What do we want teachers to understand about Number and Operations in Base Ten?

What is unitizing?
What are place-value based strategies for addition, subtraction?
What models might students use to think and show thinking?

Start with this video:

As a presenter, you should understand that this video is meant to create cognitive dissonance in teacher thinking.
The questioning, context, and manipulative used are less than optimal on purpose. The questioning assumes understanding of the manipulative by the child, and the task is decontextualized.

Questions for discussion:

What does this student understand?

What place value understanding does this student demonstrate?

What was the purpose of the questioning?

How did the questioning develop understanding?

How did the manipulative assist the student in showing their thinking?

How did the context support student thinking?

What does it mean to have an understanding of place value?

Why is that understanding crucial?

What does it look like when students understand?

Facilitator notes:

Place value understanding: each of the places/digits in a numeral represents a value ten times more than the place to its immediate left, and tens times less than the place to its immediate right.

Show the place value progression in the standards (unitizing, composition and decomposition of tens, hundreds, and thousands). This should be articulated, standard by standard. Teachers could either be given the standards as determined by the team, or be allowed to determine which standards are the best fit through discussion.

Unitizing: seeing ten ones as a unit called one ten, ten tens as a unit called one hundred, and ten hundreds as a unit called one thousand, and so on.

Present teachers with the following situation:

My friend makes necklaces using beads. Her beads come in singles, strings of ten on a pipe cleaner, and in packages of ten pipe cleaner strings.
My friend has 5 packages, 9 strings, and 6 singles.
I want to borrow 2 packages, 13 strings, and 8 singles. Does my friend have enough beads to share with me? If she does, how many will she have left over after she shares?

Teacher task:

What understanding do you need to begin working on this task?

What understanding do students need prior to working on this task?

What foundation is being built? What standards are developed through this task? Create questions which would support student understanding.

What manipulatives would support student thinking and modeling? Why would these manipulatives work? What models would be useful to students as they grapple with this problem?

In your team, work together to create a situation which requires students to compose and decompose tens, hundreds, and/or thousands.

What structures must exist in your classroom before students can be expected to confidently attempt this task?

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What do we want teachers to understand about Number and Operations in Base Ten?What is unitizing?

What are place-value based strategies for addition, subtraction?

What models might students use to think and show thinking?

Start with this video:As a presenter, you should understand that this video is meant to create cognitive dissonance in teacher thinking.

The questioning, context, and manipulative used are less than optimal

on purpose. The questioning assumes understanding of the manipulative by the child, and the task is decontextualized.Questions for discussion:Facilitator notes:

Present teachers with the following situation:My friend makes necklaces using beads. Her beads come in singles, strings of ten on a pipe cleaner, and in packages of ten pipe cleaner strings.

My friend has 5 packages, 9 strings, and 6 singles.

I want to borrow 2 packages, 13 strings, and 8 singles. Does my friend have enough beads to share with me? If she does, how many will she have left over after she shares?

Teacher task: