Renaming Numbers
(Beginning Subtraction)
Objective/Goal: Students will learn to connect the abstract representation of regrouping, by creating a
model of a numeral using base-10 blocks. Students will draw the representation in their notebooks and then
show the representation of regrouping one ten.
Touch on These Benchmarks
K.1.1.1, K.1.1.2, K.1.1.3, K.1.2.1, K.1.2.2
1.1.2.1, 1.1.2.2
2.1.2.1, 2.1.2.2
Benchmark Emphasized
Subtraction
1.1.2.2 Compose and decompose numbers up to 12 with an emphasis on
making ten.
2.1.2.1 Use strategies to generate addition and subtraction facts including
making tens, fact families, doubles plus or minus one, counting on,
counting back and the commutative and associative properties. Use the
relationship between addition and subtraction to generate basic facts.
Possible Misconceptions from Scimathmn.org:
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The number sentences in a fact family are isolated facts. Students may not recognize the
relationships between addition and subtraction.
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Estimation means the "correct" answer.
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The only correct format for a problem is a + b = c or a - b = c, not recognizing that it can also be
c = a + b or c = a - b.
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A number can be decomposed in only one way. For example, they see 47 as 40 + 7, but not 30 +
10 + 7.
Materials:
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Base-10 blocks
Math notebooks
Student Sentence Frames
Vocabulary card: Sum, Regroup, Subtract, Difference, Ones, Tens, and Numeral visible to
students
Pencil
Directions:
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Given a two-digit numeral, students represent the numeral using base-10 blocks.
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Students draw this representation in their math notebook and show the sum (prove the
quantity is the same.)
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Students then regroup one ten into ten ones with the base-10 blocks.
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Students draw this second representation in their math notebook by crossing out one ten and
adding ten ones to the ones column.
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Students represent the regrouping by crossing out one ten and recording the new number of
tens above the representation.
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Students then prove that the quantity is the same by adding this representation.
Purposefulness of Chosen Problems:
By counting objects first by ones, then grouping objects and checking to see that the quantity remains
the same, and finally grouping by tens with ones “left over”, students acquire the necessary conceptual
skills for understanding place value and get a clearer sense of how to rename numbers (when
subtracting) or regroup them (when adding) when using the traditional or an invented algorithm.
Student Math Notebooks
Written at the top of the page: Renaming Numbers
Examples: (see the illustrations below.) Students draw a picture to represent their base-10 example.
Given the numeral 52:
Note: Another way to represent the regrouping and the quantity is the same:
Other Numbers to Use:
36 (practice organizing more than 5 in ones place)
40 (seeing the renaming as a group of ten)
22 (practice organizing less than 5 in ones place)
19 (important to solidify understanding of teen numbers)
Directions for Partner Work:
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Once all students in the flex group have explained their thinking, students continue the activity
with their partner.
Students decide who is Partner A and who is Partner B.
Give students a stack of cards using only cards 0-9. Partner A chooses two cards to represent the
first 2 – digit number that Partner A will use and Partner B will check for accuracy.
Once the number is chosen, students create the base-10 model to represent this number.
Partner A and B check their partner’s model to verify that they are the same.
Partner A describes the numeral using the Student Sentence Frame below.
Both Partners draw the representation in their notebook and show the sum.
Both Partners then regroup one ten into ten ones with the base-10 blocks.
Partner A describes the regrouped numeral using the Student Sentence Frame below.
Both Partners draw this second representation in their math notebook.
Both Partners represent the regrouping by crossing out one ten and recording the new number of
tens above the representation.
Both Partners then prove that the quantity is the same by adding this representation.
Student Sentence Frames: (what the students say to each other)
• Who is Partner A and who is Partner B?”
• Partner A: “My numeral is 52. I have 5 tens and 2 ones. “
• Partner B: “When you add ___ tens and ___ ones, the sum is ____________.”
• Partner A: “I regrouped one ten so now I have ______ tens and _____ ones.”
• Partner B: “When you add ___ tens and ____ ones, the sum is ___________.”
Vocabulary Cards
sum
sum
sum
regroup
regroup
regroup
subtract
subtract
subtract
difference
difference
difference
tens
tens
tens
numeral
numeral
numeral
ones
ones
ones
Student Sentence Frames for Renaming Numbers
Student Sentence Frames: (what the students say to each other)
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“Who is Partner A and who is Partner B?”
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Partner A: “My numeral is 52. I have 5 tens and 2 ones. “
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Partner B: “When you add ___ tens and ___ ones, the sum is ____________.”
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Partner A: “I regrouped one ten so now I have ______ tens and _____ ones.”
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Partner B: “When you add ___ tens and ____ ones, the sum is ___________.”
Student Sentence Frames: (what the students say to each other)
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“Who is Partner A and who is Partner B?”
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Partner A: “My numeral is 52. I have 5 tens and 2 ones. “
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Partner B: “When you add ___ tens and ___ ones, the sum is ____________.”
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Partner A: “I regrouped one ten so now I have ______ tens and _____ ones.”
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Partner B: “When you add ___ tens and ____ ones, the sum is ___________.”
Student Sentence Frames: (what the students say to each other)
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“Who is Partner A and who is Partner B?”
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Partner A: “My numeral is 52. I have 5 tens and 2 ones. “
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Partner B: “When you add ___ tens and ___ ones, the sum is ____________.”
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Partner A: “I regrouped one ten so now I have ______ tens and _____ ones.”
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Partner B: “When you add ___ tens and ____ ones, the sum is ___________.”
Student Sentence Frames: (what the students say to each other)
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“Who is Partner A and who is Partner B?”
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Partner A: “My numeral is 52. I have 5 tens and 2 ones. “
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Partner B: “When you add ___ tens and ___ ones, the sum is ____________.”
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Partner A: “I regrouped one ten so now I have ______ tens and _____ ones.”
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Partner B: “When you add ___ tens and ____ ones, the sum is ___________.”
Student Sentence Frames: (what the students say to each other)
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“Who is Partner A and who is Partner B?”
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Partner A: “My numeral is 52. I have 5 tens and 2 ones. “
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Partner B: “When you add ___ tens and ___ ones, the sum is ____________.”
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Partner A: “I regrouped one ten so now I have ______ tens and _____ ones.”
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Partner B: “When you add ___ tens and ____ ones, the sum is ___________.”