Adding and Regrouping
NCTM Principles and Standards for School Mathematics
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Uses models to develop an understanding of place value and the base-ten number system
Connects words and numbers to the quantities they represent using various
representations
Recognizes equivalent representations of the same number and generates them by
composing and decomposing numbers
Develops and uses strategies for whole number computations
Uses a variety of methods and tools for computing with whole numbers, including objects
and paper and pencil
Grade Level: 2-3 (Ages 7-9)
Teacher Instructions
Students often memorize procedures for working with multi-digit numbers, such as “carrying”
and “borrowing,” without a conceptual understanding of such procedures in the context of place
value. In this Kidspiration® activity, students will work with Kidspiration Base Ten Blocks ™
and solve multi-digit addition problems with visual models. They will discuss and translate their
models to the standard procedure, and learn about regrouping as it relates to place value.
1. Open Adding with Regrouping.kia from Kidspiration Starter>Activities>Math.
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©2008 Inspiration Software, Inc.
Adding and Regrouping
The first page of the activity
is an example. It may be
helpful to walk through the
example from the beginning
as a class. If so, the first
page of the activity can be
unlocked ahead of time
from the Teacher menu,
allowing deletion of the
base ten blocks and text
inside the blue explanation
box. From the Math
palette, bring out base ten
blocks to represent each
addend, distinguishing them
with color. Ask the class
how many ones are present.
Is it possible to regroup?
Select 10 ones and use the
Group button on the bottom
toolbar to exchange or
regroup the ones for 1 ten.
Ask students where on the
place value mat the ten
should live, moving as needed.
Now how many tens are
present? Is it possible to
regroup the tens?
represent each addend
regroup to “make tens”
Collaborate as a class to
write an explanation of the
steps used to solve the
problem in the blue
explanation box, as well as
the solution.
“carry a one”
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Adding and Regrouping
2. Complete the same problem on the board or overhead projector without manipulatives. If
students are familiar with the standard procedure for adding multi-digit numbers, discuss
the relationship between each step of the procedure to the model that they just used. How
does starting at the right, recording a 2 and “carrying a 1” relate to their model with base
ten blocks? What does “carrying a 1” mean in the context of place value?
3. For pages 2-4 of the activity, assign students to work in small groups or independently,
depending on computer availability.
4. Re-convene as a class and go over each problem in the activity, paying special attention
to the order in which steps are taken, when and why regrouping does or does not occur,
and the relationship between the standard procedure and the visual model. Are ten ones
equivalent to 1 ten? What does “carrying” really mean? Does regrouping always occur
with ones, or can it occur in other columns?
Assessment
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Assess students’ process and accuracy during independent work, as well as their
contributions to the initial problem and class discussions.
Completed activities can be assessed for completion and correctness, paying careful
attention to correct use of regrouping and a thorough explanation of steps taken. See
Regrouping Exemplar.kid for a sample completed activity.
Individual students can present their solutions to the three problems. Presenters can be
assessed on the accuracy of their solution and the description of their process to the class.
Lesson Adaptations
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Increase the level of difficulty by adding and interspersing pages containing problems
that require regrouping twice and problems that do not require any regrouping.
Include problems that deal with thousands by choosing a four-column place value mat.
Delete the blocks on each page of the activity, requiring students to represent each
addend by bringing out the appropriate blocks and distinguishing them with color.
If the activity is used as a starting point for learning the standard procedure for adding
multi-digit numbers, facilitate a discussion in which students begin to develop their own
procedures after working with the visual models.
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©2008 Inspiration Software, Inc.