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Learning about Number
Relationships and Properties of Numbers Using Calculators and Hundred
Boards: Patterns to 100 and Beyond
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Patterns
to 100 and Beyond
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A major learning goal
for students in the primary grades is to develop an understanding of properties
of, and relationships among, numbers. Building on students' intuitive
understandings of patterns and number relationships, teachers can further
the development of number concepts and logical reasoning as described
in the Number and Operations and Reasoning and Proof Standards.
In this two-part example, virtual hundred boards and calculators furnish
a visual way of highlighting and displaying various patterns and relationships
among numbers. Using calculators and hundred boards together, teachers
can encourage students to communicate their thinking with others, as discussed
in the Communication Standard. In
the first part, Displaying Number Patterns, the same patterns are displayed
on a calculator and on a hundred board simultaneously. In this second
part, Patterns to 100 and Beyond, students examine number patterns, using
a calculator to move beyond 100.
Task
Explore different counting
patterns using the interactive calculator below. Notice the scroll feature
that allows the patterns on the hundred board to go up to 1000.
- Skip-counting by
what numbers will include 100 as part of the pattern? (If counting by
threes, start with 3. If counting by eights, start with 8.)
- What pattern do
you see when you count by twos and begin with 2?
- What do you notice
when you count by twos and begin with 1? Why?
- Will there be a
pattern if you skip-count by fives and begin with 3? Why?
- What happens if
you skip-count by tens and start with 37? What do you notice?
- How does adding
10 to any number relate to skip-counting by tens beginning with that
number?
[How
to Use the Interactive Figure]
[Stand-alone
applet]
Students expand their
intuitive understandings as they experiment with different counting sequences
and identify the resulting numerical patterns. Calculators are an important
tool for students to develop an awareness of the order of numbers. Learning
to count with a calculator will naturally lead to counting backward as
well as counting forward. Counting backward with the calculator may contribute
to students’ understanding of subtraction and can introduce them
to negative numbers.
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Patterns
to 100 and Beyond
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