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Philippians 2:5-11

Christ Jesus who, though he was in the form of God, did not count equality with God a thing to be grasped, but emptied himself, by taking the form of a servant, being born in the likeness of men.

And being found in human form, he humbled himself by becoming obedient to the point of death, even death on a cross.

Therefore God has highly exalted him and bestowed on him the name that is above every name.

So that at the name of Jesus every knee should bow, in heaven and on earth and under the earth, and every tongue confess that Jesus Christ is Lord, to the glory of God the Father.

At some point during the process of teaching multiplication to our children, we really need to come to terms with this question:

What IS multiplication?

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“What’s my answer? It’s not one that society’s going to like. Because society expects — demands, even — that mathematics be concrete, real-world, absolute, having definitive answers.

I can’t give a definitive answer.

Multiplication manifests itself in different ways. So maybe the word ‘is’ there is just too absolute. And it’s actually at odds with what mathematicians do.

Mathematicians do attend to real-world, practical scenarios — by stepping away from them, looking at a bigger picture.”

Continuing on my theme of times table facts, here’s the inimitable James Tanton:

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“If our task is to memorize this table, please make it about mathematics — about thinking your way through a challenge, and what can I do to make my life easier.”

You may also enjoy my blog post series about working through the times tables, paying attention to mathematical relationships (and a bit of prealgebra) along the way.

A comment from a friend got me playing around with multiplication. I found a few videos from some of my favorite math people, so I’ll be sharing over the next few days.

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“When students have to drill multiplication facts, it’s frustrating, unproductive and it makes them hate math. A better way to master the multiplication table is work on the skills that allow students to multiply quickly and efficiently.”

Making doubles and halves are a great foundation for all sorts of math.

Do you ever play the doubling game with your children? One player picks a starting number, and then you take turns doubling it until your mental math skills run out. How far can you go?

Or try the halving game: One player chooses a starting number, and you take turns cutting it in half. How tiny can you go?

As Sonya demonstrated, these skills help your child master their multiplication facts. And they are fantastic preparation for exponents and logarithms, too!

Each monthly Playful Math Education Blog Carnival brings you a great new collection of puzzles, math conversations, teaching tips, and all sorts of mathy fun. It’s like a free online magazine of mathematical adventures, helpful and inspiring no matter when you read them.

Sonya put together this wonderful collection of mathematical games, art projects, holiday activities, paper crafts (LOTS of snowflakes!), and more.

She writes:

“It doesn’t matter where you look, there are always things to count and lots of things to wonder about. How many snowflakes in a snowman? How many points are on a star? How many turkeys do we eat every year? Does anyone actually eat all the fruitcake that is sold each year?

“Here is Winter and her holidays by the numbers…

“This was probably my favorite Playful Math Education Blog Carnival to write. There is so much out there to explore that I’m sure I’ve barely scratched the surface.

“Come back because I’m going to keep adding to this post…”

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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.