Math 392 Test 2
In the video, Rachel calculates 45×36 in the following way: 45×36 =(40+5)×(30+6) =(40×30)+(40×6)+(5×30)+(5×6) =1200+240+150+30 =1620 A. (20×10)+(20×7)+(3×10)+(3×7) B. (2×17)+(3×17) C. (2×1)+(2×7)+(3×1)+(3×7) D. (2x10)+(2x7)+(3x10)+(3x7)
A. (20×10)+(20×7)+(3×10)+(3×7)
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. The goal is not just quick recall, but also flexibility and use of strategies. C. Games and activities are effective ways to practice strategies and work toward mastery. D. Timed tests are not effective and there are better ways to assess students' progress in learning basic facts.
A. Calculators can interfere with learning the basic facts and they should not be used until after the facts have been mastered.
Which of the following strategies is a foundational strategy that must precede the learning of the others? A. Combinations of 10 B. Near doubles C. Add zero D. Making 10
A. Combinations of 10
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. Adding zero C. Story problems D. Quick images
A. Explicit reasoning
How can the multiplication table be used to solve division problems? A. Find the row for either factor, if possible. Within this row, find the entry corresponding to the other factor. The quotient is the number of the corresponding column. B. Find the row for the quotient, if possible. Within this row, find the entry corresponding to either factor. The other factor is the number of the corresponding column. C. Find the column for the first factor, if possible. Then find the row corresponding to the second factor. The quotient is the entry diagonally up and to the right of the corresponding entry. D. Find the column for either factor, if possible. Within this column, move down n rows, where n is the other factor. The resulting entry is the quotient.
A. Find the row for either factor, if possible. Within this row, find the entry corresponding to the other factor. The quotient is the number of the corresponding column.
Sue claims the following is true by the distributive property, where a and b are whole numbers. 5(ab)=(5a)(5b) A. Her claim is false; consider the example when a=1 and b=2. B. Her claim is true; consider the example when a=1 and b=2. C. Her claim is true; consider the example where a=1 and b=0. D. Her claim is false; consider the example where a=1 and b=0.
A. Her claim is false; consider the example when a=1 and b=2.
All of questions below would be ways to connect real-world ideas to support students understanding of place-value concept except which one? A. How many numbers on a thousands chart? B. How many girls in the second grade have long hair? C. How many cartons of chocolate and plain milk are served in the cafeteria each month? D. How many minutes a day do second graders spend on mathematics?
A. How many numbers on a thousands chart?
Place parentheses, if needed, to make each of the following equations true. 4+3•4=28 A. Parentheses are needed. The corrected equation is (4+3)•4=28. B. Parentheses are needed. The corrected equation is (4+3•4)=28. C. Parentheses are needed. The corrected equation is 4+(3•4)=28. D. Parentheses are not needed to make the equation true.
A. Parentheses are needed. The corrected equation is (4+3)•4=28.
What is the main reason for teaching addition and subtraction at the same time? A.Reinforce their inverse relationship B.Problem structures C.Subtraction as think addition D.Use of models
A. Reinforce their inverse relationship
What is the correct way to say 32 using base-ten language? A. Three tens and two ones B. Thirty-two ones C. Three tens and some more D. Three and two
A. Three tens and two ones
Which of the following statements about names for numbers is true? A. When a student writes "three hundred fifty-eight" as "300508," the student may be at an early stage in moving accurately between oral three-digit numbers and written three-digit numbers. B. There are many more errors saying the names of three-digit numbers than four-digit numbers. C. Whenever you refer to a number in the tens, hundreds, or thousands (or beyond), make sure you just say "six," rather than referring to it with its place-value location, such as 6 tens (or 60). D. 106 should be read as "one hundred and six."
A. When a student writes "three hundred fifty-eight" as "300508," the student may be at an early stage in moving accurately between oral three-digit numbers and written three-digit numbers.
Consider the odd number 35 shown in the multiplication table. Consider all the numbers that surround it. Note that they are all even. Does this happen for all odd numbers in the table? Explain why or why not. A. Yes. The only way for a product of two numbers to be odd is if both factors are odd. Therefore, the surrounding row(s) and column(s) will contain products of even numbers, which are even. B. No. A product of two numbers is odd if at least one factor is odd. Therefore, the surrounding row(s) and column(s) will contain products of odd and even numbers, which are odd and even. C. Yes. An odd number has the form 2k+1, where k is a whole number. Therefore, the entry to the right will equal 2k+1+b, where b is the number of the corresponding column, and 1+b must always be an even number. D. No. An odd number has the form 2k+1, where k is a whole number. Therefore, the entry to the right will equal 2k+1+b, where b is the number of the corresponding row, and 1+b can be even or odd.
A. Yes. The only way for a product of two numbers to be odd is if both factors are odd. Therefore, the surrounding row(s) and column(s) will contain products of even numbers, which are even.
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)
Identify the problem structure that one group is a particular multiple of the other. A.Comparison problems B.Part-part-whole problems C.Combination problems D.Area problems
A.Comparison problems
Equal group problems involve three quantities. Which of the following would not be a part of equal group problem? A.Difference between groups B.Total of all groups C.Number of groups D.Size of each group
A.Difference between groups
To support knowledge about the commutative property teachers should do what to help the students' focus on the relationship? A.Pair problems with same addends but in different orders B.Have students just reverse the piles of manipulatives on the part-part-whole mat C.Help students identify combinations of ten D.Use terms like "flip flop" and "ring around the Rosie"
A.Pair problems with same addends but in different orders
Base-ten riddles are a method for showing equivalent representations. Identify the base-ten riddle what would not equal 42. A. I have 22 ones and 2 tens. Who am I? B. I have 20 ones and 2 ten. Who am I? C. I have 32 ones and 1 ten. Who am I? D. I have 12 ones and 3 tens. Who am I?
B. I have 20 ones and 2 ten. Who am I?
Which of the following assessments can be used to determine students' understanding of base-ten development? A. Observe if students can immediately state the value of a quantity on a ten-frame. B. Observe students counting out a large collection of objects and see if they are grouping the objects into groups of ten. C. Observe students skip counting on a hundreds chart. D. Observe students counting on from a number less than ten.
B. Observe students counting out a large collection of objects and see if they are grouping the objects into groups of ten.
Place parentheses, if needed, to make each of the following equations true. 5+4+9÷6=3 A. Parentheses are needed. The corrected equation is (5+4)+(9÷6)=3. B. Parentheses are needed. The corrected equation is (5+4+9)÷6=3. C. Parentheses are needed. The corrected equation is 5+(4+9)÷6=3. D. Parentheses are not needed to make the equation true.
B. Parentheses are needed. The corrected equation is (5+4+9)÷6=3.
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.Product C.Start D.Result
B. Product
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. Take from 10 C. Down under 10 D. Five as an anchor
B. Take from 10
When introducing place value concepts, it is most important that base-ten models for ones, tens, and hundreds be: A. pregrouped (models cannot be taken apart or put together). B. proportional (model for a ten is 10 times larger than the model for a 1). C. virtual models (such as computer representations of base-ten blocks). D. used in a pocket chart.
B. proportional (model for a ten is 10 times larger than the model for a 1).
Which reasoning strategy below would require students to know their addition facts to effectively use it for subtraction facts? A. Down under 10 B. "Think-addition" and "missing addend." C. Five as an anchor D. Take from 10
B. "Think-addition" and "missing addend."
Which of the following open number sentences represents partition division? A.3 + 6 = 9 B.3 × = 18 C.3 × 6 = 18 D. × 6 = 18
B.3 × = 18
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.Area B.Array C.Comparison D.Combination
B.Array
State the name of the property illustrated. 2+[5+(4)]=(2+5)+(4) A.Commutative property of addition B.Associative property of addition C.Identity property of addition
B.Associative property of addition
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 focus on sense making and the development of the meaning of the operations. C.The structures help students memorize their basic facts. D.The structures help students develop a key word strategy.
B.The structures help students focus on sense making and the development of the meaning of the operations.
Which of the following is an example of the identity property of addition? A. 345=3•10^2+4•10+5 B. 4(7+5)=4•7+4•5 C. 3+0=3=0+3. D. (3+2)+4=3+(2+4)
C. 3+0=3=0+3.
The integration of whole-number place-value involves using precise language. What statement below would confuse students about the groupings of tens and ones? A. 53 is five tens and three ones B. 53 is five tens and three C. 53 is the digits five and three D. 53 is fifty and three
C. 53 is the digits five and three
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= students doubles 6 to get twelve and then adds the 3 left over from 9 to make 15 C. 9 + 6 = student thinks 10 + 6 is 16 and 9 is one less so the answer is 15 D. 9 + 6= student knows that 8 + 6 is fourteen so they add one more to make 15
C. 9 + 6 = student thinks 10 + 6 is 16 and 9 is one less so the answer is 15
Explain how the distributive property of multiplication over addition would be helpful to mentally perform the following computation. 54•17+54 x8 A. After factoring out 17, the product has a remainder of 0. It is easier to divide with a remainder of 0. 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 54, the other factor sums to 100. It is easier to multiply by 100. D. After switching the order of the terms, 17 can be written as 10+7. It is easier to multiply by 10 than to multiply by 17.
C. After factoring out 54, the other factor sums to 100. It is easier to multiply by 100.
Which of the following student explanations uses the Making 10 strategy to solve 8 + 9? A. I knew that 8 + 10 was 18, and then I took one off 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 added 8 + 8 + 1 to get 17.
C. I took 9 + 1 and added on 7 to get 17.
John claims that he can get the same answer to the problem below by adding up (begin with 1+5) or by adding down (begin with 6+5). He wants to know why and if this works all the time. How do you respond? 6+5+1= A. It does not always work. While the associative property holds, the commutative property does not 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 work all of the time. This is because 6,5, and 1 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. Neither the commutative or associative properties hold for all values.
C. It does work all of the time. This is because 6,5, and 1 are whole numbers, so the commutative and associative properties hold and allow the three numbers to be added regardless of their order.
Which of the following statements would not be evidence of about teaching the basic facts effectively? A. It is important to explicitly teach students strategies for solving basic fact problems. B. Story problems can help students develop fluency with the basic facts. C. Memorizing facts is important to mastering the facts. D. Fluency includes being able to select appropriate strategies and answer problems quickly and correctly.
C. Memorizing facts is important to mastering the facts.
Models are important to guide students' conceptual understanding and the relationships of ones, tens, and hundreds. Identify the model below this is considered nonproportional. A. Ten-frames B. Electronic base-ten manipulatives C. Money D. Connecting cubes
C. Money
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. Explicitly teaching reasoning strategies C. Providing more fact drill and worksheets D. Identification of student fact knowledge
C. Providing more fact drill and worksheets
If a student was asked to count a container with 45 counters and you asked how many cups would you need if you placed 10 counters in each cup? What action below would provide the best evidence of the students' knowledge of place value? A. Student asks for some cups to put the counters into B. Student makes a random guess C. Student goes back and counts to 10 and then starts again at 1 D. Student goes back and recounts them by ones
C. Student goes back and counts to 10 and then starts again at 1
State the name of the property illustrated. 4+[3+(7)]=(4+3)+(7) A.Identity property of addition B.Commutative property of addition C.Associative property of addition
C.Associative property of addition
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.Work a simpler problem C.Look for key words D.Use a model, diagram, or materials
C.Look for key words
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. Call it "the answer is" symbol. C.Use the language "is the same as" when you read an equal sign. D.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.
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 the only two operations that can be performed on the number line. 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 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 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.
Which problem structure is related to the subtraction situation "how many more?" A.Take away B.Start unknown C.Part-part-whole D.Comparison
D. Comparison
Which of the following is not a strategy for supporting students' learning of basic facts? A. Explicit strategy instruction B. Guided invention C. Memorization D. Drill
D. 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. Know which facts students do and don't know C. Integrates assessment into instruction D. Easier to implement
D. Easier to implement
Number sense means that students have a grasp on the size of numbers. What does the term relative magnitude mean? A. Numbers easy to compute mentally B. Number of minutes dedicated to mathematics instruction C. Numbers that can be used as signposts for a numbers location D. Number relationships—is it larger, smaller, close, or about the same
D. Number relationships—is it larger, smaller, close, or about the same
Place parentheses, if needed, to make each of the following equations true. 12 ÷4+1=4 A. Parentheses are needed. The corrected equation is (12÷4)+1=4. B. Parentheses are needed. The corrected equation is (12÷4+1)=4. C. Parentheses are needed. The corrected equation is 12÷(4+1)=4. D. Parentheses are not needed to make the equation true.
D. Parentheses are not needed to make the equation true.
Place parentheses, if needed, to make each of the following equations true. 5+6÷2+4=12 A. Parentheses are needed. The corrected equation is (5+6)÷(2+4)=12. B. Parentheses are needed. The corrected equation is 5+6÷(2+4)=12. C. Parentheses are needed. The corrected equation is (5+6)÷2+4=12. D. Parentheses are not needed to make the equation true.
D. Parentheses are not needed to make the equation true.
What method below would students be able to infuse reasoning strategies, select appropriate strategies and become more efficient in finding the answer? A. Fact worksheets B. Time fact tests C. Fact drills D. Playing games
D. Playing games
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
D.2(5+3)= 2×5+2×3
Strategies for building a good lesson around a context problem include all of the following for student with the exception of which one? A.Focus on few problems to solve B.Discussion about multiple methods for solving C.Use physical materials and drawings to solve D.Use only paper and pencil to solve
D.Use only paper and pencil to solve
Which property is illustrated in each of the following: a. 8•(3•6)=(8•3)•6 b. 8•(3•6)=8•(6•3) c. 8•(3•6)=(3•6)•8 d. 1•(3•6)=3•6 e. (5+1)•0=0 f. (8+3)(5+6)=(8+3)5+(8+3)6
a. associative property b. commutative property c. commutative property d. identity property e. zero property f. distributive property