Sacramento Homeschool Math By Hand

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 211

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math. Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”

And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times. Why ambient? A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful. Today’s post features the Jewish harvest holiday of Sukkot.

Sukkot is a wonderful way to begin the Grade 3 year!  When I taught a Waldorf Grade 3 in Michigan, I had a class Dad help us build a lashed, open-walled structure with tree branches and a thatch-ready roof.  We kept the walls open and thatched the roof with willowy, leafy tree branches, then enjoyed a traditional harvest meal in our sukkah.  Here are several excerpts re Sukkot from Tori Avery’s blog.

“Temporary structures known as “sukkah” can range in size from small (just large enough for two people) to enormous. A sukkah is constructed with three or four walls and a roof known as a “schach” made from natural organic materials. It must be at least three feet tall, and you must be able to see the sky through the roof—if you can’t, the sukkah is not considered “kosher.” Traditionally, Jewish families decorate the sukkah with a variety of decorations including homemade ornaments, paintings, and streamers. Often decorations are inspired by harvest foods and the seven species of Israel mentioned in Deuteronomy: grapes, figs, pomegranates, olives, dates, wheat and barley.

Sukkot is a harvest holiday, which means that the foods served are seasonal in nature. The Sukkot menu generally features vegetables and fruits that are harvested at the turn of the season—apples, squash, eggplants, grapes, etc. As a food lover, this holiday is one of my favorites because we are encouraged to create dishes from fresh and delicious seasonal ingredients. The arrival of Sukkot ushers in the autumn season; Sukkot foods are inspired by the bounty of the harvest.”

Since the Old Testament, gardening, and housebuilding are all included, this is a perfect fit with the Grade 3 curriculum!  The comfort and satisfaction my third graders felt was palpable as they helped build and then enjoyed their “harvest house.”  See below for a quick and easy sukkah, built with recycled lathe and large, metal can lids.  This dome sukkah, from Volecipede, is partially thatched and quite spacious inside.

Above all, help your third graders build a home on this earth, and all else will fall quite beautifully into place.  Remember as always, that knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of knowledge as a worthy goal. Tune in tomorrow for more Grade 3 fun!

The post Common Core’s Done: Time for Some Grade 3 Fun! (#211) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 210

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math. Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”

And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times. Why ambient? A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful. CCSS math standards are listed here in blue, followed by ambient math suggestions.

Geometry 3.G
Reason with shapes and their attributes.
2. Partition shapes into parts with equal areas.  Express the idea of each part as a unit fraction of the whole.  For example, partition into 4 parts with equal area, describe the area of each part as 1/4 the area of the shape.

Again, form drawing more than adequately addresses this standard with forms that are divided into symmetrical parts, horizontally, vertically, or both.  Though fractional terms are not directly used, the foundations for fractional thinking are built.  Here are several examples taken from the Math By Hand / Form Drawing/Stories book (the small letters indicate colors).

Here, the form is begun by finding 4 equally spaced points on a circle and marking them.  The contrasting straight line and curved forms are then built off the 4 corners.  Note how the differences resonate: the top left is crystal-like and the bottom right, flower-like.

Here, the square is tilted on end to form a diamond, then the space is divided equally in 4 parts with the cross.  Each quarter part is then further divided with the triangles.  This form could also be transformed into a curved form, similar to the one above.

Here, the space is again divided equally into 4 parts, but without the square border.  The curved half-circles contrast with the straight line form, and can also be drawn without the cross guidelines.

As always, form drawing is an excellent exercise in flexibility, creativity, and self control.  And the foundations are wonderfully built for approaching geometry with instruments later on, but not until Grade 6.

Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of knowledge as a worthy goal. Now the fun begins!  We have come to the end of the Common Core Grade 3 math standards, and so will devote some time and posts to exploring the joys of “homesteading” in the third grade.

The post 3.G 2: Divide Shapes Into Equal Parts, But Without Fractions (#210) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 209

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math. Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”

And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times. Why ambient? A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful. CCSS math standards are listed here in blue, followed by ambient math suggestions.

Geometry 3.G
Reason with shapes and their attributes.
1. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).  Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Form drawing nicely covers this standard by focusing on squares that can be fitted within a perfectly-drawn circle.  Hand-drawn forms are key, until formal geometry is taught in Grade 6.  That’s time enough to learn the formal names and terms.  No need now to be so explicit that each shape is identified by name.  More effective, much deeper learning is possible if the first interface with a concept is intuitive and broad, not specific.

Confidence and solid knowledge are built on just such a foundation.  Waldorf education parallels the stages of child development with the stages of human development.  For this reason, perspective drawing is not taught until Grade 7, paralleling the cultural context of the Renaissance when art images first reflected the leap into 3-dimensional seeing.

Plane forms are appropriate at this time, but not yet dimensional forms.  So the Rhombus needs to wait till a later grade, because its complex angles make it a dimensional rather than flat, plane figure.  Many variations on the square are experienced with form drawing, and this variety engenders a flexibility of thinking which spills over into all other areas.

Another invaluable quality of form drawing is that the forms are experienced on a much deeper level because they are created from virtually nothing.  Each form is described either verbally or with a picture story first, then moved, large and with whole-body movement.  The form is then “drawn” in the air before committing it to paper.

All of the square forms are accurately drawn because they’re based on the circle.  A yellow crayon or pencil is used to draw many circles, filling up the whole page, until the perfect circle is “found” then darkened.  After the corners of the square are located on the circle, the square is drawn with exploratory lines until the “right” lines are found.  This sort of freehand drawing is so much more empowering than tight, technical drawing because the forms are artfully built.  See below for contrasting examples of finding the “square spiral” within nested squares.

As always, knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of knowledge as a worthy goal. Tune in tomorrow for more Grade 3 math CCSS and their ambient counterparts.

The post 3.G 1: Geometry Squares But Not Rhombuses (#209) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 209

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math. Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”

And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times. Why ambient? A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful. CCSS math standards are listed here in blue, followed by ambient math suggestions.

Geometry 3.G
Reason with shapes and their attributes.
1. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).  Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Form drawing nicely covers this standard by focusing on squares that can be fitted within a perfectly-drawn circle.  Hand-drawn forms are key, until formal geometry is taught in Grade 6.  That’s time enough to learn the formal names and terms.  No need now to be so explicit that each shape is identified by name.  More effective, much deeper learning is possible if the first interface with a concept is intuitive and broad, not specific.

Confidence and solid knowledge are built on just such a foundation.  Waldorf education parallels the stages of child development with the stages of human development.  For this reason, perspective drawing is not taught until Grade 7, paralleling the cultural context of the Renaissance when art images first reflected the leap into 3-dimensional seeing.

Plane forms are appropriate at this time, but not yet dimensional forms.  So the Rhombus needs to wait till a later grade, because its complex angles make it a dimensional rather than flat, plane figure.  Many variations on the square are experienced with form drawing, and this variety engenders a flexibility of thinking which spills over into all other areas.

Another invaluable quality of form drawing is that the forms are experienced on a much deeper level because they are created from virtually nothing.  Each form is described either verbally or with a picture story first, then moved, large and with whole-body movement.  The form is then “drawn” in the air before committing it to paper.

All of the square forms are accurately drawn because they’re based on the circle.  A yellow crayon or pencil is used to draw many circles, filling up the whole page, until the perfect circle is “found” then darkened.  After the corners of the square are located on the circle, the square is drawn with exploratory lines until the “right” lines are found.  This sort of freehand drawing is so much more empowering than tight, technical drawing because the forms are artfully built.  See below for contrasting examples of finding the “square spiral” within nested squares.

As always, knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of knowledge as a worthy goal. Tune in tomorrow for more Grade 3 math CCSS and their ambient counterparts.

The post 3.G 1: Geometry Squares But Not Rhombuses (#209) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 208

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math. Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”

And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times. Why ambient? A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful. CCSS math standards are listed here in blue, followed by ambient math suggestions.

Measurement and Data 3.MD
Geometric measurement: understand concepts of area and relate area to multiplication and addition.
6. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
7. Relate area to the operations of multiplication and division.
a) Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
b) Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real-world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
c) Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b plus c is the sum of a x b and a x c.  Use area models to represent the distributive property in mathematical reasoning.
d) Recognize area as additive.  Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems.
Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
8. Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

I chose to list and address the rest of the measurement standards in one go because I feel that the application is similar for all.  As said in yesterday’s post, a bit of reality goes a long way, and the reality needs to be really real.  A fake reality just will not do.  One online lesson plan suggested having a group of third graders collaborate in designing a fictional clubhouse.  Such ruses are easily seen through and disaffection sets in, making understanding and successful learning elusive if not impossible.

So be real.  Design garden plots in shapes that fulfill the requirements of the standards, then build your garden using various units of measurement, first on paper, then for real.  Or design a game with a shape that fulfills the standard’s requirements, and draw it with sidewalk chalk on the pavement, then play the game!  Cut the required shapes out of fabric and sew a quilt that you and the children will be measuring as you go along.

The possibilities are endless, and it’s vitally important to ground learning in life.  A lifelong love of learning is built on just this sort of solid ground.  Worksheets, apps, and applets alienate.  They remove human interaction from the mix.  There may be a fear-driven motivation to consume (most workbooks are termed “consumable”) reams of standards-aligned worksheets to insure that when the questions show up on the high-stakes tests they will be recognized, and answered correctly.

But what lives beyond this sort of fear?  Faith.  A belief that if the concept is covered globally and holistically, just once or twice, it will stick.  And it will translate when the relevant questions appear on the test.  Out of such stuff the kind of heroes needed to address the towering challenges awaiting them in this fragile, cliff-hanger of a world are built.  Let love and humanity trump fear.  Give your children the gift of real things, not virtual, digital, or computerized.

Norman Davidson, Director of Teacher Training at the Waldorf Institute in Spring Valley, NY, summed it up with this.  “Go to the library, get what you need to teach the lesson, and then enliven it.”  Using the most mundane sources so your teaching is grounded, apply love and creativity to translate lessons into the language your child needs and understands: that of love and beauty.

Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of knowledge as a worthy goal. Tune in tomorrow for more Grade 3 math CCSS and their ambient counterparts.

The post 3. MD 6, 7 a) b) c) d), 8: Area & Perimeter, Make It Real (#208) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 207

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math. Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”

And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times. Why ambient? A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful. CCSS math standards are listed here in blue, followed by ambient math suggestions.

Measurement and Data 3.MD
Geometric measurement: understand concepts of area and relate area to multiplication and addition.
5. Recognize area as an attribute of plane figures and understand concepts of area measurement.
a) A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.
b) A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

I remember struggling with my daughter as we wrestled with the area and perimeter problems in the Grade 6 Saxon math textbook.  We sat in the kitchen every night attempting to master area and perimeter, using the foot square floor tiles as prompts.  It was a mighty struggle for her at age 12.  Granted, her strengths lie in the history/literature rather than the math/science camp but still, the struggle was real.

If the CC sees merit in pushing academics down to lower and lower grades in the name of “rigor” so be it.  But as an advocate for the voice of reason and patience I say, “Wait.  Just wait.”  Isn’t mastering all the times tables, long division and multiplication, while honing skills in the 4 processes enough?  Along with basic measurement skills, yes.

This may be enough for the 9 year old who is experiencing the pangs and loss of childish innocence as an inevitable facet of growing up, but the Common Core’s way of teaching and learning does not take into account that real sustenance is needed to weather not only this storm but all of the many storms that are each experienced deeply at the different ages and stages for every child.

A first glimpse into area and perimeter may be experienced with the building projects taken on this year.  Back to the chicken coop.  How much floor space is needed for each chicken?  And how is that figured out?  If each chicken needs 4 square feet of coop space (I just googled it, it does), how large does the coop need to be to accommodate 5 hens?  There you go, area and multiplication.  But concretely and with LOTS of adult help and support.  Gotta love this hobbit coop by inhabitat.com!

Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of knowledge as a worthy goal. Tune in tomorrow for more Grade 3 math CCSS and their ambient counterparts.

The post 3.MD 5 a) b): Too Soon for Area Measurement? Yes. (#207) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 207

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math. Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”

And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times. Why ambient? A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful. CCSS math standards are listed here in blue, followed by ambient math suggestions.

Measurement and Data 3.MD
Geometric measurement: understand concepts of area and relate area to multiplication and addition.
5. Recognize area as an attribute of plane figures and understand concepts of area measurement.
a) A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.
b) A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

I remember struggling with my daughter as we wrestled with the area and perimeter problems in the Grade 6 Saxon math textbook.  We sat in the kitchen every night attempting to master area and perimeter, using the foot square floor tiles as prompts.  It was a mighty struggle for her at age 12.  Granted, her strengths lie in the history/literature rather than the math/science camp but still, the struggle was real.

If the CC sees merit in pushing academics down to lower and lower grades in the name of “rigor” so be it.  But as an advocate for the voice of reason and patience I say, “Wait.  Just wait.”  Isn’t mastering all the times tables, long division and multiplication, while honing skills in the 4 processes enough?  Along with basic measurement skills, yes.

This may be enough for the 9 year old who is experiencing the pangs and loss of childish innocence as an inevitable facet of growing up, but the Common Core’s way of teaching and learning does not take into account that real sustenance is needed to weather not only this storm but the many storms that are each experienced differently at the different ages and stages for every child.

A first glimpse into area and perimeter may be experienced with the building projects taken on this year.  Back to the chicken coop.  How much floor space is needed for each chicken?  And how is that figured out?  If each chicken needs 4 square feet of coop space (I just googled it, it does), how large does the coop need to be to accommodate 5 hens?  There you go, area and multiplication.  But concretely and with LOTS of adult help and support.  Gotta love this hobbit coop by inhabitat.com!

Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of knowledge as a worthy goal. Tune in tomorrow for more Grade 3 math CCSS and their ambient counterparts.

The post 3.MD 5 a) b): Too Soon for Area Measurement? Yes. (#207) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 206

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math. Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”

And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times. Why ambient? A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful. CCSS math standards are listed here in blue, followed by ambient math suggestions.

Measurement and Data 3.MD
Represent and interpret data.
4. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch.  Show the data by making a line plot, where the horizontal scale is marked off in appropriate units, whole numbers, halves, or quarters.

Before teaching the nuts and bolts of measurement, create a fascination for it.  Where did the units of measurement come from?  How did they get their names?  What endearingly funny anecdotes can be related about our collective relationship to measurement?  Here are some examples from the Math By Hand Grade 3 binder:

Colorful historical facts and anecdotes in story form, along with practical applications and experiences are fun and effective teaching tools.  It’s surprising how relatively recently we’ve adopted our weights and measures standards.  When we lived more simply, before commerce and trade, there was little to no need to measure or weigh anything accurately.  Many peoples or tribes used individual systems of measurement in their local communities.  

The first known unit of universal measurement was the Egyptian cubit.  Its length was based on the length of the arm and hand, from the elbow to the extended fingertips.  Everyone’s arm measures differently, so in ancient Egypt the Standard Royal Cubit (used to check the accuracy of all measuring rods) was made of black granite and preserved at the Royal Court.

The human body was also used as the basis for smaller measurements.  Digits (fingers or sections of fingers), the palm, and the whole hand were used as smaller increments of the cubit.  Later on, the king’s foot was used as the first standard for our modern “foot.” 

And here are a couple of examples of the origins of units of measurement’s names:

Yard
from the German gierd (pronounced gyard) meaning girth, to encircle. One theory is that the yard originated as the waist measurement of the king (36 inches).  Another is that King Henry I of England decreed that a yard should be equal to the distance between his nose and extended thumb!

Mile
from the Latin mille meaning 1,000. The mile was first measured as 1,000 paces.

This sort of exploration and discovery can make for a much stronger start than diving right into the abstract bare bones of the subject.  As always, hands-on experience is invaluable.  The Math By Hand Grade 3 Kit 4 includes all the materials needed to make a 36″ tape measure, by hand of course!  

The instructions guide the student to mark whole, half, and quarter inches on the tape measure.  Much enthusiasm and willingness to learn is generated by the experience of making one’s own tools, and the inclination to use the tools more prolifically engenders a more successful relationship with measuring in general.

As for making line plots of random objects that are measured, the make-work nature of this endeavor will tend to make it less valuable and interesting.  How much more vital would it be to first create a situation that requires this sort of measuring, so the project itself has integrity, before setting about to measure and record otherwise random objects?

Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of knowledge as a worthy goal. Tune in tomorrow for more Grade 3 math CCSS and their ambient counterparts.

The post 3.MD 4: Tell Stories About Measurement First! (#206) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 205

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math. Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”

And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times. Why ambient? A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful.  Today’s post focuses on a Grade 3 building project at the Roseway Waldorf School near Durban, South Africa.

This was a practical application, teaching both housebuilding and measurement.  What child would choose to sit in a classroom toiling over worksheets or testing for hours on end over building something with his or her own two hands (and as it happens, feet)?  No child, it seems.  But why is this so-obvious fact so consistently ignored as we move progressively closer to digital and virtual learning, accompanied by rigid, grey, prisoning school policies?

Watch the youtube here, as you listen to the words of the Cold Play song, “We Live In A Beautiful World” . . . and know that we could indeed.  Choosing beautifully simple options over hi-tech, complex ones is key.  Get real.  The world is dying for you to do just that, with your children, its future.

Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of knowledge as a worthy goal. Tune in tomorrow for more Grade 3 math CCSS and their ambient counterparts.

The post Grade 3 Break: Building a Thatched Cob Hut (#205) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 204

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math. Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”

And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times. Why ambient? A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful. CCSS math standards are listed here in blue, followed by ambient math suggestions.

Measurement and Data 3.MD
Represent and interpret data.
3. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories.  Solve one-and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs.  For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

What?  5 pets?  Too many artificial scenarios created for the purpose of learning through repetition and “busy work” can be alienating and a turn-off.  John Holt said something to the effect that we cannot expect children to do what we as adults would refuse to do.  Think about it.  Would you willingly agree to spend roughly six hours a day solving problems for made-up situations?  And then take test after test to prove that you learned something?

Or would you rather do something real.  Here’s an example of a real bar graph, courtesy of veggieharvest.com (better than lots of 5 pet squares):

A child-friendly version of this chart could easily fulfill all of the above standard requirements while at the same time serving a very nutritious purpose!  Helping to plan the family garden and learning about seed-starting, planting, and harvesting is the goal, while learning about graphing data is secondary.  But so much more effective when it’s real.  Real data rocks!

Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of knowledge as a worthy goal. Tune in tomorrow for more Grade 3 math CCSS and their ambient counterparts.

The post 3.MD 3: Real Data: Garden Bar Graphs (#204) appeared first on Math By Hand.