Critical Foundations, Part 2
back! As noted in my previous post and worth repeating here, to me, the
“signature expectation” of any pre-K–grade 6 mathematics experience is the
ongoing nurturing and development of a sense of number, and the ongoing
instructional development and understanding of place value and fraction
equivalence (I refer to these as pillars of a sense of number sense) are must-haves
for all mathematics learners.
blog entry, I offer additional activities and tasks that connect place value to
mathematics topics within a continuum that begins with counting and essentially
extends counting to understanding numbers greater than 9, then presents the
need for a direct focus on place value related to two-digit whole numbers, and
extends to comparing and ordering such numbers as well as early work with
addition and subtraction. I hope that what you will read below, and in the previous post will generate
discussion and a literal swap shop of comments and ideas of what works for you,
as well as questions to help all of us in our efforts to deepen place-value
provides additional activities and tasks and once again seeks your comments,
thoughts, and your own activities and ideas. Try
these new activities:
1. Turn-around numbers. Select any two-digit number (e.g., 67). Ask, “If
we turn the digits around, what is the new number?” (76) Have students try 89. Then
have them try 54. Ask, “How do you know when the turn-around number will be
larger than the start number? How do you know when it will be smaller?”
2. True or False? Such questioning promotes early work with
estimation. Have students represent the numbers with base ten materials, if
3. Digit Card Activities. (You will need digit cards with the digits 1–9
on the cards; 0 may be used at times, too.)
a. Have students draw a digit card (from digit
cards 1–9) and place that number of ones blocks in the ones column on a grid
like the one below. Then have them draw another card and place that number of
tens rods in the tens column. What is the new number? What is the number if you
took a one away? What is the number if you took a ten away?
b. Have students draw two digit cards from 1–9, using those two cards
to represent ones and tens digits. Ask, “What’s the largest and smallest
two-digit numbers that could be created?” Have students represent each number
using base-ten materials.
c. Have students think about the digit cards 1–9. If they drew two
cards, what would the smallest and largest two-digit numbers they could create?
What if a student drew three cards—What would be the smallest and largest
numbers that could be created?
think decimals now. Consider the following.
4. What’s Wrong? Have students discuss and show why the following are
5. Close to One. Have students determine which of the following is
closest to the number 1:
6. Ask students to share their thinking, perhaps comparing the
amounts using representations (possible representations: number lines or hundred charts).
sampling of place-value–related opportunities would not be complete without
some tasks for students to consider. Try the following.
7. Task: Which major league baseball stadium holds the largest crowd? The
smallest crowd? Have students go to http://ondeckcircle.wordpress.com/2013/10/14/major-league-baseball-stadiums-largest-to-smallest/ to find out. Then have them
complete the following:
8. Task: The number 3 is the smallest whole number greater than 2. But
is there a smallest decimal that is greater than 2? If so, what is it? If not,
why not? Have students discuss their solutions, which should provide an
interesting beginning to work with density of fractions, these particular
Once again, it’s your turn. An abridged rationale (see Place
Value—Part 1 for the full discussion) for the foundational importance of
place value and a half dozen +1 sets of
activities and tasks has been provided for you to consider. Try them.
you think? What works? How do you
develop place-value understandings? How does what you do connect to developing
the level of flexibility with number so necessary for developing and
establishing a sense of number?
As with the Place Value—Part 1 blog,
we want to hear from you! Post your comments below or share your thoughts on
Twitter @TCM_at_NCTM using #TCMtalk, or get to me personally on Twitter
@SkipFennell; or at firstname.lastname@example.org.
Feel free to visit the following websites for information, resources, or just
Fennell, email@example.com, is the L. Stanley Bowlsbey Professor of Education and
Graduate and Professional Studies at McDaniel College in Westminster, Maryland,
where he directs the Brookhill Foundation–supported Elementary
Mathematics Specialists and Teacher Leaders Project
(http://www.mathspecialists.org). He is a past president of NCTM and a
recipient of NCTM’s Lifetime Achievement Award. Skip is interested in the work
of mathematics specialists, implementation of the CCSSM, teacher education,
number and fraction sense, and educational policy.