NUMBER SENSE

K-2 Math &

Science C

ollaborative at the Allegheny

Intermediate U

nit

REFLECTING ON NUMBER SENSE

Go to mscsummercourses2013.wikispaces.com and then to the number sense page.

Respond to the discussion prompt “Visual Representations”.

Math &

Science C

ollaborative at the Allegheny

Intermediate U

nit

AGENDA

Response to wiki prompt Sharing of Number Sense Visual

Activity Do these children have number sense?

– videos Games to Develop Number Sense Mental Math Videos Article discussion Planning

Math &

Science C

ollaborative at the Allegheny

Intermediate U

nit

COMMUNITY OF LEARNERS

Building a strong and supportive community of learners is essential in making number sense routines beneficial and productive for everyone.Students share out thinking Work through misunderstandings in front

of peers Have time to think for themselves

Math &

Science C

ollaborative at the Allegheny

Intermediate U

nit

SHARING: NUMBER SENSE VISUAL ACTIVITY

With your group, share the activity you used.How did the students respond to the

activity?What challenges, if any, did you

encounter?What role did the visual play in the

success or challenge of the activity?

Math &

Science C

ollaborative at the Allegheny

Intermediate U

nit

LEARNING PROGRESSION: K-5 OPERATIONS AND ALGEBRAIC THINKING

Read the learning progression for the grade level assigned to you.Make note of how it is

connected to number sense.

Math &

Science C

ollaborative at the Allegheny

Intermediate U

nit

K1 – dot cards and ten framesWhich students are able to subitize and unitize five and which ones are not? What evidence do you have?How do the visual representations support students’ in developing number sense?

How does the ten-frame with seven dots provide opportunities for students to use five as a unit?

How does the teacher elicit and support students’ uses of different strategies?What evidence did you find of the students engaging in the Standards for Mathematical Practice?How does what you saw in the video connect to what you read about in the progression?

DO THESE STUDENTS HAVE NUMBER SENSE?

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K2 – rekenreks How does the warm-up with four and six provide the teacher with information to guide her instructional decisions?What examples of one-to-one correspondence and conservation of number surface in the lesson?Are there specific number combinations that seem more accessible to students? How does the teacher build on this foundation?How does the rekenrek support students’ in developing number sense?What evidence did you find of the students engaging in the Standards for Mathematical Practice? How does what you saw in the video connect to what you read about in the progression?

DO THESE STUDENTS HAVE NUMBER SENSE?

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IMPLICATIONS FOR TEACHING AND LEARNING

What kinds of activities do you think these children were engaged in prior to these lessons?

What evidence is there that they used these tools prior to the lessons we viewed?

Math &

Science C

ollaborative at the Allegheny

Intermediate U

nit

GAMES TO DEVELOP NUMBER SENSE

Play each of the games. After you play each game, answer the following questions:

What concept(s) is the focus of each game? What tools might students use to support to

solve the problems? Discuss the strategies students might use. Might

they reason with facts they know? Use landmark strategies? Use make-a-ten? Use the 5- or 10-structure? How might you promote the use of more efficient strategies?

Is there any way to adapt these games for older students to play?

Math &

Science C

ollaborative at the Allegheny

Intermediate U

nit

Finding DoublesMake 10Capture 10

Rack 10CombineBear Tracks

GAMES TO DEVELOP NUMBER SENSE

What evidence will you look for to see if students understand the underlying mathematics of the game?

What evidence will you look for to see if students are using number sense as they play the game?

Math &

Science C

ollaborative at the Allegheny

Intermediate U

nit

LEARNING PROGRESSION: K-5 NUMBER AND OPERATIONS IN BASE TEN

Read the learning progression for the grade level assigned to you.Make note of how it is connected to

number sense, specifically, composing and decomposing numbers.

Math &

Science C

ollaborative at the Allegheny

Intermediate U

nit

MENTAL MATH

When students solve a problem in their heads, they usually use what they know about place value, number relationships, patterns, and visual images to figure it out.Problem contextNaked numbers

Math &

Science C

ollaborative at the Allegheny

Intermediate U

nit

VIDEO: 8 + 6

What are examples of how the ten-frame model supports student strategies for 8 + 6?

How does the ten-frame encourage students’ understanding of 10 as an important number in computation?

What seems to be a core strategy throughout this number talk?

8 + 6 is considered to be a basic addition fact. What role can number talks play in helping students build basic fact knowledge?

Math &

Science C

ollaborative at the Allegheny

Intermediate U

nit

VIDEO: 26+27 Did any of the students use the strategies we did? How do the strategies demonstrate that children

have built an understanding of place value? In each strategy the students start from the left and

work to the right. How does this help build number sense and a sense of reasonableness for the answer?

What role does the hundred chart play in helping children understand place value?

How are students using their understanding of number relationships in their strategies?

A major focus of kindergarten is to build fluency with small numbers. How is this ideas incorporated in the students’ strategies?

Is there any evidence that students were engaged in the Standards for Mathematical Practice?

Math &

Science C

ollaborative at the Allegheny

Intermediate U

nit

MENTAL MATH

Given that 48+37=85, what is the answer to 49+36? Show why this is true using the number line.

Math &

Science C

ollaborative at the Allegheny

Intermediate U

nit

VIDEO: 70-59 How does the number line provide support for

understanding Grant’s Constant Difference strategy? In what other ways could you model this strategy to help students understand why it works?

The students share several subtraction strategies: Constant Difference, Adding Up, Removing in Chunks, and Adjusting One of the Numbers. Discuss how these strategies are similar and different?

When Andrew shared his strategy, students were unsure whether 1 should be added or subtracted. Share your observations about the student and teacher roles during the class discussion. How could you help students understand his thinking?

Is there any evidence that students were engaged in the Standards for Mathematical Practice?

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DEVELOPING NUMBER SENSE THROUGH REAL-LIFE SITUATIONS

How does thinking about numbers in real-life situations help develop and/or improve children’s number sense?

Math &

Science C

ollaborative at the Allegheny

Intermediate U

nit

LEARNING FROM EACH OTHER

Read chapter 7, p. 119, in Number Sense Routines.

In your small group, discuss the following questions:How does math talk support the

development of number sense?How do visual representations support

math talk?How can you help students see mistakes

as learning opportunities and how does that support the development of number sense?

Math &

Science C

ollaborative at the Allegheny

Intermediate U

nit

FLUENCY IN PA CORE STANDARDS M

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cience Collaborative at the A

llegheny Interm

ediate Unit

SORTING ACTIVITYM

ath & S

cience Collaborative at the A

llegheny Interm

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Sort the cards into two piles. Be ready to tell us how you sorted.

WHAT DOES FLUENCY MEAN TO YOU

Math &

Science C

ollaborative at the Allegheny

Intermediate U

nit

On a large post-it, write down your thoughts about fluency. What is it?

NUMBER SENSE AND FLUENCY

How does number sense support the development of fluency?

Math &

Science C

ollaborative at the Allegheny

Intermediate U

nit

ARTICLE DISCUSSION

Read the article “10 Is the Magic Number.”

Math &

Science C

ollaborative at the Allegheny

Intermediate U

nit

PLANNING

Plan task focusing on one standard and one standard for math practice involving the use of visuals to develop/extend number sense.Include a mental math activity and

a game.

Math &

Science C

ollaborative at the Allegheny

Intermediate U

nit

HOMEWORK Read chapter 5, P. 79 in Number Sense

Routines. Read Why Children Have Difficulties

Mastering the Basic Number Combinations and How to Help Them.

Complete task, if necessary. Plan task focusing on one standard

and one standard for math practice involving the use of visuals to develop/extend number sense.Include a mental math activity and a

game.

Math &

Science C

ollaborative at the Allegheny

Intermediate U

nit