Place Value Curriculum Map (published version)

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Place Value Curriculum Map Grades K-2
Becky Kimball

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The topic for this curriculum map is place value. In the Utah Core State Standards, math
standards about place value is placed under the domain of numbers and operations in base ten
(Utah State Office of Education, 2010). Teaching about place value starts in kindergarten and
proceeds throughout elementary school grades. While there is several standards about place
value, I will only cover one place value standard per grade in this paper. Standards, skills,
assessments about teaching place value regarding ones and tens for numbers 11 to 19,
hundreds and two digit and three digits numbers for grades K to 2 is covered in this curriculum
map.
The kindergarten standard for place value is under the cluster, “Work with numbers 11–
19 to gain foundations for place value.” (Utah State Office of Education, 2010, p.13). The
kindergarten students are introduced to numbers 11 to 19 naming the numbers, grouping
objects to represent the numbers, and reading and writing the numbers 11 to 19. When the
children have mastered these skills, they are ready to be introduced to place value. The
standard K.NBT.1 is written “Compose and decompose numbers from 11 to 19 into ten ones
and some further ones, e.g., by using objects or drawings, and record each composition or
decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are
composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.” (Utah
State Office of Education, 2010 p. 13 ).
The students learn the skills to group the objects representing the numbers 11 to 19
into groups of tens and ones. For example, for the number 14, the children would create a
group of ten objects and a group of 4 objects, counting out the objects as the objects are

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grouped together. The children would need to identify the collections of objects as a group of
ten ones and a group of four ones. The children would then be able to see that the group of
ten plus the group of four represents fourteen. The children then learn to work with drawings
of the groupings to record the grouping.
Children will also be taught skills to decompose the groups of objects. The children
could be given a group of 15 objects and sort the objects into a groups of ten and 5. The
children could count the groups of ten objects and five objects. The children remove one of the
group of ten objects. The children could then count the remaining group of five. The children
could see how 15 minus 10 equals 5. Drawings of the groupings could also be used. The
children would then be taught to read and write the equation 15-10=5 .
The standard 1.NBT.2 is about place value for first graders. The standard is “Understand
that the two digits of a two-digit number represent amounts of tens and ones. Understand the
following as special cases: a. 10 can be thought of as a bundle of ten ones—called a “ten.” b.
The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven,
eight, or nine ones. c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three,
four, five, six, seven, eight, or nine tens (and 0 ones)” ((Utah State Office of Education, 2010 p.
16).
The children in first grade learn the skills to work with place value in creating
representations of two digit numbers in the tens and ones. The first grade students learn that
the placement of a number in a two digit number determines the value of the number. In the
ones place, the numbers are 0-9 representing the number of ones in a group. However in the

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tens place of a two digit number, the students learn a something special. The number is no
longer a one or a set of ones, but the number represents a set or sets of ten. The students
learn to identify multiple sets of ten by the number in the tens place and the number of ones in
the tens place in a two digit number. They learn that zero is place holder for when there is no
groups of ones, just groups of ten.
This concept of place value grows to include the 100’s place in three digit number for
students in second grade. For the second grade students, the standard, 2. NBT.1 states,
“Understand that the three digits of a three-digit number represent amounts of hundreds, tens,
and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special
cases: a. 100 can be thought of as a bundle of ten tens—called a “hundred.” b. The numbers
100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight,
or nine hundreds (and 0 tens and 0 ones).
Second grade students learn skills about the 100’s place value in three digit numbers.
They already understand about place values for 10’s and ones, and now add on how to work
with a 100 place value in three digit numbers. The children come to learn the 100’s place
represents a grouping of ten tens. Ten tens equal 100. They need to apply the knowledge of
using zero as a place holder for when no groups of tens or ones are in the number. 100 is a
group of ten tens, 0 tens, 0 ones. They then learn to apply this to other numbers above 100 all
the way up to 900. The children also apply their knowledge of tens and ones to three digit
numbers by combining this with the knowledge of 10 tens make up 100. The children learn the
place value for 100, tens and one in a three digit number. 145 is a group of 100, 4 tens, and 5

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ones. They learn to read and write these numbers using place value which becomes valuable
knowledge to use in learning to add and subtract three digit numbers.
A number of formative assessments are available for the teacher to use in teaching and
evaluating the understanding of the students about place value concepts and skills. I am
including some observational questions for the teacher while working with the students.
Some observational questions for kindergarten during teaching activities include Are
the children grouping objects into a set of ten and a set of ones, counting the objects in each
group for a given number? Can they place a number card with the correct number in front of
the objects? Can they write the number? Can they write the correct numbers in the equation
for a total number and the numbers for a group of ten and a group of ones? Can they write the
correct symbol for the equations?
For first grade, the teacher observes if the students are able to identify the two digit
numbers as a set or set(s) of ten and a group of ones. The students may be working with
manipulative objects, so the teacher will have to look for the correct number of manipulative
objects in a object group the students are working with. The teacher will also need to observe
if the students are writing the numbers correctly during math sessions. Students can confuse
numbers with teen or ty at the end of a number, so teachers need to watch for this problem
(Rivera, 2014).
The second grade teacher will need to observe if the students are applying the concepts
of place value in the 100s. They also need to look for the student’s use of zero as a place

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holder. According to Riveria (2104), students often will skip the zero as a place holder in three
digit numbers while writing, resulting in one hundred fifteen being written as 15.
Formative and Summative Assessments Kindergarten
Number books- numbers between 11 and 19. The children have pages to glue the
number 11 on the page. The children put 11 stickers on the page. The process is repeated
each day with the next number in line ( 12, 13, 14, 15…19) with objects the children stick,
draw, paint or stamp pictures on the pages representing the numbers. When the page with 19
is completed, the pages are collected together. The children can choose the colors of the front
and backs of their books and decorate the fronts and backs of the books. Punch three holes in
all the fronts, backs, and pages. Thread colored yard through the holes on the pages to bind
the books. Number books are completed! Children can read their books with their parents.
Plan about 2 weeks for this activity.
Grouping fun. The teacher shows a number between 11 and 19 written on a card to a
small group of children. The students then count out the number on the card with objects into
a group. They group 10 of the objects onto a square. The children place a card with the
number 10 in front of the objects on the square. The rest of the objects are grouped into
another group on a circle. The children then count the number of objects in the smaller group
on the circle. The children place a card with the number of objects circle. The teacher and
children count all the objects in both sets to confirm the number is the same, even divided into
a group of ten and ones. The process is repeated with another number and more objects to
group. Once the children learn the process, they can do the activity on their own.

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To extend the activities, add some cards with a plus signs and equal signs. After placing
down the number cards, have the children put the plus sign between the numbers and the
equal sign after the numbers and the final number after the equal sign. Talk about how
__+___=____ . The children can write the equation on a paper using markers, crayons or
pencils.
Decomposing numbers 11-19 can be taught by putting the ten objects on the square
and ones on the circle. Place the number in front of the groups. Put a minus sign next to the
number. The children can choose which group of objects to take away. Place the number of
objects being taken away next to the minus sign. Place an equal sign next to the number being
taken away. Count the number of objects left. Place that number after the equal sign. Talk
about how ____-__=__. The children can write the equation on a paper with markers, crayons,
or pencils.
Picture groups. On a sheet of paper a number of pictures divided into groups. There
are two lines under each picture. The numbers ten and ones is written under the lines. The
children must circle ten pictures of each picture group. With the children, the teacher counts
the number of pictures not circled in each group. The children then write the counted number
in the ones place on the two lines. The teacher and children count the group of ten (which will
be one) in each group and write the number one in the tens place on a line under the picture.
Talk about how the number in that place represents one group of ten. Name the number
written.

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Number cards and Object groups (Summative assessment). Show a number card
between 11 and 19. The children are to count out the number, sort into a group of ten and a
group of ones, and write the equation on paper.
First Grade Formative Assessments
Legos Bundling the 10’s. With a group of legos the children are to put together groups
of ten legos. They can build up the legos in a line, or create a shape out of ten legos. The
group must contain 10 and only 10 legos. After the children finish putting their groups
together, they count the number of lego groups. Any extra legos are put back into the box of
legos. They are to write down the number of lego groups and then add zero to the number.
Have the children name their number.
Legos, bundling the 10’s plus ones. With the lego tens groups and leftover legos, have
the children counting the number of legos left over that did not fit into their groups of ten.
Have the children write down the number of leftover legos next to their groups of ten number.
Name the number.
Writing equations for bundling the tens and bundling the tens plus ones. The
children write down the number on paper for their tens bundles, write a plus sign, write the
number for the ones legos, write and equal sign and then the total number of legos.
Chicken Scratch Pictures- Tens and Ones. When the teacher shows a picture of bundled
ten objects and some single objects, have the children write down a x for each ten bundle and a
line for each object not in a bundle. On a paper is written lines with tens and ones written

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under them. Count the number of x’s and place the number in tens place. Count the number
of lines and put the number in the ones place. Name the number.
Boxes for writing an expanded version of an addition or subtraction equation could be
on the paper. There could be a place for the equation too.
Second Grade Assessments
Treasure Chest Game. A treasure chest picture is on a card stock or on foam board.
Several of the treasure chest pictures can be made for groups of children playing. Many
papers in the shapes of diamonds, rectangular gems, and circular gems are placed in groups
nearby. The diamonds are labeled with one hundred, the rectangular gems have a 10 and the
circular shapes have a one. The children can choose several of each type to place on the
treasure chests up to 9 gems each.
When the gems are in place, the children then count the number of each gem on the chest.
They then use a laminated card stock playing card with three boxes on the card next to each
other. With a dry erase marker the children write down the number of diamonds with one
hundred written on it, the number of rectangular gems with ten and the circular gems with
ones in the correct places for tens and ones. The children can then pull out another card with
a hundreds box +tens box+ones box= total number box.
100’s Book. The children are going to make a book of 100 using groups of ten. The
book will be an accordion book with the pages folding up like an according. Each sheet of paper
is folded in half. One edge of the page is taped to the edge of another page. Pages can be

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different colors. It will take about 5 papers to make a book. Each half of the paper is
considered a page. On each paper, the children will put 10 pictures on the page. The children
can draw, paint, stamp, color objects on the page. When the book is all put together, the
pages unfold like an accordion. The front of the book is the top page when the book is folded.
The children write 100 on the front and back pages and decorating as they please. Colored
masking tape can be used to tape the pages together.
Time frames for teaching place value varies from grade to grade. The Kindergarten
grade students learning about working with numbers 11 to 19 need to learn other concepts and
skills first. I would begin to introduce the place value later in the school year, starting
approximately in April depending on the readiness of the students and working on place value
through the rest of the year. Perhaps teaching the children in small groups depending on their
developmental readiness is a good practice. The first grade students are ready to start place
value towards the beginning the school year with a review of number concepts from
kindergarten. Learning place value concepts at the first of the year is good to build up skills
that work well with addition and subtraction concepts. The place value concepts and skills
could be applied throughout the whole school year while working with a variety of number
concepts and algebraic operations. Second grade place value concepts and skills are also good
to start with at the beginning of the year and applied throughout the school year while working
with number concepts and algebraic operations.
Place value is an especially useful skill in learning to add and subtract three digit
numbers. I only covered one standard in each grade introducing place value. There are other

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standards regarding place value that are good to teach and have the children apply in their
lessons throughout the school curriculum. Place value is an especially useful skill in learning to
add and subtract three digit numbers. Place value is an important concept and skill to teach the
children through many different types of activities that the children can learn and enjoy
learning at school.

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References
Rivera, F. D. (2014). Teaching to the Math Common Core State Standards : Focus on
Kindergarten to Grade 5. Rotterdam: Sense PubliAunola, K., Leskinen, E., Lerkkanen, M.,
& Nurmi, J. (2004). Developmental Dynamics of Math Performance From Preschool to
Grade 2. Journal Of Educational Psychology, 96(4), 699-713. doi:10.1037/0022-
0663.96.4.699
Utah
State
Office
of
Educati
on,
(2010).
Utah
Core
State
Standar
ds for
Mathe
matics.
Retriev
ed from
http://www.uen.org/core/core.do?courseNum=4210

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Appendix
Curriculum Map, Place Value, Grades K-2
Boxes page
Tens and Ones page

Place Value Curriculum Map (published version)

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