Math Test (multiple choice)
ch. 9) Which of the following is NOT a true statement regarding mathematical symbols? a) It is important that very young children understand the symbols +, -, and = to learn about addition and subtraction concepts. b) Great care should be taken to assure students understand = means "is equal to" rather than "the answer is." c) By first grade, symbolic conventions are important for children to know. d) Frequently, the meaning of the equal sign confuses students.
a) It is important that very young children understand the symbols +, -, and = to learn about addition and subtraction concepts. - very young needs content and understanding of concept before labeling and symbols.
ch. 9) Which problem 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? - had _(original)_ got _(joined)_ more... how many now _(result)_
ch. 11) 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 - to abstract
ch. 10) Which of the following is a frequently used strategy to help students learn basic multiplication facts? a) Nifty nines b) Using unknown facts to reason and figure out the ones that are known c) Tripling numbers and then adding one d) Making students see there is no relationship between multiplication and division
a) Nifty nines - multiplying 9's - only b would make sense other wise, but it isn't specific to multiplication
ch. 12) Which of the following is NOT a benefit of student-developed strategies? 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. - no memorization
*ch. 9) Which problem is an example of the comparison, product unknown (multiplication) 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 1 meat and 1 kind of bread for each? c) Barry saved $12 and Jill saved $6. Barry saved how many times as much money as Jill? d) -answer is already been taken, so ti is not this one. process of elimination.- d) Barry saved $24 total, and he saved $6 each month. For how many months had he been saving?
a) This month, Barry saved 8 times as much as last month. Last month, he saved $3. How much did Barry save this month? - comparison (this month and last month) and product unknown (?) b) not comparison c) Barry saved $12 and Jill saved $6. Barry saved how many times as much money as Jill? - comparison (Barry and Jill) and product unknown (how many times as much more) -I would say c, but she said a in class.
ch. 10) When is drill appropriate? a) Never b) As a practice tool, only once students are effectively using reasoning strategies that they conceptually understand c) When every student is drilled at the same pace d) Only when students are given for practice a set of facts that have no relationship to one another
b) As a practice tool, only once students are effectively using reasoning strategies that they conceptually understand - makes the most sense. - definitely not a. and d.
ch. 11) 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. - textbooks should not decide content
ch. 11) 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.
b) Can be helpful for students who are ELLs because many other countries routinely use base-ten language. - remember in class, other languages refer to numbers as 60 and 3.
ch. 8) Part-part-whole concepts a) Are usually taught through introductory activities that require the student to break apart several different numbers during one activity. b) Consist of activities in which students can break apart a number into two or more parts or compose a number from two or more parts.- adding c) Must be taught using very specifically designed materials. d) Do not include as an important category of activities missing part activities.
b) Consist of activities in which students can break apart a number into two or more parts or compose a number from two or more parts.- adding - this and this is THIS - part-part-whole
ch. 8) Which of the following represents a true statement about the number 0? a) It is a concept that is easily understood by small children without an adult having to intentionally build understanding. b) Developing students' understanding of it is crucial, due to its important role in the base-ten number system. c) Because early counting involves touching an object, 0 is usually included in the count. d) A zero dot plate is not useful in initiating dialogue about the concept.
b) Developing students' understanding of it is crucial, due to its important role in the base-ten number system. - 0 plays a huge role in the number system and can be difficult to understand
ch. 9) 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. - most applicable answer. really, read them. :)
ch. 13) The compatible numbers strategy a) Is one of the least helpful strategies for estimating division problems. b) Involves changing the numbers in the problems to make them more "friendly" to work with. c) Is not easily applied to situations involving fraction, decimals, and rates. d) Is not appropriate for estimating multiplication problems.
b) Involves changing the numbers in the problems to make them more "friendly" to work with. - using our anchor numbers, more compatible
ch. 12) Which of the following is a true statement regarding computational estimation? a) We can use calculators, so it's not really that necessary. b) Its under representation in many textbooks can cause someone to incorrectly assume it's not very important. c) Teachers should define for and accept from students only one correct estimation. d) Examples of real-life context are not needed.
b) Its under representation in many textbooks can cause someone to incorrectly assume it's not very important. - the rest are ridiculous - makes sense
ch. 9) Which problem represents the separate, 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 books does she have? d) Maryann had 9 library books and Jim had 4. How many more did Maryann have than Jim?
b) Maryann had 5 library books before she returned 2 of them. How many does she have now? - had _(original)_ returned/lost/gave _(separated)_... How many now _(result)_
ch. 9) The relationship between addition and subtraction a) Can confuse children and should not be addressed in class. b) Should be developed for children by providing them with examples of the same number sets appearing in different contexts. c) Is not an example of an inverse relationship. d) Can prevent students from developing flexibility in the methods they use to solve problems.
b) Should be developed for children by providing them with examples of the same number sets appearing in different contexts. - exposure
ch. 11) 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.
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. - student led
ch. 12) 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) Student-to-student conversations should be discouraged, in order to provide students with a quiet environment to think. d) The degree to which students feel safe to make mistakes is not an important factor.
b) The teacher should attempt to move unsophisticated ideas to more sophisticated thinking through coaching and questioning. - promote deeper thinking
ch. 9) Which of the following is a true statement about contextual problems? a) They are connected more to what is referred to as "school mathematics" than they are to children's lives. b) Their origin could result from recent experiences in the classroom. c) Their language orientation can make them inappropriate for ELL students. d) Enhancing them with visual aids or students acting them out would be inappropriate.
b) Their origin could result from recent experiences in the classroom. - EXPERIENCE= context. learning experiences give content context.
ch. 10) Games can be appropriate to support mastery because a) They can be less engaging than other forms of practice. b) They frequently have aspects that allow students to self-check their answers. c) They are frequently much more stressful than other forms of practice. d) They rarely allow teachers methods to differentiate, based on individual student needs
b) They frequently have aspects that allow students to self-check their answers. - they aren't non engaging or more stressful, they can allow differentiation, so this is the best answer.
ch. 10) Which of the following is NOT a strategy that helps students master basic facts? a) One more than/two more than b) Using 6 as an anchor number c) Near doubles d) Doubles
b) Using 6 as an anchor number - 6 doesn't make sense as an anchor, the rest are very helpful.
ch. 12) All of the following could be examples of student-developed 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.) - will NOT solve answer, only provide estimation
ch. 13) 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) 27 × 4 is about 30 (27 + 3) × 4 = 120; then subtract out the extra 3 × 4, so 120 -12 = 108 (using estimation) d) 46 × 3 = 46 × 2 (double) + 46 = 92 + 46 = 138
c) 27 × 4 is about 30 (27 + 3) × 4 = 120; then subtract out the extra 3 × 4, so 120 -12 = 108 (using estimation) - compensating with anchor numbers
ch. 13) Calculators a) Are not appropriate to use when students are learning to become more fluent estimators. b) Don't help students check the reasonableness of their estimates. c) Are one of the reasons that estimation skills are so important, because students frequently make mistakes involving hitting the wrong keys. d) Can greatly reduce student engagement.
c) Are one of the reasons that estimation skills are so important, because students frequently make mistakes involving hitting the wrong keys. -
ch. 8) Which of the following is a true statement about developing the concepts of more than, less than, and same? a) A child who enters kindergarten unable to pick the set that has "more" is representative of the norm. b) The concept of "more" is frequently more troublesome for students to grasp than "less." c) Children should practice constructing sets of different amounts and comparing them. d) Activities that use dot cards and counters are not appropriate to develop these concepts.
c) Children should practice constructing sets of different amounts and comparing them. - establishes less than more than within comparing
ch. 9) What number property is illustrated by the problem 16 × 12 = 6(10 + 2) = 160 + 32 = 192? a) Associative b) Commutative c) Distributive d) Identity
c) Distributive - 6 is being distributed/pulled out
ch. 8) Which of the following is NOT (key word NOT!!!) a research-based strategy for helping teachers develop high-quality activities for children ages 3-6? a) Build on students' previous experiences and knowledge. b) Base mathematics curriculum on a solid understanding of child development. c) Greatly limit the amount of play time students have with mathematics to ensure there is ample time to cover the curriculum. d) Regularly assess students' understanding, knowledge, and skills.
c) Greatly LIMIT the amount of play time students have with mathematics to ensure there is ample time to cover the curriculum. -you want to allow every student to play around, and experiment with numbers
ch. 10) What statement most accurately describes a person who has mastered basic facts? a) He or she can use a model or a picture to figure out the answer to a basic fact problem. b) He or she has a conceptual understanding of the basic facts and can access her background knowledge to, with some time, figure out the answer to a basic fact problem. c) He or she has obtained a set of essential understandings and progressed through a set of stages so that she just "knows" the answers to certain basic fact problems. d) He or she can use a set of manipulatives and reasoning to figure out the answer to a basic fact problem.
c) He or she has obtained a set of essential understandings and progressed through a set of stages so that she just "knows" the answers to certain basic fact problems. - all other answers that doesn't require assistance/manipulatives or a beginning understanding.
ch. 13) Which of the following is a true statement regarding using estimation strategies? a) It is much more useful to focus on the estimated answer than it is to focus on the process students used to obtain the estimate. b) The more practice students have with finding a variety of estimates for the same problem, the more confused they will become. c) If the teacher has ELL students, he or she should ensure the students understand the context of the problem, then provide the numerical information before asking for an estimate. d) The front-end strategy has been shown to be one of the most difficult for students to learn to use.
c) If the teacher has ELL students, he or she should ensure the students understand the context of the problem, then provide the numerical information before asking for an estimate. - ELLs often have difficulty with estimation. be clear with them.
ch. 12) 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. - reasoning and logic are required when inventing strategies
ch. 12) Modern technology has made computation easier 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. - mental computation will ALWAYS be considered better in an elementary math class
ch. 8) Which of the following is an example of a tool that will promote instant recognition (subitizing)? a) Dot plates b) Spinners c) Fraction bars- not early number d) Base ten materials- not early number (comes on later)
a) Dot Plates -various possibilities for representing numbers shown
ch. 10) Which of the following is NOT one of the phases in the process of learning basic facts? a) Drawing strategies b) Counting strategies c) Mastery d) Reasoning strategies
a) Drawing strategies - you don't NEED to draw it out. count, yes. master, yes. Reason, yes.
ch. 10) All of the following are recommendations that can support students' ability to quickly recall basic facts EXCEPT a) Drilling for extended periods of time b) Involving families c) Using technology d) Encouraging students to self-monitor
a) Drilling for extended periods of time - extended periods of drilling are NOT effective, so take a break. lol
ch. 8) Anchoring numbers a) Is the process of relating a given number to another benchmark number.- Comparing numbers to 5 and 10. 8= 5 and 3 b) Is best introduced using the numbers 3 and 6. c) Is not well-taught using five- and ten-frames. d) Is a skill that can't be assessed through a diagnostic interview.
a) Is the process of relating a given number to another benchmark number.- Comparing numbers to 5 and 10. 8= 5 and 3 - anchor numbers are the "easy" numbers, numbers your students may find it easier to work with
ch. 11) 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. - face value= correlation (like one-to-one) possibly 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.
ch. 13) Which of the following is NOT a useful strategy for multiplying by single digits? a) Doubling b) Compatible numbers c) Partitioning d) Complete number
c) Partitioning - dividing
ch. 13) When developing the standard algorithm for division, a) Teachers should avoid using a confusing algorithm based on repeated addition. b) Teachers should have students use models after developing the written record. c) The process of recording explicit trades can be less confusing to students than the more common bringing down. d) The expression "goes into" is very meaningful for kids.
c) The process of recording explicit trades can be less confusing to students than the more common bringing down. -
ch. 11) 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. - zero's are tricky for kids regardless
ch. 10) When supporting students' ability to quickly recall basic facts, avoid a) Only working on a few facts at once. b) Allowing ample time before moving from reasoning to memorization. c) Using public displays of mastery (bulletin boards, etc.). d) Limiting the length of timed tests.
c) Using public displays of mastery (bulletin boards, etc.).
ch. 9) Which would NOT be a good statement/question from a teacher to help a student realize why he or she can't divide by 0? a) "What happens when you take these 25 pennies and divide them into 0 groups?" b) "Can you show me how to share 8 apples between no people?" c) "What can you multiply by 0 to get 7?" d) "Just memorize that you can't divide by 0.
d) "Just memorize that you can't divide by 0. - others get kids thinking, memorizing a fact is NOT ideal.
ch. 9) 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 1 meat and 1 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? - equal groups ($24), unknown groups (how many months)
ch. 11) 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. - helpful and makes sense
ch. 12) Which of the following is NOT an example of a method used to compute a solution? a) Standard algorithms b) Student-invented strategies c) Discourse modeling d) Computational estimation
d) Computational estimation - estimation is not solving/looking for solution
ch. 10) Despite the fact that many learners in the past learned basic facts from memorization, it is not an effective strategy for all of the following reasons EXCEPT a) There are just too many facts to memorize, and it's an inefficient process. b) When students are taught to simply memorize, they usually don't go back and make sure that their work is reasonable. c) Students don't develop efficient reasoning strategies and use inefficient ones, such as counting by ones. d) It greatly increases student motivation.
d) It greatly increases student motivation. - memorization has nothing to do with motivation. - all other answers are true. re-read them. a) is VERY true. Can I get an AMEN?
ch. 9) 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? - "A" had _(given)_, "B" had _(given)_. How many more/less did _A/B_ have?
ch. 12) Which of the following is NOT true about strategies for developing the subtraction algorithm? a) Students should begin with models only. b) The teacher should anticipate that there will be difficulties with zeros. c) After the procedure is completely understood with models, then students should begin developing the written record. d) The general approach is completely different from that used to develop the addition algorithm.
d) The general approach is completely different from that used to develop the addition algorithm. - subtraction is "think addition" and algorithms are very similar
ch.8) 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 will 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. - place value is needed later, not core idea here
