Math Chapter 10
What statement below would represent a child that has yet grasped the knowledge of recognizing groups of ten? A) Counts out sixteen objects and can tell you how many by counting each piece. B) Counts out sixteen and puts the 10 in one pile and 6 in another and tells you there are sixteen. C) Counts out sixteen and makes two piles of eight and tells you there are sixteen. D) Counts out sixteen and places 6 aside and tells you 10 and 6 are sixteen.
Answer: A) Counts out sixteen objects and can tell you how many by counting each piece.
What is the primary reason for delaying the use of nonproportional models when introducing place-value concepts? A) Models do not physically represent 10 times larger than the one. B) Models like abacus are hard to learn how to use. C) Models like money provide more conceptual than procedural knowledge. D) Models do not engage the students as much as the proportional models.
Answer: A) Models do not physically represent 10 times larger than the one.
What is the major challenge for students when learning about three-digit numbers? A) Students are not clear on reading a number with an internal zero in place. B) A different process is used than how students learned with two-digit numbers. C) Students are not competent with two-digit number names. D) An instructional process that values quick recall and response.
Answer: A) Students are not clear on reading a number with an internal zero in place.
The multiplicative structure of a number would help students in acquiring skill in all of the following EXCEPT: A) Writing numbers greater than 100. B) Reading large numbers. C) Knowing ten in any position means a single thing. D) Generalizing structure of number system.
Answer: A) Writing numbers greater than 100.
The statement below are all helpful when guiding students to conceptualize numbers with 4 or more digits EXCEPT: A) Students should be able to generalize the idea that 10 in any one position of the number result in one single thing in the next bigger place. B) Because these numbers are so large, teachers should just use the examples provided in the mathematics textbook. C) Models of the unit cubes can still be used. D) Students should be given the opportunity to work with hands-on, real-life examples of them.
Answer: B) Because these numbers are so large, teachers should just use the examples provided in the mathematics textbook.
What mathematical representation would help students identify patterns and number relationships? A) Blank number line. B) Hundreds chart. C) Place value chart. D) 10 × 10 Multiplication Array.
Answer: B) Hundreds chart.
Complete this statement, "Number sense is linked to a complete understanding of..." A) Problem solving. B) Place-value. C) Base-ten models. D) Basic Facts.
Answer: B) Place-value.
What would be a strong indication that students are ready to begin place-value grouping activities? A) Students understand counting by ones. B) Students have had time to experiment with showing amounts in groups of twos, fives and agree that ten is a useful-sized group to use. C) Students have only worked with small items that can easily be bundled together. D) Students are able to verbalize the amounts they are grouping.
Answer: B) Students have had time to experiment with showing amounts in groups of twos, fives and agree that ten is a useful-sized group to use.
A calculator activity that is good assessment to see whether students really understand the value of digits is titled "Digit Change." Students must change one number without putting in the new number. What place value would a student need to know in order to change 315 to 295? A) Ones. B) Tens. C) Hundreds. D) Tens and ones
Answer: B) Tens.
Describe an activity that would help students to better conceptualize very large numbers. How would this activity build conceptualization? (essay question)
Answer: Better conceptualization of large numbers by creating references 1. Paper models of base ten can be taped together to make larger models 2. Chalk lines on the playground to make 100 meters × 10 3. 10,000 grid paper 4. collections of some type of object 5. activities that can involve distance and time (Literature Connections)
As students become more confident with the use of place value models they can represent them with a semi-concrete notation like square-line-dot. What number would be represented by 16 lines, 11 dots and 5 squares? A) 16,115 B) 5,171 C) 671 D) 32
Answer: C) 671
All of the activities below would provide opportunities for students to connect the base-ten concepts with the oral number names EXCEPT: A) Using arrays to cover up rows and columns and ask students to identify the number name. B) Lie out base-ten models and ask students to tell you how many tens and ones. C) A chain of paper links is shown and students are asked to estimate how many tens and ones. D) Students need to show with fingers how to construct a named number.
Answer: C) A chain of paper links is shown and students are asked to estimate how many tens and ones.
Base ten riddles engage students in what type of mathematical demonstration? A) Part-part-whole representation. B) Commutative representation. C) Equivalent representation. D) Nonproportional representation.
Answer: C) Equivalent representation.
The ideas below would give students opportunities to see and make connections to numbers in the real world. The statements below identify examples that would engage students with large benchmark numbers EXCEPT: A) Measurements and numbers discovered on a field trip. B) Number of milk cartons sold in a week at an elementary school. C) Number of seconds in a month. D) Measurement of students' height in second grade.
Answer: C) Number of seconds in a month.
The statements below are true of patterns and relationships on a hundreds chart EXCEPT: A) Count by tens going down the far-right hand column. B) Starting at 11 and moving down diagonally you can find the same number in the ones and tens place. C) Starting at the 10 and moving down diagonally the numbers increase by ten. D) In a column the first number (tens digit) counts or goes up by ones as you move down.
Answer: C) Starting at the 10 and moving down diagonally the numbers increase by ten.
What is the valuable feature of what hundred charts and ten-frame cards demonstrate? A) The meaning behind the individual digits. B) The identity of the digit in the ones place and in the tens place. C) The distance to the next multiple of ten. D) The importance of place-value.
Answer: C) The distance to the next multiple of ten.
The mathematical language we use when introducing base-ten words is important to the development of the ideas. Identify the statement that consistently connects to the standard approach. A) Sixty-nine. B) Nine ones and 6 tens. C) 6 tens and 9. D) 6 tens and 9 ones.
Answer: D) 6 tens and 9 ones.
Three section place-value mats can help students see the left to right order of the pieces. What statement below would correctly depict 705? A) 7 hundred blocks and 5 tens. B) 7 hundred blocks and 0 tens. C) 7 hundred blocks and 0 units. D) 7 hundred blocks and 5 units.
Answer: D) 7 hundred blocks and 5 units.
What does the relational understanding of place value begin with? A) Counting by ones and saying and writing the numeral. B) Counting by ones, making a model and saying and writing the numeral. C) Counting by tens and ones and saying and writing the numeral. D) Counting by tens and ones, making the model, saying and writing the numeral.
Answer: D) Counting by tens and ones, making the model, saying and writing the numeral.
All the examples below are examples of proportional base-ten models EXCEPT: A) Counters and cups. B) Cubes. C) Strips and squares. D) Money.
Answer: D) Money.
Place-value mats provide a method for organizing base-ten materials. What would be the purpose of using two ten-frames in the ones place? A) Show the left-to-right order of numbers. B) Show how numbers are built. C) Show that there is no need for regrouping. D) Show that there is no need for repeated counting.
Answer: D) Show that there is no need for repeated counting.
What are proportional models and discuss how they can contribute to students understanding of place-value? (essay question)
Answer: What are proportional models and how do they contribute to conceptual understanding? 1. Most clearly reflect the relationship of ones, tens and hundreds 2. Ten can be made from the single pieces 3. Pre-grouped models cannot be taken apart or put together 4. 10 single pieces must be traded or exchanged for a ten 5. Ten frames show the distance to the next ten All of the models provide physical evidence and practice with the concept of the ten-to-one relationship.
