# Video Clips catalog

Watch the videos, analyze what students know, and answer each of these questions:

- What did the student do?
- What can be inferred about what the student knows because of what they did?
- Where in a sequence of learning might the student's understanding fall? What evidence can you give to support that placement?
- What activities, from the book, could be used to build on their understanding and move toward mathematical literacy?

## Getting Ready: Classification, Number sense, and Counting

Group 1. Preschool counting - counting, number value, place value - How many starfish?

Group 2. Class meeting - counting, number value, place value - How many milks needed for the class?

Group 3. Counting candy person 1 - counting, number value, place value - How many candies in the can?

Group 4. Counting candy - person 2 - counting, number value, place value - How many candies in the can?

## Place value and number value 10-100

Group 2. Cena- place value, estimation, number value - circles and stars - Classroom procedural 49, Interview write number 18, represent with tiles, group tiles into tens and ones (24), 24 how get to 16[18], what does the 18 mean? represent 13 tiles with written numerals and what does the written numeral 13 represent in tiles?

Group 3. Brandon - place value, estimation, number value - how many beans would fit in the cup?

Group 4. Catrina - place value, estimation, number value - how do the tiles represent 16 and 21? how do the numerals on paper represent 16?

Group 1. Jonathan - place value, estimation, number value - circles and stars in class procedural count by tens..., interview tiles estimate tens, represent 24 with tiles and written numeral, represent 16 with tiles and written numeral, eyes, represent 21 written numeral imagine represent with tiles. again eyes.

Group all. Rudy - place value, estimation, number value - skip count, represent 24 with numerals, tiles, 16, (24-8=16), 27, beans estimate half jar, count - suppose counted by tens what would get?

## Addition and Subtraction of Whole Numbers

Counting dots on dice - addition?

Transition - adding two numbers less than 100 - number value, place value, and addition -

Mental addition and subtraction of two numbers less than 100.

Constance Kamii explaining student's invented solutions for addition and subtraction using deconstruction and construction of numbers.

## Addition and Subtraction Whole Number Algorithms

Algorithm samples - (clip 1) two digit subtraction using a traditional algorithm. (clip 2) two digit subtraction using a traditional algorithm, manipulatives, and 100 chart. (clip 3) three digit addition student invented algorithm and base ten blocks.

## Multiplication and Division of Whole Numbers

Additional mutiplication and division samples - (clip 1) Dozens of eggs you say? (clip 2) How many cards in a packet? (clip 3) When is multiplication multiplication and not repeated addition?

## Multiplication and Division Algorithms

Newly added - Constance Kamii explaining student's invented solutions for division with deconstruction and construction of division problems using addition.

## Representation of Rational Numbers and Adding and Subtracting them

clips 1 - 3 fractional parts of a candy bar (first 3 clips)

Clip - improper fractions, procedural Vs. conceptual, great facilitation and student empowerment.

## Chapter 11 - Security it Knowing why: Multiplying and Dividing Rational Numbers

Clips with decimal values fractions interview

## Geometry Ideas

This clip, which creates a problem involving fractions - what part of a larger cube is a smaller cube? However, cnocepts related to geometry volume, area, visual spatial; as well as fractional parts, problem solving, reasoning, multiples are needed to be successful.

## Measurement

Group. Tiles - estimation, place value, number value, problem solving - Notice the 99 chart on the wall!

Three videos with students estimating tiles:

(clip 1) Cheeto counts 16 tiles,

(clip 2) class how many tiles in this cup? If it is half full and it holds 99 tiles when it is full, how many?

(clip 3&4) How many tiles in cup? How many piles of ten? (99, 8, 9...)

Video Brandon estimating beans

## Collect, Represent, Interpret and Predict (Analyzing Data and Using Probability)

clip 1 - circles and stars chart discussion - data analysis, multiples, probability, problem solving, reasoning, estimation - graph of number of stars possible in the game circles and stars. Concerns about the data?

#### Algebra videos

Odd plus Odd - proof - student demonstrates at the board with drawings to represent how it works for ALL odd numbers. View concrete, iconic or picture, formal operational infinite proof.

Equations - equality - whole number addition - sequences

Equations - equality and multiplication - sequences