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Exploring Math:
Breaking Numbers Apart
in a Base-Ten System
Created by Patrice Covino and Megan Stein, 2013
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Solve.
27 + 42=
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Solving Strategies, Mathematical
Thinking
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27dffffffhhffffxxxxxxxxxxxxxxxwwwwwwwwwwwwwwwww+
42
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(20+40)+ (7+2)
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30 + 42 – 3
Goal: To provide children with a strong foundation in number
sense so they can work with numbers fluently.
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What is Base-Ten?
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Base-Ten is a “place value” system where any single digit
can represent a different value depending on it’s placement
in a number.
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Example:
Note the value of the digit 5 in each number below.
325
152
578
5 vs. 50 vs. 500
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Decomposing Numbers
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Children need a strong sense of numbers to be able
compose and decompose them comfortably.
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Decomposition/ Composition of Numbers:
325
300 + 20 + 5
Understanding
325
the place value of 325 entails knowing that:
is closer to 300 than 400
It
is 100 more than 225
It
is 25 more than 300
It
is 5 less than 330
It
is composed of 32 groups of ten and 5 ones
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How might this look in
Kindergarten?
16 =
10 + 6
1 group of tens and 6 ones
★★★★★★★★★★
★★★★★★
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Why learn about it as early as
Kindergarten?
Common Core Kindergarten Math Standards
Work with numbers 11–19 to gain foundations for place value.
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1. Compose and decompose numbers from 11 to 19 into a group of ten 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.
Becoming comfortable with Base 10 in Kindergarten allows
children to build a solid number sense foundation, which they
can later rely on as they approach more challenging work.
+ Kindergarten Base-Ten Goals Across the Year
Number and Operation in Base Ten
January
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June
March
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Explain that counting tells how many items there are altogether—when
counting, the last number tells the total number of items; it is a cumulative count
Understand that numbers exist in a specific order (number line)
Understand that a number corresponds with a group of objects and the
marching numeral
Create an equivalent set for a given number up to 10
Understand that the distance between any two consecutive counting numbers
on a given number line is one
Understand that we begin counting a set of objects with the number one
Understand that numbers can also be used to tell the position of objects in a
sequence and numbers represent a quantity
Count to 100 by ones and tens
Count on from a given number within 100
Count backwards from 20
Write numbers 30
Skip count by fives to 100
Skip count by twos to 20
Compare two written numbers between up to 10 using language such as
greater than, less than, or equal to
Compose and decompose numbers 11-19 into groups of 10s and 1s
Understand that zero is a number that represents a group with no object
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What does Base-Ten look like in
the classroom?
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Repeated counting practice and developing mental images for
quantities up to 10
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Days in School Count (by 1s, 2s, 5s, and 10s)
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Morning Meeting choral counting
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Ten Frames (games on Ten Frames- memory, build a number)
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Base-10 Blocks
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Connecting cube towers (one more, one less, ordering)
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Drawings organized for Base-Ten
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How can I support my child at
home?
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Provide FUN opportunities for your child to compose and
decompose numbers in the form of tactile or visual supports.
Consider using the following materials:
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Play-doh or Clay
Dried Pasta
Cereal, Pretzels, etc.
Markers, crayons, paper
Base 10 Flash Cards
Sponges cut into longs and cubes
Rekenrek- home-made or store-bought!