Learning about Area and Volume

Students have been working hard to learn concepts about area and volume.

Last week, we learned that we can find the area of a square by multiplying the length by the width. A=L * W a formula we may remember from our school days. Students are also thinking about how we may find the number of pieces that cover that "square area"--including using the fractional parts.

For example:
How many 1/2 ft squares or parts would you need to fill one square foot?
It would take four 1/2 square feet pieces to create one square foot.

We were looking for a pattern to help us solve other problems. Some noticed that if we multiply the denominators, we will get the number of pieces needed to cover the square foot.  In the second example, it would take nine 1/3 square feet pieces to cover one square foot.

This week, we transitioned to volume. Students have been working to find the volume using either of the following formulas:

V = L * W * H   or V = B * H

Students were also working to visualize the size of various cubic units. We have worked with cubic centimeters, cubic decimeters, and cubic meters. Below, you can see us building a cubic meter. 

These first few days in math have been challenging. However, it is exciting to see students think deeply about math!  

Getting started with Math

This school year, all of Columbia Public Schools are implementing new math materials. The series that we are using is called Everyday Math.  This new program is rigorous and rich with opportunities to see math being applicable to life.

Introducing variables and expressions

Students were introduced to a series of "staircases". You can find detailed ideas on how to use in the classroom, across multiple grade levels, here .  You can tell that I am an exceptional artist when it comes to representing something in 3-D.

Students went to work. They recorded the height of the staircase and the number of cubes that matched each term. While most students used cubes, many were able to establish some sort of pattern pretty quickly and abandoned the cubes.

It is hard to see here but a student is trying to draft an expression in word form. 

Another student suggests that we try using a variable to express the pattern. We tried using one for n but it was not quite something that worked when n changed. 

I introduced how we can use a variable, or a letter, preferably n to help us communicate an expression. The wheels were turning. We shared our ideas as a class and tested them out. 

A few students were beginning to make connections as to how this could be represented and that it might take more than one operation to do so. The investigation will continue!

Please note, the learning target was purposefully absent. I have moments where I think it is helpful and can support student understanding. However there are times that I think it blows the whole inquiry down the drain.  Want to consider another perspective? Read this blog post here: Joe Bower's Blog

Stumping us in math!

Using this as a starter....

She's on to something!

Step Right, Up!

Finding points of ordered pairs on a coordinate plane

Students are extending their graphing from a coordinate grid to a coordinate plane.

It is hard to see in the photograph, but students had to name the ordered pairs for each point on the coordinate plane.

Then, students had a turn to locate the point after being provided with the ordered pair. This was the a little more of a challenge as students were working with negative numbers as well. 

We will continue to provide experiences to practice this skill!

Rolling Sixes

Students worked with a partner to play a math game. One person rolled a die. When they landed on a six, they stopped rolling and switched with their partner. The partner was writing the numbers-- hoping to reach 100 before the partner rolled a six. So fun!