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Sunday, November 1, 2015


Elsewhere on this site, I gave some general times tables tips. Here, we'll have a closer look at the six times tables. You can use this page to show your kids the hidden patterns in the nine times tables, and make it easier for them to learn. Keep in mind that these patterns will mean infinitely more to your children if you can somehow coax them to realize the rule for themselves, rather than just pointing it out to them.
Here's the six times table. By the way, you might like to download the printable six times table chart on this site, and stick it to the wall of your classroom, or your kid's bedroom!

If you have a look at every second row, you might notice an interesting pattern. Inspect carefully the ones digit.

Did you see the pattern?
The ones digit of six times something is the ones digit of the something, at least if the something is even.

What about odd 'somethings'?
6x1=6(and 6-1=5)
6x3=18(and 8-3=5)
6x5=30(and 5-0=5)
6x7=42(and 7-2=5)
6x9=54(and 9-4=5)
6x11=66(and 6-1=5)
There you have it!
For odd 'somethings', the ones digit of six times something is five more or less than the ones digit of the something.

Some other facts about the answers in the six times table :
  • Since the answers are always even, the last digit must always be 0, 2, 4, 6 or 8.
  • If you add the digits together, and do that again and again, you'll eventually get 3, 6 or 9. For example :
    • 6 x 1 = 6...
    • 6 x 2 = 12, and 1 + 2 = 3...
    • 6 x 3 = 18, and 1 + 8 = 9...
    • 6 x 4 = 24, and 2 + 4 = 6...
    • 6 x 5 = 30, and 3 + 0 = 3...
    • 6 x 6 = 36, and 3 + 6 = 9...
    • 6 x 7 = 42, and 4 + 2 = 6...
    • 6 x 8 = 48, and 4 + 8 = 12, and 1 + 2 = 3...
    • 6 x 9 = 54, and 5 + 4 = 9...
    • 6 x 10 = 60, and 6 + 0 = 6...
    • 6 x 11 = 66, and 6 + 6 = 12, and 1 + 2 = 3...
    • 6 x 12 = 72, and 7 + 2 = 9...
    Amazingly, this pattern, 6,3,9,6,3,9,... continues forever.
    • 6 x 5468 = 38208, and 3+8+2+0+8=21, and 2+1=3...
    • 6 x 5469 = 38214, and 3+8+2+1+4=18, and 1+8=9...
    • 6 x 5470 = 38220, and 3+8+2+2+0=15, and 1+5=6...
    • 6 x 5471 = 38226, and 3+8+2+2+6=21, and 2+1=3...
    • 6 x 5472 = 38232, and 3+8+2+3+2=18, and 1+8=9...
How's that for an interesting pattern?
Before I close this page, if your child can easily multiply by 5, or by 2 and 3, there are a couple of easy ways to multiply by 6.
  • 6 times something is twice 3 times something. So if I want 6 times 9, I can say 3 times 9 is 27, then 27+27 is 54. Not easy for every kid, but maybe it'll work for yours.
  • Probably, it's easier to use this trick : 6 times something is 5 times something, plus another something. So to work out 6 x 7, I'd remember 5 x 7 is 35, then add another 7 to get 42. Or to find 6 x 12, I'd remember 5 x 12 is 60, then add another 12 to get 72.

Monday, August 3, 2015

Opinion Writing as a Response to "Junie B. Jones Is Not a Crook"

Using the book, Junie B. Jone Is Not A Crook,  I wrote a reader response to the question: If you saw something in the Lost and Found at school would it be okay to take it?

You are welcome to copy my idea, or you can purchase all the needed pages so your students can create the fan book themselves, in my Teacher Pay Teacher store. They are having a 10% off sale today and tomorrow. This item is only $1.99 in my store.
The unit includes the fan template in two formats: lined and unlined. In addition, 2 activities are also included: 
1) Whole Group Oral Activity To Work on Adding Reasons to Support Their Opinion
 2) Supporting Your Opinion with Good Reasons from your Schema or Personal Experience. 

Check it out by CLICKING HERE

Created to address the following Common Core Standards:
CC.3.W.1  Write opinion pieces on familiar topics or texts, supporting a point of view with reasons.
CC.3. W. 1.a   Introduce the topic or text they are writing about, state an opinion, and create an organizational structure that lists reasons.
CC.3.W.1.b   Provide reasons that support the opinion
CC.3. W.1.c   Use linking words and phrases (e.g., because, therefore, since, for example) to connect opinions and reasons.
CC.3.W.1.d    Provide a concluding statement or section.

Let me know what you think about the fan book in the comment section of this post.  I read everyone of your comments and respond to your questions.

Friday, July 10, 2015

Eureka Math Taught in Guided Math Groups

I'm going to a Eureka Math Training at the end of the month. 

Has anyone used this curriculum in a Guided Math Format? 
 Please leave me a comment as I would love to hear how it worked...
I've also been considering how to use it with
 Multi-grade/Split  Classes.


Monday, June 29, 2015

Opinion Writing for a Multi-Grade Classroom: Conclusion

I've been working on a unit for 3rd, 4th, and 5th Graders about Opinion writing based on the Common Core Writing Standards.

  My goal is to create a unit that can be used in a
 Multi-Grade Classroom. 
 Here's an example of one of the activities.

To make it work for a Multi-Grade classroom, there are 3 different paragraphs that are appropriate for different grade levels. 

 The whole class has a mini-lesson about writing a conclusion to an opinion paragraph.   The teacher then divides students into small groups, and that group receives one paragraph based on their reading level.


Monday, June 8, 2015

Clarifying the Differences Between Opinion, Persuasive, and Argument Writing

While developing materials to assist a 3rd Grader as she learns how to write an opinion piece that supports a point of view with reasons, I had to step back and clarify the difference between 
opinion, persuasive, and argument writing for myself.

Here is a simple chart from that helped me. Click on the chart to take you directly to their website.

Opinion Chart

Then I came upon this very informative  post written by 
the Six Traits Gurus, and I realized that the big difference between these different types of writing is evidence.

For the 3rd Grader that I am working with, I need to concentrate on just having her learn to state her opinion well but with her own voice.

Grade Level Differences: Opinion Pieces versus Arguments
Up through grade 5, the CCSS call for students to write opinion pieces, not arguments per se. The defining characteristics of an opinion piece are as follows:
  • The writer makes a claim
  • The writer offers reasons to support that claim (School uniforms are not a good idea because they are expensive)
  • The writer offers facts or details to strengthen his/her reasons (School uniforms can cost over $100 each, and every student needs at least two of them)
  • The writer uses transitions (For example, To illustrate, Consequently, On the other hand, In addition) to link reasons or details to the main claim
  • The writer sets up the paper by making the issue clear and closes by reinforcing his/her position or otherwise guiding the reader toward a good decision
After reading this post, I also realized that I don't want my 3rd Grader to get sucked into the conclusion pit where they just restate the 3 reasons.  I want them to start to think about a powerhouse ending that contains those reasons without the step by step writing that is so boring (and yet so easy to do). Here's an excerpt from the blog post that started me thinking:

  • A powerhouse ending. Endings matter. They need to stick in our minds, wrap up loose ends, give us new things to think about—and perhaps, in the case of argument, suggest new thinking or action. An ending must be more than a summary of what we’ve read. It is condescending to simply summarize what’s been said, as if the reader were inattentive or not very quick. It’s lazy to leave things dangling, or toss the choice of options to the reader—the old “What do you think?” way out. A good argument might close with a call to action, a summary of the consequences of inaction, or even with the most powerful piece of evidence—one the writer has held back until this moment. A good question to ask is, What doesn’t the reader know yet that will push him/her to a good conclusion?
 She also discusses implications for higher grades as they focus on argumentative writing and on using evidence to support those arguments.  Click HERE to read the whole article.  It's really worth your time! 

Lastly, I did more research on this topic using multiple sources and an old language arts textbook (dry reading)  and the definitions concurred with the above discussion. I didn't want you to think I just found one source on the internet and took that information as the "holy grail."


Sunday, June 7, 2015

Opinion Writing : Common Core Standard CC.3.W.1a

 I am working with a 3rd Grader on the
 Common Core Writing Standard CC.3.W.1.a

Introduce the topic or text they are writing about, state an opinion, and create an organizational structure that lists reasons.

We've been talking about the organizational structure that help us write a well-written opinion.  
Together we wrote down some of her thoughts that answer the topic: Is ballet a healthy activity?
Example of a completed Opinion Structure
Example of an individual Page
If you would like a fan pattern to use in your classroom, click HERE TO GO TO MY GOOGLE DOC FILE

This document has both lined and unlined fan pages. It also includes the organizational graphic organizer that we used while talking about the structure of an opinion writing piece.
 (More on that in another post)

Leave a comment and let me know if you find it helpful or not. Share your OPINION

Monday, April 27, 2015

Comparing Surface Area and Volume

A great activity for those "talented students" that you are urging to think about ideas on their own.

Give the student sentence strips that contain the above phrases.  In small groups, they create the Venn Diagram.  Then, challenge them to create their own Double Venn Diagrams that compare two mathematical concepts.  

Have the students generate a list of pairs of mathematical concepts that they could compare, and then confer with their teacher
 for final approval of their basic idea.

Lately, I've been thinking about this poem.

Perhaps we need to let our "Talented Learners"  FLY?


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