Maria's Math News, Vol. 81, April 2014

I love teaching, and I love math. This newsletter is my way of reaching out and helping you to teach it, too.

It's April but not April fool's day, and I wouldn't want to fool you anyway.

In this newsletter, you'll get to peek at some challenging puzzles, think about grading, read a story of a girl who changed her hatred towards math, ponder some thoughts about the Common Core, and learn how to find the whole when the fractional part is known.

Later in this month I'll run a GIVEAWAY for my products -- stay tuned!


Step One: Read
Whether your child likes fantasy books, grand adventures, historical fiction, or biographies, Spidersmart has plenty of choices. There are more than 2,000 titles from which to choose.
Step Two: Write
Every book has a corresponding, easy-to-use online writing assignment with three sections: vocabulary building, reading comprehension question, and an essay based on the book's themes.
Step Three: Revise
A teacher will check your child's work, giving comments about every answer. The teacher will then review the revision to ensure that the writing shows improvement.
Real Teachers, Real Results


1. Favorite challenging puzzles (grades 7-12)
2. Grading tests and math homework (grades K-12)
3. A story of a girl who hated math (grades K-12)
4. Common Core and common sense (grades K-12)
5. Finding a total when the fractional part is known (grades 4-7)

1. Favorite challenging puzzles

Have you ever encountered this well-known puzzle about the missing $1?

Three people rent a room at $30. They pay $10 each and go up to the room. The owner realized he charged too much and it was only supposed to be $25. He sends the bell hop up with the $5. Each of the people keeps $1 and they give the bellhop $2 as they can't share it. So now each person has paid $9 for the room (total $27) and the bell hop has $2... where is the other $1???

See the solution to this and find many more puzzles on my new page of favorite challenging puzzles.

Have fun!


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Go to Mathematics Lessons to see a list of our lessons, lesson objectives, see what we are about, and watch video math lessons.

2. Grading tests and math homework

A few days ago I got a question from Jennifer concerning GRADING a child's math work, and I think it's a good question!
How do recommend that parents grade when using Math Mammoth? Should I score every assignment? Or just tests? Before we pulled our children out of public school, only tests were being counted for their grade. What do you recommend? Thanks


I don't actually give any exact grading recommendations regarding Math Mammoth but leave it up to parents/teachers. I do include a grading rubric for the tests, but that's all.

Personally, I feel that grading needs to be such that it doesn't discourage the child. It really depends on the child. Some children are better off without any scores but just feedback on where they need to work more, how to fix errors, etc.

All grading probably should be accompanied with notes like "You worked hard and I appreciate that!" "Here you show you've learned this topic and worked hard in it." etc. so that the emphasis is on the hard work, appreciating that, praising the work, giving feedback on specifics, and not on the actual percent score.

On the other hand, if a child is getting a "big head" (too proud) over their accomplishments, you could find a really hard test so they can learn they have room to improve. But this is not nearly as common than the opposite side where children are discouraged and think they "can't do math".

I would definitely NOT grade any of the day-to-day work with percent scores or letter grades.  Of course you need to find where the child made an error, but that should be sufficient.

Also, when when you assign a final mark for a whole grade, don't look ONLY at the tests but also the overall accomplishments, work, etc. I like to give children assignments outside of tests that count towards the final mark. In math, it could be a neatly written solution to a hard word problem, for example. Or, a set of definitions for geometry terms accompanied by drawings. It could be a description or exact instructions for a math game (tying in with writing/ language arts). Those can then go to their portfolio if you use such.

Most children in our society tend to get the idea that math is about "speed" and getting correct answers, and thus math test scores become really important to them. We need to discourage that line of thinking.

See also

Hope this helps!

3. A story of a girl who hated math

This is one of the entries to the Great Math Moment(s) contest I ran in January 2014 -- a story of a girl who used to hate math but that all changed!

I am homeschooling my kids.  The kid I'm writing about is my oldest--a unique, amazing, beautiful, extremely bright 8-year-old.  She has light red hair and a giant smile that shows all of her teeth and gums.  She's outstanding. I know that everyone says that about their child, but really, she's outstanding. She is the best big sister I could have ever have hoped for, she's loyal, she's funny... and she's smart.  She caught onto reading very, very  early, and is well advanced at that subject for her age.

But she hated math. Oh, how she hated math.  Her smile and loyalty would vanish at the mere sight of her math book. She'd snap at her precious little brother and the tears would freely flow.  Our days would turn from joyous to sad on a dime.  
And since we are a no-tears-in-school-when-they're-little kind of family, I decided to pull way back on math towards the end of last school year. When we did do math (twice a week or so), we did a spiral curriculum.  I thought that made the most sense so that she wouldn't be overwhelmed.  But the problem was, every single day my precious carrot-top would fail.  She would encounter something she didn't remember or know.  And the tears would always come back.  I tried coaxing, bribing, cajoling... everything.  And finally I quit teaching her math altogether, because her sister (2 years younger) was catching up with her. I didn't want this bright, beautiful girl to start to believe she wasn't good at math.  I knew that simply wasn't true.  So I stopped math last year, and then I took a chance on Math Mammoth.  It pretty much came down to the cost and the reviews.  I wanted something simple, different from what she was doing, and that she could "win" at.  
I'd be lying if I said that it was a total shift.  Still some tears.  Still discouragement.  But slowly, I saw her actually gain confidence because she began to truly learn her math.  And I can't tell you when it happened, but one day I realized that she was no longer fussing.  She was no longer crying.  Our days were no longer lost to frustration and failure.  My child was actually LEARNING. 

Today I sat on my bed with her and showed her a flashcard of two two-digit numbers.  I said, "This is what's coming up for you sometime soon. Do you think you can do it?"  My child looked at me, looked at the problem, thought for a while, and told me the answer.  She added two digit numbers before she even got to them in her curriculum.  Why?  Because she UNDERSTOOD how.  I was so proud of her.

The joy is back in my sweetie, the smile is back on her face.  She doesn't LOVE math, but she is confident that she can do it and sticks with it because of Math Mammoth's simple and logical teachings.  I actually found your contest because I wanted to write you this note anyway.  I don't have a photo of her doing her math or of the moment it started to click, but I do have a photo of her smiling and having fun.  Since that's really all I wanted this whole time, anyway, that's the photo I'm including. 

Katie Brown

4. Common Core and common sense

I wrote somewhat of a long piece about Math Mammoth's position concerning the Common Core Standards, and some bad examples of supposed "common core math" or "new math" as some call it. Math Mammoth and the Common Core Standards

I hope it is helpful to at least some of you!

5. Finding a total when the fractional part is known

Someone asked me recently,
I have had great success with the Grade 4 Light Blue Series with my twin daughters and we have been breezing through the curriculum. ... For the most part, they get how to find the fractional part but we did have some trouble on problems 4 on page 59 Worktext 4-B and problem 7 on page 60 in Worktext 4-B.
They have to do with finding the total number of something when you are given a fractional part.

I had a hard time teaching the concept of "working backwards" and was wondering if you have any additional resources or problems we could use to practice.

Working backwards is of course perfectly FINE but I feel using the BAR MODEL is easier for children who have not worked through these kinds of problems before. The model shows them clearly HOW we "work backwards" to get the total.

Here's an example from the previous page (page 58 in Math Mammoth 4-B):

This is the problem #4 they had trouble with

One cold day, 1/8 of a company's workers were sick and stayed home. 84 people showed up at work. How many workers does the company have?

You can simply teach the children to make a bar model for these types of problems. Then once they get used to that, they may also start solving them without the model, but the model is the starting point so they can see clearly the relationship between the fractional parts and the total.

For this problem, draw a bar divided into 8 parts. Mark on it the 84 people (which is seven  parts).

←------------  ? --------------→
←------------ 84 ----------→

Mark the whole bar with a question mark so it is clear THAT is the unknown.

Then the solution should be easy to see! The 84 people correspond to seven parts in the model. Find how much one part is: 84 ÷ 7 = 12. Then, the total is eight of those parts: 8 x 12 = 96.

Now try this one. Let's change 1/8 into 5/8 in the above problem: One cold day, 5/8 of a company's workers were sick and stayed home. 84 people showed up at work. How many workers does the company have?

This time you mark three of the eight 'blocks' as being 84:

←------------- ? ---------------→
←--- 84 ---→

The solution: first divide 84 ÷ 3 = 28 to find the value of one "block". Then, multiply that by 8!

This topic comes up later in the curriculum, too. For example, the lesson Problem Solving with Bar Models 4 in Math Mammoth Grade 5-A concentrates on these types of problems.

I don't currently have any additional worksheets that would concentrate on these types of problems but you can make questions like these to practice the basic idea:

2/9 of a number is 66. What is the number?
5/7 of a number is 35. What is the number?

Hope this helps!

Feel free to forward this issue to a friend/colleague! Subscribe here.

Till next time,
Maria Miller
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