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The Promise

Posted on by Denise Gaskins

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Romans 4:13-25

For the promise to Abraham and his offspring that he would be heir of the world did not come through the law but through the righteousness of faith.

For if it is the adherents of the law who are to be the heirs, faith is null and the promise is void.

That is why it depends on faith, in order that the promise may rest on grace and be guaranteed to all his offspring — not only to the adherent of the law but also to the one who shares the faith of Abraham, who is the father of us all — in the presence of the God in whom he believed, who gives life to the dead and calls into existence the things that do not exist.

In hope he believed against hope, that he should become the father of many nations … That is why his faith was “counted to him as righteousness.”

But the words “it was counted to him” were not written for his sake alone, but for ours also.

It will be counted to us who believe in him who raised from the dead Jesus our Lord, who was delivered up for our trespasses and raised for our justification.

Scripture quotations are from the ESV® Bible (The Holy Bible, English Standard Version®), copyright © 2001 by Crossway, a publishing ministry of Good News Publishers. Used by permission. All rights reserved. ESV.org.

Hello, Food TV

Posted on by Denise Gaskins

I didn’t get anything written to share today, so here’s a cat picture instead. My favorite shot from Puck’s babyhood.

He’s grown about two years’ worth since then.

Still full of puckishness, though. He had a time of it today, “helping” me put up the Christmas tree.

Mathy Christmas Cards

Posted on by Denise Gaskins

I always wait too long to put cards in the mail. Maybe these creative beauties will inspire me to get started right away?

For More Holiday Math

CREDITS: Reindeer photo (top) by Norman Tsui via Unsplash.com.

What Are Mixed Numbers?

Posted on by Denise Gaskins

I just discovered a fascinating fact: In some places in the world, mixed numbers apparently don’t exist.

So that made me curious about my blog readers:

  • Did you learn about mixed numbers in school?
  • Do you ever use mixed numbers in daily life?
  • Are your children learning to work with them?

And if you DO know mixed numbers, can you simplify this mess:

[If you enjoy dry math humor, the answer is worth the work.]

Continue reading What Are Mixed Numbers?

The Principality of Mathematics

Posted on by Denise Gaskins
quotation from Charlotte Mason: The principality of mathematics is a mountainous land, but the air is very fine and health-giving

Here’s the full quote:

“The Principality of Mathematics is a mountainous land, but the air is very fine and health-giving, though some people find it too rare for their breathing. People who seek their work or play in this principality find themselves braced by effort and satisfied with truth.”

— Charlotte Mason, Ourselves

Charlotte Mason and Math

Math was not one of Charlotte Mason’s primary interests. She didn’t think or write as deeply about it as she did other subjects.

She even wrote, “It is unnecessary to exhibit mathematical work done in the P.U.S. as it is on the same lines and reaches the same standard as in other schools.”

This leaves us modern parents and teachers having to read our own interpretations into her words. It should be no surprise when we come to different conclusions. Someday, perhaps, I’ll publish my own vision for a Charlotte Mason approach to homeschooling math.

In the meantime, the following articles describe a method that allows even the youngest children to explore the Principality of Mathematics:

In the years since writing those posts, Sonya and Lacy combined all their ideas into an easy-to-implement program that I think Mason herself would have enjoyed. Here’s my review:

CREDITS: Quote background photo (top) by Kalen Emsley via Unsplash.com.

Mathematical Days of Christmas

Posted on by Denise Gaskins

Enjoy this bit of seasonal fidgeting from Vi Hart.

If you don’t understand some of the references, that’s normal! Pick a phrase, Google it, and relish the fun of learning something new.

Did your device hide the video? Find it on YouTube here.

For More Holiday Math

CREDITS: Lamppost photo (top) by Aaron Burden via Unsplash.com.

Math Advent Calendars for 2020

Posted on by Denise Gaskins

Would you like to add some no-preparation-required fun to your math lessons this month?

Check out these creative mathematical Advent calendars, each featuring one puzzle or activity per day for December 1–24.

Some of the calendars may show a previous year’s date. (This is 2020 after all!) But the puzzles are evergreen — you can enjoy them anytime.

For more Advent-math links, visit Colleen Young’s Mathematical Advent Calendars post. And don’t miss my massive blog post Holiday Math Puzzles and Activities for Christmas, Winter Break.

I Wonder

Posted on by Denise Gaskins

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Romans 5:6-11

For while we were still weak, at the right time Christ died for the ungodly.

For one will scarcely die for a righteous person — though perhaps for a good person one would dare even to die — but God shows his love for us in that while we were still sinners, Christ died for us.

Since, therefore, we have now been justified by his blood, much more shall we be saved by him from the wrath of God.

For if while we were enemies we were reconciled to God by the death of his Son, much more, now that we are reconciled, shall we be saved by his life.

More than that, we also rejoice in God through our Lord Jesus Christ, through whom we have now received reconciliation.

Scripture quotations are from the ESV® Bible (The Holy Bible, English Standard Version®), copyright © 2001 by Crossway, a publishing ministry of Good News Publishers. Used by permission. All rights reserved. ESV.org.

Can You Do the Math Salute?

Posted on by Denise Gaskins

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How Is This Math?

The idea that math is only about numbers, calculations, and textbook exercises is one of the greatest lies we learn in school. Of course, nobody ever comes straight out and actually says that. But the whole system teaches us every day what counts for math and what doesn’t.

James Tanton’s math salute is a physical puzzle.

How in the world did he do that?

Physical puzzles don’t fit into our cultural understanding of math. But the process of figuring out the puzzle is the same problem-solving process we use to figure out other puzzles — including the puzzles we call math.

In fact, real mathematics is all about figuring out puzzles without a teacher showing you what to do. Problem-solving is a universally useful skill.

As master teacher W. W. Sawyer said:

“Everyone knows that it is easy to do a puzzle if someone has told you the answer. That is simply a test of memory. You can claim to be a mathematician only if you can solve puzzles that you have never studied before. That is the test of reasoning.”

—W. W. Sawyer, Mathematician’s Delight

So tackle the puzzle of the math salute. Show it to your kids. (And don’t be surprised if they figure it out before you do!)

[THE FINE PRINT: I am an Amazon affiliate. If you follow the link and buy something, I’ll earn a small commission (at no cost to you). But this book is a well-known classic, so you should be able to order it through your local library.]

O Come

Posted on by Denise Gaskins

Today, we celebrate the traditional beginning of the Christmas music season…

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Isaiah 11:1-10

There shall come forth a shoot from the stump of Jesse,
and a branch from his roots shall bear fruit.

And the Spirit of the Lord shall rest upon him,
the Spirit of wisdom and understanding,
the Spirit of counsel and might,
the Spirit of knowledge and the fear of the Lord.

And his delight shall be in the fear of the Lord.
he shall not judge by what his eyes see,
or decide disputes by what his ears hear,

but with righteousness he shall judge the poor,
and decide with equity for the meek of the earth.

… They shall not hurt or destroy
in all my holy mountain;
for the earth shall be full of the knowledge of the Lord
as the waters cover the sea.

In that day the root of Jesse shall stand as a signal for the peoples — of him shall the nations inquire, and his resting place shall be glorious.

Scripture quotations are from the ESV® Bible (The Holy Bible, English Standard Version®), copyright © 2001 by Crossway, a publishing ministry of Good News Publishers. Used by permission. All rights reserved. ESV.org.