Welcome to: “Framing” Numeration Concepts in k -1

Welcome to: “Framing” Numeration Concepts in k-1

Room: EBC511:40 a.m.-12:45 p.m.Presenter: Lori Baldwin

Contact information: [email protected]

Major Resource(s) for this presentation came from the text:

Teaching Student-Centered MATHEMATICS; Grades k-3

By: John A. Van de Walle & LouAnn H. Lovin

&

The presenter’s participation in the grant, “Partners in Mathematics”.

mailto:[email protected]

Early Concepts of Number Sense...

When do children first begin their quest in understanding counting and numbers?

Many children begin learning number concepts in their homes as early as at the age of 2 and 3 years old.

Early Concepts of Number Sense...

What are some ways children learn these concepts while at home?

Counting their fingers

Seeing that their snack is running out and asking their parent for “more”.

Counting people at the table etc…

The language of More/Less/Equal

According to Van de Walle & Lovin, “…the word less proves to be more difficult for children than the word more.”

pg. 38

Why is the term, less, more difficult for students to understand and apply than the term, more?

One reason may be that students have more chances, in daily life, to use the term, more,than the term, less.

How do we facilitate understanding the terms, more/less/equal?

Anytime we use the term, more, we can pair it with the opposite, less, so students develop a stronger understanding of just how opposite they are in relation to one another.

Early Counting & Cardinality….Let’s sequence the order of the development of the

concept of counting. Read through the list below and sequence these

skills from 1st – 8th.

Touching objects and saying the number name. Rote counting (saying numbers aloud, beginning with 1 and going as

high as what’s currently known) maintaining correct sequence.Reading a numeral and matching it to the set, after counting the set.Matching objects within two sets and being able to tell which set has

more (or less, or is equal) and “how” they know. Counting objects in 2 separate sets and being able to tell you which

group has more or less.Counting objects in a set. Being able to answer how many at the end

without having to go back and recount the set, from 1.

Counting objects in a set. And when asked are unable to answer how many at the end without having to go back and recount the set, from 1.

Being able to start at any given number within the range of 0-100, and end at a target number (start counting sequence at a number other than 1).

1

2

3

4

5

6

7

8

Principle of Cardinality…

“Children will learn how to count (matching counting words with objects) before they understand that the last count word indicates the amount of the set or the cardinality of the set.”

page 39 Teaching Student-Centered MATHEMATICS; Grades k-3

Determining if a student has the Principle of Cardinality….

After a student counts a loose set of objects, ask him or her, “How many are there?”

The student should answer, “Nine.”

Proceed with the question, “How do you know there are nine?”

The student should say something like, “I know there are nine because I counted them.”

If the student cannot answer “because I counted them” & has to go back and recount the set, starting from 1, then you know that he or she does not have the principle of cardinality (which is only taught in kindergarten using the Common Core). The student needs more time counting sets within the range of 1-5.

The Fives Frame

Look at the fives frame below. What sorts of statements can you make about the frame?

Why the Fives Frame?

The fives frame serves as a visual tool for arranging a set of 5 objects (like two-sided, red/yellow plastic chips).

“Since ten plays such a large role in our numeration system and because two fives make up 10, it is very useful to develop relationships for the numbers 1 to 10 to the important anchors of 5 and 10.”

-page 42 Teaching Student-Centered MATHEMATICS; Grades k-3

What do you notice?

Let’s look at a series of fives frames. What do you notice about these frames?

What do you notice?

What do you notice about this frame?

What do you notice?


What do you notice?


What do you notice?


What do you notice?


What do you notice?


What do you notice?

In the version of “What do you notice?” that just played before you, it was out of numerical sequence.

Using a fives frame, do you think that it matters whether or not students learn to build numbers 0-5 in sequence? Why or why not?

How could this game be used in a classroom with students?

Let’s build some models….

For this next set of activities you will need…

10 plastic chips

A fives frame mat

Is this what you built?








Check for conservation: Is this value still worth 3?



Teaching “Five and some more”

What does this slide show?How would you describe this value in terms of “Five and some more”?

“Five and some more…”

Teaching students about the values of 6, 7, 8, 9, & 10 as “Five and some more” provides a strong foundation for understanding how each of these values relates to the anchor of Five.

6 is five and one more7 is five and two more8 is five and three more9 is five and four more10 is five and five more….something special….

Teaching “Five and some more”

What does this slide show?How would you describe this value in terms of “Five and some more”?

Before moving onto Tens Frames…

How can educators use Fives Frames to model the term more?

“Show me a value that is more/greater than what I am showing you on my fives frame.”


How can educators use Fives Frames to model the term less?

“Show me a value that is less than what I am showing you on my fives frame.”


How can educators use Fives Frames to model the term equal?

“Show me a value that is equal to what I am showing you on my fives frame.”

Connecting a variety of Models to the Fives Frame

2

Build this value

On your Fives Frame, show me a value EQUAL to…

Build this value


Build this value


Build this value


Build this value


Build this value


6

Build this value


3

Build this value


1

Build this value


4

Build this value


5

Build this value


2

Build this value


0

Tens Frames connections

“Five and Some More” Tens Frames

The focus changes from the value of 5 to 10.

Tens Frames

Many of the same activities used with the Fives Frames can, & should, be used with the tens frames to

develop concepts about how numbers relate to ten.

Concepts of Cardinality for values 6-10. Building sets 6, 7, 8, 9, & 10

Building sets more, less, & equal to 6, 7, 8, 9, and 10

Teen Numbers seen as Ten and Some More

What do you see? Describe values seen and the empty frames…how many more ‘til 10?

Tens Frames

What do you notice about this Tens Frame?

It is good for the teacher to point out that the top row is worth five and that five more chips will fill the frame. How many more are needed to make 10?

Tens Frames

What do you notice about this Tens Frame?

It is good for the teacher to point out that the value on the frame is 7. How many more are needed to make 10?

Tens Frames: Part-Part WholeThe part-part-whole relationship is when a student

is able to conceptualize that a number (whole) is made up of two or more parts. This is the most important concept that can be developed about numbers. Pg. 43 Teaching Student-Centered MATHEMATICS;

Grades k-3

What is this part-part-whole relationship?

Teen Numbers…”Ten and some more”

Many young students rely on the names of numbers when writing them. Teen Numbers are tricky b/c

their names don’t match how we write them.

Many young students write teen numbers this way. Can you find the six-teen? Nine-teen? Fif-teen?

Teen Numbers = “Ten and some more”

Fifteen is a group of 10 and 5 more.What is the benefit of allowing students to see the “some

more” on the outside of the tens frame and not on another frame?

Pointing out the obvious…

Teen number names are tricky.

Using a tens frames to show “ten and some more” helps provide logic to writing numerals to show place value.

1 8

Eight ones (some more)One full tens frame

Transitioning from one tens-frame to two tens frames…

When do you think you would transition students from a tens frame “and some more” with teen numbers TO two tens frames?

As students start to become fluent in their understandings of how teen numbers relate to both 10 and 20, then they are ready to transition to using two tens-frames to move towards 30.

The same is true as we move into numbers greater than 20. Ten within the whole is underlying concept we want to build upon, as our number system is based on ten.

As we end…remember…

Keep it simple.Go slow to go fast. Be thorough.Allow time for exploration and questioning.Ask good questions that require explanation from

students.Show how we apply new knowledge to daily life.

Thank you for attending: “Framing” Numeration Concepts in k-1

Presenter: Lori Baldwin

Contact information: [email protected]

Major Resource(s) for this presentation came from the text:

Teaching Student-Centered MATHEMATICS; Grades k-3

By: John A. Van de Walle & LouAnn H. Lovin

mailto:[email protected]

Documents

Welcome to: “Framing” Numeration Concepts in k -1