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.