Category Archives: Grade

From Cooking to Counting

  By drawlins • May 9, 2017 , ,

First Graders Cook, Question, and Count

By Julie Kim, First Grade Associate teacher

In the real world, we confront daily math problems through a process of noticing and wondering. After our mind has determined a question about a scenario, whether it is counting how many more blocks you need to walk or how many servings to cook for dinner, we proceed to the next step: plan, search, and gather. We plan for what steps we are going to take in order to answer the question. We search for the separate variables and pieces of information that we need in order to solve the question. We gather these pieces of information then puzzle them up in a way that will help us solve the problem. Will we, as mathematicians, get the answer we are looking for the first time around? Not always. Will we get an answer immediately? Not guaranteed. Will we persevere and try over and over again until we do? We should. Through real world work, first graders develop stamina and perseverance as they attack the challenges and questions that they are eager to solve. This is where the real work happens.

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Expanding Geometry Beyond the Equilateral Triangle

  By drawlins • March 3, 2017 , ,

Is It Still a Triangle if it’s Not Pointing Upward? 

When young children are first introduced to shape categories, like the triangle, they are presented with symmetrical models such as an equilateral triangle (all sides and angles equal in measure). Children are usually shown the equilateral triangle positioned only one way- with one vertex pointed upward, and a horizontal base.

However, research suggests that as soon as these typical examples are introduced, a variety of different positions and sizes should also be shown to children so that their notions of triangles don’t become rigid and limited to only one type of triangle, or a single example of a shape. “Children two to three years of age are not too young for this type of learning” (NCTM, 2010).

“There’s lots of ways you can make a triangle”

Examining various triangles and determining whether or not they are, in fact triangles, leads children to grapple about specific attributes that define what a triangle is (three sides, three corners, straight lines, etc.). As children experience a broader variety of each shape, they begin to build more accurate geometric concepts and ideas. Through this investigation process, the Fours are laying the foundation for geometric discussions that will take place in later grades, such as transformations (rotations, flips, slides), symmetry, and angles.

Observe the Fours as they explore and debate what it is that makes a triangle a triangle, and in the process, redefine their ideas of triangles. 

The Math Relationship of Blocks

  By drawlins • February 26, 2017 , , ,

What can a student in the fours do when they run out of a certain sized block? 

They can use the “recipe” or conversion chart they made to create the block size they need from other blocks.

Students in Pre-K used classroom blocks to estimate, and then test, how many of each of the same size smaller blocks it would take to cover one double unit block. The class worked in pairs on this investigation, and then the class created posters of their mathematical conversions. They have found this conversion chart, or “recipe” useful to refer to when they run out of a certain block size because they can now create the size they need by combining (composing) other blocks. Continue reading

Cooking Up Arrays

  By drawlins • January 31, 2017 , ,

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.

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How Many Sides Does A Circle Have?

  By drawlins • January 30, 2017 , , ,

Teachers posed this question to first graders during their study of geometry.

First graders went beyond naming basic two-dimensional shapes to exploring specific characteristics, or attributes, that define them. Their conversations evolved from seeing a shape as a “whole” such as a triangle, to analyzing and deciding the specific features that prove that it is a triangle. Students decided that a shape can only be called a triangle if it has three straight lines that make up the sides, three corners, or vertices, and does not have any openings (it needs to be closed).  Through this specific definition, they discovered that there are many types of triangles. They used this critical thinking foundation to explore a variety of two-dimensional shapes.

“Does a Circle Have Sides?”

 This was an interesting question to ponder. First grade teachers, Sarah and Ariane, posed it to their students to see if they could apply the skills they had learned about defining geometric attributes to this question. It turns out that it wasn’t an easy question to answer! Continue reading

Math, Push Carts, & City Hall Protest in New York

  By drawlins • February 24, 2016 , ,

Math with Social Justice Relevance

food samplingIt was a chilly day in January.

Fourth grade students and teachers went downtown to walk the streets of the busy financial district to meet food cart vendors. They were able to observe the variety of international selections that vendors were selling, and sample the delicious-smelling food.

Over 90% of the food vendors in New York City are first generation, or recent immigrants. This field trip gave students the opportunity to talk directly to the people who stood inside these carts, cooking food that reflected the cuisine of their home countries. Students were curious to hear the stories of where they immigrated from, and how they happened to enter into the business of selling food on the street. Continue reading

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Family Math Night at LREI

  By drawlins • November 30, 2015 , , , , ,

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