Basic Operations of Fractions and Decimals Self-Assessment

 This year I am teaching sixth grade math to a group of fifth grade gifted students.  One of the units in our curriculum taught basic operations of fractions and decimals.  It was a cumbersome unit, so I took it apart by skill and made sure my students knew their strengths and weaknesses.

I created this document for students to keep track of their progress throughout the unit.  I would give a pretest, reteach small groups using whiteboards, and then retest to ensure mastery.

To download Basic Operations of Fractions and Decimals Self-Assessment, please click here.

Converting Fractions to Decimals with a Meter Stick Number Line

One of the key math concepts in fourth grade is placing fractions and decimals on a number line. It helps to have a strong visual model the students can manipulate.  I realized that I already had a class set of number lines I could use for the activity: meter sticks.

Meter sticks are a way of representing tenths, hundredths and thousandths.  One meter stick is the whole.  Each decimeter is a tenth, each centimeter is a hundredth, and each millimeter is a thousandth.
(You can purchase 12 meter sticks by clicking the affiliate link below.)
 
I started with modeling half.  Students could visually see that I had marked half way across the stick.  Fourth graders know that 50 is half of 100 so the clothespin marked the 50 cm point.

Next, I marked the tenths.  On one side of the clothespins I have tenths in fraction form.  On the other side I marked the equivalent decimal.

I made additional clothespins with fifths, fourths, and eighths.  On the other side of each I marked the equivalent fractions.  I am using this tool as an independent station for some students and an intervention for others.

Compare, Add, and Subtract Fractions

Here is an activity that I use with students who have learned how to work with fractions, but need practice.  I allow them to use any strategy they need to in order to compare, add, and subtract two fractions.

Students receive the half sheet shown above and find equivalent fractions with like denominators.  Next, they show which fraction is greater, then add, and then subtract the two fractions.  The finished paper would look something like the figure shown below.

To download four "Compare, Add, and Subtract Fractions" activities, please click here.  I have included an answer key to save you time.

To purchase my expanded version of "Compare, Add, and Subtract Fractions," please visit my Teachers Pay Teachers store or my Teacher's Notebook store.


Happy Friday!

Fractions and Decimals Number Line

Last year, I posted a series of posts about fractions and decimals.  I used a meter stick as a number line and had students create their own set of fraction bars.  I created a worksheet to go along with the lessons, but I realized I never shared it with you.

To download the fractions and decimals number line worksheet, click here. 
To see all my blog posts about teaching fractions in an upper elementary classroom, click here. 

 
Happy Friday!

Gomoku with Improper Fractions

To download the game board for Gomoku: Improper Fractions, click here.

Like Gomoku: Simplifying Fractions, students play this game by rolling two dice and dividing the answers.  This game board has whole numbers and improper fractions, because the larger number is divided by the smaller number. 

Students place a marker on an open place with the answer.  The winner is the one who places five markers in a row.

Gomoku Games: Five in a Row is available for free at Teachers Pay Teachers and Teacher's Notebook.

Quilt Square Codes -- Math Spies Episode 7

Have you visited Math Spies lately?  Math Spies is my math problem-solving website.  I post a problem a week each Wednesday.

Episodes 7 has seven problems with an extra example problem to show students how to solve the others.  I call it Quilt Square Code Problems, because, students determine the fraction of each color of a square like the one above.  They use those fractions to solve a code word.

Click here for the example problem on Math Spies. To solve the other seven problems in the series, click here. 

I made a set of task cards with these codes and 24 more available here at Teacher's Notebook and available here at Teachers Pay Teachers.

Gomoku -- Simplifying Fractions

 To download the game board for Gomoku Simplifying Fractions, click here.

Frequent readers of this blog know I love creating math games for my students to practice their facts.  I created Gomoku Games, a freebie in my Teachers Pay Teachers store where students can follow a few basic directions to play different versions of the game.  The change in difficulty comes in the operation performed on the numbers rolled.  For example, I have introduced addition, subtraction, and multiplication versions of this game. 

When I got to division, I wanted my students to work with fractions.  For this version, have the students roll two dice.  The smaller number becomes the numerator, the larger number becomes the denominator.  (There is another game board where this pattern is reversed.)

If your students haven't learned how to simplify yet, I would recommend a "cheat sheet": a list of possible fractions with their simplified forms.  As you can see from the list below, their aren't that many of them that need simplifying.

1 = 2/2 = 3/3 = 4/4 = 5/5 = 6/6
1/2 = 2/4 = 3/6
1/3 = 2/6
2/3 = 4/6

Once a player has figured out the answer, he/she places a marker on a square with that answer.  The objective is to get five markers placed in a row.

Gomoku Games: Five in a Row is available for free at Teachers Pay Teachers and Teacher's Notebook.

Improper Fractions and Mixed Numbers

Last week I shared a short set of fraction quizzes with an answer key.  I focused on fractions of a group.  This week I am sharing a similar set of quizzes where students convert improper fractions to mixed numbers and vice versa.  I have included an answer key as I do with all my math products.

I did not write the directions on the quiz to save room.  Please tell the students (or write it on the board) that if they see an improper fraction, they convert it to a mixed number.  If they see a mixed number, they convert it to a fraction.  I know this may seem blatantly obvious, but having tried these out on actual students, I found I needed to be explicit in my directions.

Another quiz in this series is located on this post: Adding and Subtracting Fractions with Like Denominators.

Fractions of a Group

When I solve a problem in my classroom, I assume others might have the same problem.  I know the trend is to have students solve rigorous problems with lots of vocabulary, but sometimes I just want to know if my students understand how to manipulate the numbers.

Last year I created a series of  short math quizzes for different aspects of fractions.  The first set I posted last spring called: Adding and Subtracting Fractions with Like Denominators.  This week I want to share Fractions of a Group. 

This document from my Google Drive has three short quizzes with answer keys.  I can use them for monitoring the progress of my students.  I like having three for pretest, mid-unit, and post-test.

I know it may seem obvious, but I have math materials that students can use to form equal groups using the denominator and then collecting the number of groups in the numerator.  This physical manipulation is necessary even in the upper elementary grades where we think they should compute abstractly. 

Next week I will share Converting Mixed Numbers to Improper Fractions and Back.

Developing Number Sense Round Up

Over the last several weeks I have posted several lessons I use to teach number sense.  Here is a list with the links in case you missed one or two.

First I wrote about using a meter stick to teach students the relationships between fractions and decimals.  (I recently updated this post here.

I wrote a follow up post here about other concepts I teach using the meter stick as a model.

You can purchase 12 meter sticks from Amazon by clicking the affiliate link below.

 
 Next, I wrote about creating a Magnified Inch and using this as a model for fractions between 0 and 1. 

I followed that up with how I extend the lesson to include mixed numbers.  My students have placing mixed numbers on a number line and creating their own helped.

 I wrote two posts about having students create their own set of fraction bars.  The first week I showed halves, thirds, and fourths.  The next week I wrote about creating sixths, eighths, and twelfths.

Last week I asked the question, "Can Calculators Boost Number Sense?". I would love some discussion about this issue.

Student Created Fraction Strips Part 2: sixths, eighths, and twelfths

If you missed the first part of Student Created Fraction Strips, click here. 

Depending on the experience level of the students, I may introduce sixths, eighths and twelfths on the second day.  If I have already taught the Magnified Inch lesson, some of the fractions may go more quickly.

I don't try to have students fold the sixths.  We talk about the whole as 12 inches and dividing that equally in six pieces is the same thing as 12 ÷ 6 = 2.  Each piece will be 2 inches.  I hold up sixths next to the thirds and we see how there are two sixths for every third.

I have students fold the eighths instead of measure.  Each piece will be 1 1/2 inches and that is a little beyond what my students were capable of doing.  Instead we fold half, then half of each half, and then half of each fourth. 

 

Holding up a finished copy and showing the relationship between halves, fourths and eighths helps.  As a final step, label the fraction strips you made today with the words and numbers for each fractions.

 

Student Created Fraction Strips Part 1: whole, halves, thirds, and fourths

Note: the picture above is the set I made with the students this past year.  In the photos below, I used different construction paper.  When I create fraction strips with students, I keep the colors consistent for each fraction each year.

Although I have a printable set of color-coded fraction/decimal strips that is a best selling item in my store, I find that having students create their own set by cutting, measuring, and folding, assists my students in understanding fractions.  I also know that they need meaningful reasons to measure with a ruler.

I keep the printable version for my math stations and have students keep a copy in their notebooks.

I start by cutting a set of 3 X 12 inch strips for each student.  (Some teachers want a laminator at home.  I want my own paper cutter.)

 

I reserve one strip to represent the whole.  We measure its length -- 12 inches.

 



Next we fold and cut the color we are using to represent half.  I have them measure the half -- 6 inches.  I ask what is 2X6?  Notice that I have cut one and left the other uncut.  I find that some students need fraction bars that they can manipulate.

Next we fold, cut, and measure the color representing thirds.  Each piece should be 4 inches.  What is 3X4?

Then we fold, cut, and measure fourths.  What is 4X3?

I do take time to have them write the words and numbers on each part.  As we use these to solve problems, it helps to have both. 

Next week I will continue with sixths, eighths, and twelfths.

The Magnified Inch for Mixed Numbers

Last Monday, I shared how I used the Magnified Inch lesson to introduce fractions.  This week I am explaining how I extend the lesson for mixed numbers.

This came about, because so many problems for Common Core fractions required students to plot fractions and mixed numbers on a number line.  My students struggled with this, and I believe that when they construct the model with my guidance, it helps them so much more than just viewing a model an adult has already constructed.

So I redid the original Magnified Inch and then had them make a second one in a different color.  As you can see in the picture above, we added ones before each of the fractions.  I had them tape the two strips together to make a continuous number line.

(I didn't do this last school year, but I was thinking about extending this number line with mixed numbers up to 4.  I don't know that I would do this with every student.  I'll get back to you on that.)

It still didn't sink in for most students until we started reading the numbers left to right aloud as a class.  They could see the pattern in the numbers.

If any part of this isn't clear, or you have questions, please ask in the comments.  I hope you find this lesson helpful.

The Magnified Inch for Fractions

I heard about the Magnified Inch lesson from a colleague about ten years ago and then read about it in a book called Family Math.  The authors put this lesson in the measurement category, but I find it helpful when teaching fractions.  Here is my version of the lesson:

I start by cutting an eighteen inch strip of construction paper for each student.  ( I always make extras.)  I have students fold the ends together to make half.  I label it with a fairly long line, but I leave enough room to show equivalent fractions.

 

 

Next, I have the students fold each end to the center.  We talk about cutting each half into half.  I label each part with a slightly shorter line like you would see on a ruler and mark the lines 1/4 and 3/4 respectively.  I tell them that 2/4 is the same thing as 1/2 and write in that label as well.

 

 

The next part is where I lose some students.  I need to fold each fourth into half.  I have found that the simplest way to do this is to fold each end of the strip to the 1/4 mark and then to the 3/4 mark.  I label the new marks 1/8, 3/8, 5/8 and 7/8.  I explain that 2/8 = 1/4, 4/8= 2/4=1/2, and 6/8 = 3/4.  Decide how much guidance your students need with labeling equivalent fractions based on how much experience they have had.

 

I use this tool as a number line.  We talk about which fractions are greater or less than others.  I let them use it as a tool as we go through the unit. I find that because my students have created this tool, they understand it better than a number line printed in a book.

 

Next week I will explain how I have extended this lesson to include mixed numbers.