place value training: number sense using 10-frames thursday, january 29, 2015 kathleen wilson

Place Value Training:

Number Senseusing

10-Frames

Thursday, January 29, 2015Kathleen Wilson

Goals

a) Link standards to the activitiesb) Demonstrate progression of place value across

grade levelsc) Deconstruct activities explicitly through student

and teacher lensd) Show how you could use activities during Part 2

flex groupse) Capture misconceptions and show how an

activity can be scaffolded up or down depending on the learner's needs

Agenda

• Welcome, Introductions, Vision, and Goals• Human Bar Graph• Scavenger Hunt Using SPPS Math Website

Resources• Video Clips• CRA (Concrete – Representation – Abstract) • Ten-frames for Building Number Sense

Stay EngagedOur learning time here is BRIEF- Be

present in this moment.

Speak Your Truth Please honestly own your

experience. Experience Discomfort

It is in our un-comfortableness that we achieve growth.

Expect and Accept Non-ClosureOur learning time here is BRIEF- Every question

will not be answered, every rock will not be overturned.

Our Norms

Golden Ticket

Vehicle Line Up

Turn in Ticket

Debrief the Activity

Share with a partner who is in the same

position as you the connections you

saw with the 4Rs and this activity

Concrete

Pictorial=

Abstract

2 + 1 + 1 = 2 + 2

Research-Based Math Instructional Strategies

Concrete

Doing

Students who use concrete materials

develop more comprehensive mental

representations and conceptual

understanding

Representational

Drawing/Connecting

Move to this level after students have successfully used concrete

materials

Abstract

Symbolic

Moving to abstract without a strong

foundation in concrete & representational

may cause misconceptions and

student errors

Does this build number sense?

What is Number Sense?It is difficult to define precisely, but broadly speaking, it refers to “a well organized conceptual framework of number information that enables a person to understand numbers and number relationships and to solve mathematical problems that are not bound by traditional algorithms.” (Bobis, 1996)The National Council of Teachers (1989) identified five components that characterize number sense: number meaning, number relationships, number magnitude, operations involving numbers and referents for numbers and quantities. These contribute to general intuitions about numbers and lay the foundation for more advanced skills. Researchers have linked strong number sense with skills observed in students proficient in the following mathematical activities:

• Mental calculations• Computational estimation• Judging the relative magnitude of numbers• Recognizing part-whole relationships and place value concepts and • Problem solving

The Development of Base-Ten Arithmetical Strategies

Jim Martland, et. al, in their book Teaching Framework in Number, outline a three level model for the development of base-ten arithmetical strategies.

Level 1: Initial Concept of Ten The student does not see ten as a unit of any kind. The

student focuses on the individual items that make up the ten. Student counts forward or backward by ones in addition or subtraction tasks involving tens. At this level, the student can identify numbers in the range of 1 to 10.

The Development of Base-Ten Arithmetical Strategies (cont.)

Level 2: Intermediate Concept of Ten Ten is seen as a unit composed of ten ones. The student

is dependent on representations of ten such as open hands of ten fingers. The student can perform addition and subtraction tasks involving tens when they are presented with materials but not when presented as written number sentences.

Level 3: Facile Concept of Ten The student can solve addition and subtraction tasks

involving tens and ones without using materials or representations of materials. They can solve written number sentences involving tens and ones by adding or subtracting units of tens and one.

Activity: Patterns Through Number Sense

Instructions for activity: Ten volunteers stand at the front.

1.Each has a sheet of colored paper (yellow).2.Ask the group questions about the Quantity/value of ten. How many people do

you see? How many yellow? Have participants record what they see in their notebook.

3.Take away a yellow sheet of paper and distribute a green. Then ask the group how many are still there? How many yellow? How many green? Record what they see

4.Take away another sheet of yellow and add another green (now 8 yellow and 2 green). Ask the same questions, but lead more towards the relationship between yellow and green. Record what they see

5.Take away another yellow, add another green, and so on until you feel like the group has a handle on where you are going with the activity. Record what they see

6.The group should be able to see that relationship between yellow and green, that in all they still make ten, that as one goes up in value – the other goes down, etc.

Yellow Green Total10 0 10

9 1 10

8 2 10

7 3 10

6 4 10

5 5 10

4 6 10

3 7 10

2 8 10

1 9 10

0 10 10

Number Sense Routine

Ten Frames

Ten Frames help develop…

• the five-structure and ten-structure of a number

• a visual model of numbers• an understanding of composing and

decomposing numbers with the structure of ten

• the part-part-whole relationship of numbers• a visual image for the make ten addition

strategy

Effective Ways to Use Ten Frames

• quick images to help students visualize quantities

• tool for composing/decomposing teen numbers

• tool for modeling part-part whole relationship of teen numbers

• tool for learning the make ten strategy for addition

• tool for learning math facts

Ten Frames as Quick Images

Procedures:– Show the frame for 3-4 seconds– Hide the frame – Ask: How many? How do you know?– Allow think time– Create the visual with counters– Partner Share– Call on 1-2 students to share their thinking– Repeat

Get Ready…

What did you see?How do you know?

Recreate it with your tools

Get Ready…

What did you see?How do you know?

Recreate it with your tools

Get Ready…

What did you see?How do you know?

Recreate it with your tools

Get Ready…

What did you see?How do you know?

Recreate it with your tools

Get Ready…

What did you see?How do you know?

Recreate it with your tools

Get Ready…

What did you see?How do you know?

Recreate it with your tools

Get Ready…

What did you see?How do you know?

Recreate it with your tools

Get Ready…

What did you see?How do you know?

Recreate it with your tools

Differentiation to Personalize

Learning

Making 10

iPad App “10-Frame Fill”

Number Sense Resources

http://thecenter.spps.org/number_sense.html

Mastering Math Facts

Double Ten Frames

Double Ten Frames help develop…

• the five-structure and ten-structure of a number • a visual model of teen numbers• an understanding of composing and decomposing

numbers up to 20 with the structure of ten• the part-part-whole relationship of teen numbers• a visual image for the make ten addition strategy

TD#3Professional Development Department 2012

Effective Ways to Use Double Ten Frames

• quick images to help students visualize quantities

• tool for composing/decomposing teen numbers

• tool for modeling part-part whole relationship of teen numbers

• tool for learning the make ten strategy for addition

Double Ten Frames as Quick Images

Procedures:• Show the frame for 3-4 seconds• Hide the frame • Ask: How many? How do you know?• Have students build what they saw• Allow think time• Partner Share• Call on 1-2 students to share their thinking• Repeat

Get Ready…

What did you see?How do you know?

Recreate it with your tools

Get Ready…

What did you see?How do you know?

Recreate it with your tools

Get Ready…

What did you see?How do you know?

Recreate it with your tools

Get Ready…

What did you see?How do you know?

Recreate it with your tools

Get Ready…

What did you see?How do you know?

Recreate it with your tools

Get Ready…

What did you see?How do you know?

Recreate it with your tools

Get Ready…

What did you see?How do you know?

Recreate it with your tools

Get Ready…

What did you see?How do you know?

Recreate it with your tools

Get Ready…

What did you see?How do you know?

Recreate it with your tools

Get Ready…

What did you see?How do you know?

Recreate it with your tools

Ten Frames as Quick Images

Math Review Key Ideas:

• Double ten frames help us see quantities quickly

• When both ten frames are full there are twenty

Transitioning from Ten Frames to Base Ten Blocks

• Representing teen numbers to twenty with ten frames and base ten blocks side by side.

• Staying with numbers in the twenties to make sure student can soundly move beyond Level 2: Intermediate Concept of Ten.

Debrief the Activity

Share with a partnerthe connections you

saw with the 4Rs and this activity

Four “Rs” of Culturally Responsive Teaching

How will I build

relationships with teachers,

students, and families?

In what ways will I message to ALL students that they are expected to attain high standards?

What strategies will I use

to make sure students

and adults are able to

show up as their

authentic selves?

How will I make sure the curriculum relates to students’ experiences, interests and backgrounds?

Clean Up :D

Please return 2 towers of 10 unifix cubes,

two 10-frames, &one 5-frame,

to the ziplock bag and

organize large bag of materials