Midterm Ch. 7-13
Modern technology has made computation easier. Identify the true statement below. A) But mental computation strategies can be faster than using technology. B) And recent studies have found that a very low percentage of adults use mental math computation in everyday life. C) And mental computation contributes to diminished number sense. D) So the ability to compute fluently without technology is no longer needed for most people.
A) But mental computation strategies can be faster than using technology.
16) Which one the statements below is not a part of the progression of a child's understanding of ten? A) Child understands 30 as 3 tens. B) Child understands ten as ten ones. C) Child understands ten as a unit with materials or representations. D) Child solves tasks involving tens with using materials or representations.
A) Child understands 30 as 3 tens.
10) A blank number line and numeral cards can be used to support the development of numeral identification and what other concept? A) Counting sequence. B) Place value. C) One-to-one correspondence. D) Cardinality.
A) Counting sequence.
What statement below describes the cluster problem approach for multidigit multiplication? A) Encourages the use of known facts and combinations. B) Encourages the manipulation of only one of the factors. C) Encourages the use of an open array. D) Encourages the use of fair sharing.
A) Encourages the use of known facts and combinations.
Complete this statement, "Constructing models of arrays draws attention to..." A) Factors connection with rows and columns. B) Factors and product. C) Number of rows and columns. D) Connection with measurement of area.
A) Factors connection with rows and columns.
What strategy for computational estimation after adding or subtracting do you adjust to correct for digits or numbers that were ignored? A) Front-end. B) Rounding. C) Compatible numbers. D) Over and under.
A) Front-end.Complete the statement, "A mental computation strategy is a simple..." A) Left-handed method. B) Invented strategy. C) Standard algorithm. D) One right way.
An open number can be used effectively for thinking about addition and subtraction. All of the reasons below support the use of an open number line EXCEPT: A) Is less flexible than a numbered line. B) Eliminates confusion with hash marks and spaces. C) Less prone to computational errors. D) Helps with modeling student thinking.
A) Is less flexible than a numbered line.
Identify the problem that represents the join, result unknown structure. A) Maryann had 3 library books before she checked out 2 more. How many did she have all together? B) Maryann had 5 library books before she returned 2 of them. How many does she have now? C) Maryann had 4 nonfiction books and 2 fiction. How many more nonfiction books does she have? D) Maryann had 9 library books and Jim had 4. How many more did Maryann have than Jim?
A) Maryann had 3 library books before she checked out 2 more. How many did she have all together?
Why is it significant for students to use think-addition for subtraction rather than take-away? A) Mastering subtraction facts. B) Mastering symbolic representations. C) Mastering problem solving strategies. D) Mastering model-based solutions.
A) Mastering subtraction facts.
6) Verbal counting requires separate skills. Identify the statement that represents one of them. A) One-to-one correspondence. B) Last word names the quantity. C) Greater than, less than and equal to relationships. D) Anchor numbers.
A) One-to-one correspondence.
What invented strategy is just like the standard algorithm except that students always begin with the largest values? A) Partitioning. B) Clusters. C) Complete number. D) Compensation.
A) Partitioning.
Identify the reason why the equal sign can confuse children. A) Relational symbol not operations. B) Means the answer is coming up. C) Operations symbol not relational. D) Means the answer is the same as.
A) Relational symbol not operations.
What is the reason why mental calculations estimates are more complex? A) They require a deep knowledge of how numbers work. B) They require a solid knowledge of division procedures. C) They require a deep knowledge of partitioning. D) They require a solid knowledge of multiplication procedures.
A) They require a deep knowledge of how numbers work.
All of the statements below are considered a benefit of invented strategies EXCEPT: A) They require one specific set of steps to use them, which makes them easier to memorize. B) They help reduce the amount of needed re-teaching. C) Students develop stronger number sense. D) They are frequently more efficient than standard algorithms.
A) They require one specific set of steps to use them, which makes them easier to memorize.
9) Reading and writing numerals is similar to teaching children the alphabet and reading. Identify the statement below that would be developmentally inappropriate for early learners. A) Worksheets with numbers to trace. B) Writing numbers on interactive whiteboard. C) Tracing numbers with shaving cream. D) Pushing numbers on calculator.
A) Worksheets with numbers to trace.
There are important things to remember when teaching the standard algorithm. Identify the statement that does not belong. A) Good choice in some situations. B) Require written record first. C) Require concrete models first. D) Explicit connections are made between concept and procedure.
B) Require written record first.
The Common Core State Standards states that student should learn a variety of strategies. These strategies should be based on all of the following EXCEPT: A) Place value. B) Sophisticated thinking. C) Properties of operations. D) Prior to the standard algorithm.
B) Sophisticated thinking.
A good lesson built on a context or related to a story would have all of the qualities listed below EXCEPT: A) Words, pictures and numbers are used to explain solution. B) Students can easily find a solution with mental mathematics. C) Students can find mistakes in other's written solutions. D) Designed to anticipate and develop mathematical models of the real world.
B) Students can easily find a solution with mental mathematics.
Complete the statement, "When creating a classroom environment appropriate for inventing strategies..." A) The teacher should immediately confirm that a student's answer is correct, in order to build his/her confidence. B) The teacher should attempt to move unsophisticated ideas to more sophisticated thinking through coaching and questioning. C) The teacher should discourage student-to-student conversations in order to provide students with a quiet environment to think. D) The teacher should encourage the use of naked numbers as a starting point.
B) The teacher should attempt to move unsophisticated ideas to more sophisticated thinking through coaching and questioning.
1) Which of the following is a description of Number Sense? A) Counting tells how many things are in a set. B) Thinking about different sized quantities and use number relationships. C) Relating through comparing quantities. D) Operations with numbers based on the world around us.
B) Thinking about different sized quantities and use number relationships.
What statement below is the description of a Part-part-whole? A) Involve comparison of two quantities. B) Two parts that are conceptually or mentally combined into one whole. C) The change is the amount being removed. D) Initial action of joining start amount, a change amount and resulting amount.
B) Two parts that are conceptually or mentally combined into one whole.
What is the purpose of using a side bar chart in multidigit division? A) Easier to come up with the actual answer. B) Uses a doubling strategy for considering the reasonableness of an answer. C) Increases the mental computation needed to find the answer. D) Uses the explicit trade notation.
B) Uses a doubling strategy for considering the reasonableness of an answer.
When using place-value mats, drawing ______________ in the ones place will make it very clear to students how many ones there are so they can avoid recounting the ones.
x's or ten frame
All of the following could be examples of invented strategies for obtaining the sum of two-digit numbers EXCEPT: A) Adding on tens and then ones (For example, to solve 24 + 35, think 24 + 30 = 54 and 5 more makes 59.) B) Using nicer numbers to estimate (For example, to solve 24 + 47, think 24 is close to 25 and 47 is closer to 45 so 24 + 47 = 25 + 45 = 70.) C) Moving some to make 10 (For example, to solve 24 + 35, move 6 from 35 to make 24 + 6 and then add 30 to the remaining 29.) D) Adding tens and adding ones then combining (For example, to solve 24 + 35, think 20 + 30 = 50 and 4 + 5 = 9 so 50 + 9 = 59.)
B) Using nicer numbers to estimate (For example, to solve 24 + 47, think 24 is close to 25 and 47 is closer to 45 so 24 + 47 = 25 + 45 = 70.)
When helping students to conceptualize numbers with 4 or more digits, which of the following is NOT true? A. Students should be able to generalize the idea that 10 in any one position of the number results in one single thing in the next bigger place. B. Because these numbers are so large, teachers should just make due with the examples that are provided in textbooks. C. Models, such unit cubes, can still be used. D. Students should be given the opportunity to work with hands-on, real life examples of them.
B. Because these numbers are so large, teachers should just make due with the examples that are provided in textbooks.
The following statements are true regarding computational estimation EXCEPT: A) Use the language of estimation- about, close, just about. B) Focus on flexible methods. C) Focus on answers. D) Accept a range of estimates.
C) Focus on answers.
Remainders have an effect on all of the following EXCEPT: A) Discarded leaving a smaller whole-number answer. B) Rounded to the nearest whole number for an approximate answer. C) Fractional part left over and not included in the whole-number answer. D) Force the answer to the next highest whole number.
C) Fractional part left over and not included in the whole-number answer.
The use of model-based problems that students can use counters, bar diagrams, or number lines helps with their problem solving skills. Identify the statement below that describes what the use of bar diagrams can demonstrate. A) Modeling two parts in two separate piles. B) Measuring distances from zero. C) Generating mean-making space. D) Breaking the shape apart to show multiple parts.
C) Generating mean-making space.
20) Graphs clearly exhibit comparisons between numbers. What question below would require a comparison response? A) Which snack is the most liked? B) How many people like apples as a snack? C) How much is the difference between apples and oranges? D) Which snack is the least liked?
C) How much is the difference between apples and oranges?
Which of the following is a true statement about standard algorithms? A) Students will frequently invent them on their own if they are given the time to experiment. B) They cannot be taught in a way that would help students understand the meaning behind the steps. C) In order to use them, students should be required to understand why they work and explain their steps. D) There are no differences between various cultures.
C) In order to use them, students should be required to understand why they work and explain their steps.
One strategy for teaching computational estimation is to ask for information, but no answer. Which statement below would be an example of NOT gathering information? A) Is it more or less that 1,000? B) Is it between $400 and $700? C) Is one of these right? D) Is your estimate about how much?
C) Is one of these right?
Which problem represents the separate, start unknown structure? A) Maryann had 3 library books before she checked out 2 more. How many did she have all together? B) Maryann had 5 library books before she returned 2 of them. How many does she have now? C) Maryann had some nonfiction books and 2 fiction. She now has 8 books. How many did she begin with? D) Maryann had 9 library books and Jim had 4. How many more did Maryann have than Jim?
C) Maryann had some nonfiction books and 2 fiction. She now has 8 books. How many did she begin with?
An intuitive idea about long division with two digit divisors is to round up the divisor. All of examples below support this idea EXCEPT: A) Think about sharing base-ten pieces. B) Underestimate how many can be shared. C) Pretend there are fewer sets to share than there really are. D) Multiples of 10 are easier to compare.
C) Pretend there are fewer sets to share than there really are.
2) Research-based recommendations for high quality learning activities in the first six years of life include all of the following EXCEPT: A) Enhance children's natural interest in mathematics. B) Use formal and informal experiences. C) Provide experiences for children to become procedural fluent. D) Assess children's mathematical knowledge.
C) Provide experiences for children to become procedural fluent.
A number line can be helpful with teaching this estimation strategy. A) Front end. B) Compatible. C) Rounding. D) Mental computation.
C) Rounding.
4) Children explore quantity before they can count. What is the word for children being able to "just" see how many there are without counting? A) Quantifying. B) Relating. C) Subitzing. D) Enumerating
C) Subitzing.
Students who have learned this strategy for their "basic facts" can use it effectively with solving problems with multidigit numbers. A) Jump strategy. B) Shortcut strategy. C) Think addition strategy. D) Split strategy.
C) Think addition strategy.
Identify the statement that represents what might be voiced when using the missing-factor strategy. A) When no more tens can be distributed a ten is traded for ten ones. B) Seven goes into three hundred forty-five how many times? C) What number times seven will be close to three hundred forty-five with less than seven remaining? D) Split three hundred forty-five into 3 hundred, four tens and five ones.
C) What number times seven will be close to three hundred forty-five with less than seven remaining?
When students are being introduced to three-digit numbers A. The process should be quite different from introducing students to two-digit numbers. B. They have normally not yet mastered the two-digit number names. C. They frequently struggle with numbers that contain no tens, like 503. D. Their mistakes when attempting to write numeric examples should not be discussed, in order to avoid embarrassment.
C. They frequently struggle with numbers that contain no tens, like 503.
18) One of the best ways for children to think of real quantities is to associate numbers with measures of things. What concept would not emerge from using estimation? A) More or less than ________. B) Closer to ________ or to ________. C) Is ________ reasonable? D) Exactly how many ________.
D) Exactly how many ________.
The general approach for teaching the subtraction standard algorithm is the same as addition. What statement below would not be a problem when using the standard algorithm for addition? A) Develop the written record. B) Begin with models. C) Trades made after the column in the left has been done. D) Exercises with zeros.
D) Exercises with zeros.
What compensation strategy works when you are multiplying with 5 or 50? A) Clusters. B) Partitioning the multiplier. C) Array. D) Half-then-double.
D) Half-then-double.
Cultural differences are evident in algorithms. What reason below supports teaching for mathematics? A) Notational algorithms. B) Customary algorithms. C) Mental algorithms. D) Invented algorithms.
D) Invented algorithms.
When developing the written record for multiplication computation it is helpful to encourage students to follow these suggestions EXCEPT: A) Use sheets with base-ten columns. B) Record partial products. C) Record the combined product on one line. D) Mark the subdivisions of the factors.
D) Mark the subdivisions of the factors.
Which problem represents the compare, difference unknown structure? A) Maryann had 3 library books before she checked out 2 more. How many did she have all together? B) Maryann had 5 library books before she returned 2 of them. How many does she have now? C) Maryann had 4 nonfiction books and 2 fiction. How many books does she have? D) Maryann had 9 library books and Jim had 4. How many more did Maryann have than Jim?
D) Maryann had 9 library books and Jim had 4. How many more did Maryann have than Jim?
3) The National Research Council identified three foundational areas in mathematics content for early learners. Identify the core that is more applicable for experienced learners. A) Operations core. B) Relations' core. C) Number core. D) Reasoning core.
D) Reasoning core.
The models listed below are used to support the development of invented strategies EXCEPT: A) Jump strategy. B) Split strategy. C) Take-Away strategy. D) Shortcut strategy.
D) Shortcut strategy.
All of the statements below are related to teaching multiplication and division EXCEPT: A) What to do with remainders. B) Symbolism as a way to record thinking. C) Physical models, drawings and equations. D) Think addition as multiplication and take away as division.
D) Think addition as multiplication and take away as division.
Identify the statement that is describes the importance for children to know the relationship between addition and subtraction. A) Writing symbolic equations. B) Using the associative property. C) Mental mathematics. D) Using the same models or pictures.
D) Using the same models or pictures.
15) While developing students' understanding of the relationships for numbers 10 through 20, all of the following should be kept in mind EXCEPT: A) Even though students experience numbers up to 20 regularly in real life, it should not be assumed that they would automatically extend the relationships they learned for numbers 1 to 10 to bigger numbers. B) These relationships are just as important as the ones involving numbers 1 to 10. C) Children should learn that there is a set of ten involved in any number between 10 and 20. D) While learning about these relationships, students should develop a complete understanding of the concept of place value
D) While learning about these relationships, students should develop a complete understanding of the concept of place value.
Making the transition from base-ten to standard language A. Can be made more confusing by using base-ten materials when verbalizing the number names. B. Should not include the teacher using a mix of base-ten and standard language, C. Should not include a discussion of the "backwards" names given to the teens, as they can be confusing. D. Can be made less difficult by using a word wall to provide support for ELLs and students with disabilities.
D. Can be made less difficult by using a word wall to provide support for ELLs and students with disabilities.
According to NCTM, it's not necessary for students to have fully developed place value understandings before giving them opportunities to solve problems with two and three-digit numbers. True or False
False
Base ten blocks are the only material that should be used to model place value concepts. True or False
False
Nonproportional models should be used only after students understand that ten units makes a "ten." True or False
False
Describe the three types estimation and give an example of how they could be used in teaching computational estimation.
Measurement, quantity, computational ways of estimating. M: Finding the size of a room in sqft, Q: students in a gym or guessing how much candy is in a jar, CWoE: estimating population for word problems or figuring out approx. how much of money is spent or needed to purchase something
21) Identify the first three levels of thinking from the trajectory for counting and give an example of what the child demonstrate at that level.
Precounter: Child will say ball when presented with a group of balls instead of saying the quantity. Reciter: Child will verbally count but it's possible its not in the right order or they may repeat a number or skip a number Corresponder: Child can count one to one, but when asked the number after counting, they may have to recount.
In order to help students to understand the way the two digits of a number and a base ten model of it are related, models of tens should be grouped on the left, and units should be on the right, to reflect the structure of the numeric version. TRUE or FALSE
True
Identify two or more ways that an open number line can be used to support the use of invented strategies.
You can fit any number on it, more flexible, works with any numbers, elements confusion with hashmark
What number property is illustrated by the problem 16 × 12 = 16(10 + 2) = 160 + 32 = 192? A) Associative. B) Commutative. C) Identity. D) Distributive
D) Distributive
A _____________ is an important tool that can hang on a wall, be displayed on a smart board, or can be given to students as paper copies, which students can use to discover numerous place-value-related patterns
100s chart
Cluster problems are an approach to developing the missing-factor strategy and capitalize on the inverse relationship between multiplication and division. All of equations below represent clusters that would help solve 381 divided by 72 EXCEPT: A) 81 × 70 B) 10 × 72 C) 5 × 70 D) 4 × 72
A) 81 × 70
Which of the following is NOT an example of a proportional model that can be used for place value? A. Money B. Beans in cups of ten and single beans C. Base ten blocks D. Stir straws bundled in groups of ten and with single straws
A. Money
Statements/questions from a teacher can support children's understanding of why one can't divide by 0 EXCEPT: A) "What happens when you take these 25 pennies and divide them into 0 groups?" B) "Just memorize that you can't divide by 0." C) "Can you show me how to share 8 apples between no people?" D) "Put 12 blocks in 0 equal groups."
B) "Just memorize that you can't divide by 0."
Representing a product of two factors may depend on the methods student experienced. What representation of 37 × 5 below would indicate that the student had worked with base-ten? A) An array with 5 × 30 and 5 × 7. B) 5 groups of 30 lines and 5 groups of 7 dots. C) 5 circles with 37 items in each. D) 37 + 37 + 37 + 37 + 37 + 37 + 37.
B) 5 groups of 30 lines and 5 groups of 7 dots.
Which problem is an example of the comparison, product unknown (multiplication) structure? A) Barry's sandwich shop offers 3 kinds of meat and 2 kinds of bread. How many different sandwiches could he make if he uses one meat and one kind of bread for each? B) Barry saved $12 and Jill saved $6. Barry saved how many times as much money as Jill? C) This month, Barry saved 8 times as much as last month. Last month, he saved $3. How much did Barry save this month? D) Barry saved $24 total, and he saved $6 each month. For how many months had he been saving?
B) Barry saved $12 and Jill saved $6. Barry saved how many times as much money as Jill?
11) The concepts of more, less and same are basic relationships that contribute to children's understanding of number. Identify the one relationship that if a child is unable to use they may be at educational risk. A) Choose the set that is equal. B) Choose the set that is more. C) Choose the set that is less. D) Choose the set that can be subitized.
B) Choose the set that is more.
19) Complete this statement, "The early stages of number development, the use of graphs is primarily for..." A) Learning the counting sequence. B) Connecting numbers to real quantities. C) Bench mark numbers. D) Part-Part-Whole.
B) Connecting numbers to real quantities.
5) Which of the following represents a true statement about the concept of 0? A) Understanding of 0 comes easily understood by small children. B) Developing understanding of 0 is important with its role in the base-ten number system. C) Counting involves touching an object, 0 is rarely included in the count. D) Discovering 0 is not useful for small children.
B) Developing understanding of 0 is important with its role in the base-ten number system.
Which of the following is a strategy that is more applicable for multiplying single digits than multidigits? A) Compatible numbers. B) Doubling. C) Partitioning. D) Complete number.
B) Doubling.
What is the importance of students knowing the commutative property? A) Applies to addition and subtraction. B) Helps students master basic facts because, if they really understand it, it reduces the number of individual facts they have to memorize. C) Should be demonstrated with problems that have the same sums but different addends. D) Is a term that even very young students should memorize?
B) Helps students master basic facts because, if they really understand it, it reduces the number of individual facts they have to memorize.
Complete the statement, "A mental computation strategy is a simple..." A) Left-handed method. B) Invented strategy. C) Standard algorithm. D) One right way.
B) Invented strategy.
The ten-structure of the number system is important to extend students thinking beyond counting. All of the activities below reference a strategy for calculation EXCEPT: A) Using decade number. B) Odd or even. C) Up over 10. D) Add on to get to 10.
B) Odd or even.
14) Here is a possible list of the kinds of things children should learn about any number up to 20 while in pre-k or kindergarten. All of them are appropriate EXCEPT: A) Count and know the number words in their order. B) Reading three digit numbers. C) State more and less by one and 2. D) Relates to the benchmark numbers.
B) Reading three digit numbers.
When a problem has a number that is a multiple of ________ or close to ________ it is an example of a problem that you leave one number intact and subtract from it. A) 85 - 35 B) 85 - 64 C) 85 - 29 D) 85 - 56
C) 85 - 29
13) An important variation of part-part-whole activities is referred to as missing-part activities. Identify the statement below that describes a missing part activity. A) 2-3-4. B) Making a bar of two color connecting. C) A dot plate showing 5 and say, "I wish I had seven." D) Saying a 10 fact, six and four equals 10.
C) A dot plate showing 5 and say, "I wish I had seven."
This model uses a structure that automatically organizes proportionate equal groups and offers a visual demonstration of the commutative and distributive properties. A) Clusters. B) Missing Factor. C) Area. D) Open array.
C) Area.
Problems with the join and separate structures, with the start or initial amount unknown, tend to be the hardest for students to understand and accurately solve. Identify the reason for they are more challenging for children to use. A) Children can model the physical action. B) Children can act out the situation. C) Children cannot use counters for the initial amount. D) Children cannot grasp a quantity represents two things at once.
C) Children cannot use counters for the initial amount.
What statement identifies the importance of using contextual problems as a primary teaching tool? A) Children demonstrate procedural fluency. B) Children identify the structure of the situations. C) Children construct richer understanding of the operations. D) Children connect problems to school mathematics.
C) Children construct richer understanding of the operations.
Division may be easier for students if they are familiar with the concepts. All of the statements below are related to division of whole numbers EXCEPT: A) Partitioning. B) Fair sharing. C) Compensating. D) Repeated subtracting.
C) Compensating.
What invented strategy is represented by a student multiplying 58 × 6 by adding 58 + 58 to get 116 and then adding another 116 to get 232 and then adding another 116 to find the product of 348. A) Partitioning. B) Clusters. C) Complete number. D) Compensation.
C) Complete number.
17) A hundreds chart is an essential tool for early exposure to numbers to 100. All of the reasons below are benefits of using hundreds chart EXCEPT: A) Highlight number patterns. B) Recognize and count with two digit numbers. C) Conceptualize numbers greater than 100. D) Locations of numbers.
C) Conceptualize numbers greater than 100.
7) The learning trajectory for counting has levels of thinking. What level below would represent a child that can count objects and know which have been counted and which have not, and respond to random arrangements. A) Corresponder. B) Reciter. C) Counter and Producer. D) Skip Counter.
C) Counter and Producer.
All of the following provide an example of a method used for computation EXCEPT: A) Standard algorithms. B) Student-invented strategies. C) Discourse modeling. D) Computational estimation.
C) Discourse modeling.
The key word strategy sends a wrong message about problem solving. Identify the statement below that would be offered in support of the key word strategy. A) Encourages children to ignore meaning and structure of problems. B) Many problems do not have key words. C) Encourage children to use a list of key words with corresponding operations. D) Many problems have key words that may be misleading.
C) Encourage children to use a list of key words with corresponding operations.
Often siblings and family members are pushing the use of the standard algorithm while students are learning invented strategies. What is the course of action for a teacher? A) Insist on invented strategies. B) Require students demonstrate both standard and invented strategies. C) Expect them to be responsible for the explanation of why any strategy works. D) Memorize the steps.
C) Expect them to be responsible for the explanation of why any strategy works.
A student who has place value understanding at the face value level, when asked to explain the digits of the number 45, would most likely A. Be unable to identify the meaning behind the individual digits, and would see the number as one unit. B. Be able to identify the digit in the ones place and in the tens place, but be unable to relate the meaning of the two digits to two separate amounts. C. Match up four blocks to go with the 4 digit and five blocks to go with the 5 digit. D. Verbalize that the 4 represents forty and the 5 represents five units.
C. Match up four blocks to go with the 4 digit and five blocks to go with the 5 digit.
When it comes to beginning grouping activities A.Because students usually understand counting by ones, teachers should skip directly to grouping by ten. B. Teachers should let students experiment with showing amounts in groups until they, perhaps, come to an agreement that ten is a useful-sized group to use. C. Students should only work with very small items that can easily be bundled together. D. Teachers should not worry about having students verbalize the amounts they are grouping.
C. Students should only work with very small items that can easily be bundled together.
8) Children who can count successfully orally, but do not understand that the last word stated is the amount of the set are not demonstrating what principle? A) Subitize. B) Quantify. C) Enumerate. D) Cardinality.
D) Cardinality.
Which is an example of the compensation strategy? A) 63 × 5 = 63 + 63 + 63 + 63 + 63 = 315 B) 27 × 4 = 20 × 4 + 7 × 4 = 80 + 28 = 108 C) 46 × 3 = 46 × 2 (double) + 46 = 92 + 46 = 138 D) 27 × 4 is about 30 (27 + 3) × 4 = 120; then subtract out the extra 3 × 4, so 120 -12 = 108
D) 27 × 4 is about 30 (27 + 3) × 4 = 120; then subtract out the extra 3 × 4, so 120 -12 = 108
Developing the standard algorithm for division teachers should use all of the following guides EXCEPT: A) Partial quotients with a visual model. B) Partition or fair share model. C) Explicit trade method. D) Area model.
D) Area model.
Which problem is an example of the equal groups, number of groups unknown structure? A) This month, Barry saved 8 times as much as last month. Last month, he saved $3. How much did Barry save this month? B) Barry's sandwich shop offers 3 kinds of meat and 2 kinds of bread. How many different sandwiches could he make if he uses one meat and one kind of bread for each? C) Barry saved $12 and Jill saved $6. Barry saved how many times as much money as Jill? D) Barry saved $24 total, and he saved $6 each month. For how many months had he been saving?
D) Barry saved $24 total, and he saved $6 each month. For how many months had he been saving?
All of the statements below represent the differences between invented strategies and standard algorithms EXCEPT: A) A range of flexible options. B) Left-handed rather than right-handed. C) Number oriented rather than digit oriented. D) Basis for mental computation and estimation.
D) Basis for mental computation and estimation.
12) Experience with number relationships will guide children beyond counting by ones to solve problems. Name the relationship 10 plays in developing number sense. A) One and two more. B) One and two less. C) Part-part-whole. D) Benchmark numbers.
D) Benchmark numbers.
Using base-ten language A. Is demonstrated when the teacher says "We have fifty-three beans." B. Can be helpful for students who are ELLs because many other countries routinely use base-ten language. C. Is frequently confusing for students, and it is best avoided. D. Looks only like this format: ____tens and ____ones.
D. Looks only like this format: ____tens and ____ones.
Describe an activity that would help your students to better conceptualize numbers that are very large.
Describe how this activity would build conceptualization. Length of the room in unifix cubes as compared to length of the playground or hallway. A guessing game with large candy amounts in different jars.
Because students can often hide their lack of conceptual understanding, a more in-depth assessment tool, a ______________________ , can be used to determine what they really know.
Diagnostic assessment
Present and discuss two reasons for using contextual problems to teach addition, subtraction, multiplication and division.
Helps to practice reasoning skills Relates to real world problems, for instance I use my math skills often for tipping service workers.
How do the commutative and associative properties relate to children's understanding of the basic facts?
If a student were to be presented with an equation, such as 1+2=3, then is asked to solve 2+1=... The answer is still 3, you just switched the terms around. It helps in order to scaffold to more advanced facts if they know the basics.
Multiples of 10, 100, and sometimes 25 are called __________________, which work especially well with hundreds charts and number lines to help students find the distances between numbers.
Landmark Numbers
22) Discuss why the concept of "less" is more difficult than "more."
The concept that less is more difficult than more is because we use the word "more" very often in real life with children. We don't often say the word "less" to say that were finished.
