number sense and place value by jessica rodriguez
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Number Sense and Number Sense and Place ValuePlace Value
Number Sense and Number Sense and Place ValuePlace Value
By Jessica RodriguezBy Jessica Rodriguez
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What is Number Sense?
• An understanding of numbers and their relationships (Van de Walle, 2007)
• A flexibility in thinking about numbers, including their size representations, and effects with operations (addition, subtraction, multiplication, division) (Van de Walle, 2007).
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What is Number Sense?
Understanding Numbers
• Five is more than three and less than ten.
• When I add, the number increases.
• When I subtract, the number decreases.
Flexible Thinking• The number 6 is two
groups of three. It is also three groups of two.
• If 10+5= 15, then 9+5= 14 because 9 is one less than 10.
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Developing Number Sense…
• Children need many, varied opportunities to work with numbers.
• Use hands-on counters and representations of numbers
• Use real-world opportunities to teach number sense
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Question: Brainstorm some real-world
math activities for children developing number sense…
Example: counting oranges at the grocery store.
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More, Less, and the Same Amount
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Question:
How can we develop an understanding of quantity (more, less, and the same)?
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Virtual Field Trip…Let’s take a trip to “Count Us In!”• Open a new Internet window and go
to http://www.abc.net.au/countusin/default.htm
• Explore some of the games offered at this website.
• We will meet back in 5 minutes…
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Virtual Field Trip Question…
Share a game or activity you found at this website…
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Question: Why are visual
representations (beans, counters, blocks, etc.) so important in developing an understanding of numbers?
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Flexible Thinking…A number has
many representations…
Let’s take the number 9. It can be a set of 9…
It can also be…• A set of five and
four• A set of 2 and 7• 12-3• One away from
ten• And on…
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Part-Part-Whole Activities
Use counters to find as many ways as you can make the number 10.
Examples:● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ●
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Missing Part Activities
Use counters to find the missing part. You have 3 counters, you get some more. You have a total of 10. How many did you get?
Examples:● ● ● + ____ =
10
● ● ● ● ● ● ● ● ● ●
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Virtual Field Trip…Let’s take a trip to “Ten Frame”• Open a new Internet window and go
to http://illuminations.nctm.org/ActivityDetail.aspx?ID=75
• Play the game for a few minutes. • We will meet back in 3 minutes…
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Virtual Field Trip Question…
How does a ten frame help develop flexible thinking with the quantity 10?
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What is Place Value?• The basis of how our numbers are
written and spoken. • Each number has a value that is
based on its place (hundreds place, tens place, ones, place, etc.)
• Our system is a base-ten system; each place is a multiple of ten.
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Place Value Is Number Groupings…
Tens Ones
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Examples of Base Ten Models for Numbers
25 19
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Base Ten ManipulativesGroupable base ten
models: ones that the children can put together into groups of ten and take apart, like beans or connecting cubes.
Pregrouped base ten models: ones that are already grouped for the students and the students cannot take apart.
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Virtual Field Trip…Let’s take a trip to “Base Ten Blocks”• Open a new Internet window and go to
http://nlvm.usu.edu/en/nav/frames_asid_152_g_1_t_1.html?from=category_g_1_t_1.html
• Explore the activity for a few minutes. • In order to make the number, you have to
click on the blue blocks at the top of the chart.
• We will meet back in 4 minutes…
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Virtual Field Trip Question…
How does this type of activity support understanding of place value?