July Links: Math Mania

I love teaching math! That's hardly a surprise since math was always my favorite subject before I discovered the even greater thrill of applied math in the study of chemistry. Faith, a senior this year, is exploring the possibility of studying secondary math education in college. Woohoo!

Since we're all gearing up for a new school year, I figured this was as good a time as any to share some great links about math education.

Articles Worth Reading

Six Reasons Why Singapore Math Might Just Be the Better Way
We've been using Singapore Math for fifteen years, and this article lays out why it is superior to most other approaches for elementary math. Any decent math program should teach numerical literacy. But math ought to be about so much more, including building logical thinking patterns. (Watch, for example, the answer to a Singapore math question which went viral which is highlighted in this article.)

"Who Says Math Has to Be Boring"  - New York Times article with some reasons why so many kids get turned off to math somewhere between kindergarten and high school. (Not that all the suggested "fixes" are all that great. For instance, the writer wrongheadedly seems to think full-day preschool is a solution!) But there's still some interesting stuff. Here's a bit:
A new study, by researchers at the University of Missouri, showed that the most important factor that predicted math success in middle school and upward was an understanding of what numbers are before entering the first grade. Having “number system knowledge” in kindergarten or earlier — grasping that a numeral represents a quantity, and understanding the relationships among numbers — was a more important factor in math success by seventh grade than intelligence, race or income.
Math manipulatives (counting bears) have taken on new life as game counters in our family


Some help for this essential topic, one that trips up many students.

From the Wall Street Journal : "New Approaches to Teaching Fractions"
Fractions create a wall which many students fail to conquer. And without knowing how to manipulate ordinary fractions, handling algebra becomes impossible.

Here's a sample:
A child's knowledge of fractions in fifth grade predicts performance in high-school math classes, even after controlling for IQ, reading achievement, working memory, family income and education, and knowledge of whole numbers, according to a 2012 study led by Bob Siegler, a professor of cognitive psychology at Carnegie Mellon University.

Visual Fraction Games - Teaches fractions via a number line (as suggested in the article above) with games like  "Find Grampy."

Free Fraction Strips - printable fraction "bars"

Mastering the  Facts

"Dad's Eight Simple Rules for Mastering the Times Tables" : Seven simple rules such as
Rule #7: The Nine Rule - Tens is Number Minus One, Ones is Nine Minus Tens
Using these rules will cut the number of facts to memorize from 100 down to 10.

Teach your kids how to use their 9's calculator! (Yes - your two hands make a "Nifty Nine's Calculator." And you always have it with you.) All of our kids have used this simple, fun trick.
7 x 9 = 63Fingers are numbered 1-10 from L -> R
Finger 7 is bent because we are multiplying by 7
# fingers to left = 6 (tens); # fingers to right = 3 ones = 63

John Woodward's site for Teaching Math Facts: This one is not visually exciting, but if you can wade through it, you'll find gold in the helpful articles on a logical plan for teaching math facts along with downloadable PDFs worksheets. There's good stuff here!

Triangle flashcards color coded by family
(Here: teal = square numbers; green = x 3s; purple = x 9s.)

Triangle Flashcards: Triangle flashcards are more versatile than traditional rectangle ones because you use one set for inverse operations. Which means the same card can be used for both addition and subtraction (or another for multiplication and division) by covering a different part of the card. You can print these for multiplication/division and these for addition/subtraction. Or simply cut out your own triangles from manila file folders and craft your own. Doing that allows you to color code the cards in a way that matches how your child has learned the facts: 2s, 3s, 4s, doubles, etc.

Living Math (Teaching math with literature)

Living Math
Teach math from literature? You've got to be kidding! No, really. But maybe instead would be a nice way to provide a change of pace for a few weeks.

Living Math Book List. Search by categories such as calendars, multiplication, metrics, and estimation. You'll find several book titles for each topic. (Some of this website seems to be down for maintenance, but I was still able to access the book lists.)

Living Books Library Top Picks for Living Math

Just for Fun:

This is really sweet! Make 9 square cookie puzzles with chocolate and vanilla cookie dough as you help build spatial skills. Find instructions at Almost Unschoolers blog.

Hexaflexagons! What is a hexaflexagon? Watch the video, and I'll bet you'll want to make one yourself. Very cool!


Ten Free Math File Folder Games: cute games for young children will help as they learn to count, fractions, addition, skip counting, and more.

Math is Fun: games (such as chess), puzzles (including the famous Tower of Hanoi), and activities organized topically

Multiplication.com : Games for multiplication drill

And More...

I've mentioned this before, but my favorite math blog is Math=Love. If you are teaching algebra, look no further for incredibly helpful tips on teaching this subject, especially if you would like to have your students create Interactive Notebooks.

"Favorite Free Resources for Teaching Math" from Karen at Living Unabridged. Online games, printables, algebra help, and more from one of my favorite bloggers.

Some of my previous math posts:

Choosing a Math Curriculum

Super Supplements for Math

Resources for Teaching Logic and Thinking Skills to PK-Elementary Students

Algebra Love  (Interactive Notebooks)

Co-op Book Club: 2014-2015

Students toss eggs as part of our Around the World in 80 Days book club

Book Club, Book Club - oh how we love you!

Once a month instead of having our regular co-op activities, we meet for Book Club. This past year we again had two levels: older students from  5th  -8th grade and younger ones from 4 years-3rd grade. (Books for the younger ones are listed at the end of this post.)

We're about to start in on Year 4 of Book Club, so I figured it's high time I write a bit about Year 3.

As always, Book Club provided excellent discussions about everything from the meaning of real courage to  plus plenty of active fun!

Does the idea of leading a literary discussion intimidate you? It does me at times! This summer a few of us have been going through Adam Andrew's excellent Teaching the Classics seminar. We chipped in together to buy the DVDs, and then each one purchased her own workbook. If you need help in knowing how to lead book discussions and using literature to inspire deeper thought and analysis, this is a great course! If possible, watch it with some friends. That way you can share not only the cost, but also have the opportunity for some great discussions yourselves.

OK, here's a rundown of where the older group has been this past year. We were finishing our second year of a 2-year world geography course, so again our books have something of an international flavor.

The House of Sixty Fathers by Meindert DeJong
1957 Newbery Honor book

I love this heartwarming story set in China during WWII. We follow the travails of Tien Pao (and his pig - Glory of the Republic!) as they become separated from his family in Japanese-controlled China. An American airman befriends Tien Pao, but there are many heart-wrenching ins and outs before all is resolved. This is based on true story of a young boy adopted by a squadron of American flyers though in real life things weren't quite as neat and tidy as in the book.

Activities included taste testing some of the foods Tien Pao survived on: leaves, grass, and dirt. Yum. The kids also had a contest to see who could consume a portion of rice most quickly.

Call it Courage by Armstrong Sperry
This short book set in Polynesia features Mafatu, a Polynesian boy who fears the ocean. The 1941 Newbery winner, this short book led to a good discussion about whether or not Mafatu showed courage in leaving his home and sailing out to the unknown.
Our children then watched the Disney movie based on this book and mostly laughed at it, especially when they noticed silly "extrabookular" details like goggles made bones.


The King’s Fifth by Scott O’Dell

A historical fiction piece, The King's Fifth tells the tale of Esteban de Sandoval, a young 
mapmaker with Cornado. Esteban, writing from prison, tells how he and six others had 
set out in search of treasure and the famous cities of Cibola in the American Southwest. 
Characters include an Indian girl, Zia, and a desparate gold-hunter, Captain Mendoza. 
Over time, readers will see the bitter fruit that comes from greed in the lives of each of 
the characters except for Zia.

Our students sampled homemade beef aspic (muleskin stew) and were surprised to learn that stock made from animal bones takes on a gelatinous consistency. To wash away the taste of the beef gelatin, they then had a delicious berry crumble. Esteban was a cartographer, so the students tried a craft which replicated the way he signed his maps. We made bookmarks by painting designs on thick paper, and then drying the egg white with a hair dryer, sprinkling cork ash on top, and rubbing it all with wool.


Pearl Buck story: Christmas Day in the Morning

In December we gathered all the children together to listen to this short story written by Pearl Buck. 

Grade 3-5-Originally published in 1955, this story has been illustrated and brought to life for a new generation. A man remembers a great discovery he made when he was 15 and living on his father's farm. A few days before Christmas he overhears his dad saying how much he hates having to wake his son at dawn for morning chores. As a special gift for his father, the boy gets up at a quarter to three on Christmas morning and does the milking by himself. Buehner illustrates these scenes, many taking place at night and illuminated by lanterns or by moonlight, with a sturdy, folksy, old-fashioned solidity. The hard life on a farm, the struggle to keep the family and animals warm and fed, is reflected on the parents' faces. Moving and tender, this is a fine choice for reading aloud or family sharing.-S. P.

We played a number of parlor games including a shadow guessing game. One child was chosen to be the guesser and sat in front of a suspended bed sheet. All the other children stayed out or sight around a corner. One (or two) were chosen to stand behind the sheet, making some kind of silly actions which would disguise the identity of the poser. The guessing child had to try to determine who was behind the sheet. Great fun!


Otto of the Silver Hand by Howard Pyle

Howard Pyle is best known as an illustrator, but he also wrote a number of wonderful books including Men of Iron, The Merry Adventures of Robin Hood, and Otto of the Silver Hand, all of which are set in the Middle Ages.

Pyle's books are all public domain, so it is easy to find free ebooks. However, since his illustrations are top-notch, make sure to find versions with the pictures or just go with a print copy. Often you can find reasonably priced old hardbacks.

Discussion this time focused on when exactly did the climax occur? Who were the protagonist and antagonist? (After watching some of Teaching the Classics lessons, we realized that "it depends." There can be a number of different conflicts within a given piece of literature. And each separate conflict might have a different climax.) Anyway, this was one of those books which led to a vigorous, involved back and forth between the students, which is always great to see!

And what did we DO? Make silver hands, of course!

From what? What else than duct tape!

Showing off their removable silver hands


Heart of a Samurai by Margi Preus
Shipwrecked by Rhoda Blumberg]

This month we had two related titles. Both tell the true story of a young Japanese sailor, who in 1841, along with several sailing companions, was shipwrecked and washed up onto a tiny island far from their homes. An American whaling ship rescued the men, and Manjiro eventually ends up living in New England as the adopted son of the American captain who found him.

Eventually Manjiro ends up returning to Japan and he was instrumental in the opening of Japan to westerns. Absolutely fascinating story!

What do my sons remember from the activities this book club? Throwing "harpoons" into snowbanks!


The Endless Steppe: Growing Up in Siberia by Esther Hautzig

Yet another true story, this one tells what happened to Esther and her family when
they were arrested and taken to Siberia in 1941, leaving behind their very privileged 
life in Poland. From 10-14 she lived with her mother and grandparents in harsh conditions, 
but as the book progresses, Esther learns how to do more than merely survive.

During Book Club, the children learned more about the author and watched a documentary 
based on her life.

I'm getting long-winded, so I'll finish this summary off in a bit with one more post about our last two books.

Books the younger kids enjoyed:

Lionel and the Book of Beasts by E. Nesbit
A Bear Called Paddington by Michael Bond
Mrs. Piggle Wiggle by Betty MacDonald 
The Velveteen Rabbit by Margery Williams
Milly-Molly-Mandy by Joyce Brisley
Pippi Longstocking by Astrid Lindgren  
The Reluctant Dragon by Kenneth Grahame

Links to posts about previous years' book club meetings:

Homer Price, Survival books, An Old Fashioned Thanksgiving, The Best Christmas Pageant Ever, Snow Treasure, Peter Pan, The Enchanted Castle, Bears of Blue River

Part I :Twenty-One Balloons, Betsy-Tacy, Red Hugh, House of Arden

Part II: Stories of Don Quixote; Carry On, Mr. Bowditch; Just So Stories + Rikki Tikki Tavi; Star of Light

Part III: A Wrinkle in Time

Part IV: The Hobbit

The Duties of Parents

Tim carries a reluctant hiker in western Canada some years ago.

Parenting takes courage. It requires stamina and fortitude. Above all, it necessitates faith.

Book after book has been written telling us how to raise children. Under the "Family" tab at Christian Book Distributors, I came up with 507 pages! In the 30 years we've been parents, Tim and I have read a number of such books. But of all these there is one that stands far, far above all the rest. I believe it to be the most important book on Christian parenting ever.  It's not new, trendy, or heavily marketed. In fact, you can read it for free. And did I mention that it is very short?

What book(let) is this?

J. C. Ryle's The Duties of Parents

Bishop Ryle, a 19th century evangelical Anglican pastor, describes what parents must do in seventeen statements which he then explains more fully. Here are the seventeen points:

1. First, then, if you would train your children rightly, train them in the way they should go, and not in the way that they would.

2. Train up your child with all tenderness, affection, and patience. I do not mean that you are to spoil him, but I do mean that you should let him see that you love him.

3. Train your children with an abiding persuasion on your mind that much depends upon you.

4. Train with this thought continually before your eyes--that the soul of your child is the first thing to be considered.

5. Train your child to a knowledge of the Bible.  

Screensaver recently put on family computer by the formerly moody hiker.
He's growing up!

6. Train them to a habit of prayer. 

7. Train them to habits of diligence, and regularity about public means of grace.

8. Train them to a habit of faith.

9. Train them to a habit of obedience.

10. Train them to a habit of always speaking the truth.

11. Train them to a habit of always redeeming the time.

12. Train them with a constant fear of over-indulgence.

13. Train them remembering continually how God trains His children.

14. Train them remembering continually the influence of your own example.

15. Train them remembering continually the power of sin.

16. Train them remembering continually the promises of Scripture.

17. Train them, lastly, with continual prayer for a blessing on all you do.

Print yourself a copy of Ryle's exceedingly helpful book. (It should take only around 20 pages.) Then read it. Pray through it. And consider re-reading annually!

Because I'm An Undependable Blogger

Butterfly bush

Each week I faithfully check in with my favorite blogs. Rachel Houser's Stitched in Color blog is my go-to quilting inspiration site. For book and homeschool insights, I turn to Living Unabridged. And just for fun I read Better  After, a witty home and furniture make-over site.

One of the things I love about these blogs is that the author of each one faithfully follows a pattern of posting. Rachel puts up something new every Monday, Wednesday, and Friday. Karen at Living Unabridged almost always puts up a "Weekend Wandering" post on Saturdays (plus other thoughts as time allows.) And Lindsey at Better After posts every weekday.

Posts from these bloggers come faithfully. Predictably. Dependably.

Alas, Nonnie's Notes is anything but dependable.

No matter how good my intentions, I've never been able to find a rhythm of posting. Some months I've put up eight pieces and other months just one. Sometimes I have other writing responsibilities, but most of the time when I'm not posting it is because I'm too busy doing. Life. I never want to be guilty of writing about life but not living it. So my first order of business is to be present. Here. Now.

Net result - I'm inconsistent in writing in this space. And I don't see anything changing any time soon. Life is still just really, really full. I'm very thankful for that!

But here's a solution! (Proposed by a reader. Thank you, friend!):

Now you can subscribe to Nonnie's Notes. Just type your name in the little box up at the right hand side of the blog. You'll have to follow a few directions including confirming your email address. But then you should receive an email when I put up a new post. Whether that is tomorrow. Or next month.

Looping and Block Scheduling: Help for Busy Homeschool Moms

What are you doing for "professional development" this year?

Bricks and mortar teachers spend time each year attending seminars to keep their skills sharp and give them new ideas. Summer makes a great time for us homeschool teachers to do the same by putting more tools in our toolboxes. Happily, opportunities abound to do this right at home!


Recently I "attended" a webinar on Looping given by Sarah Mackenzie (from the popular blog Amongst Lovely Things) and one of her "Schole Sisters," Pam Barnhill.

You can watch it here: Looping webinar

Looping is a powerful strategy for fitting in those things that fall into the cracks of your day. Some subjects are essential for every day - especially the 3Rs. If you skip out on math just once a week, by the end of the year, you've only accomplished 80% of what you might have done by hitting math daily. But other subjects like history or science, nature study or art, music or P.E. don't necessarily need to be daily ones. Looping allows you to do what you can each day and then pick up where you left off the next day. (After first accomplishing those essential subjects!) Sarah Mackenzie has written about looping here and here and here.

Moms with little ones may find looping most powerful. By junior and senior high school, flexibility diminishes as schedules become necessarily more rigorous.

However, looping has other applications besides organizing your school day! I've been playing around with the idea of using looping as I structure house cleaning. I think it has real potential, especially in the future when I don't have young helpers living at home to do most of the work.

(Listen also for the part where Pam B. discusses "procedures." That was what I found most useful of all, and I've been working on developing some simple procedure sheets to remind myself of just how I want various subjects to flow.)


Another strategy for covering many bases without lots of stress is using block scheduling. And - good news! Pam Barnhill will be giving a free webinar this week on this topic! If you want to join the live webinar on Tuesday, July 14 at 3:30 EST, sign up here. If you miss it, don't worry! The webinar should become available for later viewing as well.

Prayer Tools: More on using colored note cards (Prayer Part V)

It's been a while since I last wrote about my index card system for organizing my prayer times. (See this post.) And I've promised to explain more about how I use various colored cards to keep things organized, so here goes.

To recap -
You'll need a 3x5 file box, 3x5 dividers marked 1-31, and colored index cards.

Colored cards come in many varieties such as these:

Lined cards with colored tops

How many colors will you need? That depends on the categories you decide to go with. It's also easy to make cards from manila folders or cardstock, and that gives you access to a larger variety of colors.

Next, you'll need to think of your cards in two categories:

Moving cards vs. Stationary cards

STATIONARY CARDS - these stay in place behind their day of the month divider.

MOVING CARDS - these are ones I cycle through very frequently. So after praying through them on a particular day, I then move them forward either 1, 3, or 5 days.

Today I'll explain the moving cards.

Each day I start with some scripture to help me focus on and worship the LORD. (I'll explain more about that next time.) And I also want to always remind myself to STOP and give thanks. So I use this traveling card to prompt me to do that:

This card reminds me to think through the previous day, reflecting on and giving thanks for God's daily mercies!

Cards for Tim and the grandgirls - these cards are light peach
Every day I pray for my husband, so after I pray through his card, I move it one slot forward.

Normally I divide my children and grandchildren cards into three stacks and rotate through them every three days. After using, they just proceed forward three spots.

Finally, there are other people and things I wanted to pray for, but I knew if I tried to do all every day, I would become overwhelmed. (And likely quit.) So I divided these prayer needs over five days. Naturally, each category has its own color.

Category Color Days of the month
Prodigals and others who need Jesus Blue 1, 6, 11, 16, 21, 26, 31
Friends (also struggling marriages and single moms) Pink 2, 7, 12, 17, 22, 27
Church Green 3, 8, 13, 18, 23, 28
Small group Purple 4, 9, 14, 19, 24, 29
Missionaries and Ministries Yellow 5, 10, 15, 20, 25, 30

On the top of these colored cards I write the numbers which indicate the days they will be used. That helps me know where to move them. (But since the card dividers fit five across, each time the colored cards simply move back one layer. In other words, #1, 6, 11, 16,  21, 26, and 31 all line up, front to back. As do the numbers for each of the cards.)

Oh - I should mention another reason I've found this card system SO very useful in every day life. You know those times a friend asks you to pray for something, and you agree to? But maybe you pray a couple of times and then forget. The prayer cards give you a place to capture that request and then faithfully follow through in prayer!

When I first set up my prayer cards, these are the ones I began with. But after a while, I wanted to add more cards with scripture to help guide my prayers. I'll explain about those next time!

What's Your Job Description?

Daughter Faith with granddaughter Jenny

"So, what do you do?"

This simple question sometimes catches me off guard. How to describe succinctly a mother's duties? Last week when I fielded this question at Purdue orientation, I mumbled something about homeschooling my nine children. Maybe next time I should try something like this:

"I dispense the honey of the Holy Scriptures,
          the old wine of the classics,

          the fruit of grammar,
and the dazzling splendor of the stars.” 
                            - Alcuin, monk who tutored Charlemagne and his sons