Warning! Are You Sabotaging Your Students? PART 3

If you haven't heard by now, you might still be teaching your students some outdated skills.  In Part 1 and Part 2 of this 3-part blog post, I examined such skills as, telling time on an analog clock, counting coins and using reference or library skills.


Are they outdated? What's the conclusion so far?  It's a mixed bag.  Because our society is changing so rapidly at a pace far more furious than we can keep up with, this has made teaching time and money more difficult because children are not using those skills on a daily basis anymore compared to kids 20 years ago. We've got digital watches everywhere, including on our phones and other gadgets.  Most electronic billboards and such have only digital clocks.  When I was a kid 40 years ago, if mom said to be home at 5:00, you were home at 5:00 or face serious consequences.  So we HAD to know how to tell the time on an analog clock.


Today, kids rarely see their parents fumble with coins or cash because we just swipe our credit card or hit ApplePay®.  Kids today don't even get cash anymore.  They're given gift cards, so that makes all the money virtual money that is not actually held in your hand or jingled in your pocket.


On the other hand,  teaching time on an analog clock and counting money also reinforces other critical math skills.  My conclusion is to keep teaching those skills for now.  Ask me again in five years, though.

As for reference skills, they will always be needed in this information-packed world.  But we need to be realistic and not waste time teaching kids to look in print encyclopedias or dictionaries when these can be accessed digitally or within an App.  However, we do have to show them how to use reliable sources of information.

So what else is out of date or rapidly becoming so?


Ok, this is one of those topics that gets everyone riled up.  I'll admit it.  I was one of these geeky kids who tried very hard to perfect his cursive writing.  I mean we spent A LOT of time learning how to write in cursive.  We even had our very own book for practice!  By junior high, you were expected to write in cursive full time.  Since I am a baby boomer, all my essays and assignments were done in cursive for high school. But that was 40 years ago!


It's 2018 and what about now? Should we continue to teach cursive writing? Is it needed ANYWHERE in our society?  Will it be required in ten years?  Are there any benefits to learning how to write in cursive?  You could spend hours Googling all the research on this issue.  But here's the real world answer.

As a mostly third grade teacher (though this year I'm teaching second grade), it was always my job to introduce and teach cursive writing.  Teaching cursive was fun.  But since I've been teaching for over 30 years, every year the curriculum got more and more crowded.  Something had to give.  That's why cursive writing got pushed to the very end of the year, usually during or after state testing season.  After taking a difficult and lengthy test, students were eager to just learn something fun like cursive writing.


There were videos on ACTUAL VHS tapes we could watch and learn how to write in cursive.  My school even purchased a cursive writing program for all the third-grade teachers.  So what happened? Why have we stopped teaching cursive?  In California, cursive writing was added when the state adopted the Common Core State Standards (3L.1.j, Write legibly in cursive or joined italics, allowing margins and correct spacing between letters in a word and words in a sentence.) so it's not like we can ignore it.

What happened is that it comes down to time.  There just isn't enough time in the day to teach everything.  Something has got to give.  And that give is cursive.  We justify it by saying that keyboarding is a more appropriate skill.  And I agree!  Keyboarding is a skill that will be needed by my second graders for the rest of their lives.  Cursive writing, not so much.

Think about when you as an adult needed to use cursive writing? Probably when you went to sign your name on an important document or on a credit card receipt.  I really can't think of any other place I use cursive writing, except to myself on notes.  But even then it's "pursive" or a combination of printing and cursive.


So, if all they need to do is to learn how to write their name in cursive so they can sign their names on important documents, then let's just teach them to write their name in cursive.  It's not likely they will encounter the need to read cursive writing in their school careers.  When was the last time you received a letter in cursive writing from grandma?

Let's face it, cursive writing is a polarizing issue, and there are many arguments for and against it.  But in the real world of my classroom, I feel like this should almost be an elective in high school... like calligraphy!  This is one skill we need to put on the shelf and leave it there.


Keyboarding.  If we're not swiping here or there, we're texting with our thumbs or typing on a keyboard.  Even entering information on those newfangled TVs requires your to expertly go up and down and across on a virtual screen keyboard.  So yes, by all means, teach keyboarding skills.


When I was in high school in the 70s, I took a typing class because I knew that typing would serve me in the future in college.  And it did.  I became an expert typist and could center a title or syllabicate words at the end of a line with no problem.  In college, I typed all my assignments and essays.  When personal computers finally came on the scene, centering and syllabication became automated.  But learning the keyboard has not.  And that's what we need to teach our students.  Teach them to find the location of the keys.

My second graders have small hands. Even on their Chromebook, they are not able to reach all the keys if we teach them proper keyboarding skills like keeping your fingers on the home keys.  And developmentally, they just can't keep from looking down or holding their hands in place.  So for now, just finding the location of the keys is fine with me.


As they grow older, I do think it's important for kids to take an actual typing (or is it called keyboarding?) class.  Hunting and pecking are not going to get them into college or a get a good job.  Now it could be that in ten years, voice recognition will be the norm and students can dictate their writing.  Just look at all the virtual assistants out there now like Siri, Alexa, and others.

But keyboarding will still be needed as not everything needs to be done through voice recognition technology.  Also, I tell my students:  texting is NOT typing.  They are two different skills though they use the same keyboard.  But yes, learn how to keyboard (or type as we used to say!).  It will serve you well as it did me when I took that typing class more than 40 years ago!


Here is a 21st-century skill that is necessary for EVERY student in school today and for future students:  digital citizenship.  Today's students are growing up in an increasingly digital world where interaction with netizens and information from all over the world is instantaneous.  To be a productive and responsible citizen, you also have to be a responsible digital citizen as well.


Students will need to understand how to be a responsible digital citizen. They'll need to know the protocols for posting someone's or their own private information and the consequences it could engender.  They need to know that posting inflammatory or even innocent information can result in unforeseen blowback.


They'll need to know how to spot unreliable or sketchy sources.  They'll need to understand the differences between opinion, speculation, wishful thinking, gossip, outright lies and HARD, COLD, PROVEN FACTS.  They'll need to learn that was is omitted is just as important as what is included.  They need to know when they're being trolled.  Don't feed the internet trolls.


For that, they'll need to have critical thinking skills that help them spot red flags and photoshopped sources.  They'll need to know how to communicate effectively while understanding that communicating digitally is different than an in-person conversation.  Emojis don't count as body language!

They'll need to know what cyberbullying is and how to combat it.  They'll need to know how to keep themselves safe from online predators and scams.  They'll need to know the procedures for reporting inappropriate and dangerous content.  They'll need to know that's it's OK to let an adult know that their friends are posting improper or illegal images and content.  They'll need to know that their cyber behaviors have real-life consequences at home, at school, and in the workplace.


Understanding and abiding by your school's acceptable use policy are critical to understanding that even in the workplace, employers have the right to terminate employment if they can document that you have violated their acceptable use policy or workplace rules.  Remember, the internet is forever.  Things can be saved through screenshots or cached files making nothing truly deleted from the internet.


They'll need to learn that digital friendships are nice, but having a "real friend" to hang out with in person is more rewarding and crucial for learning how to be a friend.  We need to have people we can depend on in our lives, and a real friend is one of those.

They'll need to understand privacy issues.  How and where information about their online activities is collected and shared.  They'll need to follow the rules for copyright and trademarks.  Just because it's on the internet doesn't mean you can co-opt it and use it for your own purposes without permission.

They'll need to learn how to disconnect from the virtual world and live in the real world so they can realize their potential and not be isolated in a make-believe fantasy world that bears no resemblance to their real world.


Finally, they'll need to understand the power of social media.  Social media is relatively new in the internet age.  It can literally make you famous overnight or destroy you utterly.  It's like the public square of years gone by.  Just like in a public square, social media can give you the virtual key to the city or put you in a virtual stockade for public shame.  Teenagers especially need to understand the power of social media if they are going to be allowed to use it.  Schools need to educate students on the use of social media because let's face it, their parents were of a younger generation and really cannot relate to the power it can yield.


You can agree or disagree whether teaching time on an analog clock, counting coins, learning reference skills and teaching cursive writing are skills worth teaching.  But I think we can agree that the future is changing rapidly and technology is advancing at a rate that outpaces educational reform.  We say we want to prepare students for college and the workforce.  But what will college be like in 10 years when my second graders graduate from high school? What kinds of jobs will they hold?

Think about this.  It took about 40 years to go from the constructing the first mainframe computer to having a personal computer in your house.  From there it took another 20 years to get to mobile computing on cell phones and tablets.  It took another 10 years for it to be common to have appliances and even your car connected to the internet.  Everything in your house can be controlled in the palm of your hand through a mobile device.  So as you can see the rate of technological advance and the use of technology is increasing at an ever-quickening pace.


Taking into account that in five years things will advance even more, what skills should we be thinking about adding, changing, fine-tuning or also eliminating?  We don't want to sabotage our students' futures by teaching them skills that won't be needed.

Share your thoughts about which skills we should add or eliminate completely? Share below in the comments.

Warning! Are You Sabotaging Your Students? PART 2

Are you still wondering what other skills students are being taught that may just be outdated?  In PART 1, I examined the concept of teaching time on an analog clock.  Though it is clear that the future will be digital, students should still be exposed to using an analog clock because it does help teach other skills such as, counting on or counting backward.  But other aspects such as teaching the archaic language of "20 till" or "half-past" or "quarter after" might not be a good use of our time.


Let's examine other skills we teach that may just be outdated in this rapidly changing world.  What about coins and money? What about reference skills? What about cursive writing?  What about keyboarding?


I discovered with my own children that when it came time for them to learn about money, they struggled while learning it in school.  But I couldn't understand why.  I tried to remember how I learned to identify the coins and count money.

When I was a kid, you could buy a lot with pocket change!  I could buy a candy bar or soda for 25¢ or less.  So any coin, whether they were pennies, nickels, dimes or quarters would be valuable to any kid back then.  Taking glass bottles back to the store to get the deposit was also another way to get pocket change.  And of course, washing cars for 50¢ also helped!  I also remember skimming a nickel or a dime from my lunch money and saving it to visit the 7-11 after school!  Since it was rare to have any bills as a kid, coins were the de facto currency for any kid in the 60s and 70s.


Fast forward to the 2000s.  I hate carrying around change.  I pay with credit cards or ApplePay.  I rarely have cash in my wallet.  Even the book fairs at school take checks and credit cards.  When my kids eat in the cafeteria, they don't need money to pay.  I've already prepaid online and they have a credit.  I don't pay with checks anymore.  I pay all my bills online through online banking.  I have direct deposit for my paycheck.  I can transfer money anytime with an App.  So essentially, my kids and I NEVER see the actual money used in daily transactions.  It's all virtual, prepaid or plastic.  My kids also don't get an allowance.  I never got one while growing up and in my culture, allowances are not part of it.  If you wanted money, you earned it.


So what does that mean for students in our classrooms?  They're probably experiencing the same scenario as my own children.  So think about it.  We are moving towards a cashless society.  I predict in ten years or less, cash will be an exception, not the rule.  Maybe we should be teaching our students how to manage an online bank account or use a debit card!  My son is on a trip to the East Coast with his 8th-grade class to tour America's historic sites.  I did give him some cash, but he also has a newly minted debit card.  So for the week prior to traveling, I had him practice paying for groceries, gas, fast food using his debit card.  Trust me, you'll want to teach your teenager how to use that debit card correctly!


In my second grade class, we are currently learning about money and I encountered the same situation.  My students really did not know any of the coins!  So we spent some extra days just learning to identify the coins and their values before learning how to count different money amounts.  It also doesn't help when all the backs of the new quarters are different!  And did you know the new Jefferson nickel has Thomas Jefferson facing forward rather than in profile?  Even that was a surprise to me (shows you how long I've been NOT carrying around change).


So the big question is:  do we continue to teach coins and money?  My answer is yes.  Even though I'm sure that when my current second graders graduate high school in ten years it'll be a mostly cashless society, think about all the math skills they learn while learning to count money!


They learn value vs quantity (5 pennies is the same as a nickel).  They learn to count by 1s, 5s, 10s, 25s, and even 50. They use mental math to add quantities.  They learn the value of saving money.  They even learn some history when you examine who and what is on each coin.  When teaching about bills, I taught them the correct way to fold bills and store them in a wallet or purse.  I remember as a kid being told: "don't fold, spindle or mutilate your dollar bills!"  Google the origin of that phrase!

Keep on teaching money, though it's soon to go out of style!


Since I was born before the internet was actually invented, I remember the days of using the Encyclopedia Brittanica (my parents had bought a set), dictionaries, and the library index card system.   In school, we were taught explicitly how to use the Dewey Decimal System in the library.  Those skills carried me through college as the internet was not much more than a collection of BBS that was accessed through dial-up (Google it!).


But once the internet became popular (though still dial-up), students and others began using it for research.  But we all know that anyone can publish a web page and fill it with misinformation or incorrect information.  Reliability and trustworthiness became the key.  That's not something we really had to deal with in earlier times just using encyclopedias, dictionaries and library books.

What kinds of reference skills should we teach students today?  We should probably scratch off print encyclopedias.  Finding access to a set is sometimes hard and when you do find one, it's usually very much out of date. There was a time that print encyclopedias were published on CD-ROMS (remember those?).  But even a CD-ROM can be out of date with the information.


Instead, we should focus on identifying reliable and trustworthy online encyclopedias.  Yes, Brittanica has an online encyclopedia, but it is not free.  Most of the free online encyclopedias are ad-supported.  Using an online encyclopedia can be daunting unless a school, a district, or parent wishes to pay for services like Brittanica for Kids online.  Ad-supported sites can present their own problems as the ads presented can be content inappropriate for children.

The best alternative is for teachers, curriculum specialists, district specialists and parents to organize a list of websites by topic or subject that has been examined for appropriateness, reliability, and trustworthiness by adults.  Since children can not expertly identify unreliable and untrustworthy sites that task should be left to adults while we teach them to understand the concepts of trustworthiness, reliability, and accuracy.


As for dictionaries, there are many online dictionaries and some online Apps like Google Docs and Slides have built-in dictionaries and thesauruses.  Dictionary skills that should be taught include understanding the part of speech, alternate definitions (multiple meaning words) and synonym/antonyms.

The library index card system has been replaced by computers.  Children still need to know how a library is organized by subject and author.  The Dewey Decimal System is still in place and should be learned.


The Millenials were the first generation to grow up in the Age of the Internet.  The iGen generation is now firmly entrenched in the digital world and expects answers immediately.  I predict that in the next ten years, personal assistants like Siri and Alexa will be the norm.  But learning how to search on the internet is an art form.  Children should be taught how to use boolean terms for searching (adding quotation marks, separators, terms, etc.).  They should also be taught how to separate paid content from search results.  Understanding how to narrow search results is the key to finding information that is relevant.


Coming soon is PART 3 that examines the role of cursive writing and keyboarding skills as well as, what new skills should be included for the future.

If you missed PART 1, click here to view it.

Warning! Are You Sabotaging Your Students?

Ok, maybe the headline was a little TOO dramatic.  But I started to think about this the other day when I began teaching telling time and counting money to my second graders.  In ten years, these little second graders are going to be seniors in high school!  So here I am teaching them to tell time on an analog clock.  And now, using the fake plastic money to learn how to count money.


But think about it?  In ten years, will there be ANY analog clocks around other than Big Ben?  Pretty much everywhere you look you see digital clocks.  I remember my younger brother always going to the digital clock in our house when he needed to know the time (and that was more than 30 years ago!).  My own kids do the same!  They did learn how to tell time on an analog clock. But because they weren't obligated or had the need to use an analog clock (other than the one in school), they literally started to forget how to tell time on it.  But are there still advantages of using an analog clock?

Uhg! I'M GETTING OLD! (when did that coin change?)

Let's talk about coins and money.  True story.  I had no idea the new nickel had Jefferson facing forward!  Since I have been mostly teaching third grade the past ten years, teaching second grade is new to me this year.  I haven't taught lessons on money in a LONG time.  And I hate carrying around change! So I never really paid attention to the difference in the coins.  Ok, I did know about the new quarters.


So here I am teaching my students how to count coins.  What's the biggest hang-up or obstacle so far?  Recognizing the coins!  So to my surprise, the new nickel has Thomas Jefferson looking forward instead of a profile. I guess I hadn't been paying attention to coins for a LONG time.  As I said before, I hate carrying around change. If I ever have any, I just put them in a box and collect it until I can take it to coin counter (free coin counting at my credit union, btw).   So when my students asked me what a coin was in their math book, I said to look at the resource chart that we made together or to look in their math journal.  Of course, it had the old nickel!  So a quick lesson on the new nickel.  But think about it.  In ten years, will we STILL be using coins or will we be a cashless society?

THE iGENs (they're in your classroom right now!)

What skills are we teaching today that will NOT be needed in ten years by this generation?  By the way, they are called the iGen generation.  Fitting name!  Unlike their older brothers and sisters who are the Millenials who GRADUALLY went from laptops to tablets to phones, this generation is glued to a portable screen (tablets and phones) full time.


They are growing up in a world we can not even imagine what it will be like in ten years. The first tablet, the iPad, was introduced in 2010...the year my second graders were born!  They've grown up around screens and swiping.   What skills will they need by the time they graduate from high school?  It's hard to predict the future, but there are trends we see coming.

In this THREE part post, let's examine some skills that may or may NOT be needed in ten years time (2028).  Part THREE will look at some recent skills that will be of critical importance in any future that comes (think digital citizenship).


As I explained above, the only analog clocks we see anywhere nowadays seem to be in classrooms and grandfather clocks (oh yeah, they might have Roman numerals, too!).  Yes, I still have one in my classroom.  But you know what, the school Chromebooks also display the time digitally.  Guess which one the students prefer to use?  Is it a losing battle?  Do we choose between analog or digital?  If you're proficient at telling time using an analog clock, the switch to a digital clock is no big thing.


But think about all that went into learning how to tell time on an analog clock.  The movement of the hands on a clock vs numbers just changing on a display.  You could actually SEE the progression of time.  Granted that on a digital clock, you can usually use a stopwatch function to see the passage of time. But looking at an analog clock allowed us to do mental math (counting on or counting backward).

How many more minutes or hours do I have to wait?  You could visualize the hands moving on that clock.  It is very hard to imagine or visualize the numbers on a digital display changing to figure out how much time is left of how long I'll have to wait.  That involves adding and subtracting in your head, while with an analog clock, it's a matter of just counting on or counting backward.


But in ten more years, will there be mostly analog or digital clocks on display in public areas?  What about on screens?  Probably more digital than analog displays.  Digital just takes up less space and is easier to change or adjust.  So if students looking at a digital display can mentally add or subtract, then that's probably just as skillful as counting forward or backward on an analog clock.


In the meantime though, I still think it's important to continue teaching time on an analog clock because it is just more than just learning how to tell time.  It's using mental math and visualizing, which are still essential math skills no matter what century you live in.  Other math skills can be strengthened or taught through an analog clock:  counting by fives, understanding quarters or fourths, and the concept of am and pm.


What I do think we should stop teaching are all the VARIOUS ways of saying the same time.  You know...half past, quarter to, 10 'till.  Does anyone other than our grandparents even use that terminology today?  Ok, they might hear it more often in different parts of the country, and they will definitely read it in older stories, but do we get our "bang for the buck" when we take so much time to teach these archaic phrases?  I'm happy with my second graders just knowing it's "two-thirty" rather than "half past 2."  The only term that should be taught is o'clock!


Take a look at Part Two, to examine some more skills such as counting money and reference skills such as library skills and dictionary skills.

What do you think so far?  Do you feel you teach skills you know won't be relevant in ten years? Or maybe they won't be relevant, but are necessary to develop OTHER skills?  Or are we ONLY teaching them because they will appear on state standardized tests? Share your thoughts in the comment section below!

Frustrated That Students Don't Know the Multiplication Facts? Part 3 The Derivative Strategies

In the final part of this three-part series on multiplication fluency, let's explore the Derivative Strategies.  These are the strategies that are taught AFTER the student has demonstrated proficiency in the Foundation Strategies (see the previous post for an explanation of the Foundation Strategies).  

The Derivative Strategies are the final steps that will eventually lead to multiplication fluency as well as, a better conceptual understanding of multiplication.



These are the strategies that continue to build that conceptual understanding of multiplication while building fluency over time.  The first strategy to teach is the halving and doubling strategy.  Why?

This strategy works with even factors.  So, if a student has learned and has fluency with the facts for the two times table, then he or she is ready to use this strategy to learn the facts for the four multiplication table.

Watch this example of a student using the halving and doubling strategy.

As you can see, knowing the 2s helps with learning the 4s because two is half of four.  The same strategy can be applied to learning the eight times table (though other strategies can be used as well).


This is the second strategy to teach students to use.  Once the 2s and 4s are learned by doubling and halving, students can move on to learning the three times table by learning to add a group.  If the student knows the 2s timetable, then teach the student to use this strategy to learn the 3s.

Watch this video of a student using the Add a Group Strategy.

THE DERIVATIVE STRATEGIES:  The Distributive Property Strategy

Of all the Properties of Multiplication, this is one of the hardest to teach.  Conceptually, students need to understand decomposing a number, partial products, and writing equations.  Not an easy task. Obviously, students need to be taught explicitly the Distributive Property of Multiplication.   I use this resource to teach the Distributive Property every year.  But whatever resources you use, once students are familiar with it, they can then practice the strategy for multiplying by seven and eight.

Before teaching this strategy, students really should be proficient in the facts for five.  Why? It is easier to decompose a number when one of the factors is five.  Multiplying by five leads to products with zero and five, which when added to the other partial product is easier to do mentally.

Watch this video of a student using the Distributive Property of Multiplication.


There are several other strategies to teach which include subtracting a group, using a nearby square and the patterns for the nine times table.


There is a definite sequence of teaching the multiplication tables.  I've created a resource that has everything you need to teach these strategies over time.  

Click to see the full product preview!

The Multiplication Fluency Strategies Resources includes teaching posters, student templates, practice pages, and games. See below for examples of each!

Click to see the entire resource!

I've also included sample lesson plans for the Foundation Strategies and Derivative Strategies.  It also includes the teaching sequence for the multiplication tables and well as, explanations for each of the strategies.



Click to see the entire resource!

Check out my Facebook page as well, as I will be posting more information and teaching multiplication, fact fluency, and more common core math topics!

Want more ideas and tips for teaching multiplication?  Check out my Pinterest Board for Multiplication and Division.

What are you go to strategies for teaching multiplication fluency? 
Share them below in the comments!

Frustrated That Students Don't Know the Multiplication Facts? Part 2 The Foundational Strategies

In the first part of this post, I wrote that we need to teach mental math strategies for multiplication just as we do for addition and subtraction.   But first, students need to learn about the concept of multiplication through arrays, equal groups, and repeated addition.  Then it is time to start memorizing the multiplication facts.


What usually happens is that some students are good at memorizing and can recall them on demand.  But most will learn a multiplication table and then start forgetting it soon thereafter.  Yes, there are ways to improve memorization skills and I do teach my students those tips.  Memorization is part of being fluent in the facts.  As we probably already know, we will have many students who will battle with memorizing all the multiplication facts.


But what if there was a different way to address multiplication fluency?  How? By teaching students multiplication mental math strategies that will help them arrive at the product more efficiently WHEN or IF memory recall fails.

These mental math strategies are first practiced with paper and pencil, but eventually (just like the addition strategies) they begin to use them mentally with more efficiency.  There are two categories of strategies:  Foundational Strategies and Derivative Strategies.

In part 2, let's explore the Foundation Strategies.


The Foundation Strategies must be taught first as they are the foundation for the later Derivative Strategies.

The Foundation Strategies involve basic mental math skills such as skip counting, finding a pattern, knowing the Identity and Zero Properties of Multiplication and learning by memory the all-important square numbers.  Here's a chart comparing the Foundation Strategies for both Addition and Multiplication.


If a student uses these strategies, the student will know about 50 facts on a multiplication chart.  That is a great start to eventually learning the rest and being fluent in the computation of multiplication facts.  The student must have these skills under control in order to advance to the next level of strategies, the Derivative Strategies.

Let's take a look at how the Foundation Strategies can be taught.


Skip counting is one of those mental math skills that begins early in kindergarten.  By second grade children should be able to count by 2s, 5s, and 10s.  Counting by 2s, 5s, and 10s will enable students to quickly learn the multiplication facts for those tables.  


Skip counting can be done with songs (https://youtu.be/SCBwSSDk9Mg) are a great way to motivate kids and keep them engaged while learning.  Counting dimes and nickels is another way to motivate students to learn to count by 5s and 10s.  A game for learning to count by 2s is thinking of things that come in pairs.  How many pairs of eyes are in our class? How many shoes?  There are lots of possibilities!  Games, flash cards, multiples strips, and bookmarks also help with learning to count by 2s, 5s, and 10s.


Teaching and learning the Properties of Multiplication lay the foundation later for Algebra and more advanced math.  So it is important that we explicitly teach these building block properties.  Start with the Identity Property and the Zero Property,

I like to teach these two properties in a fun way by making Zero a Hero and One a Bum.  Zero can obliterate any factor to produce a product of zero while One is a bum because he's lazy and produces a product equivalent to the factor.


Finally, the products of squares (2 x 2, 3 x 3, 4 x 4, etc.) should be learned and memorized.  The square numbers run diagonally along a multiplication chart.  The resulting line of squares produces a mirror image of the other products (3 x 4 = 12 and 4 x 3 = 12). That is why it's important to memorize these square number products.  It reduces the number of facts to learn!

To teach the square numbers is to make cards with all the square factors (1 x 1, 2 x 2, 3 x 3, etc) on one card.  Then on other cards write all the products of those squares.  Then hand out one card to each student.  On a signal, they are to quietly get up and find their partner to match the square factors to the square product.  When they've found their match, the pair stands back to back.  You can practice this multiple times in a 5 - 10 minute period by giving students a different card each time.  You can even time the class to see how fast all the pairs can partner up.


Students should practice the Foundation Strategies until they are proficient because they will be needed later to develop the Derivative Strategies.

In Part 3, we'll take a look at the Derivative Strategies including video of strategy use in action!

/>https://twoboysandadadteacher.blogspot.com/2016/09/how-i-present-back-to-school-night-with.html type='text/javascript'/>