# Teaching with Materials

## 20-Tray

The 20-Tray demystifies the difficult teen numbers by demonstrating that the sequence and concepts they have internalized regarding numbers 1 to 10 extend to higher numbers, as well. Children discover that the numbers 11-20 are made of ten and some ones, and that the combinations of ten apply to make combinations making twenty e.g. (4+6=10, so 14+6=20).

The 20-Tray is used to demonstrate:

• Understanding of teen numbers
• That all teen numbers are made of a ten and some ones
• Counting forwards and backwards within 20
• Fluency with adding 10 and 9 to any number
• Combinations of 20

## Building the 20-Stair

Children discover the role of 10 in each teen number as they build the stair from 1 to 20. They name the blocks in each step, such as 10 and 5, and then give their sum, 15. In this way they all understand the composition of each number from 11 to 20.

## 20-Track

The 20-Track provides children with an introduction to the number line and gives them the opportunity to discover addition and subtraction facts for numbers 1 to 20. Children can also see how the structure of the facts they learned about from numbers 1 to 10 have a similar structure in the numbers 11 to 20.

The 20-Track is used to teach:

• Concept of teen numbers using a linear representation
• Place value of teen numbers (one 10 block and another block)
• Addition and subtraction within 20
• Fluency with adding 10 and 9 to any number
• Fluency with making a 10 to add two numbers

## Whole Class Lesson on Adding 9

Temple Ary with a whole class of second graders at the Ramaz School in New York City. She is working with the 20-Tray to teach what happens when you add a number to 9. You will notice that each child has a white board to write on and that the children are regularly asked to explain their thinking about how they got to a particular answer, thereby building their conceptualizing, problem solving skills and vocabulary for math.