place value training: number sense using 10-frames thursday, january 29, 2015 kathleen wilson
TRANSCRIPT
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Place Value Training:
Number Senseusing
10-Frames
Thursday, January 29, 2015Kathleen Wilson
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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
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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
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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
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Golden Ticket
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Vehicle Line Up
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Turn in Ticket
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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
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Concrete
Pictorial=
Abstract
2 + 1 + 1 = 2 + 2
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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
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Does this build number sense?
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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
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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.
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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.
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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.
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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
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Number Sense Routine
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Ten Frames
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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
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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
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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
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Get Ready…
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What did you see?How do you know?
Recreate it with your tools
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Get Ready…
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What did you see?How do you know?
Recreate it with your tools
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Get Ready…
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What did you see?How do you know?
Recreate it with your tools
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Get Ready…
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What did you see?How do you know?
Recreate it with your tools
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Get Ready…
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What did you see?How do you know?
Recreate it with your tools
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Get Ready…
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What did you see?How do you know?
Recreate it with your tools
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Get Ready…
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What did you see?How do you know?
Recreate it with your tools
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Get Ready…
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What did you see?How do you know?
Recreate it with your tools
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Differentiation to Personalize
Learning
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Making 10
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iPad App “10-Frame Fill”
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Number Sense Resources
http://thecenter.spps.org/number_sense.html
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Mastering Math Facts
Double Ten Frames
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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
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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
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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
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Get Ready…
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What did you see?How do you know?
Recreate it with your tools
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Get Ready…
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What did you see?How do you know?
Recreate it with your tools
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Get Ready…
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What did you see?How do you know?
Recreate it with your tools
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Get Ready…
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What did you see?How do you know?
Recreate it with your tools
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Get Ready…
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What did you see?How do you know?
Recreate it with your tools
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Get Ready…
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What did you see?How do you know?
Recreate it with your tools
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Get Ready…
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What did you see?How do you know?
Recreate it with your tools
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Get Ready…
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What did you see?How do you know?
Recreate it with your tools
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Get Ready…
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What did you see?How do you know?
Recreate it with your tools
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Get Ready…
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What did you see?How do you know?
Recreate it with your tools
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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
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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.
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Debrief the Activity
Share with a partnerthe connections you
saw with the 4Rs and this activity
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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?
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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