Sacramento Homeschool Math By Hand

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 178

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 is all about wrapping up with a play from the stories shared all year.  

Many Waldorf plays are centered around Saints or Heroes and the legends that grew up around them.  But the fables are another fertile field for harvesting, with fun plays that are fairly simple to produce, with costuming, scripts, and scenery. Simple masks will do for most fables’ characters, and basic outfits of neutral or dark colored t-shirts and cotton pants help to direct the focus to the characters through their masks.  Here’s a Pinterest post from one of my favorite blogs: Picklebums, featuring egg-carton masks.  The possibilities are endless with these!  Paint and embellish them for many different fables’ characters.

Generic outdoor scenery will do, since most of the action takes place in the woods!  Create a simple scene of trees and sky on a plain, white cotton sheet.  You might try using sidewalk chalk and water for a subtle effect, or paints and wide brushes for something bolder.  Make this a community project, everyone will want to get into the act.

Or here’s another option.  Get a free “end roll” from your local newspaper (they give away the rolls that are too small to use on the presses), available in newsprint or heavier white paper.  The heavier paper is obviously sturdier.  This allows you to paint (or chalk or crayon) the scenery in panels for more flexibility.  Roll up the paper (or fold the sheet) for another time, another play.

The fables are super simple to script.  Just create a basic dialog from the story, staying as faithful to it as possible.  Some of the fables might lend themselves to a chorus rather than individual speaking parts.  Taking three to four weeks at the end of the year to put on a play is soooo worth the time and effort.  I reposted something on Facebook recently that was very sad.  It seems a certain school (I’m imagining there are many more like it) wrote a letter to parents stating that because of the pressure to fit in enough academics to meet Common Core demands, the Kindergarten class play was being cancelled.  Tragic.

In Waldorf schools, performance skills are built up through the years so that a brief 10 to 15 minute first grade fairy tale play becomes a full-on 90-minute seventh or eighth grade performance (most often Shakespeare).  My daughter’s wonderfully memorable eighth grade play was “You Can’t Take It With You,” an excellent choice for that particular group!  

So do recruit family and friends to help with this crowning achievement, and have mountains of fun with it.  Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of that knowledge as a worthy goal.  More Grade 2 fun tomorrow, stay tuned!

The post Fun! The End-of-Year Play: Scripts, Costumes, Scenery (#178) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 178

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 is all about wrapping up with a play from the stories shared all year.  

Many Waldorf plays are centered around Saints or Heroes and the legends that grew up around them.  But the fables are another fertile field for harvesting, with fun plays that are fairly simple to produce, with costuming, scripts, and scenery. Simple masks will do for most fables’ characters, and basic outfits of neutral or dark colored t-shirts and cotton pants help to direct the focus to the characters through their masks.  Here’s a Pinterest post from one of my favorite blogs: Picklebums, featuring egg-carton masks.  The possibilities are endless with these!  Paint and embellish them for many different fables’ characters.

Generic outdoor scenery will do, since most of the action takes place in the woods!  Create a simple scene of trees and sky on a plain, white cotton sheet.  You might try using sidewalk chalk and water for a subtle effect, or paints and wide brushes for something bolder.  Make this a community project, everyone will want to get into the act.

Or here’s another option.  Get a free “end roll” from your local newspaper (they give away the rolls that are too small to use on the presses), available in newsprint or heavier white paper.  The heavier paper is obviously sturdier.  This allows you to paint (or chalk or crayon) the scenery in panels for more flexibility.  Roll up the paper (or fold the sheet) for another time, another play.

The fables are super simple to script.  Just create a basic dialog from the story, staying as faithful to it as possible.  Some of the fables might lend themselves to a chorus rather than individual speaking parts.  Taking three to four weeks at the end of the year to put on a play is soooo worth the time and effort.  I reposted something on Facebook recently that was very sad.  It seems a certain school (I’m imagining there are many more like it) wrote a letter to parents stating that because of the pressure to fit in enough academics to meet Common Core demands, the Kindergarten class play was being cancelled.  Tragic.

In Waldorf schools, performance skills are built up through the years so that a brief 10 to 15 minute first grade fairy tale play becomes a full-on 90-minute seventh or eighth grade performance (most often Shakespeare).  My daughter’s wonderfully memorable eighth grade play was “You Can’t Take It With You,” an excellent choice for that particular group!  

So do recruit family and friends to help with this crowning achievement, and have mountains of fun with it.  Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of that knowledge as a worthy goal.  More Grade 2 fun tomorrow, stay tuned!

The post Fun! The End-of-Year Play: Scripts, Costumes, Scenery (#178) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 177

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 is all about chalkboard drawing.  1) Why do it?  2) How complicated and difficult is it?  3) Will your children benefit from it?  4) Will you grow into it and grow to actually enjoy it?  Resounding yes! on #’s 3 and 4, not very for # 2, and see below for # 1′s response.

Chalkboard drawing was one of my favorite things as a Waldorf teacher.  Ok, so I’m an artist to begin with, but the blackboard and colored chalk is a wonderfully forgiving medium and it’s quite possible for even the art-intimidated to succeed.  My husband once subbed for a week in my second grade classroom and his drawing of the fable, “The Milkmaid and Her Pail” was very good.

She wore a bright red dress and the essence of the story (the milkmaid’s foolish vanity as her undoing) was palpably present in the drawing.  My point here is that no matter how skilled (or not) you are as an artist, your drawings will be wonderful.  One of the most valuable ideas I took away from Waldorf education is that the teacher’s striving means more to the children than almost anything else s/he does.  They will not only love you for your efforts, but will gain so much from your example that they will pour on the extra effort in everything they do as well.

You can construct your own blackboard fairly economically and simply.  On the large side is nice, because you want it to sort of dominate the room.  It imparts a great deal of the subject at hand or the general mood of the year (i.e., the fables’ animals or the heroes/saints).  A piece of 1/2″ plywood is fine, but you may want to choose a better grade for a smoother surface.  Cover it with several coats of blackboard paint, then frame it with a simple (stained or painted) molding.  Prop and lean it or hang it on the wall with several large picture hooks and heavy picture wire.  You’re all set!  A new drawing only once a month is sufficient.

Here’s an excellent resource to inspire you, a website by Catie Johnson called Chalkboard Drawings in the Waldorf Classroom.  This is the Essence of Grade Two page, but do wander around to the different grades, look at the Why Do Chalkboard Drawings, and the Gallery of Drawings pages.  I guarantee you’ll be inspired to try your hand at a few of your own drawings.  Oh, and there’s the “Tibetan sand mandala” element as well, which conveys a valuable message all its own: that nothing is too precious to let go of, and then begin again with a clean slate.  (Do photograph and save them however.)

When I began the Waldorf teacher training, several specters haunted me.  One was how was I ever going to teach music?  And knitting?  I had little to no experience or talent with either.  And math?!  (Actually, getting to learn math the Waldorf way and teaching it hands-on, with games, language arts, and movement is what inspired me to create Math By Hand.)  But my very insecurity, vulnerability, and being able to conquer my fears and succeed was one of the best lessons I was able to teach my students!

Homeschooling parents teach most of what they teach this way anyway, but I encourage you to take that extra stretch into unfamiliar territory.  You will love it, you’ll see.  As always, it’s movement, story, art and playfulness that win the math day!  Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of that knowledge as a worthy goal.  More Grade 2 fun tomorrow, stay tuned!

The post Fun! Chalkboard Drawing Made Easy (#177) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 176

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 standard will be listed in blue, followed by its ambient counterpart.

Geometry 2.G
Reason with shapes and their attributes.
3. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths.  Recognize that equal shares of identical wholes need not have the same shape.

Again, form drawing covers this nicely, with the circle being the basis for many, many forms.  The circle is drawn with a yellow crayon, lightly at first until the perfect circle is “found” than darkened.  Partitioning happens the same way, with the equal shares marked lightly, then darkened as the best spacing is found.

Note the pentagon/pentagram and hexagon/hexagram below.  They were drawn with the method cited above, and the hexagram is further divided into 12 equal shares.  Though a feel for the whole and parts of a whole is there, it is not made conscious yet.  That’s reserved for fractions in Grade 4, when there’s an optimal readiness for “fractioning” or the fracturing it represents.  As mentioned earlier, wholeness should only gradually give way to separation as the child moves through the grades.

As always, it’s movement, story, art and playfulness that win the math day! Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of that knowledge as a worthy goal.  This is the last Grade 2 Common Core standard tune in tomorrow for the fun part!  

The post 2.G 3: Divide Circles & Squares Without Fractioning (#176) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 174

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 standard will be listed in blue, followed by its ambient counterpart.

Geometry 2.G
Reason with shapes and their attributes.
2. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

It’s not clear how to get rows and columns of squares by folding a rectangle into smaller versions of itself.  I’d think you’d need to start with a square to get squares.  Aside from that though, there’s the activity itself.  Does it have a purpose, or is it busywork, as are so many of the lessons and activities imposed on children as part of a school day.  Here’s what John Holt has to say about this:

The very first Grade 2 lesson is making an oversized times tables wall chart.  A 36 inch square piece of poster paper is folded: in half twice (4 columns), then in thirds (12 columns).  Then the paper is opened up and the same folds are repeated the other way, yielding 144 same-sized squares.

The children then fill in the tables they know.  They’ve learned the 2′s, 5′s, and 10′s in Grade 1 and of course they know the 1′s.  They can be told that the 11′s are just double numbers (up to 9), and they are happy to see how much of the chart is completed!  A prompt is used to copy from, as the rest are penciled in.

After all the tables are checked for accuracy, the children color the numbers in each row a different color with colored pencils.  Many patterns are found, like the square numbers running along a diagonal line from 1 to 144.  The chart is posted in a prominent place so the times tables can be painlessly and gradually absorbed.

Many squares were made from a large square, and used for a good purpose.  This chart can used until all the times tables are learned.  Basic skills like this are the bedrock of math success and proficiency.  And the chart is created with pride and enjoyment, qualities that are so essential to any teaching and learning worth its salt.

As always, it’s movement, story, art and playfulness that win the math day! Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of that knowledge as a worthy goal.

The post 2.G 2: Making Squares On Purpose (#175) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 174

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 standard will be listed in blue, followed by its ambient counterpart.

Geometry 2.G
Reason with shapes and their attributes.
1. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.  Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

Form drawing!  It fills the bill nicely.  With the exception of the beginning and end, this standard is totally appropriate for Grade 2 (beginning with “reason” and ending with “cubes”). At this age, foundations are built for future learning, with an eye toward the concrete rather than the abstract.  And since reasoning is by nature abstract, it doesn’t fit.

Cubes are a whole different genre than flat, 2 dimensional shapes.  The latter is nicely addressed with form drawing, but drawing 3-dimensional shapes needs to come later.  A playful approach to solid geometric forms could continue.  Math By Hand offers materials to make a cube ball (see below).  Similar 3-dimensional shapes could be sewn, sculpted, or knitted.  But technically correct, 3-dimensional geometric drawings are way too complex for now.

Math By Hand offers a comprehensive progression of form drawings through the grades.  The collection of 16 drawings for each of the grades 1-4 is included in a book with grade level stories.  See this slideshow overview of the Stories / Form Drawing books.

Form drawing could be taught in a block of one to three weeks at the beginning of the year and brought back as a main lesson once a week.  It’s a valuable discipline for many reasons, including building confidence, flexibility, and creativity.

See below for examples of a triangle, quadrilateral, hexagon, and pentagon/gram, all associated with numbers and fairy tales in the Math By Hand / Grade 1 / Quality of Numbers block.  The exposure through form drawing to varied geometric forms begins in Grade 1 and continues, becoming more complex with each grade, until formal geometry in Grade 6.

As always, it’s movement, story, art  and playfulness that win the math day!  Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of that knowledge as a worthy goal.

The post 2.G 1: Form Drawing & Geometry (#174) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 174

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 standard will be listed in blue, followed by its ambient counterpart.

Geometry 2.G
Reason with shapes and their attributes.
1. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.  Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

Form drawing!  It fills the bill nicely.  With the exception of the beginning and end, this standard is totally appropriate for Grade 2 (beginning with “reason” and ending with “cubes”). At this age, foundations are built for future learning, with an eye toward the concrete rather than the abstract.  And since reasoning is by nature abstract, it doesn’t fit.

Cubes are a whole different genre than flat, 2 dimensional shapes.  The latter is nicely addressed with form drawing, but drawing 3-dimensional shapes needs to come later.  A playful approach to solid geometric forms could continue.  Math By Hand offers materials to make a cube ball (see below).  Similar 3-dimensional shapes could be sewn, sculpted, or knitted.  But technically correct, 3-dimensional geometric drawings are way too complex for now.

Math By Hand offers a comprehensive progression of form drawings through the grades.  The collection of 16 drawings for each of the grades 1-4 is included in a book with grade level stories.  See this slideshow overview of the Stories / Form Drawing books.

Form drawing could be taught in a block of one to three weeks at the beginning of the year and brought back as a main lesson once a week.  It’s a valuable discipline for many reasons, including building confidence, flexibility, and creativity.

See below for examples of a triangle, quadrilateral, hexagon, and pentagon/gram, all associated with numbers and fairy tales in the Math By Hand / Grade 1 / Quality of Numbers block.  The exposure through form drawing to varied geometric forms begins in Grade 1 and continues, becoming more complex with each grade, until formal geometry in Grade 6.

As always, it’s movement, story, art  and playfulness that win the math day!  Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of that knowledge as a worthy goal.

The post G.2 1: Form Drawing & Geometry (#174) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 173

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 standard will be listed in blue, followed by its ambient counterpart.

Measurement and Data 2.MD
Represent and interpret data.
10. Draw and picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories.  Solve simple put-together, take-apart, and compare problems. 

The following is a re-post from Grade 1, Day 113:

This needs to be very informal. Excel spreadsheets, or formal charts and graphs for that matter, should not be the venue here. More like, three or four small shoeboxes perhaps painted or covered with kraft paper to hold collections, will suit the purpose nicely.  Or use open, wide-mouth mason jars, since they are see-through and easily added to and taken from.

Children are natural collectors, and do not need much encouragement to organize and categorize their treasures. Nature walks are the perfect occasion to gather various specimens like acorns, pine cones, stones, shells, and many more wonders. All children relish the opportunity to look closely at the minutiae of their surroundings in the natural world.

This collection could be accompanied by a small, colorful record keeping notebook. Sections could be created for each category, with the data updated as more specimens or additional categories are added. A color-coding system may be useful, using a different colored pencil for each category. Matching colored index tabs could be added for easy perusing.

All junior scientists are more than happy to talk about their collections, and could be guided to be consistent in their documentation. One large page (kept separately and inserted into the notebook) could list all of the categories side by side, color coded and updated as needed.

Using legos or duplos is a wonderful, 3-D way to introduce the concept of bar graphing, and could be used as a visual for solving simple put-together, take-apart, and compare problems.  Do keep word problems vital, concrete, alive and real, however.

As always, it’s movement, story, and art, along with gifts of the natural world, that win the math day! Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of that knowledge as a worthy goal.

The post 2.MD 10: Using Bell Jars & Legos to Graph Data (#173) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 173

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 standard will be listed in blue, followed by its ambient counterpart.

Measurement and Data 2.MD
Represent and interpret data.
10. Draw and picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories.  Solve simple put-together, take-apart, and compare problems. 

The following is a re-post from Grade 1, Day 113:

This needs to be very informal. Excel spreadsheets, or formal charts and graphs for that matter, should not be the venue here. More like, three or four small shoeboxes perhaps painted or covered with kraft paper to hold collections, will suit the purpose nicely.  Or use open, wide-mouth mason jars, since they are see-through and easily added to and taken from.

Children are natural collectors, and do not need much encouragement to organize and categorize their treasures. Nature walks are the perfect occasion to gather various specimens like acorns, pine cones, stones, shells, and many more wonders. All children relish the opportunity to look closely at the minutiae of their surroundings in the natural world.

This collection could be accompanied by a small, colorful record keeping notebook. Sections could be created for each category, with the data updated as more specimens or additional categories are added. A color-coding system may be useful, using a different colored pencil for each category. Matching colored index tabs could be added for easy perusing.

All junior scientists are more than happy to talk about their collections, and could be guided to be consistent in their documentation. One large page (kept separately and inserted into the notebook) could list all of the categories side by side, color coded and updated as needed.

Using legos or duplos is a wonderful, 3-D way to introduce the concept of bar graphing, and could be used as a visual for solving simple put-together, take-apart, and compare problems.  Do keep word problems vital, concrete, alive and real, however.

The post 2.MD 10: Using Bell Jars & Legos to Graph Data (#173) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 172

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 standard will be listed in blue, followed by its ambient counterpart.

Measurement and Data 2.MD
Represent and interpret data.
9. Generate measurement data by measuring lengths of several objects to the nearest whole unit or by making repeated measurements of the same object.  Show the measurements by making a line plot where the horizontal scale is marked off in whole number units.

In searching online for lesson plans and activities aligned to this standard, I found many that obviously resulted from much effort and energy on the part of master teachers in a cooperative effort.  There’s a big push to create lesson plans that match the standards and are aligned to the CCSS standardized tests.  Authenticity is a challenge since so many teachers are scrambling to create or find ways to implement these standards that many feel were too hastily rolled out, without enough substance.

At any rate, most of what I found was disappointingly divorced from meaning, in real life or in the context of a larger focus of study.  One plan required presenting two pencils of different lengths to the “scholars,” asking how to find out which pencil is longer.  The teacher was instructed to call on one or two scholars who then suggested s/he use a ruler to measure both of them.  Then the teacher walked the scholars through the process of finding the difference between the two lengths by using a subtraction sentence.

Does this lesson seem boring to you, or is it me?  This is what comes of letting standards run the show, and coming at learning abstractly, through the front door.  Instead, couldn’t measurement be incidental, taking a back seat to life, and learning about who we are as a culture or a race? Here’s another Grade 3 sneak peek to illustrate the point.  

After learning about Noah’s Ark, students measure it in a large, open space using a cubit as the measuring unit.  This is after learning about the cubit, one of the earliest measuring tools.  It really is astonishing to the third graders to see just how huge the ark was!  Nothing as mundane as measuring pencils (why on earth would you need to measure your pencils anyway?), ir’s literally monumental and riveting.  Just another example of how lessons could be brought to life and made compellingly interesting.

See below for a picture of an exact replica of Noah’s Ark, built according to exacting Biblical specifications by John Huibers of the Netherlands.  As a Waldorf third grade teacher, I had the students make their own cubit replicas (see below for a picture of a Cubit Rod that is currently housed in the Louvre.)

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 the last Common Core measurement standard and its ambient counterpart.

The post 2.MD 9: Using Cubits vs. Rulers to Measure, Large! (#172) appeared first on Math By Hand.