Numeracy–Fundamental Questions


The only picture I could think of to post with this concept, is the Hello Numbers Discovery Pack.  Not that numeracy discussions are for early learners and their teachers and parents.  In fact numeracy is the center of the future of mathematics.  I created the plush numbers with magnets to create multi-digit numbers in response to teachers asking for tools to assist children with numeracy and understanding place value.  Putting 10 on the board or on a worksheet does NOT have the same impact as constructing 10 with 1 and 0 using magnets in your small hands.  Numbers become Friends You Can Count On! and friendly.  They want to engage you in stories of their relevance and how you will interact with them throughout life.

Stories will be coming as to how they came to be and how arithmetic came to where it is today.  Geometry is a critical aspect of the history of math and should be integrated from the beginning rather than left to proving logical relationships visually.  Why did the Greeks use geometry to prove relationships?  This is a great history lesson related to the 3rd question below.


When I meet with teachers, parents and students, I open with some of these questions for them to ponder:

What is math (maths)?  Where did it come from?  If you were to invent a numbering system, what would it look like/what characteristics would it have?

These three questions are fundamental to understanding numeracy.  I have never had folks ask me these questions, but I began asking them when I was a top math/statistics student.  Although I could “do” the work I complained that I did not understand what math was about.  Numeracy is fundamental to understanding math, yet we avoid discussing these three and other similar questions because they demand we are more comfortable returning to preparing folks to answer test questions without concern as to they understanding of what and why they are doing the work.

If anyone has ideas as to responses to these questions, please send them to me:  I am collecting ideas and passing them on to others.  We must address these issues to ensure that what we pass on is relevant to the future.  Even math will move on the respond to the new questions we will face.

When writing, please also discuss what aspects of math you use on a daily basis.  Using does not mean what you teach, but what you use for daily living.  Please also note your profession and how that influences the aspects of math you use.

To fundamental numeracy and math for today and tomorrow!





The Globe Celebrates the Common New Year


NumbersAlive! hopes you all have a wonderful transition from 2017 to 2018.

As 2018 begins, consider how the change in the year utilizes numbers in an understood global manner   How and why did this happen?  Many cultures have their own calendars, but the world celebrates the new year with the same numbering system.  Among the numbers 0-9, 8 is happy to replace 7, who hung on as long as possible as part of time’s name.  Like the US presidency, the transition should be smooth.   Numbers are part of every discipline/concept necessary for transforming young children into citizens

Geometry should be linked to numbers and our efforts to do so created Number Linx which was named the best invention of North America at the iCAN invited inventor conference in Toronto last August.

We are here to help all educators, parents and children understand what math is about and where it came from.   We are focused on such questions and embrace historic and forward-thinking fundamentals to make math meaningful and real.  Being everywhere you look we use actual photos, locations, quotes, etc. to demonstrate its usefulness.  We encourage learners of all ages to observe, discuss, design, create, and make math!  How and why were the systems we use today developed?


Importance of Exercising Your Right to Vote

As a citizen you have an obligation to vote.

If everyone votes would America unite?
Knowing each vote is a light in the night.
Would commenters have less need to “spin”
Reasons why voters decided who will win?

If everyone voted, would leaders do more?
And listen to voters like never before?
If everyone voted would the hungry be fed?
Would the homeless have shelter, each child his own bed?

Our vote is our voice that can’t be dismissed
It’s a shout and a prayer, our heart and our fist.
Our vote is our right, that makes our land great.
It’s a duty and joy; our privilege, our fate.


Let’s look at the most recent election for two governors.  Did citizens exercise their right to vote?


Look at the two pie charts.  What are the largest pieces?  The purple pieces are the registered voters who did NOT exercise their right to vote or voted for something other than the three identified candidates.  And this was considered a “large turnout”!

The lesson of November 7, 2017 should be that fewer than half of all registered voters voted.  Why?  What does that mean? Would their votes have been similar to those who did vote?

A great numeric civics exercise would be to consider how different possibilities of additional voters could have changed the outcome.  Chart those possibilities and see how important everyone’s vote is.

Other issues to discuss and investigate include the following:

  1.  What are the types of data systems used to determine the total number of registered voters?
  2. How could weather affect the number of citizens who exercise their right to vote?
  3. What procedures do voting locations use to know that the voter is registered to vote?
  4. Why do so few citizens actually exercise their right to vote?


New Jersey registered voters as of 11/7/17: 5,754,862
New Jersey Gubernatorial results Source:
Murphy, Philip Dem 1,119,516 55%
Guadagno, Kim GOP 858,735 43%
Genovese, Gina Ind 11,131 1%

Commonwealth of Virginia 5,489,530 registered voters as of 10/31/2017:
Virginia Gubernatorial Race results
Ralph S. Northam
Democratic 1,405,007 53.87%
Edward W. “Ed” Gillespie
Republican 1,172,533 44.96%
Clifford D. Hyra
Libertarian 29,303 1.12%




Candy Calculations

Halloween cndy bag 1Halloween candy bag 2








Bag 1 of 100 pieces                                                   Bag 2 of 100 pieces

Like most kids, Halloween was one of my favorite days each year. It still is.
I’d collect a huge bag of treats, then spill and sort my spoils on the living room floor. I’d make separate piles of Hershey bars, candy corn packets, lollipops, Three Musketeers, etc. or fruit, sorting and counting to determine the size of my Halloween haul.
Unconsciously, I was developing important math skills with each bag of candy or type of fruit I threw into a pile.
Halloween is a great and painless opportunity to help children hone their early math skills – number sense, sorting, patterns, and estimation – and more advanced arithmetic competences, like multiplication and percentage. Here’s how.

Sorting: Kids will sort their stash into categories most important to them — candy or fruit, lumpy or smooth bags, what I’ll keep or will trade away. You can suggest other categories, like size, color, calories, weight, treats Mom will let you eat every day or just once a week. Remember, no category is wrong. The world needs thinkers who bring unique approaches to solving common problems.
Look at the two pictures of the loot from two different bags of 100 pieces of candy. What do you notice between bag 1 and bag 2? If your favorite is Almond Joy, which bag would you prefer the house to have for you to pick a piece? Why?

Then order the four kinds of candy by type (Most? Least? 2nd most? 3rd most?) for each bag. How easy is it to estimate the order from most to least, or least to most without actually counting?

Counting: Halloween is all about counting. How many doorbells did you ring? How many treats did you get? How many tricks did you perform? How many M&Ms in each package? The counting opportunities are endless.

Number recognition: Students can pick out all the numbers on a bag of candy – total weight, ounces/serving, calories/serving, grams of sugar or fat, percentage of Recommended Daily Value. Not only will students practice their number recognition skills, but they’ll learn about nutrition, too.

Weighing/Measuring: Grab a scale and measuring cup and let students practice weighing and measuring their loot. Does every M&M weigh the same? Do 4 grams feel heavier or lighter than 4 ounces? How do you convert one into the other?

Multiplication: At Target, a 4.4 oz. Hershey’s Milk Chocolate bar costs $1.59. How much would 1 oz. cost? Search each label for the total number of ounces in each chocolate treat, then multiply to determine the total value.

Math is so much fun when you tie it to a holiday kids already love. Have a happy, safe, and mathematic Halloween!

By the Way:
Bag 1 included 100 mini candies:  9 Almond Joys; 16 Reese’s, 45 Kit Kats; and 30 Hershey’s.
Bag 2 also included 100 mini candies:  14 Almond Joys; 22 Reese’s; 54 Kit Kats; and 10 Hershey’s.

Learn With Urns!

Grecian Urn

A beautiful artifact, this Grecian urn.

Around the amphora the patterns turn,

Made for a funeral, the art is so fine,

It showcases beautiful Grecian design.

With shapes of triangles, squares and rhombi,

Ancestor’s ashes don’t become zombies.

Archaeologists worked hard to recreate

This puzzling urn—it’s once again great.

Although the long-buried urn is quite old,

Diggers found all pieces –its artwork still bold.

The classic style is still made today,

As well as modern vessels made of clay.

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