math

Helping Your Child With Math HW: Some Don’ts and A Lot of Do’s

Jen Moffett, , Leave a comment

The struggle is real. Your child is frustrated, you are frustrated, and the homework you both have been working on STILL is not complete. Your child screams, “You aren’t doing it RIGHT…That’s NOT how my teacher showed me…I HATE math!”

Here are the 2 mistakes we as parents make. Since it is the beginning of the school year, let’s really make an effort to abide by these Golden Rules. These are followed by helpful hints to make it a successful year in mathematics.

Golden Rule #1 (Even if you dislike math A LOT) Never Ever say negative remarks regarding your abilities in math or about math in general. I cannot tell you how many Student Study Team meetings began with a parent saying, “Well I was never good at math”…That is your golden ticket for your child to say the same thing, and think it is okay to just give up. It is not okay. Would you admit that you couldn’t read? No. So just don’t say it. Don’t say the homework is “stupid” or disrespect your child’s teacher in front of her. The results will not improve her performance or her efforts in her math class. If you have a problem with the mathematics coming home or with your child’s teacher, discuss it with the teacher.

 Golden Rule #2 Do not do your child’s homework for her. I often tutor my family and friends. My favorite comment is, “I don’t get (insert child’s name) math homework. Can you come explain it to me?” Though I would love you (the parent) to understand the mathematics as well, you should not be the one doing the work. Your child needs to do the work, needs to struggle and figure out where he is lost, and needs to feel what it’s like to finally “get it”. That is the goal of the homework, not just completing the problems.

Ways to Help Your Child With Mathematics

  1. Set a schedule. Your child should do his homework at a regular time each day. My son’s schedule is crazy: Cross Country in the am two days, in the pm two days, and Youth Group one night. Yet the schedule is the same every day. Whatever time he gets home, he eats something (whether it’s a snack or dinner) then gets down to homework. He knows this is the routine, so there is no griping.
  2. Set a standard place to complete HW. It is a pain, but I like him to do his homework at the dinner table. He can spread out, and I am usually fixing (or cleaning up) dinner nearby to ask questions when needed. We have a side tray table with materials he may need (paper, calculator, pencil, colored pencils, etc) set up for him so there is no reason to leave the space.
  3. Encourage. Encourage. Encourage. The students whom I hear the most from aren’t the ones who got it the fastest. They are the ones who put in the effort, with me cheering them on through their frustrations and never giving up on them or their learning mathematics. It means the world to your child to know you are rooting for them to be successful (Even if they won’t admit it!).
  4. Give directives/Ask questions FIRST. Here is a list of prompts and probing questions to move you along.
    • Tell me what you are doing (or working on).
    • What did you do in class that was like this problem? Do you have an example in your notes we can look at? Let’s re-read your notes and see if that helps you remember.
    • Could we call someone from your class? (This is great with social media. They can facetime, Skype, Google Hangout, etc. Get your kids to make study groups from friends in their classes!)
    • Let’s look in your math book and see if the examples from the section you are working on will help us.
    • Does your math book have video tutorials? (Most do! Get the login and password from your teacher BEFORE a crisis!) Let’s watch it and see if it helps us understand more.
    • What did you try first?
    • How did you get that answer? Explain it to me.
    • What is the pattern?
    • What doesn’t make sense? Where did you get stuck?
    • Does your teacher offer tutoring tomorrow morning? Let’s get you there!
  5. Email me the math! Love to blog about math problems in REAL time! jarguelovesmath@yahoo.com
  6. If none of this is helping, and your child has worked on her math homework for over 30 minutes will little (or no) understanding, STOP. I would email her math teacher and ask for advice. Explain the attempts made and where your child is stuck. Most teachers will be understanding and give her more time. If the teacher does not, request a meeting with just the two of you to discuss the difficulties your child is having and intervention options the teacher (or school) offers.

Good luck and have a great year support your child’s success in mathematics!

Helping Your Child With Math HW: Some Don’ts and A Lot of Do’s

Start Smart! 6 Things Your Child Can Do To Start The Year Right

Jen Moffett, , Leave a comment

You know it’s almost here! The smell of newly sharpened pencils and the odor of dry erase pens…The aisles of school supplies in the local stores…Sales on children’s clothing…School is upon us! Here are some tips for you to encourage your child to do to get the year off to a great start in their math class!

Greet the Teacher1. Greet your teacher the first day. I cannot stress the importance of making a good first impression. This is especially important in middle school, where we teachers have over 180 students to remember!  Encourage your child to make eye contact with his teacher and shake her hand. Say, “My name is ________ and I look forward to being in your class!”

2. Sit in the front! Now, some teachers choose your seats for you. If they do not, choose a seat in the first two rows. It forces you to listen, and you have first crack at your teacher if you don’t understand something.Sit in Front

3. S.L.A.N.T. This is a behavioral routine (I learned about it when I was an AVID teacher) used by many school districts to encourage positive engagement in class. (For more information, visit http://www.powayusd.com/teachers/lharvey/path/slant.htm)

S– Sit Up – Sitting with your feet flat on the floor, back straight, and facing forward focuses you and puts you in the right mindset to work and take part in discussions.            

L– Lean Forward- Leaning forward shows you are engaged in the lesson, which often encourages teachers to ask you questions, see how you are doing,  and keep you engaged.

A–Ask Questions- I can guarantee you are not the only one with your question. However, by being the bold one to ask it, the teacher knows you are listening and that you care. In turn, she will take more time with you to make sure you understand.

N–Nod Yes/No- The simple act of nodding when you agree/disagree lets the teacher know you are listening and what you are thinking.

T–Talk With Teachers- We are real people. Talk to us. The more we know you, the more we care about you.

HW4. Write your homework down. The most common reason I get for students not doing their HW is that they didn’t know what it was. Get in the habit of coming in and immediately pulling out your planner to write down your HW. When you do your HW, highlight it to indicate it is complete.

5. Do your homework! Start off right. Get in the habit of doing your HW. If you don’t understand it, try it for at least 20 minutes and email your teacher to let her know what you tried and where you got stuck. Just putting in the effort will let your teacher know you care. The more you care, the more we care about helping you.

6. Don’t be absent. Miss school, miss out. You simply cannot make up the discussions and learning that took place on a day you missed. The more school you miss, the more you don’t understand, the more you dislike school, the more likely you will drop out.Absent

Have a great first week of school!

Up next: Questions to Ask Your Child To Help With HW!

Start Smart! 6 Things Your Child Can Do To Start The Year Right

Beyond Counting: Ideas and Activites For Your Little Ones

Jen Moffett, , , , , , Leave a comment

While waiting for his big brother at the orthodontist, my little boy, C,  had the following conversation…

Dr. T: How old are you, cutie?

C: I’m three!

Dr. T: How old is your brother (pointing towards my thirteen year old)

C: Four!

This was such a proud mama moment for me!

Now you may ask yourself, “Why is she getting all excited over this? Clearly, he is not four. Why is she so proud of her little boy?”

There are a number of reasons why this is a critical step towards numeracy. I truly believe that if you start children purposefully thinking about numbers early on, their chance for success in mathematics increases dramatically. So let’s highlight a few of the big ideas C is working towards.

bears

1. Cardinality– This is the idea that the number being used is measuring some amount. It answers the question, “How many?” For example, I can ask my son, “How many bears do you see?” He would count them one by one until he got to the number six. That last number, 6, tells you the number of bears in the set. This is a big deal! The child is no longer counting from memorization; he is recognizing that the number relates to a certain amount of “things”. The more things you have, the further you have to count. C recognized that his brother was older (or “bigger”). Therefore, his brother was tagged to a number after the one he identified with, three. He did not know how many more to go, just that he had to choose a number beyond his own. Cool.

2. Inclusion– This is the idea that the number labeling “how many objects” in a group includes all of the preceding numbers. So even though we have six bears, we can also think of it as “one and some more”, “two and some more”, “three and some more”, and so on. This is critical for addition and subtraction. If I have the number 14, I can think about it as “ten and four more”, which helps me when I want to add or subtract and regroup to make the problem easier. C knew that his brother was older, and therefore had to include his age (three) and some more. Again, he isn’t at the point of knowing how much more, but is on his way. Awesome.

3. Magnitude– The size of the object. In this case, a number (or value) given to a quantity (age) for the purpose of comparing with another quantity. This idea is instrumental for estimation, particularly with very large and very small numbers. In fact, one of the posts requested of me to write is helping students compare fractions. If a child does not know the relative size of the number they are considering then it is very difficult to compare, operate or manipulate it with any real fluency or number sense. How do I know my answer is reasonable if I haven’t a clue what the numbers I am working with represent??? For C, he was able to recognize that his brother had to be a larger quantity than three, because he is older. Super rad!

These three ideas are certainly related, but each has a different feel. You can work with them simultaneously, so long as there is purpose to the questions and tasks you present to your kids. Below are some simple, but powerful, activities you can play with your little ones to build these concepts. I choose the games that you can take on the road, to the doctor’s office, to a restaurant, etc. Instead of sitting around being squirrelly, play a game while you wait. Even five minutes will have a significant impact!

1. Count and Check: Grab a handful of ANYTHING (balls, pennies, beans, cheerios, etc) and ask your child to count how many. Make sure the amount of objects is appropriate. (For example, C is working on objects through 5.) When he finishes counting the last object, ask, “How many _____ are there?” If he cannot answer, that is okay! He is working towards cardinality. He is able to say the objects one by one (which is called one to one correspondence), but hasn’t figured out that the last number he says represents the entire amount. Have him count again, and ask again. If he cannot answer again, say, “There are (say the amount) ______ here.”  You can play this at the grocery store (count the apples, bananas, etc), setting the table (How many forks?), etc.

2. Match Me! Grab a die (one dice) and a handful of ANYTHING in a baggie. (I typically do this with pennies at restaurant.) Have your child roll the die. Let’s say she rolls a five. She takes out that many pennies and lays them out for you to see. Ask her to count them one-by-one to make sure she has five. At the end ask, “How many pennies do you have?” If she doesn’t know, that is okay! Have her recount, then ask again. If she still isn’t able to tell you, say, “I see you have five pennies.” Make sure you roll next and model for your child. Take turns until you get bored or dinner comes!

To bring the difficulty up, after playing each of these, ask, “If I gave you one more item, how many would you have?” This brings in the concepts of magnitude and inclusion! If your child has to recount with one more added in, that is fine! You know he’s got it when he can answer quickly without physically adding in another item and recounting.

Need another level of difficulty? Ask, “If I took away one of the items, how many will be left?” Same idea, but working backwards, and just as important!

Beyond Counting: Ideas and Activites For Your Little Ones

Top 5 Things NEVER to Do/Say AGAIN When Helping Your Child With Math!!!

Jen Moffett, , , 3 Comments

What we want is to see the child in pursuit of knowledge, and not knowledge in pursuit of the child.   

–George Bernard Shaw

Happy Teacher Appreciation Week!!! I had a blog all good to go with stories from my own edcuational journey, my son’s, and others. Yet it didn’t seem to fit my purpose, which is to support parents in helping their children with math. So I decided to let y’all in on some secrets. Here are the top 5 things teachers wished you would never do (or say) when helping with math. Likewise, here are the top 3 things teachers wished you would always do when supporting your child in math.

Top 5 Things NEVER To Do Again When You Help Your Child With Math

  1. 7cd05c2267bceac7ba2101dc4624d14dNever say, “I wasn’t good at math.” This goes for teachers that do not teach mathematics as well! In fact, on my most recent blog, many responded (on FB) that they were never good at math, nor would they be good at math now. This self-deprecation has to stop NOW!!! This is a cop-out, and it allows your child to think it is okay to be illnumeric (Yeah, totally made up that word.) Would you admit to your child that you couldn’t read or write? Would that be acceptable in your home for your child not to be able to read or write? Heck no! So just stop.
  2. thDVCZDEMMNEVER say the homework is stupid, boring, ridiculous, etc. in front of your child. Jo Boaler, a mathematician out of Stanford University, has done a ton of research on the correlation between student effort and performance in mathematics. Bottom line: the more effort you put in, the better you do. To learn mathematics takes effort, time, and perseverance. You may not like what your child is doing, but relay that message to the teacher, not your child. And please do not write a derogatory note on your child’s homework. This negativity leads your child to believe that he can choose to do some work and skip other work because it is uncomfortable. Would that fly in a job atmosphere? Can I choose to do some of my job-related work and ditch the rest because it is boring? NO, I cannot. Please, support your child at home. Encourage him to try his hardest. “Play” with the problems. And if he goes over the research-based homework time (According to Robert Marzano, 10 minutes per grade level. So for grade 3, 30 min.) take a break, and email his teacher.
  3. 185255772NEVER do the homework for your child! My favorite story about this was with a young lady who was perfectly capable of doing the homework, but got stuck and didn’t know what to do. She asked her father for help. He literally took the pencil from her daughter and wrote it out for her. You could see on the page where she stopped and he began. When I pulled her aside and asked her, she said, “Well, he thought I couldn’t do it so he did it for me.” What did that teach her? When it gets too tough, give up and assume someone else will do it for you? If you want to help, ask questions. But don’t give answers.
  4. stopwatchNEVER EVER attribute brilliance with speed! I am at fault for this. When a toddler can do something quickly, how do we respond? “Wow! You are so SMART.” No, you just already knew how to do it. Children are brought up thinking if they don’t know the answer to a math problem immediately, they are dumb. That is sooo not true!!! Mathematics takes deep focus, diligence, and perseverance. Encourage effort, not speed.
  5. thJ6P17D2JNEVER make excuses for your child to get out of the work. Look, life happens. We teachers get it. Things come up. We love it when you communicate with us, especially when unforeseen circumstances arise. However, your child is still responsible for the work. It may be late, but should still be done. I used to cringe when my middle school student would come in with a big ol’ grin and say, “My mom said I didn’t have to do this and here is the note!” Work it out with the teacher, not your child.

Top 3 Things To Do Right Now To Support Your Child in Math

  1. you can do itEncourage effort. When your child gets frustrated, you can absolutely say that math was tough for you too. BUT MOVE ON. What are the resources she has to support the homework? Was she given examples in notes? Did she already do some of the problems (to look at to refresh her memory)? Are there videos on-line to help? BTW: Many publishers have on-line support via tutorials. Ask your teacher for the link, login and password! Does your teacher offer tutoring? Encourage your child to attend. All of these resources will continue as she moves through education. These are great tools to learn how to access now!
  2. QuestionsAsk questions. My favorite story was of a grandfather who took care of his granddaughter after school. She ended up getting her doctorate (I believe). When asked what contributed to her success, she said it was all the help her grandfather gave her with her homework throughout her time in school. Little did she know, her grandfather was illiterate. He simply helped through questioning. You don’t have to know the math. You need to have good questions to ask.
    • What homework did you have in math today? Show it to me. (Yes, even my child has said his homework is done and…ooops! Still have a few problems left to do…)
    • Tell me what you have tried and where you think you are getting stuck. (Not a question, but a great place to start.)
    • What did you learn in class today that could help you with this? Let’s look it up in the index (if they have a book at home) and see if we can go through the lesson together.
    • Do you have notes from today? Let’s re-read them and see if they can help us.
    • Do you have a problem already done? Let’s go through the steps and see if that refreshes your thoughts.
    • What do you know? Where are you stuck in the problem?
    • Could we go online and look up how to do _______?
    • Who could you call to ask for help? Could you meet with them before school/lunch/etc? (I offered my room for study groups. Kids would come and work together on the homework. Awesome to listen to them help each other!)
    • When does your teacher offer tutoring? Let’s take you to get some support.
  3. Parent teacher ConferenceBe in communication with your teacher. You are your child’s greatest advocate. This is critical in middle and high school, where teachers have up to 200 students a day! Email the teacher when your child is stuck. When he is frustrated. When things get difficult at home. When we had our second child (ten years later), my oldest started slipping in school. I emailed his teachers what was happening, and they were super supportive, giving him the attention and help he needed to get back on track. Teachers do not know what is going on in their students’ outside lives unless you help them know. Help your child by keeping the lines of communication open!

Notice none of my suggestions encouraged you to become a mathematician. Just be a support for your child, encourage effort, and keep in contact with his teacher. These are the greatest gifts you can give a teacher (and your child!). THANKS!!!

To read more from Jo Boaler: http://www.youcubed.org/

Top 5 Things NEVER to Do/Say AGAIN When Helping Your Child With Math!!!

Taking The Distributive Property to Middle School: Making Multiplying Mixed Numbers Easier!

Jen Moffett, , , Leave a comment

The last couple of blogs have highlighted the importance of the distributive property in multiplication for grades 3-8.  Let’s refresh ourselves…

Example: 6 x 9    Try it out using the distributive property! (There are many, but I have highlighted two.)

Method 1: Think about the 9 as (10 – 1).  Distribute (multiply everything in the parenthesis by) the 6.

 6 x (10 – 1) = (6 x 10) – (6 x 1) = 60 – 6 = 54

Method 2: Think about 9 as (4 + 5). Distribute the 6.

6 x (4 + 5) = (6 x 4) + (6 x 5) = 24 + 30 = 54

So you may think, “Jen, where the heck are you going with this?! This is a waste of my time and my child’s time.” Yet here was my son’s homework earlier this year.

multiplying mixed number

He was to multiply 17 2/5 by 5. Most of us learned you MUST convert the mixed number (17 2/5) to an improper fraction, then “multiply tops/multiply bottoms”. Finally change the improper fraction BACK TO A MIXED NUMBER. What a stinkin’ waste of time!

My oldest had the problem done in less than a minute. He got 87. Do you see it? What did he do? I have to admit I didn’t see it at first, and had to ask him. This is what he said (please insert a very monotone voice, since he wasn’t pleased with having to tell his mother his strategy…)

I thought about the 17 2/5 as two parts. 17 + 2/5. I mutliplied 5 times 17 and then 5 times the 2/5. Then I put it back together. (Duh, mom.)

So what does this look like mathematically?

5 x 17 2/5 = 5 x (17 + 2/5)

                                                 5 x (17 + 2/5) = (5 x 17) + (5 x 2/5) = 85 + 10/5 = 85 + 2 = 87.

In this case, using the distributive property is MUCH faster than the rules we were taught! And it makes sense! I am using partial products. I break up my number into easier parts, multiply them by the given value, and put it back together.

Here is another example. This came from one of my intervention students (students who are brilliant but don’t excel with the traditional book method in mathematics…) :

Import 9.3.14 709

You can admire all of his fabulousness, but the piece I want to focus on is 9 1/11 x 7. In red, notice he rewrote it for everyone to understand. Please note he had done it in his head (the blue). All red work was written after to let his class know what he was thinking.

                                  9 1/11 x 7 = 7 x 9 1/11 (commutative property)

7 x 9 1/11 = 7 x (9 + 1/11)

                                     7 x (9 + 1/11) = (7 x 9) + (7 x 1/11) (distributive property)

                         = 63 + 7/11 = 63 7/11%

Why am I showing you this? As parents, you WILL see the distributive property used with fractions, decimals, and percents. It makes it faster to compute, as students can do most of it in their heads. Most important, when students use the distribute property, I have noticed less “silly” errors. They get it right because it makes sense!

What can you do to support this kind of thinking? Play with numbers. Use a whiteboard. Use the sidewalk with chalk. Use the bathroom mirror with a dry erase pen. Give one problem a day and see how easy it gets to think about multiplication this way.

Here are some starter problems…

7 x 6, 7 x 7, 7 x 8, 7 x 9, 7 x 12 (break the 12 into 10 and 2)

8 x 4, 8 x 6, 8 x 7, 8 x 9, 8 x 12

9 x 4, 9 x 6, 9 x 7, 9 x 8, 9 x 12

3 x 16 (break into 10 + 6), 3 x 17, 3 x 18, …You could go on forever!

2 x 4 1/2, 2 x 5 1/2, 2 x 6 1/2, ….and so on

3 x 4 1/3, 3 x 4 2/3, 3 x 5 1/3, 3 x 5 2/3, …and so on

4 x 3 1/4, 4 x 3 1/2, 4 x 3 3/4, … and so on

If you need more, just look up free worksheets that multiply a mixed number by a whole number. Use one a day!

Taking The Distributive Property to Middle School: Making Multiplying Mixed Numbers Easier!

Learning Multiplication Facts Fluently: Resources

Jen Moffett, , , Leave a comment

I  was hoping to have this post up a few days ago. However, I have been deeply disappointed with the lack of resources for students to truly gain an understanding of what multiplication IS. My least favorite involved rhymes for EVERY fact that had absolutely nothing to do with multiplication! (4 door x 6 chicks= denty floor, 24. Are you kidding me????)

There are a ton of “just fact” games: give the fact, type in the product, and so on. And these are fine for students who already know their facts. But if your child is struggling to learn their multiplication facts, that is the LAST place you want to go! So I am going to provide some alternatives for you to explore.

Before I do, I want you to truly ask yourself this question. Does your child REALLY know the facts, or is she merely skip counting quickly? This question could also be asked of your first grader with addition. (Does he really know his addition facts, or is he counting by ones really fast?) When you ask your child a multiplication fact, does she tap it out, count on her fingers, or (what my middle school students would do ) bounce through the multiples? Let me give you an example: 3 x 7. Does your child bounce through (3, 6, 9, 12, 15, 18, 21…21!)? If so, she was timed too early in learning her multiplication facts. Your child should not be timed until she can use a strategy or just knows the fact within three seconds. And that is one-one thousand, two-one thousand, three-one thousand. Once they can multiply that quickly, you can go to some of these fun blast ‘em multiplication games.

So how can you help get her to three seconds? Here are three games I used with my son. I used them in this order, as they get more difficult and begin to have a sort of time crunch to them. If you have others, especially great apps, please include them in the comments section. If you add a resource, please let us know if it is to review mastery or to build strategies towards mastery. Thanks!

1. Circles and Stars. I have seen this in a number of mathematics resources, but the one I love is from Marilyn Burns (see link below). This is slightly adapted. All you need are two dice, paper and a pencil (or whiteboard and marker, which is my personal choice).

Roll two dice. The first number tells you how many circles to draw. The second number tells you how many stars to draw in EACH circle. The total number of stars is your product. Play 5 rounds. The person with the most stars at the end of 5 rounds wins.

Example: Sam rolls a 3 and a 4. He draws 3 circles, with 4 stars in each circle. There are twelve stars in all. 3 x 4 = 12.

Take it one step further. Roll two dice. You choose which number represents the circles and which number represents the number of stars in EACH circle. At some point, you want to ask your child, “Does it matter?” “Will I get the same amount of stars in the total?” The answer is yes! However, 5 circles with 2 stars in each circle looks different than 2 circles with 5 stars in each circle. Yet they both give me 10 stars in all. This is a great place to discuss the commutative property. For multiplication (and addition), when I reverse the order of my factors (the numbers I am multiplying together), I will get the same result. So if your child knows 3 x 7, but thinks he doesn’t know 7 x 3, think again!

2. Math Boggle! I loved Boggle growing up. Shake up the letters, and try to find as many words as you could in the time allotted. This helped me a great deal with learning to spell. Well, we need to play with numbers just like we play with letters. We are just going to start with one fact, and try to figure out as many strategies in the time allotted to find the product (the answer to a multiplication problem). Your kids may know this as a “Number Talk” if their teacher uses them as warm-ups. (If not, encourage them to do so!)

Example: 5 x 6. You have five minutes to find as many different ways to get the value. Go!

  1. 5 + 5 + 5 + 5 + 5 + 5= 30 (Still reliable and true, but not the fastest method.)
  2. 6 + 6 + 6 + 6 + 6 = 30 (Great to have a discussion as to which method, a or b, is more efficient and discuss the commutative property yet again.)
  3. 5 x (2 x 3) = 10 x 3 = 30 (I factored the 6 into 2 x 3. You know it as taking the prime factorization of 4. It’s actually a useful tool when working with multiplication and division.)
  4. 5 x (3 + 3) = (5 x 3) + (5 + 3) = 15 + 15 = 30. This is using the distributive property. Please see prior post for details! Also notice it is 15 twice, which could lead to the next strategy.
  5. 5 x (3 x 2) = 15 x 2 = 30. Similar to c, but using the commutative property. Also, similar to d, as I have 15 two times. This leads to a nice discussion about why we break apart the 6 instead of the 5. The number 6 is composite; it can be broken into the product of primes. 5 is prime, so it cannot be broken down into smaller whole numbers through multiplication.
  6. 5 x (4 + 2) = (5 x 4) + (5 x 2) = 20 + 10 = 30. Again, using distributive property, but I broke up the 6 differently.
  7. 5 x (5 + 1) = 25 + 5 = 30. Distributive property. Notice I stopped writing in the middle step. Once kids understand what is going on (in this case, I am multiplying the 5 times the 5 and then the 5 times the 1), they can omit this step. The goal is to get as many as you can. Further, we are eventually wanting them to do most of this in their head so they know their facts.
  8. (2 + 3) x 6 = (2 x 6) + (3 x 6) = 12 + 18 = 30. You can use distributive property by breaking up the 5, but notice the partial products you get (12 and 18) are tougher to add together in your head. Great place to talk about why we naturally break apart the 6 instead of the 5.
  9. There are many others, but I am hoping you get the idea.

You can play this all day long! Just use a whiteboard and work as a team. Take 5 minutes to work alone. Discuss all of the different strategies each of you used. Perhaps work together to find one more. Go to a different fact. Play in the car (Obviously the kids are playing, not you while driving!), while waiting for an appointment, at a restaurant. The more you play with numbers with your kids, the more fun they have, and the more important they see numbers playing a role in their lives.

3. The Product Game: http://illuminations.nctm.org/Lesson.aspx?id=5729

This is the first of four different multiplication activities your child can do with you to learn multiplication fluently. I highly recommend playing this after your child has really worked with the first two activities. The directions are included on the site as well as a pdf of the game you can print out. You are basically taking two numbers and multiplying them together to earn a spot on the grid. The first person to get four in a row (like tic-tac-toe), wins. Have a whiteboard or scratch paper handy in case your child wants to use some of their strategies to figure out the products. The other activities can be found through this link: http://illuminations.nctm.org/unit.aspx?id=6104

If you only have time or energy for one of these three activities, please use #2. It gets you the most bang for your buck. Happy number playing!!!

Teachers: For a great resource for multiplication please check out Lessons for Introducing Multiplication, Grade 3 by Marilyn Burns (2001)

Learning Multiplication Facts Fluently: Resources

Fluency in Multiplication: Why Your Child Needs To Know How to Distribute!

Jen Moffett, , , 4 Comments

This is the third in a series regarding fluency of basic facts. For the introduction to this series, please read Fluency and Memorization Are Not Synonyms!!!

I am a believer that all students can be successful in understanding mathematics. Maybe not memorizing erronerous facts, but truly understanding what the numbers mean and how they relate to one another. One of my favorite interviews to do with my sixth graders is on multiplication facts. You may want to ask your child this question as well…

If I know that 7 x 6 is 42, how does that help me figure out what 7 x 7 is?

Most students will say “49”, but will not find the relationship between the two facts. Here are the common answers for my sixth graders:

1. “I just know it.”

2. (Counting each one on his/her fingers) “7, 14, 21, 28, (usually begins counting by ones), 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 49…7 x 7 is 49.”

3. Gets the answer wrong, or says he/she does not know that one.

Now don’t get me wrong, I am appreciative when a student “just knows it”, because it usually makes her life easier. The middle school years are ALLLL about multiplicative thinking and proportional reasoning. If you do not know your multiplication facts fluently, you spend sooo much time figuring out the fact (such as student #2) you get lost in the actual work you are trying to do. This leads to frustration, feelings of failure, and a negative attitude towards mathematics.

The answer I am looking for is similar to the following.

“I can just add one more group of 7 to 42 and get 49.”

Why is this important? Because many children do not see multiplication of whole numbers as simply a certain number of equal groups. 7 x 6 means that I either have 7 groups of 6 OR 6 groups of 7 (Commutative Property. Please see my blog on fluency with addition facts.) So if I have 7 x 7, I have one more group of 7 than I did before.

Mathematically, it looks like this: 7 x 7 =(7 x 6) + (7 x 1) = 42 (the fact I was given) + 7 = 49.

This type of strategy, doing your multiplication in parts, is often called in elementary books the partial products. In middle school, this particular set of partial products is called the distributive property. It means you are going to distribute (pass out) a number, multiplying it by everything it has a relationship to. This is not new. We used this in Algebra back in the day. But to use it to help with multiplication facts is a novel idea for most, though it brings understanding to what they are learning.

Here is another example: 6 x 9. (One of the most commonly missed facts.)

Let’s say I do not know my 9’s. However, I do know my x 10’s and my x 1’s. I can think about multiplying 6 by 9 as multiplying 6 by one less than 10, since 10 – 1 = 9.

6 x 9 = 6 x (10 – 1) (true)

So now I need to know how much 6 x 10 is and 6 x 1 is. (You are distributing the 6.) Those are easy facts for me!

6 x (10 – 1) = (6 x 10) – (6 x 1) = 60 – 6 = 54.

I can do this with any of the facts. Say your student struggles with 7’s. However, they know their 2’s and 5’s. They can break the 7 into 2 + 5 and use the distributive property.

4 x 7 = 4 x (2 + 5)

Now multiply 4 by the 2 and 4 by the 5 (You are distributing the 4.):

4 x (2 + 5) = (4 x 2) + (4 x 5) = 8 + 20 =28. Trust me, it looks a lot freakier on paper than just doing the partial products in your head!

Here is one for you to try: 8 x 7. Try it on paper before sneaking a peak!

There are several options. Here are a few. If yours isn’t here, please add it in the comments for others to see!

Option 1 (what I do): Break apart the 7 into 2 and 5.

8 x 7 = 8 x (2 + 5) = 16 + 40 = 56.

Option 2: Break apart the 8 into 4 and 4.

 8 x 7 = (4 + 4) x 7 = 28 + 28 = 56.

Option 3 (what my son does): Break apart the 8 into 10 – 2.

8 x 7 = (10 – 2) x 7 = 70 – 14 = 56.

There is no counting on your fingers, no tapping of feet or bopping of heads (which is what your child does to keep count if they don’t have the facts fluent yet). They just break up one of the factors (one of the numbers you are multiplying together) and multiply by parts. I really only need to know my 1’s, 2’s, 5’s and 10’s. Every other factor can be broken into these parts. It takes the number of multiplication facts to memorize from 100 (if you count 10’s) to 36.

Here’s why you really want to use this strategy with your child. If you are reading this, I bet your child is struggling with memorizing the facts. This strategy isn’t drill and kill. It isn’t a slower method that makes your child feel less than intelligent. It is actually a more sophisticated way to do the math, as it shows where the relationships are among the numbers. It is algebraic thinking in an arithmetic expression. The more your child “plays around” with numbers, the more relationships he/she will see, and the easier algebraic thinking will become. And yes, most (after using the distributive property over and over) will find that the facts will become automatic over time.

Let’s show a problem with a multi-digit number. (Another favorite of mine to use when interviewing children.) 6 x 199. Try it out. How would you solve it?

I just did it in my head. And no, I am not brilliant! Just using relationships to make the problem easier!

6 x 199 is the same as 6 x (200 – 1) = 1200 – 6 = 1194. Sooo much easier than trying to carry and multiply a bunch of numbers by 9!!!

I have to end this with a final thought. I have two dear friends that blatantly state they do not have their multiplication facts memorized. “It’s a waste of necessary brain space when all I need to know are my simple facts and build up the others in my head”, claimed the first. “Why do I need them memorized when I can figure it out quickly using partial products???” stated the second. What to know what their occupations are? The first is a mathematician and professor. The second is a statistician and psychologist. Hmmmm….

Next Blog: On-line resources and games/activities to build multiplication fluency!!!

Fluency in Multiplication: Why Your Child Needs To Know How to Distribute!

Basic Addition Facts For Fluency: Beyond Flash Cards!!!

Jen Moffett, , , Leave a comment

This is the second of a series of blogs regarding fluency of basic facts.

Memorizing any operational facts can be easy for some (who have photographic memories) and difficult for others. I tried and tried every type of “flash card” with my oldest and all it did was provide frustration, tears, and dislike for the math. We tried flash cards, memory games, on-line shoot the sum games. And none of them worked. I freaked out, knowing that if he didn’t get these facts down, it would be an uphill battle. But is it really? Do we need to focus on memorization or understanding???

This blog is about understanding and a teeny tiny bit of memorization. Please feel free to disagree, as this is a blog after all and participation is encouraged! However, at least read on before fighting the fight for memorizing only.

Depending on whether you live in a Common Core state or not, typically we want children to know fluently all of their facts to five by the end of Kindergarten and all of their single digit facts (10 + 10 is cool too) by the end of grade 1. Note I wrote “fluently” versus “to automaticity”. So what’s the difference? It means I get three whole seconds to figure it out. I may not be able to see the answer in 0.5 seconds, but using some strategic thinking I can get it. That’s the goal. Anything beyond is cool, but this is for all children.

Fun fact: If all you are going to do is memorize the sums for two single digit numbers, the amount of facts you need to memorize is 81. 81! That is a LOT! Have fun making 81 flashcards! No thank you!

So let’s dwindle the amount to memorize. Below are two strategies to teach your kiddos to make that 81 significantly less. (There are others, but if you focus on these two you are waaay ahead of the game!)

  1. Commutativity. This is a property (a rule that ALWAYS works in mathematics) of equality. Think about the distance you drive to work. And the distance you drive home. Now if you take the same route both times, you go the same distance. No matter if you start from home, or you start from work, your commute distance is the same. Commutativity works the same for numbers. I can add 3 + 5 or 5+3 and my result (the sum) is the same, 8. So if I use my commutative property, I now only have to memorize one of the two facts! I am now down to 45 facts! (You may think, “Hey, why isn’t it half of 81?” Well, the doubles such as 2 + 2 and 3 + 3 do not numerically have a commutative fact, so you are stuck with them.)
  2. Making 10. This is a big stinking deal. Your kiddos need to get under their belt the ways to make ten. (1 + 9, 2 + 8, 3 + 7, 4 + 6, 5 + 5 and the reversals based on strategy #1.) Why? For starters, we live in a base ten world. Once you hit 9, the next number literally moves over one spot to the left and now you have a double digit value. Once you hit 99, you move over one spot to the left and you now have a triple digit. And so on. Really though, let’s be practical. Is it easier to add 9 + 8 or 10 + 7? 10 + 7, because you can add the 0 + 7 easily. So if I can manipulate my digits to make a 10 +, I am good to go. Example: 9 + 6. I know that I only need one more to make 9 a 10. So I am going to take it from the 6. 9 + 6 = 10 + 5 = 15. If I know how to make a 10 + expression from the addition fact I am working with, I now go from 45 memorization facts to 25!

What are those 25 facts? 1 + 1, 2 + 1, 3 + 1, 4 + 1, 5 + 1, 6 + 1, 7 + 1, 8 + 1, 9 + 1, 2 +2, 3 + 2, 4 + 2, 5 + 2, 6 + 2, 7 + 2, 8 + 2, 3 + 3, 4 + 3, 5 + 3, 6 + 3, 7 + 3, 4 + 4, 5 + 4, 6 + 4, 5 + 5 (Notice the largest sums are 10, because all others can be made using a 10 + strategy.) So could your child learn these facts? ABSOLUTELY! Just remember to include the others for them to practice their two cool strategies with!

Next Blog: Fun games to play to work on making ten!

HUGE NOTE: Please do not time your children. For many, it stresses them out and they lose focus. Also, if you time children before they master the strategies, it will encourage them to count on their fingers. Though that may work for these small values, it will not help them in the long run when adding much larger numbers.

Basic Addition Facts For Fluency: Beyond Flash Cards!!!

Which Is Bigger? Comparing Objects Without Quantifying

Jen Moffett, , Leave a comment

One of my threenager’s (yes, I said “threenager”) favorite things to do is go to the zoo. Particularly to see the alligators and caimans. As he watches these creatures I have a habit of asking, “Which is bigger?” or “Which is smaller?” These characterizations, called attributes, are often the first way toddlers learn to compare objects. From there, they begin to quantify (How much bigger? or How much smaller?) and realize there is a need for numbers when comparing.

Yet all too often, our smart little toddlers overgeneralize and decide that EVERYTHING has an attribute of “big” (or “small”). For example, my little will tell his older brother, “You are bigger than me.” But what does he mean? Does he mean he weighs more? Is taller? Is older? Has more body hair? Each of these measures has a different attribute. In fact, Vygotsky stated that the way in which we talk about quantities and the relations between them can have a strong impact on how children think about quantities. And quantifying each of these attributes requires a different type of measurement.

My point? How we communicate with our littles makes a HUGE difference in how they look at comparing and relating objects. Not everything is bigger or smaller. Start using different attributes and introduce them to a wonderful world of vocab that will help them articulate exactly what they want to compare. For example, you are at the grocery store getting apples. Yes, have her point out the colors. Yes, have her count as you put the apples in the bag. But take it one step further. As you are waiting in line, have her hold the bag of apples versus the bag of green beans and decide which is heavier. Or which has more items. Which item is longer. Which item is wider. You get my drift.

Mathematics is not just about numbers. It also relies heavily on one’s ability to compare, estimate and see relationships, with or without numbers. Number is simply an extension of more basic ideas about relationships between quantities. Even if your child doesn’t know their numbers, you can start comparing objects NOW.

Great reference for teachers of Pre-K and Kinder:Developing Essential Understanding of Number and Numeration, NCTM (2011).

http://www.nctm.org/store/Products/Developing-Essential-Understanding-of-Number-and-Numeration-for-Teaching-Mathematics-in-Pre-K-2/

Which Is Bigger? Comparing Objects Without Quantifying

Get Ready To LOVE Mathematics!!!

Jen Moffett, 8 Comments

The essence of mathematics is not to make simple things complicated, but to make complicated things simple.  ~S. Gudder

My first math post. Well, actually, it is my seventh math post of the night, but the first one to go public. The others started with very colorful language expressing my fear and nervousness. (And those of you who actually know me, can hear me saying all of that right now!)

A little bit about me. My name is Jen Moffett, and I love math. I am actually addicted to mathematics. I read mathematical journals and books, dream about math, see mathematics in everyday life, and try to get everyone around me to love and appreciate it as much as I do. I have been in education for 20 years. In that time, I have taught elementary and middle school mathematics, worked at the county level as a curriculum specialist, and provided professional development to teachers and parents on a variety of math related ideas and concepts.

Recently, I was given the “gift” of being able to stay home with my littles. (You will hear about them more in later posts, as they are my guinea pigs for math strategies!) Emotionally rewarding, yet mentally I am needing more. I need to be teaching!!! It fulfills me in a way nothing else can. I have pimped my way into some classes through Skype, but it is still not the same. So what to do…what to do…

Yesterday, two public discussions arose about the mathematics children were bringing home, and the frustration (from the parent and child) in doing the homework. Or not doing the homework, because, really, what the heck are they asking my child to do??? These heated debates are not uncommon. Facebook has rant after rant about the struggles parents and children are feeling regarding the “new way” of doing math (Which is not new, but not the time to discuss.). I left both conversations feeling their pain. An idea sparked. I am pretty sure a lightbulb appeared above my head, but it was 1 am and no one was up to prove this.

What if I could support parents (and therefore students) through a blog?

So here it is. I am creating a blog to help you, my fellow parents. It will not be sequential, but I will provide tags so you can search for what you need. When I use great resources, I will reference them so you can check them out. There will be tasks for us to use to explore the difficult concepts, and the research supporting the strategies that may appear different than what we learned in school. Most important, I want to help you understand the “why” behind the mathematical strategies, and for you to gain an appreciation and a love (or a like for you haters) for mathematics.

Happy (math) reading!

Get Ready To LOVE Mathematics!!!