In addition to vertical multiplication and vertical (long) division (some push this to fourth grade), measurement is the primary topic of math study for grade three in Waldorf Schools. To prepare for these blocks, I listened to Eugene Schwartz’s lecture entitled Time, Weight & Measurement (found here.)
Our first math block was on time. Jamie York of Making Math Meaningful covers time in grade two, but I think there are many schools and teachers who feel the study of time fits well in grade three as a type of measurement. We began with gently reviewing the seasons and months. We talked about the origins of the months’ names and reviewed the poem “A Calendar” by Sara Coleridge which Pintail had memorized a few years ago. We mentioned days of the week and began talking about how ancient people invented ways to keep track of time. We made a sundial of clay and a pen and marked off the hours. We followed several of Eugene’s suggestions including talking about ancient clocks, water clocks and hour glasses, and how they worked. I bought a miniature hour glass to study. I also bought a wind-up analog clock that I let Pintail take apart. We watched how the gears worked and moved and then he disassembled the whole thing, leaving only the face and hands intact, which we used to practice time-telling and elapsed time, etc. I know many people make beautiful calendars during this block, but it was something I chose not to do. I used the math worksheet generating site Math-Aids.com to generate some worksheets (gasp!) to be used for practice problems. I know worksheets make people cringe, but you can use the site to give you ideas that you can write on the board or just give verbally for your child to practice. Any skill takes practice to master and if you don’t want to come up with every single problem on your own, this is a very useful math site. We spent just fourteen school days on this block, which was plenty for Pintail.
Volume, Liquid Measure and Weight
We did our dry and liquid measurement block in December. I thought it would be a good time to be in the kitchen making goodies and then learning about how the measurements relate to one another. For this block we cooked a lot, and then did some main lesson book pages regarding our learning. During this block, I had Pintail begin the Key to Measurement Book 4: English Units for Weight, Capacity, Temperature and Time. This book is recommended in the Christopherus program in grade four along with the Key to Fractions books. I felt very overwhelmed trying to do the Key to Measurement books AND the Key to Fractions books with Teal a few years ago in fourth grade, so I decided to have Pintail do the Key to Measurement books in third grade along with our measurement study. (That makes more sense to me anyway!) Any problems that I felt were too difficult or required a calculator I just had him skip. I actually like these books because they have some really fun hands-on activities for learning. Book 1 also had some time problems which allowed us to review from the previous block.
I used the linear measurement block in A Journey Through Waldorf Homeschooling Grade Three as my inspiration for this block. As suggested, we started with the story of Noah and the Ark, reading about the measurements for the ark and how they were based on the unit called the cubit. We did a lovely painting of the Ark that was inspired by a painting I did in a workshop last year with George Hoffecker. We talked about what a cubit was and made a string that was ten cubits long, then we went into our street and after marking our starting point, we leap-frogged each other until we had measured three hundred cubits. Pintail stayed at one end and I ran back to the other so we could get a sense of the length of the ark. We talked about how ancient units of measure were based on the measurement of body parts. Pintail recognized the inherent possibility for error and that led to a discussion on why units of measure were standardized. I gave examples of some of those ancient units and what things they were based on. We spent a day exploring some human body ratios, using interesting facts found here, here and here. I had Pintail lie down, so I could outline his body and then had him do a self-portrait. We checked some of the ratios using his self-portrait. After all of this hands on work, Pintail began working in the Key to Measurement Book 1: English Units of Length.
Once our measurement blocks were complete. I had Pintail continue working through the Key to Measurement Books 2 and 3. He was able to complete them all by the end of the year, getting better at calculating with long multiplication and division, too! A wonderful learning experience happened when he realized on his own that two shapes with the same perimeter can have different areas!
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