MATH 392 Test 2 Review
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. Area C. Comparison D. Combination
A. Array
Derived multiplication fact strategies can only support student learning after they have mastered what information? A. Doubles B. Commutativity of multiplication. C. Foundational facts D. Skip counting
C. Foundational facts
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. 356 + 127 =
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. Work a simpler problem B. Use a model, diagram, or materials C. Think about the answer before solving D. Look for key words
D. Look for key words
Which problem structure is related to the subtraction situation "how many more?" A. Comparison B. Take away C. Part-part-whole D. Start unknown
A. Comparison
Which of the following open number sentences represents partition division? A. 3 + 6 = 9 B. 3 × = 18 C. × 6 = 18 D. 3 × 6 = 18
B. 3 × = 18
State the name of the property illustrated. 2+[3+(7)]=(2+3)+(7) The expression is an example of which property? A. Identity property of addition B. Associative property of addition C. Commutative property of addition
B. Associative property of addition
Which of the following strategies is a foundational strategy that must precede the learning of the others? A. Making 10 B. Combinations of 10 C. Add zero D. Near doubles
B. Combinations of 10
Marek was asked to multiply 34 × 5. He said, "30 × 5 = 150 and 4 × 5 = 20, so I can add them to get 170." Which property did Marek use to solve this multiplication problem? A. Commutative property B. Distributive property of multiplication over addition C. Associative property D. Identity property of multiplication
B. Distributive property of multiplication over addition
Which of the following is not a strategy for supporting students' learning of basic facts? A. Memorization B. Drill C. Guided invention D. Explicit strategy instruction
B. Drill
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. More insights into which reasoning strategies are used B. Easier to implement C. Integrates assessment into instruction D. Know which facts students do and don't know
B. Easier to implement
What are compatible pairs in addition? A. Numbers that are even B. Numbers that easily combine to equal benchmark numbers C. Numbers that have the same number of digits D. Numbers that add or subtract without regrouping
B. Numbers that easily combine to equal benchmark numbers
Connections between multiplication and division are key for mastery of division facts. What reasoning strategy would support the mastery of division facts? A. Decomposing a factor B. Think multiplication C. Adding or subtracting a group D. Doubles and halving
B. Think multiplication
Write the complete fact family for 27/3=9. Choose the correct answer below. Select all that apply. A. 27+3=30 B. 3+9=12 C. 9•3=27 D. 3/9=0.33 E. 3•9=27 F. 27•3=81 G. 27/3=9 H. 27/9=3
C. 9•3=27 E. 3•9=27 G. 27/3=9 H. 27/9=3
Which of the following is a common model to support invented strategies? A. Geoboard B. Hundreds chart C. Open number line D. Sentence strip
C. Open number line
Invented strategies are: A. digit-oriented rather than number-oriented. B. "right-handed" rather than "left-handed" (students start on the right). C. the basis for mental computation and estimation. D. generally slower than standard algorithms.
C. the basis for mental computation and estimation.
Which reasoning strategy below would require students to know their addition facts to effectively use it for subtraction facts? A. Five as an anchor B. Down under 10 C. Take from 10 D. "Think-addition" and "missing addend."
D. "Think-addition" and "missing addend."
Illustrate the identity property of addition for whole numbers. Which of the following is an example of the identity property of addition? A. 345=3•102+4•10+5 B. (3+2)+4=3+(2+4) C. 4(7+5)=4•7+4•5 D. 3+0=3=0+3.
D. 3+0=3=0+3.
What reasoning strategy involves "unpacking" a one of the factors into two addends, multiplying each addend by the other factor and then adding them back together for the total? A. Doubling and halving B. Commutativity of multiplication C. Foundational facts D. Decomposing factors
D. Decomposing factors
Sue claims the following is true by the distributive property, where a and b are whole numbers. 5(ab)=(5a)(5b) Is her claim true or false? A. Her claim is true; consider the example where a=1 and b=0. B. Her claim is false; consider the example where a=1 and b=0. C. Her claim is true; consider the example when a=1 and b=2. D. Her claim is false; consider the example when a=1 and b=2.
D. Her claim is false; consider the example when a=1 and b=2.
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. It is important to explicitly teach students strategies for solving basic fact problems. C. Story problems can help students develop fluency with the basic facts. D. Memorizing facts is important to mastering the facts.
D. Memorizing facts is important to mastering the facts.
When asked to solve the division problem 143 ÷ 8, a student thinks, "What number times 8 will be close to 143 with less than 8 remaining?" Which strategy is the student using? A. Cluster problems B. Repeated subtraction C. Partial products D. Missing factor
D. Missing factor
When adding 10 on a hundreds chart, the most efficient strategy that demonstrates place value understanding is to: A. move up one row directly above the number. B. move to the right 10 spaces. C. move to the left 10 spaces. D. move down one row directly below the number.
D. move down one row directly below the number.
Which of the following equations illustrates the associative property for addition? A. (2+5) + 4=2 + (5+4) B. 0+7=5+2 C. 2+5=7, and 7−5=2 D. 2+5=5+2
A. (2+5) + 4=2 + (5+4)
Describe all pairs of whole numbers whose sum and product are the same. Select all that apply. A. 2 and 2 B. All pairs of whole numbers with 0 C. 0 and 0 D. 1 and 1 E. 2 and 3 F. All pairs of whole numbers with 1 G. All pairs of whole numbers with 2 H. There is no pair of whole numbers whose sum and product are the same.
A. 2 and 2 C. 0 and 0
Which of the following equations illustrates the distributive property of multiplication over addition? A. 2(5+3) = 2×5+2×3 B. 2(5+3) = 5+2×3 C. 2(5+3) = 2×5+3 D. 2(5+3) = (2+5)×(2+3)
A. 2(5+3) = 2×5+2×3
Illustrate the identity property of addition for whole numbers. Which of the following is an example of the identity property of addition? A. 3+0=3=0+3. B. 4(7+5)=4•7+4•5 C. 345=3•102+4•10+5 D. (3+2)+4=3+(2+4)
A. 3+0=3=0+3.
Write the complete fact family for 56/8=7. Choose the correct answer below. Select all that apply. A. 56/8=7 Your answer is correct. B. 7•8=56 Your answer is correct. C. 8/7=1.14 D. 56•8=448 E. 8+7=15 F. 56/7=8 Your answer is correct. G. 56+8=64 H. 8•7=56
A. 56/8=7 B. 7•8=56 F. 56/7=8 H. 8•7=56
Three statements below support students in their development of fluency with basic facts. Identify the statement that does not support basic fact fluency. A. Calculators can interfere with learning the basic facts and they should not be used until after the facts have been mastered. B. Games and activities are effective ways to practice strategies and work toward mastery. C. Timed tests are not effective and there are better ways to assess students' progress in learning basic facts. D. The goal is not just quick recall, but also flexibility and use of strategies.
A. Calculators can interfere with learning the basic facts and they should not be used until after the facts have been mastered.
Equal group problems involve three quantities. Which of the following would not be a part of equal group problem? A. Difference between groups B. Number of groups C. Size of each group D. Total of all groups
A. Difference between groups
To find 9+8, a student says she thinks of 9+8 as 9+(1+7)=(9+1)+7=10+7=17. What property or properties is she using? Select the correct choice below. A. First she separated 8 into 1+7. 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 7. B. First she separated 8 into 1+7. 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 7. C. First she separated 8 into 1+7 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 7. D. First she used the commutative property to separate 8 into 1+7. 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 7.
A. First she separated 8 into 1+7. 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 7.
Students should learn the relationship between multiplication and division. Explain this relationship. Select all that apply. A. If a/b=c, then b•c=a. B. Multiplication comes before division. C. If a•b=c, then c=a/b+b/a. D. Division comes before multiplication. E. Division is repeated multiplication. F. If a•b=c, then c/b=a. G. Division with remainder 0 is the inverse of multiplication and vice versa. H. The product of any two whole numbers is the sum of their quotients. I. Division with remainder 0 is the distribution of multiplication and vice versa.
A. If a/b=c, then b•c=a. F. If a•b=c, then c/b=a. G. Division with remainder 0 is the inverse of multiplication and vice versa.
What method below would students be able to infuse reasoning strategies, select appropriate strategies and become more efficient in finding the answer? A. Playing games B. Time fact tests C. Fact drills D. Fact worksheets
A. Playing games
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. Standard algorithms should be taught without the use of models (such as completely on a symbolic level). D. Most countries use the same standard algorithms in mathematics.
A. Teachers should spend a significant amount of time with invented strategies before introducing a standard algorithm.
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. Use physical materials and drawings to solve C. Focus on few problems to solve D. Discussion about multiple methods for solving
A. Use only paper and pencil to solve
Do you think it is valuable for students to see more than one method of doing computation problems? Why or why not? Choose the correct answer below. A. Yes. Some students may find one algorithm easier to understand or to use than others and therefore it will be easier for him or her to remember or reproduce. B. No. Some students may find it confusing to see multiple methods to produce the same result.
A. Yes. Some students may find one algorithm easier to understand or to use than others and therefore it will be easier for him or her to remember or reproduce.
One way to effectively model multiplication with large numbers is to: A. create an area model using base-ten materials. B. use repeated addition. C. use connecting cubes in groups on paper plates. D. use pennies to connect to money.
A. create an area model using base-ten materials.
The following statements are true about the benefits of invented strategies except: A. more teaching is required. B. are faster than the standard algorithm. C. basis for mental computation and estimation. D. students develop number sense.
A. more teaching is required.
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 = students takes 1 one six to make 9 at 10 and then adds 10 + 5 =15 B. 9 + 6 = student thinks 10 + 6 is 16 and 9 is one less so the answer is 15 C. 9 + 6= students doubles 6 to get twelve and then adds the 3 left over from 9 to make 15 D. 9 + 6= student knows that 8 + 6 is fourteen so they add one more to make 15
B. 9 + 6 = student thinks 10 + 6 is 16 and 9 is one less so the answer is 15
How are addition and subtraction related? Explain. Select the correct answer below. A. Addition and subtraction are the only two operations that can be performed for all natural and whole numbers, without any restrictions. 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 on the number line. 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.
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.
How are addition and subtraction related? Explain. Select the correct answer below. A. Addition and subtraction are the only two operations that can be performed for all natural and whole numbers, without any restrictions. 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 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. D. Addition and subtraction are the only two operations that can be performed on the number line.
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.
Explain how the distributive property of multiplication over addition would be helpful to mentally perform the following computation. 86•34+86•66 Choose the correct answer below. A. After factoring out 34, the product has a remainder of 0. It is easier to divide with a remainder of 0. Your answer is not correct. B. After factoring out 86, the other factor sums to 100. It is easier to multiply by 100. C. After switching the order of the terms, the first two terms make a product of 10. It is easier to multiply by 10. D. After switching the order of the terms, 34 can be written as 30+4. It is easier to multiply by 30 than to multiply by 34.
B. After factoring out 86, the other factor sums to 100. It is easier to multiply by 100.
Sue claims the following is true by the distributive property, where a and b are whole numbers. 4(ab)=(4a)(4b) Is her claim true or false? A. Her claim is false; consider the example where a=1 and b=0. B. Her claim is false; consider the example when a=1 and b=2. C. Her claim is true; consider the example when a=1 and b=2. D. Her claim is true; consider the example where a=1 and b=0.
B. Her claim is false; consider the example when a=1 and b=2.
Which of the following student explanations uses the Making 10 strategy to solve 8 + 9? A. 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. B. I took 9 + 1 and added on 7 to get 17. C. I knew that 8 + 10 was 18, and then I took one off to get 17. D. I added 8 + 8 + 1 to get 17.
B. I took 9 + 1 and added on 7 to get 17.
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 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? B. Lynn had a collection of 52 pencil and she gave 6 of them to her best friend. How many pencils does she have now? C. 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? 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?
B. Lynn had a collection of 52 pencil and she gave 6 of them to her best friend. How many pencils does she have now?
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. Have students just reverse the piles of manipulatives on the part-part-whole mat D. Help students identify combinations of ten
B. Pair problems with same addends but in different orders
Effective basic fact remediation requires three phases of intervention. Identify the statement below that would not be a part of an intervention. A. Explicitly teaching reasoning strategies B. Providing more fact drill and worksheets C. Identification of student fact knowledge D. Determining student's level of number sense and reasoning
B. Providing more fact drill and worksheets
Guiding students to develop a recording scheme for multiplication can be enhanced by the use of what tool? A. An open-array B. Recording sheet with base-ten columns C. Calculator D. Base-ten materials
B. Recording sheet with base-ten columns
What is the main reason for teaching addition and subtraction at the same time? A. Use of models B. Reinforce their inverse relationship C. Problem structures D. Subtraction as think addition
B. Reinforce their inverse relationship
When students use the break apart of decomposition strategy with division, what must they remember? A. Remember that you must record each calculation B. Remember that you cannot break apart the divisor C. Remember that you may still have remainders D. Remember that you can decompose the dividend and the divisor
B. Remember that you cannot break apart the divisor
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. Using base-ten materials to model the problem C. Reviewing the concept of greater than and less than D. Adding basic facts with sums to ten
B. Using base-ten materials to model the problem
State the name of the property illustrated. 7+[8+(6)]=(7+8)+(6) The expression is an example of which property? A. Commutative property of addition B. Identity property of addition C. Associative property of addition
C. Associative property of addition
State the name of the property illustrated. 7+[6+(4)]=7+[(4)+6] The expression is an example of which property? A. Associative property of addition B. Identity property of addition C. Commutative property of addition
C. Commutative property of addition
Identify the problem structure that one group is a particular multiple of the other. A. Combination problems B. Area problems C. Comparison problems D. Part-part-whole problems
C. Comparison problems
A child is asked to compute 9+3+7+5+11 and writes 9+3=14+5=19+5=24+11=35. Noticing that the answer is correct, if you were the teacher how would you react? Choose the correct answer below. A. Because the answer is correct, the use of the equal sign must be correct. B. The child got the correct answer, but made mistakes in his or her addition. C. Even though the answer is correct, the use of the equal sign is incorrect. Therefore, this should not be allowed. D. The child got the correct answer and solved the problem in a creative way. There is nothing wrong with this method.
C. Even though the answer is correct, the use of the equal sign is incorrect. Therefore, this should not be allowed.
To find 9+12, a student says she thinks of 9+12 as 9+(1+11)=(9+1)+11=10+11=21. What property or properties is she using? Select the correct choice below. A. First she used the commutative property to separate 12 into 1+11. 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 11. B. First she separated 12 into 1+11. 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 11. C. First she separated 12 into 1+11. 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 11. D. First she separated 12 into 1+11 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 11.
C. First she separated 12 into 1+11. 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 11.
John claims that he can get the same answer to the problem below by adding up (begin with 5+6) or by adding down (begin with 7+6). He wants to know why and if this works all the time. How do you respond? 7 6 + 5 Select the correct choice below. A. It does work all of the time. Neither the commutative or associative properties hold for all values. B. It does not always work. While the associative property holds, the commutative property does not hold for all values. C. It does work all of the time. This is because 7,6, and 5 are whole numbers, so the commutative and associative properties hold and allow the three numbers to be added regardless of their order. D. It does not always work. While the commutative property holds, the associative property does not hold for all values.
C. It does work all of the time. This is because 7,6, and 5 are whole numbers, so the commutative and associative properties hold and allow the three numbers to be added regardless of their order.
Identify the reasoning strategy that is used in high performing countries that takes advantage of students' knowledge of combinations that make ten. A. "Think-addition" and "missing addend." B. Five as an anchor C. Take from 10 D. Down under 10
C. Take from 10
Why are teaching students about the structure of word problems important? A. The structures will be on the end-of-year test. B. The structures help students develop a key word strategy. C. The structures help students focus on sense making and the development of the meaning of the operations. D. The structures help students memorize their basic facts.
C. The structures help students focus on sense making and the development of the meaning of the operations.
What is the best way to help students see the equal sign as a relational symbol? A. Say it is like a calculator—you see it and it and it gives you the answer. B. Call it "the answer is" symbol. C. Use the language "is the same as" when you read an equal sign. D. Tell students it is just like an addition or subtraction symbol.
C. Use the language "is the same as" when you read an equal sign.
How would you explain to children how to multiply 352•692, assuming they know and understand multiplication by a single digit and multiplication by a power of 10? Choose the correct answer below. A. Using the distributive property of multiplication over addition, first multiply 300 by 600 and the result by 102; then multiply 50 by 90 and the result by 10; then multiply 2 by 2 and add all the numbers obtained together. B. Using the property of place value, first multiply 3 by 6 and the result by 102; then multiply 5 by 9 and the result by 10; then multiply 2 by 2 and add all the numbers obtained together. C. Using the distributive property of multiplication over addition, first multiply 352 by 6 and the result by 102; then multiply 352 by 9 and the result by 10; then multiply 352 by 2 and add all the numbers obtained together. D. Using the definition of multiplication add 352 to 692, 692 times.
C. Using the distributive property of multiplication over addition, first multiply 352 by 6 and the result by 102; then multiply 352 by 9 and the result by 10; then multiply 352 by 2 and add all the numbers obtained together.
Fill in the blank. 2+(4+6)=2+4+6 Identify the property. A. commutative property of addition B. identity property of addition C. associative property of addition
C. associative property of addition
Explain how the distributive property of multiplication over addition would be helpful to mentally perform the following computation. 33•89+33•11 Choose the correct answer below. A. After switching the order of the terms, the first two terms make a product of 10. It is easier to multiply by 10. B. After switching the order of the terms, 89 can be written as 80+9. It is easier to multiply by 80 than to multiply by 89. C. After factoring out 89, the product has a remainder of 0. It is easier to divide with a remainder of 0. D. After factoring out 33, the other factor sums to 100. It is easier to multiply by 100.
D. After factoring out 33, the other factor sums to 100. It is easier to multiply by 100.
A student asks why she should learn the standard long division algorithm if she can get a correct answer using repeated subtraction. How do you respond? Choose the correct answer below. A. The repeated subtraction algorithm does not always produce the correct answer, however the long division algorithm is guaranteed to produce a correct answer. B. The long division algorithm is always more efficient than the repeated subtraction algorithm, especially when dividing large multiples of the divisor. C. It is always more efficient to use the repeated subtraction algorithm, however it is helpful to learn the long division algorithm to better understand the process of dividing large numbers. D. If the repeated subtraction algorithm is done with large multiples of the divisor, the repeated subtraction can be quite efficient. However, if a student uses repeated subtraction by subtracting small multiples of the divisor, the process can be very time consuming.
D. If the repeated subtraction algorithm is done with large multiples of the divisor, the repeated subtraction can be quite efficient. However, if a student uses repeated subtraction by subtracting small multiples of the divisor, the process can be very time consuming.
John claims that he can get the same answer to the problem below by adding up (begin with 2+7) or by adding down (begin with 9+7). He wants to know why and if this works all the time. How do you respond? 9 7 + 2 Select the correct choice below. A. It does work all of the time. Neither the commutative or associative properties hold for all values. B. It does not always work. While the commutative property holds, the associative property does not hold for all values. 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. This is because 9,7, and 2 are whole numbers, so the commutative and associative properties hold and allow the three numbers to be added regardless of their order.
D. It does work all of the time. This is because 9,7, and 2 are whole numbers, so the commutative and associative properties hold and allow the three numbers to be added regardless of their order.
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. Result B. Change C. Start D. Product
D. Product
When subtracting 10 on a hundreds chart, the most efficient strategy that demonstrates place value understanding is to: A. move to the left 10 spaces. B. move to the right 10 spaces. C. move down one row directly below the number. D. move up one row directly above the number.
D. move up one row directly above the number.
Each of the following equations is an example of one of the properties of whole-number addition. Fill in the blank to make a true statement, and identify the property. a. 8+5=——+8 b. 4+(5+8)=(5+8)+—— c. 8+——=8 d. 2+ (8+9) = ( 2 + --) +9
a. The completed equation is 8+5=55+8. The related property that permits the completion of the equation is the commutative property of addition. b. The completed equation is 4+(5+8)=(5+8)+44. The related property that permits the completion of the equation is the commutative property of addition. c. The completed equation is 8+00=8. The related property that permits the completion of the equation is the identity property of addition. d. The completed equation is 2+(8+9)=(2+88)+9. The related property that permits the completion of the equation is the associative property of addition.
