understanding is to: A. move down one row directly below the number. B. move to the left 10 spaces. C. move to the right 10 spaces. D. move up one row directly above the number.
D
Which of the following equations illustrates the associative property for addition? A. 0+7=5+2 B. 2+5=7, and 7−5=2 C. 2+5=5+2 D. (2+5) + 4=2 + (5+4)
D
Which of the following instructional activities would be an important component of a lesson on addition with regrouping? A. Demonstrating the commutative property of addition B. Adding basic facts with sums to ten C. Reviewing the concept of greater than and less than D. Using base-ten materials to model the problem
D
Which of the following strategies is a foundational strategy that must precede the learning of the others? A. Making 10 B. Near doubles C. Add zero D. Combinations of 10
D
