Number Sense and Number Sense and Place ValuePlace Value

Number Sense and Number Sense and Place ValuePlace Value

By Jessica RodriguezBy Jessica Rodriguez

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).

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.

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

Question: Brainstorm some real-world

math activities for children developing number sense…

Example: counting oranges at the grocery store.

More, Less, and the Same Amount

Question:

How can we develop an understanding of quantity (more, less, and the same)?

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…

Virtual Field Trip Question…

Share a game or activity you found at this website…

Question: Why are visual

representations (beans, counters, blocks, etc.) so important in developing an understanding of numbers?

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…

Part-Part-Whole Activities

Use counters to find as many ways as you can make the number 10.

Examples:● ● ● ● ● ● ● ● ● ●

● ● ● ● ● ● ● ● ● ●

● ● ● ● ● ● ● ● ● ●

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

● ● ● ● ● ● ● ● ● ●

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…

Virtual Field Trip Question…

How does a ten frame help develop flexible thinking with the quantity 10?

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.

Place Value Is Number Groupings…

Tens Ones

Examples of Base Ten Models for Numbers

25 19

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.

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…

Virtual Field Trip Question…

How does this type of activity support understanding of place value?