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.

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 math 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.

YellowGreenTotal

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

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 – Partner Share – Call on 1-2 students to share their thinking – Repeat

Double Ten Frames Mastering Math Facts

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

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? Allow think time Partner Share Call on 1-2 students to share their thinking Repeat

TD#3 Professional Development

TD#3 Professional Development 2012

How many? How do you know?

4 + 5 TD#3 Professional Development 2012

How many? How do you know?

7 + 8 TD#3 Professional Development 2012

How many? How do you know?

8 + 9 TD#3 Professional Development 2012

How many? How do you know?

How many? How do you know?

How many? How do you know?

How many? How do you know?

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.

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.

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?