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Butterfly Salad

Math on a plate.

Math on a plate.

Today my 4-year-old and I got out Cooking Is Cool: Heat-Free Recipes for Kids to Cook by Marianne Dambra. I am a little disappointed in the book because it doesn’t have step-by-step pictures for children to follow and it uses a lot of food coloring. But the full color illustrations of each recipe are nice.


Here’s our version of Butterfly Salad. The actual recipe called for dyed cottage cheese, which I thought was gross, so we used grapes instead.


  • lettuce leaf
  • pineapple rings
  • cottage cheese
  • grapes or berries
  • celery stalk (the body)
  • 1 olive (the head)
  • a carrot or bell pepper (the antennae)

Math Skills Involved:

  • counting
  • fractions (cut the pineapple rings in half)
  • comparisons (more cottage cheese, less cottage cheese)
  • ordinal numbers (first you do this, second you do that, etc.)
  • symmetry (the goal is to make the wings look the same)

This recipe took about twenty minutes to make. My daughter and I both had a lot of fun!

Cooking Is Cool: Heat-Free Recipes for Kids to Cook

Why this Kindergarten teacher is confused by Kindergarten


Here’s my “I Brake for Moms” column from today’s Everett Herald. We decided to register our daughter for half-day Kindergarten with an intent to Afterschool.


Afterschooling Plan for Working Moms


Afterschooling isn’t just for stay-at-home parents. There are a lot of ways you can provide meaningful instruction to your children using what would otherwise be dead-time.

Unfortunately, I don’t have a lot to offer teens yet, but here are some ideas for K-8:

  1. Carschooling –so easy, so effective. Ask the grandparents to buy CDs for Christmas, or else check them out from your local library.
  2. Dreambox Math –perfect for K-5. Have your kids play Dreambox while you get dinner on the table. Consider making 15 minutes of Dreambox a requirement to earn screen time.
  3. ClickN’ Read Phonics— K-3 phonics curriculum on the computer. I haven’t tried this, but it gets good reviews.
  4. Bedtime read alouds –be sneaky! For young readers, Bob Books can “unlock” stories you hate. For older readers, try using the CIA approach on your next chapter book.
  5. Hands On Equations –definitely worth the time. For older kids, if you can find an extra twenty minutes a week, Hands on Equations is really worth it. It will give them such an advantage in algebra, that you won’t believe it. Of all the math things I’ve blogged about, this is the curriculum that impresses me the most.
  6. Science Kits by mail— be a cool science mom, without having to plan anything. Seriously, almost everything you need (including a script) comes in the mail, ready for 30 minutes of fun. The catch is the kits are expensive, so you should wait for a Groupon or good deal on Homeschool Buyer’s Co-op. Sign up for my Facebook page, and I’ll keep you posted.
  7. Highlights Top Secret Adventure Kits –project based geography that come in the mail. Your 7-12 year-old solves puzzles, looks for clues, and reveals the villain while learning about that month’s county. Unfortunately, like the Young Scientist Club Kits, these are really expensive, so you’d want to watch for a special deal.
  8. Story of the World Audio CDs –history kids probably won’t get at school. SOTW is a borrow from the homeschooling world. A college professor named Susan Wise Bauer has written four volumes of world history specifically for children. They cover ancient times to the present century. These CDs can be used grades K-8. I want my kids to listen to them every two years. I have a strong suspicion SOTW will help with AP tests someday.
Don't feel guilty that you're strapped for time!

Strapped for time but with a plan, that sounds like an awesome mom to me!

An Afterschooling Plan for Half-Day Kindergarten

In our neighborhood, full-day Kindergarten costs $3,600. Half-day Kindergarten is free, but is only two hours and 40 minutes.  All of the research I’ve read says that full-day Kindergarten makes a difference. I have an “I Brake for Moms” column coming out next Sunday, explaining the issue.

If you’d like to take a look at the research yourself, here you go:

Education.com’s Full-Day vs. Half-Day

Fact Sheet from the Children’s Defense Fund

Full-Day vs. Half-Dad Kindergarten; In Which Program Do Children Learn More?

In our neighborhood, if you take out all of the minutes from lunch and recess, full-day Kindergarten means 5 hours and 15 minutes of instructional time per day. Half-day Kindergarten is 2 hours and 25 minutes. (Please note, I don’t mean to be dismissive of the importance of recess. Children learn a lot on the playground.)

So if we were to chose half-day Kindergarten, could I somehow Afterschool enough to get in the extra 2 hours and 50 minutes a day? Yes; definitely! Here’s how:

An Afterschooling Plan for Half-Day Kindergarten


Language Arts Block, 60 minutes


Choice Time, 30 minutes

  • Full-day kinders would likely be getting this at school. This thirty minute block would be a chance for my child (and I) to unwind while I got the next activities set up.


Math, 30 minutes


Specials, 30 minutes

Homework (from school), 20 minutes

TOTAL TIME = 2 hours and 50 minutes!

The cost of this Afterschooling plan would be about $350, including the uber-expensive science kits. I could splurge and get the Highlights kits too, and still come in way under $600. Or I could go the other way, and do the whole plan for practically nothing. I’d just swap about the math section for this page of free activities here.

What’s half-day Kindergarten like in your state? Are you stressing out about registering your child for Kindergarten too?

Basher Books for Grown Ups


My son Bruce(8.5) loves Basher Books so much that he reads them over and over again. I still don’t exactly understand the appeal, but appreciate how much he’s learned. If Trivial Pursuit ever becomes popular again, I want Bruce on my team.

Today at the bookstore I came across The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics by Clifford Pickford. It’s the closest thing I’ve ever seen to a Basher Book for adults.


I am very sensitive to violating copyrights, so I’m not going to share an interior picture, but this book has topics like “St. Petersburg Paradox” on the left-hand page, and then a really cool picture on the right. Sound familiar?

I bought this book for myself, but I’m pretty sure Bruce will read it too, especially if I leave it on the kitchen table next to his cereal.

FYI: My version is leather bound and cost $20 at Barnes & Noble. The paperback version on Amazon is a lot cheaper.

Making “5 Flowers”

Organizing 5 in "flowers"; girly but effective.

Organizing 5 into “flowers”; girly but effective.

Teaching kids to visualize numbers instead of just counting is one of the hallmarks of Dr. Joan Cotter’s Right Start method, which is what I’m using to introduce math to my four year old daughter Jenna.

One of my goals right now is for Jenna to be able to look at a pile of objects:


…and be able to organize them into a pattern that makes them easier to quantify:


There are many ways a child could choose to organize objects: by color, tens, twos, triangles, etc.

A very old (and bad) picture.

A very old (and bad) picture.

A classic idea from Right Start Level A would be to be to give a child a bunch of tally sticks, and ask him to create fives and tens.

Unfortunately, Jenna could care less about tally sticks, unless there’s an actual popsicle involved!

Jenna’s a girly girl, and so I was hoping colorful square tiles would capture her attention more.  That worked, for a little bit.  Then I came up with the idea of organizing the tiles into flowers.  Now all of a sudden, Jenna’s really into it!

Organizing 5 in "flowers"; girly but effective.

We’re using square tiles, but you could use crackers.


The 4 + 1 combination looks the prettiest (imo), but all of the other combinations work too.  Jenna likes to experiment with all of them.  So by making “flowers” she’s learning about 5 + 0 = 5, 3 + 1 = 5, 2 + 3 = 5, etc.

One final thought, don’t be intimidated by our fancy math manipulatives.  Crackers would work too!

Show me a picture of 10

My four-year-old's explanation of "10".

My four-year-old’s explanation of “10”.

Here’s an easy math activity to do with your preschooler.  Ask them to draw you a picture of what the number 10 looks like.  (A smaller number would also work.)

My daughter needed help tracing her hands and feet, and I helped her draw the first set of tally marks, but the thinking was all her own work.  Her picture shows five different ways to represent ten: with words, numbers, tally marks, toes and fingers.

So really, is this a picture of 50? 🙂

Repetition would make this activity boring.  (The last thing I want is for my daughter to think math is boring.)  So it’s a good thing there are infinite ways to experience numbers.

A ten triangle.

A ten triangle.

For example, check out the 10 triangle Jenna made last week with Right Start Level A!

Cheap Math

As a former teacher, I think it is really important that schools and homeschooling families use a formal curriculum to teach math. A comprehensive curriculum is also useful for Afterschooling families such as ours who are dealing with a child who is one or two grade levels above his public school’s materials. (For more about the curriculums we use, please see my main math page.)

But what if you are just testing the waters in terms of math enrichment for your child? What if your son or daughter really loves math, and you want to do encourage that at home with some cool ideas, but you don’t know where to start? Here are some of my favorite ideas for “Math on the Cheap”:

Free Comprehensive Curriculum

Math Games You Can Make

Free Math Games Online

Real Life Math

Make Your Own Math Manipulatives (Links coming!)

  • Base ten popsicle sticks with beans
  • Toothpick bundles
  • Straw bundles


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File Folder Games

When I was teaching in Ravenswood I had a classroom budget of zero, and a bunch of mismatched math books.  What our school did have however, was a laminating machine.  I put this to good use making as many file folder math games as I could.  These were a hands-on way to help my English Language Learner students learn to solve word problems, and gain conceptual understanding of multiplication and division.  

You can make file folder games at home for your children too, concentrating on any math skill you like.  Staple a ziplock bag on the back of the folder to hold all of the pieces.  I left almost all of the games I made back at my old school, but I did keep a few examples. 


Math Jumble

This is in my handwriting, circa 2000, but I don’t think I can take credit for inventing this game.  In fact, it’s been so long I don’t remember where I got this idea!   Math Jumble is a fun way to practice all sorts of math skills and you can make it at home for free.  Just be sure to use heavy paper, and if you really want the game to last, laminate the pieces or use contact paper.

Twist and Shout Multiplication

Here’s the new toy in our household this week.  So far Bruce likes it a lot and has been playing it every day.  As for me, I like that it has a headphones jack in it, so I don’t need to listen to the annoying music.  As for efficacy, Bruce does seem to be learning his x 12’s, which is an area he was weak in before.

Visualization, Not Just Counting

Today I started working on visualizing quantities 1 to 5 with Jeanna.  I say visualization, because I’m teaching her to count with quantities, instead of just counting with one to one correspondence.  The best way to explain why I’m doint this is is to read Joan Cotter’s insightful article on young children and math: http://www.alabacus.com/pageView.cfm?pageID=314 

I hadn’t read any of this when Bruce was little, so my husband and I taught him how to count with correspondance, before teaching him any visualization strategies.  But then he started at a wonderful Montessori program, nine hours a week at age three, and his math really started taking off.  By February of his second year there, when Bruce was four, he was ready for first grade math.  All of that was due to Montessori, and their wonderful focus on visualization, grouping strategies, manipulatives, a lots of fun activites to practice.  I’m very eager to try this method with Jenna here at home, and see how far it will take her.


Bruce finished off his major chapter on subtraction last month, and he wasn’t too keen on it at first.  I teach math from a Constructivist perspective, which means enabling children to develop their own meaningful strategies for solving problems, instead of just blindly teaching traditional algorithms.  Here’s a nice website that explains more about the Constructivist philosophy: http://mathforum.org/mathed/constructivism.html

Bruce, myself, his classroom teacher, and my husband were all in the trenches there for a few weeks as Bruce explored different strategies for solving triple digit, minus double digit problems with and without regrouping.  In normal classroom situations, Bruce would have been exposed to his classmate’s strategies and thinking, which would spur his own ideas, creativity (and showmanship).  But since he is working independently through the second grade book, I had to introduce some ideas to get him started.

The first strategy I introduced was solving equations on two abacuses, flipped over on side A, so that they represented 200.  (We were starting with problems no greater than 200.)  This went on for about a week, and Bruce was not impressed.  He does not like using an abacus at all, and so I never got to teach him the side B methods.  I was really bummed about this, because my husband worked with an engineer from China, who was just brilliant at math, and Chang said that when he solved problems in his head he could picture the little beads on the abacus sliding.  I wanted this for Bruce, but maybe I didn’t introduce the abacus early enough.  I’ll know better next time for Jenna. 

The second strategy I introduced to Bruce was thinking about the problems in terms of money, and then counting out the equations in pretend change.  236-89 would become $2.36- .89.  Bruce was not too thrilled with this strategy either.  He could easily solve problems this way, but under protest.

Finally I broke down and taught him one of the methods the book demonstrated, ungrouping, which uses pictorial representations of hundreds tens and ones.  I had resisted showing him this method, because Houghton Mifflin uses it as a precursor to borrowing, which I do not want Bruce to learn until later.  But I’m eating a big slice of humble pie right now because this is the method Bruce absolutely loved.

All of a sudden Bruce started tearing through his subtraction work at top speed.  He called this strategy “Busting open the hundreds”.  I’d usually draw out the squares, lines and dots for him on the white board, and he would erase them and then redraw things as he started working.  Pretty soon, he was solving problems in his head, by just looking a the picture and not even erasing anything.  Then he didn’t even need the pictures at all. 

The way Bruce would solve the above problem is that he would think: “100-89 = 11.    11+36=47  100+47=147”  He doesn’t need to do any carrying or traditional algorithms at all, which is a testament to the Constructivist method.  Constructivism encourages children to think and understand what numbers really mean, instead of just blinding computing an algorithm, which can stunt their development of number sense.  Bruce’s accuracy isn’t 100% yet, but it is on par with your typical second grader.  I’ll teach him the traditional methods of borrowing and carrying someday, but not until Bruce can do even harder problems intuitively, in his head.


Letter and Number Reversals

Letter and number reversals, what is normal?  That’s a common question teachers hear from parents.  Here’s  a picture of Bruce’s math from yesterday morning.  As you can see, he’s not quite finished with it.  I’ll go back and make him fix the last problem, which should be 130 instead of 103, but the other number reversals don’t really bother me. 

My experience has been that letter and number reversals are developmentally normal until the end of second grade.  Entering third graders might even have some reversals the first few months of school, and come out of a third/fourth grade classroom two years later just fine.

But if it’s January of your child’s third grade year (age wise, not ability level) and they are still reversing, that could potentially be a red-flag for a learning disability.  That’s when to start worrying and get your child assessed as soon as possible. 

(As a side note for those of you interested in math, Bruce solved these problems on a white board with them rewritten horizontally.  His current strategy involves “busting open the hundred” to take away tens, his terminology for “ungrouping”.)