Fraction Representations

Reinforce, reinforce, reinforce. If there's one thing that I've learned in thirty years of teaching math, it's to reinforce. Today each student in my class will select a fraction, draw it as a part of a whole, part of a group, and on a number line, as well as write a short story problem to express the fraction as division. We'll use this mini poster and display them in our room.

You can use it too! Just click on the image to grab this editable freebie from my Teachers pay Teachers store. Enjoy!

Fractions As Division

Fractions as division seems to be largely overlooked. Since we didn't learn it well as kids, it can also be hard to teach. Let's break that cycle starting today!

First, we have to wrap our heads around what this means in real life. When four children are sharing four, eight, or twelve items, division is easy. But what if we have less items than children? Here's where fractions as division come in.

You can see that we essentially divide each item by the number of children. Then each child gets one piece of each item.

My students' textbook shows it like this, which I think is confusing. Sure, adults who have fully conceptualized this topic will understand. But will kids?

I'm going to present it like this today instead. My students will understand that EACH candy bar needs to be shared equally by the students. After seeing this, we can move to the model above to prove that the amount equals 3/4.

We will also begin using the word "per" today. For this problem, we can say 3/4 candy bar per child. This will provide a springboard to my class's current science concept, speed. In order to calculate speed, we divide distance by time, and that is written as miles per hour (mi/hr) or kilometers per hour (km/hr). Yes, that little slash you see when you say per is the same slash you use in a fraction. So dividing distance (miles or kilometers) by time (hours) is written as a fraction. 

Not only do I want my students to know that a fraction represents a division problem, I want them to think of a fraction as a division problem. This takes them one step closer to becoming great mathematicians.

Fractions of Wholes, Groups, and Number Lines

Fractions come in all shapes and sizes. Kids need to be able to name fractions of a whole and group (or set), as well as on number lines to show distance and time.

Fortunately, free online resources are abundant! My students will be using worksheets from these sites to name fractions today.

Parts of a Whole - You can create your own Visual Fractions Worksheets at Math-Aids.com. Every worksheet has denominators of 2, 3, 4, and 8, but you can choose to add denominators of 5, 6, 7, 9, 10, 11, and/or 12 as well. You also have a choice between pie shapes, rectangular shapes, triangular shapes, or a combination of all three. Finally, your students can identify the fraction for a shaded area, shade the area for a given fraction, or both.

Parts of a Group or Set - Math-Drills.com offers a wide variety of fraction materials, including five worksheets for parts of a group. And with Halloween right around the corner, I'd like to mention that they have a wide variety of Halloween-related math activities! Trick or Treat Candy Probabilities will tie in nicely with the study of fractions.

Fractions on a Number Line - I found worksheets for Fractions on a Number Line at Math-Aids.com. Once again, the site offers many choices as you custom-create materials for your own class.

My math textbook offers limited practice with fractions of sets and fractions on number lines, so I definitely need these extra resources to ensure a well-rounded experience for my students. I hope you find them helpful too!

Resources for Numbers and Operations in Base Ten - Middle Grades

Are you looking for some engaging ways to reinforce all of the NBT standards? Look no farther!

Teacher-author Meredith Anderson has created a set of 32 task cards with word problems to review all Grade 4 NBT standards. Each card features a famous landmark.

Place Value Scavenger Hunt by Jonathan Pearson gets kids up and out of their seats to practice a variety of fourth grade skills related to place value: writing numbers in various forms, rounding, and comparing.

Visit the Teachers pay Teachers store of Terry's Teaching Tidbits for 5th Common Core Name Tag Centers in Base Ten. Simply fold these table toppers and allow students to rotate through the fifth grade NBT standards with a partner.

To help your students practice and conceptualize numeration skills, check out these fun activities from Scipi. Dots Fun for Everyone will give you fifteen games and three activities using dominos in math. Number Tiles, a 25-page resource, provides fifteen different activities for operations, primes and composites, exponents, and divisibility rules.

Engaging resources like these make my days as a teacher (and students' days as learners) so much more fun! I hope you'll try them!

Resources for Exponents (5.NBT.A.2)

The last sentence of Common Core State Standard 5.NBT.A.2 asks fifth grade students to "use whole number exponents to denote powers of 10." Several teacher-authors have created fantastic resources to help your students with this skill.

Multiplying and Dividing by Powers of 10, available through Mike's Math Mall, gives you an instructional PowerPoint presentation, notes, worksheets, poster, and a quiz.

Fifth grade teacher Dennis McDonald offers task cards and printables to reinforce this skill in Super Powers of Ten, Set A and Set B.

If some (or all) of your students are ready to work with negative exponents, check out Multiplying by Powers of 10 Task Cards by Hello Learning.

And for those students who are up to an even greater challenge, grab this Negatives with Exponents Dolphin Coloring Picture, created by Briana Burke.

As a teacher of fifth grade math, I can see how all of these products would work together beautifully to really reach all of my students in their study of exponents. It's time for a shopping spree!

Resources for Division (4.NBT.B.6, 5.NBT.B.6, 5.NBT.B.7)

What do the Common Core State Standards expect of middle grade students? Fourth graders must "find whole number quotients with remainders with up to four-digit dividends and one-digit divisors" (4.NBT.B.6) while fifth graders are tasked with finding "whole number quotients with remainders with up to four-digit dividends and two-digit divisors" (5.NBT.B.6), as well as dividing decimals to the hundredths (5.NBT.B.7).

I'd like to share some engaging resources for teaching and reinforcing division. Let's start with activities that help students learn their division facts. Do your students like Bingo? If so, try Fill It In Bingo by Jan Gervais. They can also play games online at Math Playground, Fun4theBrain, or SheppardSoftware.com.

Long division can be tricky. Using this Long Division Interactive Math Foldable by Creative Critters will help your students understand the process. To follow up, try some division task cards by Chili Math. These are available for division by one- or two- digit divisors. If they like to color, check out this long division picture by Briana Burke.

It's hard to separate multiplication and division. Multiplication and Division Word Problem Stations by Elizabeth Hudgins provides extra practice with practical, everyday problems while MathBall Multiplication and Division by Elements of Elementary perfects students' "game."

A variety of great activities are also available to reinforce addition, subtraction, multiplication, and/or division of decimals:

• Magnet Races - Jill Powers
• Math with Riddles Decimal Bundle - Misty Miller
• Multiplying and Dividing Decimals Task Cards for Fifth Grade - Miss Bin BK
• Multiplying and Dividing Decimals Made Easy Bundle - Mike's Math Mall
• Multiply and Divide Decimals Task Cards - Hello Learning

Thanks to all of my friends at Teachers pay Teachers for sharing their resources with us today!

Resources for Multiplication (3.NBT.A.3, 4.NBT.B.5, 5.NBT.B.5, 5.NBT.B.7)

Multiplication is a big deal for middle grade students. In third grade, the Common Core State Standards expect students to "multiply one-digit numbers by multiples of 10" (3.NBT.A.3). By fourth grade, they're tasked with multiplying "a whole number of up to four digits by a one-digit whole number" and "two two-digit numbers" (4.NBT.B.5). Fifth graders must "fluently multiply multi-digit whole numbers" (5.NBT.B.5) and multiply decimals to hundredths (5.NBT.B.7).

In my experience, students cannot multiply fluently without knowing their facts. Let's take a look at some resources. To help students conceptualize multiplication, use Multiplication Concepts PowerPoint Presentation by Two Boys and a Dad Productions and follow up with Multiplication Flip Booklets by Teaching My 3. Jan Lindley has created a 180-page Math Facts Practice Bundle to help students practice multiplication facts from two through twelve. Zoom Zoom Classroom offers Multiplication Facts Function Tables, a learning center approach to practicing facts. If your students like secret messages, check out Crypto Riddles by The Puzzle Den. An activity and board game that correlate to the book, Amanda Bean's Amazing Dream, are available at the Teachers pay Teachers store of MJcreations. As practice continues, this colorful Multiplication Chart by Page Protector Printables and More will ensure their success.

Soon students are ready to multiply two- and three-digit numbers by a one-digit number. To make learning fun, try Math with Riddles by Misty Miller and Pumpkin Patch Multiplication Task Cards - Story Problems by Amy Alvis.

Teaching kids how to multiply two digits by two digits can be really difficult. This PowerPoint presentation and related worksheets by Lindy du Plessis support student learning with a rainbow analogy.

I'd to share three great free resources for practice of double-digit by double-digit multiplication. Kadeen Whitby has created a Color by Multiplication Fun Freebie, MissKinBK shares Multiplication Task Cards, and Terry's Teaching Tidbits offers Spider Multiplication Task Cards Freebie. I'll be using all of these in my class during October!

Do you need activities for multiplying by one- and two-digit numbers? You can purchase eight sets of multiplication task cards in this bundle or pick and choose sets by visiting the Teachers pay Teachers store of ChiliMath. Jessicca Nielsen has put together an amazing 89-page Multiplication Resource Package. Check it out!

Now, especially for fifth grade teachers, we'll take a peek at a few resources for multiplying decimals. Terry's Teaching Tidbits has tackled the difficult task of conceptualization of this skill in Multiplying Decimals Using Visual Models. To extend this conceptual model and practice multiplying decimals, try Multiplying and Dividing Decimals Task Cards for Fifth Grade by MissKinBK. For some fun practice, Misty Miller has created Math with Riddles Decimal Bundle.

I'd like to thank my friends at Teachers pay Teachers for sharing all of these great multiplication resources with us! As I said before, multiplication is a big deal for middle graders - - - but engaging resources such as these can make teaching and learning so much more fun.

Resources for Adding and Subtracting (3.NBT.A.2, 4.NBT.B.4, 5.NBT.B.7)

Adding and subtracting is not just for primary kids. The Common Core State Standards ask third graders to add and subtract within 1000 (3.NBT.A.2), fourth graders to add and subtract whole numbers of all sizes (4.NBT.B.4), and fifth graders to add and subtract decimals (5.NBT.B.7). Today we'll explore engaging resources that meet these standards.

Fall has arrived in the northern hemisphere, so let's look at some seasonal products first:

• Kids will enjoy playing Fill It In Bingo, created by Jan Gervais, to practice addition and subtraction of 2- and 3-digit numbers. (Click here for a non-seasonal version.)

• For Halloween (or any time), adding and subtracting decimals will be more fun with this coloring activity, created by Briana Burke. When finished, a spider is displayed!

• Thanksgiving Menu Math by Terry's Teaching Tidbits gets students involved in real-world problem solving through addition, subtraction, multiplication, and division of decimals.

• A variety of fall-themed task cards are available in this bundle. Each set is also sold individually at the Teachers pay Teachers store of Carol's Garden.

Do you use interactive notebooks in your classroom? Creative Critters offers interactive notebook foldables for addition and subtraction, as well as Subtraction Math Game: Alien Invasion. For a comprehensive approach to addition, subtraction, multiplication, and division, take a look at Interactive Math Journal for Operations by Jane Feener. This 204-page resource includes achievement indicators, notes, foldables, QR activities, and exit cards for fourth and fifth grade learners.

Task cards are a favorite go-to for kids. Chili Math has created task cards for adding and subtracting whole numbers. (If you want a variety activities, click here for his bundle of 540 cards.) For fifth graders, why not try Add and Subtract Decimal Task Cards from Hello Learning or Adding and Subtracting Decimals to the Hundredths Place by MissKinBK?

If you're looking for a little action in your classroom, this is the one for you. Jill Powers brings new meaning to the term "board games" with her product, Magnet Races: Decimal Calculations, which includes addition, subtraction, multiplication, and division of decimals.

Practice makes perfect! Misty Miller has created motivational math riddles for for subtracting 2-digit and 3-digit numbers, as well as decimals. Oodles of additional addition and subtraction worksheets are available at Math-Aids.com and Math-Drills.com. To generate your own worksheets, go to SoftSchools.com or WorksheetWorks.com.

The availability of free and inexpensive math resources has really improved my teaching. If my class seems bored with a topic, I can find something engaging with the click of a finger. If one of my students needs more practice, I can hop on the Internet and choose from dozens of appropriate sheets (or even create my own!) I hope this blog helps you find resources that are just right for your classroom. Thanks for stopping by!

Resources for Comparing Numbers (4.NBT.A.2, 5.NBT.A.3b)

Common Core State Standard 4.NBT.A.2 asks fourth graders to "compare two multi-digit numbers based on meanings of the digits in each place." A six-minute video created by Ginny Baldwin for LearnZillion provides a wonderful lesson opener. Don't forget to click on the Guided Practice video for related story problems. Custom-made worksheets can be created at Math-Aids.com. To really motivate your class, try these games and task cards:

• Catch the Fly! and Pirates vs. Ninjas, two games created by Jonathan Pearson
• Comparing Numbers Task Cards for two digits, three digits, four digits, or five digits and above by ChiliMath

Fifth graders can learn how to "compare two decimals to thousandths based on meanings of the digits in each place" (5.NBT.A.3b) with three different LearnZillion videos created by Julie McGough: Comparing Decimals with Base-10 Blocks, Comparing Decimals with a Number Line, and Comparing Decimals Using Fractions. To practice ordering decimals, try Ordering Decimals Cards, created by Misty Miller.

Two products created for Teachers pay Teachers by MissKinBK involve students in reading, writing, and comparing decimals. Check out Place Value Task Cards for Fifth Grade and Mmmmm...Math! Sweet Place Value Practice with Decimals for some engaging practice.

As you can see, comparing whole numbers and decimals can be sweet! All you have to do is make use of all of the free and inexpensive resources floating around in cyberspace!

Resources for Reading and Writing Numbers (4.NBT.A.2, 5.NBT.A.3a)

Do you need free and/or inexpensive materials to help your students read and write numbers in standard form (numbers), expanded form, and words? If so, you've come to the right place!

Common Core State Standard 4.NBT.A.2 asks fourth graders to read and write whole numbers. Let's take a look at some free resources for these skills. Blair Turner has created a set of 27 cards showing Base-10 blocks, FREE Reading and Writing 3-Digit Numbers. Students look at the cards then write the matching number in standard form, expanded form, and words. Number Forms Foldable, available in the Teachers pay Teachers store of Misty Miller, works well with math journals. Students can show off their newfound number skills with Look! I can work with large numbers! from my September 1st blog.

Schoolhouse Divas offer a comprehensive Place Value & Whole Numbers Unit for the entire class. Or, if you need some some fun reinforcement, check out Write It: Math CCSS 4.NBT.2 Center (Amy's SMART Designs) and Large and Small Number Task Cards by Hello Learning.

Looking for a practical way to reinforce writing multi-digit numbers? Why not try Check Writing by Jonathan Pearson!

By fifth grade (5.NBT.A.3a), students are expected to read and write decimals. QR Number Sense Challenge, written by Brittany Washburn, uses technology to engage students in reading, writing, and comparing whole numbers and decimals.

A three-part animated PowerPoint presentation, printables, worksheets, and quizzes for whole numbers and decimals are all included in Place Value and Rounding from Mike's Math Mall.

Approaching a topic (even something as seemingly dry as writing numbers) in such diverse ways can bring a classroom to life. I'd like to say "thanks" to my friends at Teachers pay Teachers for allowing me to showcase their creative products today.

Resources for Place Value (4.NBT.A.1, 5.NBT.A.1)

To the left, to the left, to the left, right, left. What does this mean in regard to place value?

The Common Core State Standards require fourth graders to "recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right" (4.NBT.A.1). Additionally, fifth graders must understand that it represents "1/10 of what it represents in the place to its left" (5.NBT.A.1). Today we'll look at some free and inexpensive products to support conceptualization and practice of place value.

Conceptualization

Moving that pesky little decimal point is gaining attention in the Common Core State Standards! An earlier post suggests using Beyonce's song, "Irreplaceable," to reinforce this concept for fourth graders. Check out Placing the Value, a set of task cards and printables by Dennis McDonald, to help fifth grade students understand grasp shifts to the left and right with whole numbers and decimals.

Readiness

Just getting started with place value? Place Value Task Cards by ChiliMath and Place Value: Base Ten Basics by Tina's Teaching Treasures will give your students practice with numbers in the hundreds place. When they're ready for numbers in the thousands place, try Primary Place Value Foldable, Task Cards, Assessments, and Poster by Janet Rainey and Place Value and Number Sense by Jan Lindley.

Working with Bigger Numbers

Interactive Math Journal for Place Value, created by Jane Feener, cements students' understanding of numbers to the millions place, and Place Value Task Cards by Shari Beck allow them to practice their skill with numbers in the hundred thousands.

Do you want to go bigger still? Place It: CCSS Place Value Math Center by Amy's SMART DesignsNumbers with Decimals offers hands-on activities for three levels: one thousands, hundred thousands, and hundred millions. Interested in going even bigger? These Place Value Task Cards by ChiliMath will take your students all the way to the hundred billions!

Moving into Decimals

Now it's time to move onto the other side of the decimal point! Place Value and Value of a Digit Interactive Notebook Math Foldable by Creative Critters and Place Value and Number Sense Stations - Elizabeth Hudgins can help your students learn about and practice decimal place value.

Once your students understand the function of that pesky little decimal point, they'll be ready to move it from the left to the right (and the left, right, left!)

Resources for Rounding (3.NBT.A.1, 4.NBT.A.3, 5.NBT.A.4)

Common Core State Standard 3.NBT.A.1 asks students in Grade 3 to "use place value understanding to round numbers to the nearest 10 or 100." Fourth graders (4.NBT.A.3) must "use place value to round multi-digit whole numbers to any place." By fifth grade, the Common Core requires students to round decimals (5.NBT.A.4). Let's take a look at some free or inexpensive resources available to teach rounding.

Rounding Activities and Worksheets, created by Kholmquist, is a great place to start with third grade students. For some seasonal fun, try Pick a Pumpkin Rounding Game or Jack-o-Lantern Rounding, created by Elena Fryer. Finally, engage your third graders with some hands-on fun using Rounding to the Nearest 10 or 100 Place Value Mystery Pictures by Loreen Leedy.

Several terrific products employ technology to teach this concept. Rounding Robots PowerPoints & Printables by Jan Lindley  and Rounding Numbers Round-Up SMARTboard and Game Bundle by Amy's SMART Designs will really engage your engage third and/or fourth grade students.

Teacher-author Janet Rainey offers 65 pages of activities and assessments in Rounding Practice, Assessments, Task Cards, and Flashcards up to 10,000.

Fourth grade teachers will love Rounding the World, a product created by Dennis McDonald that includes two graphic reference sheets, 32 task cards, three activity sheets, and an answer key. MJcreations offers several games to help students practice their rounding finesse, including Rounding to the Nearest 10 and 100 - Match Game, Rounding Six Digit Numbers - Memory Match Game, and Place Value Match Game.

For rounding of decimals, fifth graders will enjoy Magnet Races: Decimals, Rounding & Order of Operations by Jill Powers and Movin' and Groovin' with Rounding by Misty Miller.

Do you need worksheets for your students? Check out these sites! They all offer great free worksheets:

• Math-Aids.Com

• Common Core Sheets

• WorksheetWorks.com

• DadsWorksheets.com

Thanks to all of the teacher-authors from Teachers pay Teachers who shared their resources for today's blog!

Understanding the Long Division Algorithm

How can we help kids understand the long division algorithm? After dividing multiples of 10 and 100, as well as estimating with compatible numbers, they are ready for a conceptual model.

In my classroom, we break out the funny money and work some simple problems like this:

For the problem 41 divided by 3, we arrange four tens and one one on the desk. A real-world problem is provided: Three children set up a lemonade stand. At the end of the day, they have forty-one dollars. How many dollars will each child receive? How many dollars will be left over?

First, how many ten-dollar bills will each child receive? If we make a stack for each child, we can move one ten-dollar bill into each stack. In our algorithm, we show that each child gets one ten by writing a one above the tens place in the dividend. Then we multiply one ten by the number of students to see that we have used three tens. We place the three below the four in the tens place and subtract to see how many tens we have left (one).

Since we cannot tear up a ten-dollar bill and give one third to each child, we go to the "bank" and exchange our ten for ten ones. In our algorithm, we drop down the one in the ones place and look down at the eleven. This shows that we now have eleven ones.

Next, we divvy up the ones. You can see that each child gets three ones. In the algorithm, we divide eleven by three (divisor) and place the three (quotient) above the one in the ones place. Now we multiply three ones by three children and see that nine ones have been used. The nine is written below the eleven and subtracted, leaving two dollar bills.

When we're all done, we go through the entire problem again (much more quickly), pointing to each step and remembering what happened with the funny money. After working a few more problems like this, it's time to take a look at the algorithm without the funny money.

I model more problems, noting each step in the algorithm. As time goes on, my students are ready to use the algorithm with support from me. Just like teaching someone to ride a bicycle, I can feel when they're balanced and pulling away. Finally, they are sailing along, free as birds, confidently solving long division problems on their own!

Common Core State Standard 4.NBT.B.6