# How many Ways Can You Make 121 Using a Combination of These Blocks?

## Students in second grade worked on this challenging open problem for several days using base ten blocks.

To understand place value deeply, students need to know that numbers can be represented more than one way. Through this problem, students explored the 10:1 base ten relationship and became flexible with decomposing hundreds, tens and ones many different ways. For example, in addition to representing 121 with 1 hundred, 2 tens, and 1 unit, students realized that 121 can be further decomposed into 12 tens and 1 unit cube, or 9 tens and 31 unit cubes.

This work provides a foundation for student strategies of breaking apart numbers by place to solve addition and subtraction problems, leading to a better understanding of the U.S. algorithm.

## Student Examples- Can you find a Pattern?

As students worked on this problem, teachers challenged them to see if they could discover a pattern, and a systematic method of finding all of the possible ways to make 121.

# Taking the Problem Further:

The openness of this problem allows students to work on many different levels and some may notice that there is a pattern with the number of blocks used (the number increases by 9), as tens are systematically decomposed, as well as an alternating odd and even number of blocks.

## Do multiplication arrays need to be introduced as a ready-made convention, or can they be “constructed” by children using concrete objects while engaged in an open-ended task?

(An action research collaborative effort by second grade lead teachers, Tasha Hernandez, Bill Miller, and Lower School Math Coordinator, Debra Rawlins)

We began this project as a way to build math relevance into the annual second grade canned food drive. The students visit Saint John’s Food Pantry and spend a morning learning about the needs of the community. Then they pitch in and help out the staff for a few hours. When they return to school, they create signs advertising the canned food drive, and place collection boxes at various locations around the school.

## Family Math Night at LREI

### Students and Parents look forward to Family Math Night every year.

Students in grades one through four celebrate mathematics, as well as continue to hone their fluency in combination facts by playing fun games. Fourth grade students create their own math games as a capstone experience, and then teach them to family and friends during Family Math Night. Continue reading

## Apollo Theater Problem

### How many New York City blocks is it to the Apollo Theater from LREI?

(The Apollo Theater is located at 125th Street in Harlem)

This problem seemed easy enough until Tasha’s second grade realized that the West Village, where LREI is located, isn’t laid out in an organized city grid system, like the rest of Manhattan is. An interesting math problem ensued, and the class enlisted Nick, LREI’s resident historian to help us understand why the streets in the West Village are so confusing! Continue reading

## Tasha’s second grade class watched the video below and came up with several mathematical questions to investigate:

1. How many steps could there be on the stairs if Robin is on the middle step?
2. Is the step Robin is on odd or even?
3. Can I count by “twos” and land on the middle step?
4. What step could Robin be on?
5. What step could Robin not be on?