## Beat Summer Math Slide: Rounding Numbers

We all know that visits to the library are an easy way to combat summer reading slide.  Keeping math skills from sliding requires a little more effort.  I’ve taught many grades, and I can say that one skill most students haven’t mastered is ROUNDING!

Every grade I’ve taught has tackled rounding early in the school year.  I think it’s supposed to be quick-and-easy review.  Well, it isn’t.  It’s a math grade killer.

If a National Board Certified Teacher is constantly surprised that kids struggle with rounding, how is a parent supposed to know?  I really don’t see how you would, so this blog post serves as a public service announcement for Rounding Awareness.

Even now, having developed many ways to teach this skill, I still don’t understand what’s so hard about rounding.  I mean, take 53.  Is it closer to 50 or 60?  Closer to 50.  How hard is that?  Very, for most students.  Don’t get them started on rounding 50,453 to the nearest tens place.  They just fall apart.

As a parent, it really helps if you’re mindful of teaching rounding in daily life.

Examples:

1. This gum costs 63 cents.  Is that closer to 60 or 70 cents?
2. I want to buy 5 drinks at the fast food restaurant.  They’re each \$1.19.  Is \$1.19 closer to \$1 or \$2?  About how much will I spend?
3. This recipe calls for 1 2/3 cup of flour.  Is that closer to one cup or two?
4. Look, this movie made \$83 million at the box office over the weekend.  What a blockbuster!  Is 83 closer to 80 or 90?
5. This meal costs \$5.85.  Is \$5.85 closer to \$5 or \$6?

A few rounding worksheets would be really helpful.  I recommend you print them from the rounding section on Dad’s Worksheets and/or Math-aids.com.  The worksheets help with something incidental real-world rounding doesn’t address: taking the same number and rounding it to the nearest tens, hundreds or thousands place.  For that skill, it really helps kids to see the number in black and white.

Your child can practice rounding on computer games.  Click here for a site with some fun games.  They are all good; my students love Rounding Sharks.

A visual technique for teaching rounding: The Rounding Hill.  As an example of rounding to the nearest 10,  this diagram shows why you round up when the ones digit is 5 or more.  Many kids think that 5 could go either way because they mistakenly believe 5 is exactly in the middle.  The Rounding Hill shows that there is no middle number, as there are 5 numbers on either side of the hill.  The Rounding Hill really helps most students, and I often see them drawing this diagram on their math tests to serve as a reference point.

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Posted in Math,Tips for Parents by Corey Green @ Jul 24, 2017

## Beat Summer Math Slide: Estimating

Students experience summer slide in every subject.  Here are some fun tips for helping your child with a difficult topic: estimating.

By estimating, I mean two different skills.  One is estimating measurements.  The other is using rounding to estimate an answer to a problem.  (526 +375 = about 900 if you round to the nearest hundred)

Fun with a tape measure*:  Simply give your kids a tape measure and challenge them to hone their estimating skills.  About how long is your kitchen?  How far to the sidewalk?  Is the length of your driveway closer to 10, 20 or 100 feet?  Should you measure the height of your cat in inches, feet or yards?  This is a pleasant way to spend a summer afternoon.

If your kids and their friends are enterprising, they could each make up their own challenges, writing little worksheets with measuring tasks.  It’s like playing school, but more active.

Fun with a scale: This is a lot like Fun with a Tape Measure, but with measurements of weight.  Your child can develop a sense of what things weigh.  How much does cereal weigh?  Dishes?  The family dog?  A book?

Shopping estimation: Running errands really does provide lots of ways to incorporate math.  Simply ask little word problems as you go.  If I buy this item for \$2.95 and that item for \$4.25, about how much will I spend?  Once your child is good at answering this type of question, challenge her to figure the rough amount of change from a nice round figure like \$10.

*Fun with whatever—a tongue-in-cheek way to make any task fun.  Sort of.  It helps!   Read the blog post for classroom examples.

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Posted in Academics,Math,Tips for Parents by Corey Green @ Jul 17, 2017

## Free Leap Year Worksheets Part 3

Leap Year Idioms

Teachers, here is a FREE Leap Year worksheet written by a National Board Certified Teacher. I hope you and your students enjoy it! Here is the Answer Key.

This worksheet helps you teach students about idioms—a commonly assessed concept on state standardized tests. Have some Leap Year fun with idioms based on the word “leap” or “year.”

If you haven’t seen them already, check out Free Leap Year Worksheets Part 1 and Part 2.

Part 1: Leap Year Reading and Writing

Part 2: “Fun with Leap Year and Leap Day” reading comprehension and Leap Year Math

Posted in FREE Worksheets,Fun With Literacy,Holidays by Corey Green @ Feb 1, 2016

## Free Leap Year Worksheets Part 2

Fun Reading Comprehension and Leap Year Math

Teachers, here are FREE Leap Year worksheets written by a National Board Certified Teacher. I hope you and your students enjoy them!

Here is an enjoyable reading comprehension worksheet called “Fun with Leap Year and Leap Day.” The passage and questions are indeed fun. What other worksheet challenges you to figure out what Pope Paul III and Ja Rule have in common? (Answer: they were both born on Leap Day.)

You and your students will enjoy learning about Leap Year luck (or lack thereof), Leap Year marriage proposals in Ireland, and the quandary posed by a Leap Year birthday in The Pirates of Penzance. The questions are all opinion based—and in my opinion, you shouldn’t grade them! Give students credit for completion, then go home and kick back to enjoy the rest of Leap Day.

Next is my fun “Was it a Leap Year?” worksheet that lets students apply their knowledge of divisibility by 4. Hints for determining divisibility by 4 are at the bottom of the page. The worksheet teaches a special case: century years. Because a revolution around the sun does not quite take 365.25 days, only century years divisible by 400 are Leap Years. The worksheet gives a student-friendly explanation and challenges them to determine if a century year was or wasn’t a Leap Year.  I also have provided an Answer Key as a separate download.

Don’t forget to download the other two worksheets in Free Leap Year Worksheets Part One.

Happy Leap Year!

Posted in Academics,FREE Worksheets,Holidays by Corey Green @ Jan 25, 2016

## How to introduce two digit multiplication

An occasional series with sample pages from the Best Multiplication Workbook EVER!

This tip comes straight from my Best Multiplication Workbook EVER!  The section on teaching 2 digit multiplication is very helpful for teachers looking to scaffold learning.  I break long multiplication into 3 sections—multiplying multidigit numbers by 1, 2 or 3 digits.  Within each section, a dozen or more lessons teach the process step by step.

Please use these two FREE sample pages with your class to introduce 2 digit multiplication.  This introductory lesson lets your students learn the Hugs and Kisses method to keep their numbers lined up when they have to put in that place holding O.  (The place holding O is the hug.  You put an X, or kiss, over a number to kiss it goodbye when you are through with it.)

The workbook lets students practice Hugs and Kisses by beginning with multiplying times 11.  This isolates the Hugs and Kisses skill, allowing students to focus on the procedure, not the math.

I wish I’d learned multiplication this way when I was a kid!  I hope this and other lessons from the Best Multiplication Workbook EVER! help your students.

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Posted in Academics,FREE Worksheets,Math by Corey Green @ Dec 21, 2015

## Bedtime Math–teach kids to love numbers and use math in real life

Bedtime Math promises to do for numeracy what bedtime stories did for literacy.

It all started when Laura Overdeck decided to help her kids love math the way she does.  And boy, does she love math!  Overdeck earned a B.S. in astrophysics from Princeton and an MBA from the University of Pennsylvania.  She combined her love of math, kids and bedtime stories into the Bedtime Math series.

Each book offers multiple evenings of Bedtime Math because they beg to be read little-by-little, with time set aside for thinking.

Bedtime Math: A Fun Excuse to Stay Up Late (Bedtime Math Series)

Bedtime Math: This Time It’s Personal (Bedtime Math Series)

Bedtime Math: The Truth Comes Out (Bedtime Math Series)

BedtimeMath.org offers FREE Bedtime Math resources to complement the books.  Check out the Daily Math for blog articles about fun real-life math topics.  You can download a Wacky Math app that brings Bedtime Math to your device–daily problems, articles, etc.

Bedtime Math has a section for educators.  The author asks educators to encourage bedtime math at home, rather than making it part of school.  She also suggests starting an after-school math club, for which she will provide ideas and curriculum.  Very generous.  However, I think the educators section should be taken with a grain of salt.  Remember, its advice is from the perspective of an accomplished mom of privileged kids, not a teacher whose students run the gamut.

Starting an after-school club opens a whole can of worms.  A) you’ll be working for free B) you have to wonder whether school liability insurance and protections extend to after-school clubs–most elementary schools aren’t set up for them C) you are responsible for making sure the kids get home safely.  If they walk, it won’t be in the safety of huge crowds of kids, and if they get picked up–well, the pickup might be an hour late or not at all.

Regarding the idea to keep Bedtime Math for home only: not everyone has a parent who loves math–or even likes it a little bit.  Not everyone has a parent who reads bedtime stories.  Heck, not everyone has a parent who actually enforces bedtime–and provides a real bed.  Plus–not everyone has a parent who speaks/reads English.

Some kids may never experience Bedtime Math unless it is at school.  Consider your school’s circumstances and decide whether Bedtime Math is something to recommend to parents or do at school.  Also consider that families may be much more interested in Bedtime Math after you whet kids’ appetites at school.

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Posted in Academics,Fun With Literacy,Math by Corey Green @ Sep 21, 2015

Many students get confused when they have to plot ordered pairs on a graph. “Run and jump” helps them remember that the first number is x and the second is y.  Teach your students to mutter “run and jump” as they first slide their pencil to the x, then slide to y.

Don’t get discouraged if your little scholars don’t quite master “run and jump” after the first lesson.  The simple catchphrase should be enough to get most kids back on track, even if it’s been a while since the class plotted ordered pairs.  Your heart will warm when you hear your students reminding each other to “run and jump.”  Teacher intervention is rarely necessary once kids know the trick.

Posted in Math by Corey Green @ Apr 27, 2015

## Spaceship Math–FREE leveled worksheets to teach basic addition and subtraction

Help kids learn math facts by using Spaceship Math, the FREE leveled worksheets with 26 scaffolded levels.

Spaceship Math is part of Dad’s Worksheets, a terrific math site that I have written about a few times.  With Spaceship Math, students learn their basic facts a few at a time.  It starts very simply.  For example, level A for addition covers 1+2 and 1+3.  That’s it, unless you count 2+1 and 3+1 as separate facts.  Level by level, students build their skills.  There are four versions of each level, plus timed tests for every two levels.  The worksheets are cumulative, so students are always reviewing old facts.

To find Spaceship Math on Dad’s Worksheets, click on the operation you want students to practice.  That opens a menu of choices for the operation, and then you can easily find Spaceship Math.

I like to give the whole class a placement test.  I choose a level in the middle, usually L.  That has 7+2 and 7+4.  From the placement test, I assign students to packets of either levels A-L or L-Z.  The students don’t exactly thank me for these packets, but they do see that the packets help them learn.  Plus, the leveled worksheets keep kids in their zone of proximal development, so it never feels too difficult.

I really like Spaceship Math for addition and, subtraction.  For multiplication, I recommend Best Multiplication Workbook EVER!–and not just because I wrote it.

Spaceship Math multiplication is very different from the way most of us learned our times tables–one table at a time.  It moves pretty quickly, and doesn’t give students a sense of how each times table works as a unit.  My Best Multiplication Workbook EVER! levels times tables in an effective way.  It provides lots of practice problems, plus word problems that show the value of each times table.

I haven’t written a Best Division Workbook EVER! yet, so for division, I give students worksheets based on the times tables.   I assign division times tables in the same order I presented multiplication tables in Best Multiplication Workbook EVER!

I hope you and your students enjoy Spaceship Math.

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Posted in FREE Worksheets,Math by Corey Green @ Mar 23, 2015

## A vertical number line makes math easier to understand

Most teachers were taught to use a horizontal number line to teach concepts.  I recommend using a vertical number line because it’s easier for students to understand.

When we add and subtract, we thinking of going up or down, not left to right.  Wouldn’t that be easier to picture on a vertical number line?  After all, to most kids, adding is going up and subtracting is going down.  Kids don’t think of numbers as going from left to right.

To teacher integers (positive and negative numbers), I like to write a vertical number line from -10 to 10.  I write the positive numbers in black and the negative numbers in red.  (In a business context, red is the color for negative numbers.)  To make 0 stand out, I write it big and blue.

Having positive numbers one color and negative numbers another helps students see the difference.  Working on a vertical number line helps them see why –2+3 = 1.

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Posted in Math by Corey Green @ Mar 9, 2015

## FREE pattern block puzzles–for online and real life

Help your students learn spatial reasoning skills with pattern blocks.  A class set of these versatile shapes can provide hours of fun and education.

Pattern blocks are mathematical manipulatives that let students see how shapes relate to each other.

In the first set, all shapes can be built from the basic equilateral triangle:

• Equilateral triangle (Green)
• Regular rhombus (Blue)
• Trapezoid (Red)
• Hexagon (Yellow)

The second set contains shapes that can’t be built of the green triangle, but can still be used in tiling patterns.

• Square (Orange)
• Small rhombus (Beige)

Click here for an inexpensive set of plastic pattern blocks available at Amazon.com

Students love to make their own patterns from pattern blocks.  Another good activity is the pattern block puzzle.  Students build complicated shapes, such as a train, using pattern blocks.  Some puzzles have interior lines to show which pieces to use.  That’s good for beginners.  More advanced students like to figure it out themselves.

I like to print the puzzles and either laminate them or put them in page protectors.  If you laminate the puzzles, I recommend taping or gluing the puzzle to construction paper for strength.

Recommended pattern block puzzles:

Complete pattern block puzzle book from LearningResources.com

Jessica’s pattern block templates

Online pattern blocks–a fun activity for the computer lab

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Posted in Academics,Math,Tips for Teachers by Corey Green @ Feb 24, 2015

## Jump rope to Best Multiplication Songs EVER!

Multiplication x jump rope = best math lesson EVER!  Take your class outside for a fun math review session or make multiplication songs part of the standard recess activities.

My Best Multiplication Songs EVER! are short songs for each times table.  Each song clocks in at 40 seconds or less, often much less.  Rhythmic and fun, they make great multiplication chants for jump rope.  You can send a CD player outside and let kids jump rope to the recordings, or kids can sing songs they have memorized.

Option one: recess fun.  In this case, jumping rope to multiplication songs is an optional activity.  Suggest to your students that it might be fun.

Option two: whole class math activity.  Figure on one jump rope for every 4-6 students.  The whole class can jump rope to the same song at the same time.  Spread out and enjoy!

How to jump rope to multiplication songs:

One or two jumpers per song: have one or two jumpers see if they can jump without mistakes for the whole song.  You can switch jumpers if there’s a mistake, or give each jumper a good 30 seconds of practice (length of a song) no matter how many mistakes he/she makes.

Jump rope like London Bridge is Falling Down: in a group of 4-6 students, you should have 2-4 jumpers.  They can practice “jumping in” during each song.  Students take turns “jumping in” and doing one or two hops, they “jumping out” and letting someone else try. An accomplished group will be doing the jump rope equivalent of London Bridge is Falling Down.

Freestyle: let your jump rope groups do their own thing.  They can jump rope however they choose, so long as everyone gets a chance to jump and turn the rope.  Maybe you’ll find a group that can Double Dutch!

Individual jump rope: maybe the PE teacher can lend you a class set of jump ropes.  Then everyone can jump to each song.  Your class will have a great time, but tire out quickly.

Your class can go through the whole album or practice certain songs over and over.  It depends if your goal is general multiplication review, or if you’re trying to practice one or two times tables.

The one rule: if you’re not jumping, you must sing the songs!

Below is a preview of Best Multiplication Songs EVER! I hope you enjoy it.

Teaching Multiplication Tables with Songs

Best Multiplication Workbook EVER! wins Learning Magazine Teachers’ Choice Award

Beat Summer Math Slide: Five tips for Multiplication

Best Multiplication Workbook EVER!

Sing Multiplication Songs During Transitions

Best Multiplication Songs EVER! on Amazon

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Posted in Academics,Tips for Teachers by Corey Green @ Oct 20, 2014

## Tips for teaching order of operations part three: online PEMDAS games

The order of operations is an important concept in math.  It’s also a frustrating concept to teach and learn.  Most students need lots of practice, multiple tips, and a myriad of ways to think about good old PEMDAS*.

Part three: online PEMDAS games

After you’ve taught order of operations until you’re blue in the face, take a break and let some online games have a crack at it.  Your students might find that practice is a little more fun when it comes in the form of a computer game.

Here are a few good order of operations games.  You can paste the links into a convenient place for your students to choose from, or let them work from this blog post.

Kids, let’s have some PEMDAS fun!  This guide is organized to help you find a game that suits your order of operations confidence level.

Good for beginners:

Order of Operations at SoftSchools.com: I like this game because it takes actual calculation out of the equation, so to speak.  Students click on which operation they should perform first.    The program models how to show your work.

Another no-calculation order of operations game: This game also lets you just deal with order of operations, not the calculations.  It’s a good way to build your confidence in knowing what to do first.

Good for practice:

The Order of Operations Millionaire Game: practice PEMDAS in the style of Who Wants to be a Millionaire?  This is a one or two player game.

Leveled order of operations game:  This game provides practice problems that are leveled.  You can choose to deal with parenthesis or just keep it simple.  This is a good game for building your skills.

Connect Four-style order of operations game: This game can be for one or two players.  It lets you solve practice problems, then place your piece for Connect Four.   You can change the level of difficulty.

Rags to Riches: build your virtual fortune as you solve order of operations problems.  It’s fun to think about making money at math practice!

Good for PEMDAS pros:

Funbrain Order of Operations game: This one asks students to place the numbers in order to create an equation that yields a predetermined result.  This is higher-level order of operations thinking.  Good for students who understand the concept, not so great for struggling students.

*PEMDAS: Please Excuse My Dear Aunt Sally.  Don’t get creative with the acronym.  This is what every math teacher after you will use.

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Posted in Academics,Math,Tips for Parents,Tips for Teachers by Corey Green @ Jun 23, 2014

## Tips for teaching order of operations part two: practicing and perfecting PEMDAS

The order of operations is an important concept in math.  It’s also a frustrating concept to teach and learn.  Most students need lots of practice, multiple tips, and a myriad of ways to think about good old PEMDAS*.

Part two: practicing and perfecting PEMDAS

Let students make practice problems.  Kids love to play teacher.  Have them create problems for the class to solve.  You can take a seat with the students and try the problems with everyone else.  Taking the part of a student is good for you, too.  You can feel the anxiety they experience as each new problem goes on the board.

Tell kids that PEMDAS is the default.  Many students get through lessons on order of operations only to disregard them when they see equations a few months later.   Many students don’t realize that they should always use order of operations.  I tell kids that they should always use it unless a problem specifically says otherwise.  (This would be a written mental-math problem on a standardized test.)

Warn kids of the PEMDAS pitfall: you’re just as confident when you’re getting it wrong.  Assuming your students know their basic facts (and that’s assuming a lot), then the math in order of operations problems won’t be hard for them.  Their competence with basic facts might lead them to think they’re doing well, even if they left PEMDAS behind a long time ago.

Warn students that if the math gets hard, they probably made a PEMDAS mistake.  Most practice order of operations problems do not involve difficult calculations and extra-long division.  If your kids find themselves mired in deep calculations, they probably made a wrong PEMDAS turn somewhere along the road.

Find practice problems online.

Math-aids.com has an excellent Order of Operations section with scaffolded lessons to help you give the kids non-intimidating practice.

Dad’s Worksheets has a great Order of Operations section, too.

I highly recommend both sites.  In fact, I have written quite a few blog posts that link to them.  Click for the post about Dad’s Worksheets and here for the post about Math-Aids.

*PEMDAS: Please Excuse My Dear Aunt Sally.  Don’t get creative with the acronym.  This is what every math teacher after you will use.

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Posted in Academics,Math,Tips for Teachers by Corey Green @ Jun 16, 2014

## Tips for teaching order of operations part one: getting started with order of operations

The order of operations is an important concept in math.  It’s also a frustrating concept to teach and learn.  Most students need lots of practice, multiple tips, and a myriad of ways to think about good old PEMDAS*.

Part one: getting started with order of operations

Don’t grade while you’re teaching.  You want to create a risk-free environment for students to learn order of operations.  Give them lots of practice, let them help each other, but don’t assess them.  Not formally, at least.  Don’t grade the homework for accuracy.  Give the kids a chance to learn before you assess them.

Plan at least a week just to get the basic concept.  Years of experience taught me that most students need a lot of time to grasp order of operations.  Students get frustrated as they are learning the concept.  Warn them in advance that most of them will take a while to learn this.

Scaffold the lessons.  Break order of operations into baby steps.  Students will need lots of practice with 3 + 2 x 4 before they deal with more complicated problems.  I recommend that you use individual whiteboards or no-budget whiteboards (page protectors) so that you can create problems that suit what your students need from moment to moment.

Give real-world examples.  One of the most common uses of order of operations is shopping.  Tell students a little story about buying 3 of one item, 4 of another, etc.  Then, add the tax to the whole thing if you think your class is ready for that.  After you’ve told the story, write the equation on the board.  Label each number.  The idea is for students to see why you can’t add the number of bananas to the cost of oranges, just because they happen to be next to each other in your example.

Teach kids to give themselves a checklist.  Model and require your students to write PEMDAS next to each problem.  They can use the acronym as a checklist to make sure they are following order of operations as they solve the problem.

*PEMDAS: Please Excuse My Dear Aunt Sally.  Don’t get creative with the acronym.  This is what every math teacher after you will use.

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Posted in Academics,Math,Tips for Teachers by Corey Green @ Jun 9, 2014

## How to Teach Coloring Maps and Map Coloring Theory

Most folks don’t know (or care) about coloring maps or map coloring theory, but today’s elementary school students are forced to take an interest.  For some reason, these subjects are often stressed on state achievement tests.  However, few textbooks provide practice or assessment for the skills.

What’s a teacher to do?

Turn to the Internet.  That’s what I did, and I found some resources that I hope will help others.

Back up and explain: coloring maps questions usually go something like this: what is the fewest number of colors needed to color this map so that no edges are touching?  (A squiggle of lines forming a “map” accompanies the question.)

Teachers and students were left to fend for themselves, drawing their best guess at sample maps, coloring them in, and trying to figure out how many colors were needed.  We never really knew if we were doing it right.

Someone already did this work for us, apparently.  My research showed that four colors are enough for any map you can draw.  Two two mathematicians, Ken Appel and Wolfgang Haken, figured this out in 1976.  If that’s not enough to convince the kids, I invite them to read about the four color theorem.  (Here’s the short version: four colors are enough!)

So, I taught my students a few things:

a)      It’s never more than four colors, according to mathematicians.

b)      On our practice tests, the answer is almost always three colors.  Ergo, this is most likely the answer to any coloring maps question life will throw at you.

c)      If the answer is only two colors, it will usually be pretty clear because the picture will look more or less like stripes.

I found an Internet tutorial on the subject that lets students practice coloring in the maps.   In our era of standardized testing, the ability to actually color in the map isn’t important, since it can’t be reduced to a bubble sheet answer choice.  However, the act of trying to color in the maps helps students understand why you never need more than four colors, and why three colors will usually suffice.

Click here to use the tutorial, from subtangent.com.  I highly recommend the tutorial as a computer lab exercise for your students.