Math Matters
Exploring Unique Strategies and Instructional Ideas around Counting, Addition and Place Value
Jen Moffett
Today’s Agenda
What do you notice? What patterns do you see?
What changed? How do the changes matter?
Number Hunt!
Using your 100 chart and a clear marker, you will be using the clues I give you to hunt down my SECRET NUMBER!!!
As we explore, think about the following:
Number Hunt
What action are you doing every time to find the number when I say, “one more than _____”?
Number Hunt
What action are you doing every time to find the number when I say, “one more than _____”? Why is it different for these numbers???
Number Hunt
What action are you doing every time to find the number when I say, “one less than _____”?
To the Left or Right? Bigger or Smaller?
Close your eyes and take a guess at what you think the number will be. Then use your 100 chart to make sure.
Number Hunt
What action are you doing every time to find the number when I say, “one less than _____”?
Number Hunt
What action are you doing every time to find the number when I say, “two more than _____”? Why is it different for these numbers???
Number Hunt
What action are you doing every time to find the number when I say, “two less than _____”?
Number Hunt
What are two different actions you could do to find the number when I say, “ten more than _____”?
Will these both work every time?
Number Hunt
Did both work every time? Which one is more efficient?
What changed each time you found ten more? What stayed the same?
Number Hunt
What do you think will happen when we find ten less?
What are two different actions you could do to find the number when I say, “ten less than _____”?
Will these both work every time?
Number Hunt
What do you think will happen when we find ten less?
Did both work every time? Which one is more efficient?
What changed each time you found ten less? What stayed the same?
Number Hunt Puzzles
Use your chart as needed. What would be the other numbers? How do you know?
4 | | | |
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| | 16 | |
Number Hunt Puzzles
Use your chart as needed. What would be the other numbers? How do you know?
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27 |
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42 |
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15 |
Number Hunt Puzzles
Use your chart as needed. What would be the other numbers? How do you know?
11 | |
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Number Hunt Puzzles
Use your chart as needed. What would be the other numbers? How do you know?
45 | |
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Number Hunt Puzzles
Use your chart as needed. What would be the other numbers? How do you know?
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| 75 |
Number Hunt Puzzles
Use your chart as needed. What would be the other numbers? How do you know?
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| 24 | |
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Number Hunt Puzzles
Use your chart as needed. What would be the other numbers? How do you know?
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| 89 | |
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Number Hunt Puzzles
Use your chart as needed. What would be the other numbers? How do you know?
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| 68 | |
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Special Attention to Computational Skills
If there are expectations of fluency with any computational skills, those skills need special attention.
Daily two- to five-minute computational previews in purposeful representations can be used weeks before formal unit of instruction for a skill.
Brief practice, strategic choice, and connections activities can be continued for several weeks after the formal unit of instruction.
Why on Earth did I just have you play with a 100 chart????
Achieving Fluency: Special Education and Mathematics, p. 114.
5 Critical Components for Math Proficiency
Adding it Up: Helping Children Learn Mathematics
https://www.nap.edu/catalog/9822/adding-it-up-helping-children-learn-mathematics
(Free download of book!)
Rationale for Reforming Mathematics Instruction
Choose one of the quotes to reflect about.
Why did it speak to you?
Do you agree/disagree?
What is Mathematical Proficiency?
Privately read page 1.
5 Critical Components to Math Proficiency
Please read your appropriate section:
3. /4. Strategic Competence/Adaptive Reasoning
Be prepared to share:
Rationale for Reforming Mathematics Instruction
Reread the quote you chose.
Where did the 100 Number Hunt fit with respect to the components?
Representational Competence
Number of The Day
Jen’s favorite number is
Crystal’s favorite number is
How does this affect…
Instructional programs from PreK through grade 12 should enable all students to understand numbers, ways of representing numbers, relationships among numbers and number systems;
Understand meanings of operations and how they relate to one another; and compute fluently and make reasonable estimates.
Achieving Fluency; Special Education and Mathematics (NCTM, 2011), p. 105
Representations for Addition
Reorganizing the Curriculum: Some Pointers
Privately read pages 114-116.
With respect to counting and addition:
Conceptual Preview
Let’s Try Some! Blank paper/Unifix Cubes
Why do these first with blank paper?
Create the Scenes
Use the “story boards” to act out the story. You may make them life-like (have cars, fish, etc) or continue using unifix or cm cubes.
Recognizing Symbols
After children have worked on verbal story problems, you can move to tagging the items/objects to symbols.
(Act it out first. Re-enact, using a whiteboard and symbolic notation.)
2. There are this many bunnies in the grass. Show me.
This many more hop over. Show me.
How many bunnies are in the grass?
If they don’t get it right away, that is OKAY! Don’t call them out in front of everyone. This is formative assessment to see who needs more time and may need different activities for tagging amounts to numerals.
Writing Numerals
Photocopy a storyboard with white paper so that half is the story board and half is blank. Place in sheet protector.
How many cars are on the road? Write that amount under your cars.
Start just with tagging sets of objects with a numeral. Build to symbolic number sentences LATER!
Check out Independent Practice
Please read pages 50-52 (1-21).
Note: We will discuss the Second Stage (p. 115 top) next time!
Symbolic Skills: First Stage
NOTE: You can build this through context and physical models!!!
Jen has 7 yellow marbles and 8 red marbles. How many marbles does she have in all?
Your turn!
You will receive a set of exercises to consider.
Check it Out!
The 5 Representations will smack you right in the face with the Kathy Richardson’s Developing Number Concepts book.
Take some time with your partner and look for 3-5 activities/tasks that you could immediately use with your students to develop their number sense with counting, cardinality and addition.
Be prepared to share your activities/tasks with others.
Final Thoughts…
Up Next: Place Value!!!�Please keep out your 100 chart!
This Afternoon’s Agenda
I’m Thinking of a Number…
I’m Thinking of a Number…
I’m Thinking of a Number…
TPT: Why IS This NOT OKAY for Our Kids?
I’m Thinking of a Number…
Ask me questions to find my number.
Work as a team! See if you can beat 10 guesses!
(What sentence frames would you have available for students to use?)
I’m Thinking of A Number…
Use your base ten blocks to represent and find my number!
My number has…
I’m Thinking of A Number…
Use your base ten blocks to represent and find my number!
My number has…
What does this do to your thinking? What questions might you ask to build understanding of the value of place?
I’m Thinking of A Number…
Use your base ten blocks to represent and find my number!
My number has…
What does this do to your thinking? What questions might you ask to build understanding of the value of place?
I’m Thinking of A Number…
Use your base ten blocks to represent and find my number!
My number has…
What does this do to your thinking? What questions might you ask to build understanding of the value of place?
Check them Out!
Explore the following riddles using base ten blocks and connecting it to a number. Think about what students will be exploring as they PLAY!
What’s Okay/Not Okay for Riddles
Supports Conceptual Understanding
Undermines Understanding
Developing Whole Number Place Value Concepts
Adapted from Burns (Lessons for Introducing Place Value), Van de Walle (Teaching Student-Centered Mathematics), and Achieving Fluency; Special Education and Mathematics
Why am I not a fan???
What is the Point of Place Value???
Extending 2-digit Number Relationships to Larger Numbers
Once students learn to count meaningfully, relationships among numbers MUST become the emphasis to build to larger numbers. (They cannot count by one’s all day long)
It is not a crime to use their fingers and hands as tens as ones! It is the informal mathematical sense making our students MUST USE to understand place value!
Part-Part-Whole Relationships
Count out 18 items as if you were a child. How many do you have?
Any student can count the number of objects. What is significant about the experience is that, through this task, it does not cause you to think about the fact that the amount you counted could be made of 2 parts.
Two of Parts!
I will give you a number.
Using your base ten blocks, find as many ways to make the number in two parts.
________ and ________ is _______.
________ + ________ = ________
Repeat with a new number, this time using ten-frame cards.
Part-Part-Whole and Place-Value
Thinking Differently About Our Questioning
Relative Magnitude
Refers to the relationship one number has with another…
For students to grasp place value, they need to understand that each place has a particular size. The sizing matters!
Who Am I?
You can use Clothesline Math for this! Or just draw a number line on the table, whiteboard, etc.
Close, Far, and In-Between
I am going to ask for 3 numbers.
Physical Models for Place-Value
You will receive a set of cards.
Integration of Grouping with Place Value Notation
It is important to be precise in your language. Students get confused when you focus on the digit rather than discussing the actual value.
Base-Ten Model
Standard and equivalent groupings used strategically to discuss quantity of numbers
Counting
Oral Names
Written Names
Base-ten language and standard language should be explored and used interchangeably
Connect to expanded notation and standard notation
Build It, Say It, Write It
Survey!