Let Your Child Make Mistakes

You’re sitting next to your son while he’s working a problem. His head is bowed over the paper and he’s in the zone. He’s finally getting it! But then….you see him make a simple math mistake. Instantly and with lightning speed, you intervene.

“Oops! What’s 9 x 7?” And you poke your pointer finger on his paper. (Imagine your boss doing that….)

And like that, he’s lost his concentration. He snaps out of his trance and erases what he was doing with angry digs of the eraser that rip at the paper. Now he’s frustrated with himself, frustrated with you, and he is OVER.IT.

Other than the simple math error, he was doing everything correctly. His work was tidy, he was showing his work, etc. So, why did you butt in? What are you afraid of? That your child will fall down and have to pick himself up?

Letting a child make mistakes is important to the math process as a whole. Every math problem has a check step. You know this because teachers and parents are always telling kids to check their work. If you demand perfection at every step of the process, there is no reason to check the work at the end! Your kids’ answers will always be correct because you, in your overbearing annoying-ness, have made it so. Why would they want to correct a problem that they know is (painfully) correct?

There is something very cathartic about checking work. When the answer works, it feels great and kids are motivated. But when the answer doesn’t work…guess what? Most of the time, kids will look back over their work and try to find the problem. And, when they see that they just messed up 9 x 7, they can make the correction without your help. They may not admit it, they may not jump for joy, but there’s satisfaction in the process.

If your child refuses to check his work, it’s probably because he’s sick of being micromanaged!  If you’re saying, “oops!” and, “uh-oh…” and, “hmmm…” every single time your child puts his pencil to the paper, he’s going to be counting the milliseconds until you leave. And I guarantee he won’t check his work.

Here’s a visual: You’re trying a new recipe that you saw on YouTube. You watched it once and you think you can do it. You want to try it out! But when you start cooking, a bossy chef suddenly appears in your kitchen and watches your every move. He corrects you. He embarrasses you. He asks questions. He makes you feel like you can’t boil water independently. He’s condescending. You can’t relax. You’re frustrated that he ruined the process, and you give up on the recipe…anything to get out of the kitchen!

The solution is to strike a deal, and his will look different for each family. With my son, we agree that I will not hover while he does his work. (Very hard for a math tutor!) If he wants help, he is to be respectful while I work with him. When he is done with his work, he is required to check three problems. If he has all three correct, he’s done with his homework! If he misses any, he needs to find and correct the errors; he can’t just copy the correct answer from the key. When those first three problems are corrected, he chooses two more to check. If he misses either of those, he promises to seek help at school the next day. Even though I know I can help him with the lesson, it’s not my job. He needs to advocate for himself at school and find clarification.

After five problem corrections, I can gauge if my son is struggling with a lesson. Let’s say a homework set has 15 problems. If my son checks five of those problems and only misses one, then statistically he has 12 out of 15 correct. That’s 80%. I’ll take it.

The goal we’ve set for my son is to get a B in Algebra. That’s realistic for our family. You may have different expectations, but be sure those expectations are realistic.








What is a Greatest Common Factor, or GCF?


The GCF is commonly used to simplify or reduce fractions. These days, kids tend to use the words “simplify” or “simplest form.” When I was a student, we used “reduce.” They are the same thing, so be sure to use the terminology your children use at school to avoid frustration and confusion. Remember, it doesn’t matter how we did it when we were kids. What matters is that we learn to use our existing knowledge in the context of what our children are trying to accomplish.

Let’s say we have the fraction 6/18. We know by looking at 6/18 that it isn’t in simplest form (it’s not reduced). We wouldn’t go into a pizza shop and order 6/18 of a pizza, would we? No! We need to find the GCF in order to simplify 6/18.

Let’s factor both 6 and 18, and then find the greatest common factor.

6: 1,6,2,3

18: 1,18,2,9,3,6

The greatest common factor, or the factor that both 6 and 18 share, is 6. (Notice that 1, 2 and 3 are common, but they aren’t the GREATEST.)

Now, what do we do with our GCF of 6? Well, we divide the numerator (top #) by 6, and we divide the denominator (bottom #) by 6.

6 ÷ 6 = 1 (new numerator) 

18 ÷ 6 = 3 (new denominator)

So, 6/18 becomes 1/3. Now, you can go into the pizza shop and order 1/3 of a pizza!

Good luck!

The BEST Math Advice Ever…

Here is the simplest, yet most basic piece of math advice I have for you, regardless of your child’s grade:

Be sure your child knows his multiplication facts, no matter what.

You’re probably thinking….seriously? Don’t they do that in school? The truth is that it really doesn’t matter what your child’s school does in the area of multiplication facts. It varies from school to school, and it varies from child to child. Some kids pick it up naturally in the second grade, and some kids still can’t rattle of 6 x 9 when they are freshmen. All that matters is that you, as the parent, step up to the plate and get the job done – especially if your child is past the 3rd grade. It may not have been in your job description, but I just added it.

When kids aren’t fluent in their multiplication facts, nearly every math function is impaired from fourth grade on. Fractions, long division & long multiplication, scale factors, money, algebra equations, exponents, area, and so much more rely on the student’s ability to multiply. If your child is churning and burning over a long division problem, it’s probably because he hasn’t learned his math facts. So, he sits there and gets frustrated (tearing the paper, slouching, burying his head in his arm, whining, complaining, procrastinating, blaming the teacher, giving up, etc) until you just break down and give him the answer so he’ll get the darn homework done and be allowed to watch tv or play video games.

If you think I sound cynical, think again. As a tutor, I see this problem several times every week. I suppose it keeps me in business to some degree, but it’s sad to see perfectly capable children lag behind their peers because they can’t recall their multiplication facts. Of course, I can tell kids and parents that this job needs to get done, but I can’t enforce it. I wish parents would tell their kids that all devices with screens will be confiscated until multiplication facts are memorized.  This proclamation would be an incentive for everyone, especially those parents who use screens as tools to get a little peace and quiet for themselves. (The truth hurts.)

So what’s the best way to teach multiplication facts? Depends. It takes several days and several ways to teach a child a new concept. Go to a learning store and get two 9-sided dice. Roll them and have your child multiply the two numbers on top. Make a game of it… if he can answer 15 correctly in a row (zero and one don’t count) he can stop practicing for the day. I also highly recommend the Kumon series of workbooks. Get the one with the tiger on the cover and have your child do 3-4 columns per school day, and 4 full pages each weekend. Try having your child skip count out loud. To skip count by 8, he’ll say: “8, 16, 24, 32, 40….” Or, just get a ball and pass it back and forth while quizzing your child on facts. Some kids learn very well when they are doing a rhythmic activity such as passing a ball or jumping on a trampoline.

Trust me. You don’t want your child to be the only one in 7th grade who can’t multiply. I’ve seen it and it isn’t pretty. A relatively small investment of your time will make the upcoming years much easier for everyone.

kumon10 sided dice

Mental Multiplication Will Make You Smarter…Instantly!

Here’s a skill your kids will use for the rest of their lives, and you might find it handy, too! Don’t let large numbers get you down – they’re easy to multiply in your head.

When multiplying numbers ending in zero, you can use this handy trick:

900 x 40 = ?

First, multiply 9 x 4 = 36

Now, count ALL of the zeros in the problem. Here we have 3 zeros. We take those 3 zeroes and stick them to the right side of 36, making the answer 36,000.

Be careful not to count zeroes that you multiply. For instance:

20 x 500 = ?

20 x 5 = 100. Now add the 2 zeros from 500 and you have 10,000

You can say that 20 x 5 is 100. Since you used the zero from 20,  you’ll only stick on the two zeroes from 500 to get 10,000….remember, you already used the zero from the 20.

More mental math next time!



Expanded Form

I never learned expanded form in elementary school. Did you? Well, I don’t know how old you are, so maybe you did. This is a third-grade concept, so that was 1984 in my case.

Anyway, when I first saw expanded form in my kids’ homeschool textbook, I was amazed! Why hadn’t I seen this before? It’s such a simple concept, but it really helped my kids understand place value.

When writing in expanded form, you break a number down into place-value chunks. Here’s an example:

Write 4876 in expanded form.

We have 4 – thousands
We have 8 – hundreds
We have 7 – tens
We have 6 – ones

So, 4876 written in expanded form looks like this:

4000 + 800 + 70 + 6

Let’s try one more, with a zero in the middle.

Write 3029 in expanded form.

We have 3 – thousands
We have 0 – hundreds (this will not show in the answer)
We have 2 – tens
We have 6 –  ones

So, 3029 written in expanded form looks like this:

3000 + 20 + 9

Love it!

Fact Families with Multiplication and Division

Did I mention that I really love fact families? It’s seriously the best way to do double-dip when teaching kids their facts. If you haven’t already read it, check out the “Fact Families Explained” article from June 2014. It goes over fact families using addition and subtraction. Some kids are really strong with division but they struggle with multiplication, or vice versa. If you teach using the fact families method, the natural relationship between multiplication and division will help strengthen both skills.

Multiplication and division are opposites.

2 x 6 = 12 and therefore, 12 / 6 = 2

If your child can’t figure out 12 / 6 = ?, try saying this: “What times 6 is 12?”

Here is the full fact family for 12, 6, and 2.

6 x 2 = 12
2 x 6 = 12
12 / 6 = 2
12 / 2 = 6

If your child struggles with one fact, such as 7 x 9, have him write out the full fact family. For older children, only have them write out the fact families for the problems they still don’t have memorized. Why? Because older kids are just like us – they don’t like to have their time wasted with trivial tasks. Get to the nitty-gritty and focus on the troublesome areas.

Good luck!

Fact Families Explained

Fact families are your friends, Mom. I mean it. When kids need to learn their basic math facts, (addition, subtraction, multiplication or division), it makes sense to think about fact families because you’ll be able to kill two birds with one stone. At some point, fact families will likely pop up on your kids’ homework. With a basic understanding of the concept behind fact families, you should be able to figure things out.

In each fact family, there are four equations. (They may be called problems, expressions, number sentences, etc…) Each of the four equations will utilize the same three numbers.

Let’s look at a simple example using addition, and therefore, subtraction.

4 + 7 = 11

Now, we use the commutative property of addition to create the second equation using the same three numbers.

7 + 4 = 11

Time for subtraction! If you start talking to your kids about subtraction early, it won’t be such a shocker later on.

11 – 7 = 4

11 – 4 = 7

So, the fact family for the original problem of 4 + 7 = 11 is:

4 + 7 = 11

7 + 4 = 11

11 – 7 = 4

11 – 4 = 7

Notice that if you read the equation from right to left and change the operation symbol, it will “un-do” the equation. Here’s a little script you can read to your kids. Insert numbers as you go.

Mom:  “So when we add 4 and 7 together, we get 11. But check this out! 11 take away 7 equals 4. It’s the opposite. Think about it. If you have 4 jellybeans, and then you add 7 jellybeans, you’ll have 11 jellybeans. But if someone eats those 7 jellybeans, you’ll have 4 jellybeans again.” 

A great way to demonstrate this (assuming you don’t have a ton of jellybeans) is to use Lego bricks. Use 4 of one color, and 7 of another.

Good luck!

Explaining Fractions to Children….It’s Easy!

Hi Moms.

Before you attempt to help your children with fractions, it helps to know what fractions really are. Many of us can solve fraction problems, but we can’t always explain what we’ve just done. To make this very easy to understand, I like to use candy bars as examples. The candy bar is merely a representation of a whole object. If you prefer to use a different example, be sure it is something that can be cut into equal pieces. Pizzas or circles work well for some examples, but I find it hard to draw equal pieces on circles.

Fractions represent two things:

1. How many pieces a whole candy bar is cut up into. This is the DENOMINATOR, or bottom number.

2. How many of those pieces are eaten. This is the NUMERATOR, or top number.

Let’s look at a fraction we all know: 1/2

  • You have one whole candy bar.
  • It is cut into two equal pieces.
  • One of the pieces has been eaten.

Here’s another one: 1 3/4

  • You have some whole candy bars.
  • All of the candy bars are cut into four equal pieces, or fourths.
  • One whole candy bar, and 3 pieces of another candy bar, have been eaten.
  • You can also say that 7/4 of candy bars have been eaten. (4 pieces in the whole, plus 3 pieces of the other.)

I hope this helps!

Summer: To worksheet or not to worksheet. That is the question.

Now that the school year has finally come to an end, my tutoring families wonder what they should do about summer study. They ask me, “What workbooks should I buy for the kids this summer?” Or, “Did you see the summer bridge workbooks at Costco? Are they any good?”

It’s normal to worry that your child will forget everything he learned in school over the summer, and that may be the case to some extent. That’s why his teacher will spend the first few weeks of the new school year reviewing material from the previous school year. Granted, it seems like a huge waste of time, but you might as well accept it. It’s been that way since forever.

Most teachers will tell you that the best thing you can do for your kids over the summer is help them perfect their multiplication and division facts. It’s so simple, yet so incredibly vital. When kids don’t know their facts, they have an especially difficult time working fractions, long division, etc. Often, when students are “slow” or “behind” in math, they’re really just getting stuck on their basic math facts. Like a line of dominos, the student thinks he’s no good at math, so he stops trying. Then he stops paying attention in class, and he gets a bad grade. The teacher emails the parent (usually Mom) to tell her that there’s a problem. Mom freaks out, and the student becomes even more frustrated and the cycle repeats itself. I see it all the time; brilliant kids who are capable of higher-level math, who can’t solve 8 x 7. Fortunately, it’s a relatively easy fix that any family can tackle over the summer.

So, instead of buying a general workbook that covers all subjects for a certain grade, try purchasing a specialized book that addresses just multiplication and division. You may find that the grade level printed on the book is below your child’s current grade level, but it doesn’t matter. Facts are facts. Your child’s teacher will be very grateful that you took this step. Reassure your older kids that working in a 3rd grade multiplication book doesn’t mean that he’s at a third grade math level.

You may be wondering why all of those general, multi-subject workbooks are in the marketplace to begin with. Well, I think it all comes down to fear. Parents today are so worried about their kids’ academic careers (this explains the freaking out) that they will buy just about anything to ease that anxiety. If it’s colorful, fun, and educational-ish..it sells. Most stores carry educational workbooks of some sort, and it’s become the norm for us to buy them like we buy bananas. Resist the allure! I urge you to purchase subject-specific workbooks! Your kids don’t need to do page after page of breaking apart compound words and “fixing” incomplete sentences. They’re boring, pointless, and your kids aren’t outside playing!

What cracks me up is that whenever I go to a yard sale or secondhand bookstore, I always find partially-completed, multi-subject workbooks with $.25 stickers on them. Yep – the kids filled out a few pages here and there, and then Mom got sick of fighting it and she let the kids off the hook. I know you’re nodding your head right now.

Here’s the plan: Identify the root issue that makes you feel that you should work with your child over the summer. For instance, if it’s long division, watch your child attempt a problem and see where he gets stuck. If he can’t seem to figure out how many times 9 goes into the 67 of 6794, then you can probably stop right there and work on division all summer. While you’re at it, be sure to address fact families: 9 x 7 = 63, and 63/9 = 7, and so on.

I grew up in the 80’s, and my mom never made me do worksheets during the summer – probably because they didn’t exist unless you robbed the elementary school and commandeered the Xerox machine. No…I got the hell out of the house so she wouldn’t make me clean it! She was pretty smart, huh? I rode my bike in the 110 degree Tucson heat without sunscreen, I built forts and I did back flips off the diving board. If we were lucky, Mom would drop me and my sister off at the Tucson Mall where we’d look at the inappropriate greeting cards in Spencer and drink Orange Julius’. Amazingly, we both graduated from college and went on to lead productive, successful lives. No summer bridge workbooks needed!

The takeaway: Make sure your kids know their facts quickly and accurately. A subject specific workbook is best for this. And remember, worksheets and workbooks don’t teach, they only reinforce.

For kids who are truly behind in a subject, or for kids with low math confidence, I suggest pre-teaching. More on that later!