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Chapter 10: Developing Whole-Number Place-Value Concepts
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
1) 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.
2) 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.
3) All the examples below are examples of proportional base-ten models EXCEPT:
A) Counters and cups.
B) Cubes.
C) Strips and squares.
D) Money.
4) 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.
5) 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.
6) 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.
7) All of the activities below would provide opportunities for students to connect the base-ten
concepts with the oral number names EXCEPT:
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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.
8) 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.
9) 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.
10) 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.
11) 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.
12) 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.
13) 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.
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14) 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.
15) 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.
16) 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.
17) As students become more confident with the use of place value models they can represent
them with a semi-concrete notations 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
18) 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.
19) 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.
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20) 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.
ESSAY. Write your answer in the space provided or on a separate sheet of paper.
21) Describe an activity that would help students to better conceptualize very large numbers.
How would this activity build conceptualization?
22) What are proportional models and discuss how they can contribute to students understanding
of place-value?
