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Chapter 11: Developing Whole-Number Place-Value Concepts
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
1) 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.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
2) 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.
3) Base ten blocks are the only material that should be used to model place value concepts.
4) Nonproportional models should be used only after students understand that ten units makes a “ten.”
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
5) 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
6) 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.
7) 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.
8) 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.
SHORT ANSWER. Write the word or phrase that best completes each statement or
answers the question.
9) 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.
10) 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.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
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.
SHORT ANSWER. Write the word or phrase that best completes each statement or
answers the question.
12) 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
13) 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.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
14) 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.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
15) 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.
ESSAY. Write your answer in the space provided or on a separate sheet of paper.
16) Describe an activity that would help your students to better conceptualize numbers that are very large.
Describe how this activity would build conceptualization.
