What is your Base-10 IQ?
Understanding the concept and algorithm of base ten is an important step in a student’s
foundation of addition and subtraction in mathematics. By continuously verbalizing the
words associated with a multi-digit number, written form, place value, and base ten
blocks through various activities, you are helping to build a strong foundation. When a
student comprehends the base-10 and place value algorithms, his or her ability in
adding or subtracting multi-digit numbers is more accurate (Fuson & Briars, 1990).
 South Carolina College and Career Ready Standards for Mathematics
 K.NS.6 Recognize a quantity of up to ten objects in an organized
arrangement (subitizing).
 K.NS.7 Determine whether the number of up to ten objects in one group is
more than, less than, or equal to the number of up to ten objects in
another group using matching and counting strategies.
 K.NS.8 Compare two written numerals up to 10 using more than, less than
or equal to.
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K.NSBT.1 Compose and decompose numbers from 11 – 19 separating
ten ones from the remaining ones using objects and drawings.
K.ATO.2 Solve real-world/story problems using objects and drawings to
find sums up to 10 and differences within 10.
K.ATO.3 Compose and decompose numbers up to 10 using objects,
drawings, and equations.
K.ATO.4 Create a sum of 10 using objects and drawings when given one
of two addends 1 – 9.
 1.NSBT.1 c. read, write and represent numbers to 100 using concrete
models, standard form, and equations in expanded form.
 1.NSBT.2 Understand place value through 99 by demonstrating that:
o a. ten ones can be thought of as a bundle (group) called a “ten”;
o b. the tens digit in a two-digit number represents the number of
tens and the ones digit represents the number of ones;
o c. two-digit numbers can be decomposed in a variety of ways
(e.g., 52 can be decomposed as 5 tens and 2 ones or 4 tens and
12 ones, etc.) and record the decomposition as an equation.
 1.MDA.4 Collect, organize, and represent data with up to 3 categories
using object graphs, picture graphs, t-charts and tallies.
 1.MDA.5 Draw conclusions from given object graphs, picture graphs, tcharts, tallies, and bar graphs.
 2.NSBT.1 Understand place value through 999 by demonstrating that: a.
100 can be thought of as a bundle (group) of 10 tens called a “hundred”;
b. the hundreds digit in a three-digit number represents the number of
hundreds, the tens digit represents the number of tens, and the ones digit
represents the number of ones; c. three-digit numbers can be
decomposed in multiple ways (e.g., 524 can be decomposed as 5
hundreds, 2 tens and 4 ones or 4 hundreds, 12 tens, and 4 ones, etc.).
 3.NSBT.4 Read and write numbers through 999,999 in standard form and
equations in expanded form.
 South Carolina College and Career Ready Standards for Language Arts
 W Standard 2-2.1 Use a combination of drawing, dictating, and writing to
compose informative/explanatory texts that name and supply information
about the topic.
 Grade 2, MC 1.2 Apply the skills of taking turns, listening to others, and
speaking clearly.
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Grades 1 and 2, MC 1.4 Participate in shared conversations with varied
partners about focused grade level topics and texts in small and large
groups.
Grade 4, LCS Standard 10.1 Use definitions, examples, and restatements
to determine the meaning of words or phrases.
Baker, C. & Ward, J. (2015). Base Ten and Place Value. National Council of
Teachers of Mathematics. Retrieved from
http://www.nctm.org/uploadedFiles/Conferences_and_Professional_Development
/Institues/Pre-K-Grade_5_Number_and_Operations/
Base10%20and%20PlaceValue%20finalslides.pdf
This presentation slide is a wonderful tool that walks through a workshop, goals,
concepts, definitions, developments, concept of place value. It shares the importance
of students learning to first count by ones, and tens, then being able to group ones and
tens. It shares the significance of presenting physical models through the area of focus,
including samples of what it said to be groupable or proportional. One students have
grasped these concepts they are able to move into decomposition of numbers. By
posing these concepts in a logical order you are guiding your students to flexibility and
computational proficiency in mathematics.
This is a wonderful presentation slide. There are so many ways to introduce various
points to one comprehending place value and base 10 concepts, to activities, to
assessing with a higher order thinking cartoon. For any student who may be struggling,
this presentation offers numerous jumping points to help reinforce understanding.
BBC: Penguins and Place Value. (2014).
http://www.bbc.co.uk/schools/starship/maths/games/place_the_penguin/small_so
und/standard.shtml
Interactive game where the player must drag a penguin into the proper place value:
tens or ones. At the end of the game, student’s results can be printed for assessment.
Duke, S. (2013). What’s the Place Value? North Mankato, MI. Rourke Educational
Media.
Duke writes and illustrates the meaning of the tens place and the ones place. Her
bright and colorful ice-pop illustrations provide a visual that reinforce the words. When a
count of 10 pops is obtain they are grouped, tied up, together. This group makes 1 set
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of ten and therefore it no longer belongs in the one’s place. The set of ten’s must shift
left into the ten’s place.
Fuson, K. C., & Briars, D. J.. (1990). Using a Base-Ten Blocks Learning/Teaching
Approach for First- and Second-Grade Place-Value and Multidigit Addition and
Subtraction. Journal for Research in Mathematics Education, 21(3), 180–206.
http://doi.org/10.2307/749373
A wonderful study in how to help students comprehend and utilize the base ten
concept. Research stressed that even though some children are able to properly carry
out algorithms procedurally correct they do not understand the reasons for the crucial
aspects of the procedure or they are unable to give the proper values of the numbers
they were writing down. Study emphasizes the importance of utilizing three word parts:
four thousand as four big cubes, two hundred as two flats, fifty as five rods, seven as
seven units, ‘4,257,’ and 4, 2, 5, 7 in their proper place value. By incorporating these
three word sets, students will be able to add and subtract multi-digit numbers more
accurately. Pre-assessments displayed that only 9 of 169 students were able to
demonstrate any understanding of trading. After instruction, with continuous modeling
and verbalization of the three sets, 160 out of 169 participants were now able to
demonstrate their ability to trade.
For a four day lesson, this study revealed the importance of creating a proper and
effective foundation four students to grow from.
Georgia standards of excellence frameworks. (2015). Retrieved from Georgia
Department of Education website https://www.georgiastandards.org/GeorgiaStandards/Frameworks/2nd-Math-Unit-1.pdf
I enjoyed the variety of activity lessons presented. These activities may be utilized for
one’s whole class, small groups, or pairs. There are numerous fun ideas that target
various academic levels. Con: Frequently, books are referenced that you wish you had
a copy of to fully comprehend what the topic referred to.
Neuschwander, C. (2009). Sir Cumference and All the King’s Tens. Watertown,
MA. Charlesbridge.
When trying to count all the countryside people who showed up for the kings surprise
party, Sir Cumference tried having random groups call out their numbers to be added
and summed together. The numbers were too random and cumbersome that they
continued to find an easy way to count all those in attendance. Finally, they realize that
by counting by 10s, in groups of 10, 100, and 1000, they could very easily tally the large
number.
I enjoyed how the characters behaved like we would when trying to count large
numbers. We seemed to always try to count straight forward, 1 to the very end count.
This book helps students see that though it may seem to be quicker, to count from 1 to
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the end, ultimately, it is best and more accurate to group our items in groups of tens and
hundreds before we sum the items up.
Poskitt, K. (1999). Murderous Maths. New York, NY. Scholastic Ltd.
Murderous Maths a wide variety of mathematical topics. The focus is on the history of
mathematic and why digits are easier to rationalize compared to that of utilizing Roman
numerals or an abacus. It explains how the 10 system works. How if you put the
numbers in various order, the number is different.
This book provides a great introduction to new mathematical topics. Sharing the
history of mathematics, compared to how it was done a hundred years ago, may help
students understand why we now solve problems with the current techniques they are
taught.
Quirk, L. (2015). Learn Zillion: How to decompose numbers video [Video
Segment]. https://learnzillion.com/lessons/2465-add-by-decomposing-numbers
Quirk provides a wonderful video that focuses on common misunderstands that occur
when one must break apart a number and put its parts in the appropriate place value.
Numbers are ‘decomposed’ to help illustrate how to add two digits numbers together.
This in turn helps students visualize and keep the tens organized while also keeping the
ones organized. By adding the sum of the tens with the sum of the ones, the digits are
maintained in their appropriate place values.
R., M. (2011). Place value math song: ones, tens, hundreds [Video Segment].
Available from https://www.youtube.com/watch?v=5W47Gh7myY&list=RD5W47G-h7myY
Mr. R provides a simple yet fun sing along video for students to learn about place
value. He demonstrates how counting 10 units you now have found what’s next,
and must move to the left (into the tens columns). He continues on by counting by
10s to see what is next (100, move left into hundreds). This is a kid friendly video.
Simple enough for younger students to understand and relate to. Tune is soft and
friendly helping to motivate students with a ‘you can do this’ too melody.
Smith, A. (2015). How to write Expanded Form [Video segment].
https://learnzillion.com/lesson_plans/8095
Smith walks students through this video in how to write a standard number in
expanded form. Video’s pace is slow enough for students to take notes on as they
watch and listen. It is not so slow that students would lose interest. The number is also
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demonstrated with the usage of Base-10 illustrations. With this Base-10 visual, zero is
displayed in the tens place, therefore, there were no rods in the illustration.
I love how Ms. Smith starts with the written form. She then adds the visuals with Base10 manipulatives. From here, she adds the appropriate Base-10 blocks up to write the
number out in expanded form.
Sparagna-LoPresti, A. (2013). A Place for Zero. Watertown, MA. Charlesbridge.
Zero seeks to find his identity in a community of numbers, addition, multiplication, and
infinite. He struggles to find his place among the other digits. Zero comes to realize his
importance through numerous additions and multiplications; he finds his place value.
I enjoyed how this book personified the numbers. We all strive feel important. It is a
story the students can easily relate to as well as learn from. Zero specifies the place
from where a group has just repositioned to the next place.
SplashMath.com, https://www.splashmath.com#sthash.r8y5xCq.dpuf
This is a wonderful site to not only reinforce your students’ academic abilities but also
assess each of their abilities. For 3rd graders, you may gain insight into how your class
is fairing their understanding of place values and expanded form, but also in rounding
their numbers to the nearest tens and or nearest hundreds.
You are required to register with a user name and password. As a teacher, the site
requests that you upload your class roster. You will be provided with a ticket for each
student. Each ticket provides the URL address, username and password for each
student named you provided in your roster. As your students utilize this site, you will
gain access to the number of problems each students answered, the overall class
accuracy, time spent, student performance, and the classrooms performance.
The Classroom Basic site is free. Premium access can be free for two months if you
invite 3 colleagues look into this site. If you continue to invite colleagues you may earn
up to 6 months of Classroom Premium which enables access to the site on your
classrooms IPad and access from your student’s home computers.
Top Marks: Place Value Charts. (2015). http://www.topmarks.co.uk/placevalue/place-value-charts
Interactive game where students find numbers in expanded form and standard form
and then they must put the digits in their appropriate place value. The reinforcing can be
utilized in just ones and tens or hundreds, tens, ones, and hundredths.
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This site also provides an interactive whiteboard mode that awards an invaluable
teaching aid. This aid provides the teacher to reset a question at any time so that
additional modeling may be inserted.
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