The class is filled with shouts of…

“No!”

“Ugh!”

“I just don’t get this.”

“Ms. E., I think I’m going to puke. Can I go to the nurse?”

“But…, I have a great new poster with key words…” Looking around the class Ms. E. sees heads drop and a few more students clutching their stomachs. Half heartily she continues, “These words will make solving word problems so much easier.”

Have you ever felt like Ms. E? I know I have. I’ve tried anything and everything to make problem solving easier for my students. I remember spending hours looking for the just right key word poster for problem solving. I knew if I could find just the right one, all my problem solving woes would be solved.

Well, they weren’t. In fact, in many ways my students became worse problems solvers then before. Here’s why I say, “No to key words for problem solving.” (Well at least some of the time.)

These are common key words we use to signal students that it is time to add. Let’s look at two examples to see why they don’t always work.

**Cars Sam Has**

**Cars Sam Buys**

Students see the key words in all. They think, “In all means to add, so I’ll add, 2 + 5 = 7.”

In this case the students have use the correct operation and find the correct answer. However, they probably didn’t think about the problem other than to look for the key words in all.

**Box 1**

**Box 2**

Students who look just for keys words see in all and write, 2 + 5 = 7.

This is an incorrect answer.

Students are looking for the keys words instead of making sense of or visualizing the problem. When students seek to understand the problem instead of just looking for key words, they write a correct equation which in this case could be one of the following:

2 + 2 + 2 + 2 + 2 = 10

5 + 5 = 10

2 × 5 = 10

5 × 2 = 10

All of these equations would be considered correct and demonstrate an understanding of the word problem.

A question for a later discussion, is which of these equation if any are more correct than the other.

These key words apply to both multiplication and division. Let’s look at a couple of examples.

Students who have been taught that each means division or multiplication might try the following.

**Might write **

5 ÷ 2 = What?

They might draw or visualize the picture below.

**Box 1**

**Box 2**

**Box 3**

Hold, it! I don’t have anymore cars.

**Box 4**

Now what do I do?

**Box 5**

I think I need to go to the restroom. Yeah, that’s what I should do.

As you can see the picture and the equation don’t match. So in the students’ mind the problem is well…going to the restroom might just be the best way to deal with the problem for them.

Without understanding the problem, students generally go automatically to multiplication. They didn’t move to multiplication because it is the correct operation but because division here just doesn’t make sense to them. Or division is too hard.

To understand this problem, students have to move beyond the key word/s and visualize or draw what is happening in the problem. In this case, it would be 5 boxes with 2 cards in each box. Like this.

**Box 1**

**Box 2**

**Box 3**

**Box 4**

**Box 5**

** **

Again correct equations could be:

2 + 2 + 2 + 2 + 2 = 10

5 + 5 = 10

2 × 5 = 10

5 × 2 = 10

Let’s try one more example. We’ll change up the numbers a bit.

Looking at just key words, students will likely write an addition or multiplication equation. (They’re easier for students.)

But when students seek understanding, they’ll visualize or draw 6 cars divide into groups of 2 until all the cars in are boxes.

**Box 1**

**Box 2**

**Box 3**

Then hopefully, they’ll write the following equation:

6 ÷ 2 = 3

And not 2 ÷ 6 = 3 (This is a problem for later.)

Hang with me for just one more example of key words, take away. I know, take away is used so much for subtraction. It really doesn’t signal any other operation. It does, however, limit students’ understanding of subtraction.

I don’t automatically say no to take away, it is a natural way for little ones to start understanding subtraction. The problem is when take away continues to be used for subtraction. Students believe that subtraction only occurs when you “take something away” from a group and the group gets smaller.

Let’s look at a word problem to see why take away just doesn’t work.

**Marco’s Cars**

**Aja’s Cars**

This is a subtraction problem that requires comparing two groups. Nothing is taken away. Because nothing is taken from either group, students will decide to add. In fact, the word more causes students to think of addition or multiplication because it implies that a group is getting larger.

Students will often write 3 + 2 = 5 instead of 3 – 1 = 1.

Next week, I’ll look at better strategies for teaching problem solving other than key words.

Drum roll please, …..

The winners are:

Robin D. and Lisa K.

Hope you are all enjoying your free product. We would love to hear how it works in your classroom.

The Folks at EdVentures 4 Kids

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At EdVentures 4 Kids, we want to say thank you for all you do.

- for tending scrapped elbows and knees
- for the sleepless nights worrying about a student
- for laughing till you cry at the corny jokes your students share
- for helping your students understand they are more than a test
- for being a cheerleader for your students as the tackle hard task
- for the hours spent planning the perfect lesson for all your students
- for the days when nothing seems to go right but you still manage a smile
- for mending the broken hearts when someone is no longer a child’s best friend
- for smiling when people say, “How hard can a job be when you get 2 months vacation?”
- for all the loving, caring, sharing, laughing, crying, reading, … you do each day

We truly thank you! You make more of a difference then you know.

To say thank you, we’re hosting a give away. (We wished we could give you millions of dollars each, but we were teachers to.)

Instead of a million dollars, we are giving away a surprise free product. (The product is great for 3rd – 5th grade.) It is one many of our TpT costumers wish list.

An email will be sent to your inbox. Confirm the subscription. After you’ve confirmed your subscription, another email will come to your inbox with a welcome letter and link to the free product.

(If you don’t see the e-mail in your inbox, check your spam. Sometimes they get redirect their.)

Use the Rafflecopter entry form to enter to win 1 of 2 $10 gift certificates from Teachers Pay Teachers. Simply enter the name of the freebie you received after subscribing to our newsletter and downloading the file.

Click submit and you’ve entered.

The drawing will be held before 1:00 p.m. EDT on May 4th. That way you use it during the sitewide Teacher Appreciate Sale at TpT.

Winners will be announced on EdVentures 4 Kids’ Facebook page and here.

May 3rd and 4th you can get up to a 28% discount on products at Teachers Pay Teachers.

Simply enter the promo code CELEBRATE as you make your Teachers Pay Teachers purchases. The discount will be automatically applied.

Check out my store and others. I’m sure you’ll find something you can’t live without.

Check back Wednesday to learn who won the Teachers Pay Teachers gift certificates.

]]>Do your students struggle with equivalent fractions like a wobbling tight rope walker?

Do they approach each assignment with a bit of fear and anxiety?

Help is on the way!

This week we’ve included step-by-step, illustrated instructions for using Equivalent Fractions at Illuminations.

Click on the link below to go to the site.

http://illuminations.nctm.org/activity.aspx?id=3510

This is a great website to help students visualize equivalent fractions in models (squares or circles), on the number line and as a number.

When using this with 3rd graders, use the Build Your Own option. (Automatic takes students too far out of 3rd grade standards. But it is wonderful for students who need a challenge.)

Once you’ve clicked on Build Your Own, start building a fraction in the red square at the top. To build a fraction move the horizontal and vertical sliders to partition the square into equal parts. Then click on equal parts of the fraction to shade it.

Here we’ve built a model showing 1/2. Notice, we moved the horizontal slider to the number 2. We clicked in 1 of the equal parts. Then the fraction 1/2 appears on the number line.

Now you are ready to build 2 fractions that are equal to 1/2 each with a different denominator.

On our model we built the fractions 2/4 and 3/6.

We moved the horizontal and vertical sliders to partition one square into 4 equal parts and the other into 6 equal parts.

Then we clicked on equal parts to shade one half of each square.

Notice with fourths we did not do the typical shading. However on the number line students can easily see that 2/4 equals 1/2. The atypical shading expands and deepens students understanding of equivalent fractions. They will move there when they are ready.

Now you are ready to check your work. Click on the check mark. If students have correctly created equivalent fractions, the equivalent fractions will appear on the table.

The example below shows our work.

If the fractions are not equal, than x’s will appear on the page. Like this.

If a student creates a fraction with the same denominator as the target fraction, (red fraction on the top of the page) an error message appears prompting the students to “Use a different denominator”.

Students can click New Fraction and create equivalent fractions for a different fraction. For the example below we chose ¾.

This example takes students outside 3rd grade denominators. The visual models make it is easier for students to find equivalent fractions.

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Yes, it is wrong. But to many 3^{rd} graders this is logical and wrong at the same time.

Here’s how a 3^{rd} grader’s reasoning for why this answer is correct.

“When I start counting, I count 1, 2 so ½ must be first. Next comes 3 and 4, so ¾ must be next. I not sure about ¼ and 4/4. But 1 comes before 4 so ¼ must be first. I’ll put 4/4 last because it is all that is left.”

Confusing, right?! Yet that is one of the many ways a 3^{rd} grader could “perfectly, logically” reason about fractions on a number line.

Because fractions on a number line are a new concept for 3^{rd} grade, you might be feeling a bit stumped as to how to help your 3^{rd} graders understand fractions on a number line. Let’s look at a few helpful tips and an activity.

Build them on the floor with tape or string.

Build them by folding sentence strips.

Build them on the wall from the floor up.

Build them with online manipulatives.

Make them huge or make them small, just build, build, build number lines.

Start by marking a 0 on the left edge of the number line and a 1 on the right.

You will add fractions as you partition the number line into equal parts. To make equal parts start folding or measuring. Make a mark where the fold is. Your students can add fractional intervals later.

(Coming soon in A Flurry of 3rd Grade Fractions an interactive notebook activity with complete directions and an activity for creating number lines with fractions.)

Make a giant floor number line with marks for the whole numbers 0 to 1.

Have students jump as far as they can on the number line. Ask, “How far did you jump?” (Your number line should be long enough that it is impossible to jump the whole distance.) Typically 3^{rd} graders will start by saying half way. As a class partition the number line into 2 equal parts. Add the number ½ at the point on the number line. Is this how far the student jumped? (You’ll add more fractions to the number line as students debate the distance.)

After marking off fraction intervals on the number line, use white boards for students to record the distance of a jump. Have all your students show their answer first before determining the “correct” or most accurate distance.

Give all your students a change to jump.

As your students jump on the number line, ask questions, questions and more questions. In fact become the Questionator. Your students might not like all the questions, but you’ll learn lots and they will too as they puzzle through the questions. Here are few question you can ask as you build number lines and jump on them.

- How can we divide the distance between 0 and 1 into 2, 3, 4, 6, or 8 equal parts?
- How do we know are parts are equal?
- What type of numbers are we working with when we divide a whole, (the distance from 0 to 1) into equal parts?
- What happens when we make more equal parts on the number line?
- How can we get the most accurate measurement for the distance you jump?
- How do we write the number to describe the distance we jump?

These are just a few of the questions you can ask to gain an understanding of your students’ reasoning.

(A Flurry of 3rd Grade Fractions contains more questions to ask your students.)

I bet you thought, I had forgotten the technology part. As promised last week, here are a few websites to practice fractions on a number line.

**Animal Rescue** http://www.sheppardsoftware.com/mathgames/fractions/AnimalRescueFractionsNumberLineGame.htm

Rescue animals that are hidden on the number line by moving the arrow to the correct location on the number line. Students can choose to play either halves, thirds, fourths, fifths, sixths, eighths or mixed.

**Math Man** http://www.sheppardsoftware.com/mathgames/fractions/mathman_fractions_numberline.htm

Played like Pac Man. Students use the arrow keys to move Math Move. Math Man can only eat the ghost with the fraction that matches the fraction on the number line.

**Find Grampy** http://www.visualfractions.com/FindGrampy/findgrampy.html

Grampy hides behind the bushes. Help Grammy find him be correctly entering the fractional distance he is behind the bushes.

**Identify Fraction on Lines** http://www.visualfractions.com/IdentifyLines/

Students are shown a number line with fractional increments. Student enter the fraction of the number line that is shaded.

We are busy, busy, busy creating **A Flurry of 3rd Grade Fractions**. This is a bundled product filled with fraction interactive notebooks, worksheets and performance task for 3^{rd} grade. Currently the section, *Understanding Fractions *is complete.

Up next are interactive notebooks, worksheets and performance task for fractions on a number line.

After that, we’ll add sections for equivalent fractions, comparing fractions and whole numbers as fractions.

As each section is added the price will increase. The current price is $9. (The completed bundle will be between $25 and $30.)

For 1 week only, we are making this an even better deal.

The total price will be $8.10. You’re saving at least $16.90

Click on the picture to grab this great deal. Time is running out, so don’t wait.

Check back next week for more fraction websites.

Want to use more internet games and activities in your 3rd grade classroom? Are your days so full you don’t have a minute to search for educational games?

Each week we’ll review internet games and activities that are:

- Easy to use
- Age and grade appropriate
- Match 3rd grade math standards

Our first internet fraction games introduce students to fractions.

Students are show a whole circle. They enter the fraction of the circle that is shaded. This is a good site to introduce writing fractions. It is also good for a review.

This site allows students to differentiate their level of play. Students can choose to play Equal and Unequal Parts; Halves, Thirds and Fourths; Simple Fractions; and Simple Fractions II. They can also choose Relaxed Mode or Timed Mode. Each of these games are introductions to fractions

- Cross the River Students help the character cross the river by correctly identifying the fraction the model represents. This is an introductory game to fractions.

Students are given a fraction. When the golf club is swung a circle appears. Students match their swing to the given fraction. This is great for introducing fraction. It is also good for developing comparing skills. Swing a fraction that is too small and the ball doesn’t fly far enough. This is a student favorite!

Students color fractional parts of flags. For example, a flag is partitioned into twelve parts. Students shade half the flag. This allows students the opportunity to see that fractions can be represented in multiple ways.

Hope your 3rd graders enjoy these fraction games.

See you back next Technology Tuesday when EdVentures 4 Kids will share internet games for fractions on a number line.