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Number Sense Workbook and Video Lessons Volume 1

 Welcome to the Number Sense Lesson page. Here you will find basic number sense tricks.  Each video follows the Number Sense Workbook.  Once you watch the vid

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eo, do the extra problems on each page of the workbook.  There is a key In the back of the booklet for each section.  I just added a new page for Errata in the book at


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If you prefer to have an invoice sent to you via email, please email  me at [email protected]  with the quantity of books you want and your contact information.Feel free to send me an email with any questions you might have.

A sample of the booklet can be found  here.

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Sample Number sense booklet

Pages 5 through 25

Page 5 – Add to 10 Ones Digit Page 6- Add to 10 Tens Digit Page 7 – Multiplying by 25 Page 8 – Multiplying by 50 Page 9 – Multiplying by 75 Page 10 – Multiplying by 125 Page 11 – Multiplying by 11 Page 12 – Multiplying by 111 Page 13 – Multiplying …

Pages 26 through 46

Pg 26 – Approximating multiplying by 142857 Pg 27 – Multiplying by 3367 Pg 28 – Multiplying by 143 Pg 29 – Add to 1 Mixed Numbers Pg 30 – Difference of Two Squares Pg 31 – Sum of Two Squares Pg 32 – Greatest Common Factor Pg 33 – Least Common Multiple Pg 34 – …

Pages 47 through 65

Page 47 – Simplifying Radicals Page 48 – % of is % of what number Page 49 – Multiplying powers of pi Page 50 – Powers of i Page 51 – If a= b and b = c then 1a = ? c Page 52 – Sum/Product of the Roots and Discriminate Page 53 – Log …


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    • Pinka on February 23, 2015 at 12:50 am
    • Reply

    This helps a lot! I took the state qualifier after watching the videos and I got a score of 327.

    1. Glad I could help. Good luck at State !!!

      • Sarah on February 27, 2015 at 1:22 am
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      Hope ya do well in state

      1. State TMSCA Champion 5A for the 30th year in a row!!!

    • Rhythm on February 23, 2015 at 5:22 pm
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    Hello Mr. Gillespey,

    I have learned and enjoyed a lot from your awesome Number Sense Workbook so far. I just wanted to let you know that I found a small error on Page 24. On the top right hand corner of that page, the example says that 23 x 38 = 924. However, 23 x 38 = 874.

    Thanks for this great book! Hopefully you write a new book, since I really love this one and will get a free copy.


    1. Nice catch. I fixed it in the problem but never the snapshot in the corner of the page. Thanks for pointing that out. Someday im going to get around to making a calculator book and Ill send one your way.

    • Synapse on February 24, 2015 at 2:07 am
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    Thanks for the videos. My score increased from a 187 to a 382.

    • Sarah on February 27, 2015 at 1:21 am
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    I love this amazing website!!! I got a 397!!! SQUEEEEEEEEEEEEE!!!

    1. Glad I could help. Mention my book to your friends : )

      • Math Rocks on April 26, 2016 at 11:37 pm
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      it’s not possible to get a 397….

      1. Thats true

    • Music to my ears on February 27, 2015 at 1:24 am
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    Could you please make a video for finding the area of a square with only the diagonal?

    1. Actually I can just tell you the formula. It’s (Diagonal 1 x Diagonal 2) / 2 or if its a squares (Diagonal squared) / 2

    • Lightning on April 19, 2015 at 7:56 pm
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    Hello. I was wondering if there was a nummber sense trick for finding the mean. Can you please tell me if there is? Thank you.

    1. Sure there is a video for this

    • Carol Stringfellow on April 28, 2015 at 7:16 pm
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    Sum of two squares (page 54). On these problems either the outer digits add to be ten and the inner digits are one apart OR vice versa. Of the two digits that are one apart, you need to choose the number with the higher digit and proceed with adding the squares of the digits and writing it twice. It is not always the first number that you square the digits and add. What if the problem were written in reverse order? Do you follow what I am saying? When I explain this to my students, I never have been able to make it less wordy. Carol Stringfellow

    1. You are absolutely right. In fact one question this year on a Number Sense test they in fact reversed the two numbers. Now the question is did the writer of the test do that on purpose? If so then we need to make sure the students understand what form it needs to be set up in to be solved. Thanks for the comment.

      • Math Rocks on April 26, 2016 at 11:55 pm
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      u have to find the number with the higher ones digit

    • Xavier Piña on May 14, 2015 at 12:57 am
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    I am currently watching these videos and my score is increasing. During the school year I was scoring in the 30’s but I started watching these videos 3 days ago and I am currently scoring in the 200’s so Thank You very very much!!!

    1. I’m glad to hear it. I have heard a lot of positive comments from you and others. Please share it with your friends and don’t forget to buy the book!!!

        • Xavier Piña on May 15, 2015 at 10:50 pm
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        Today I took a number sense test and I got a 336!!! Thank You!!!

        1. Wow that is a great score. Congrats.

            • Camille on November 20, 2015 at 3:01 am

            Thank you for all you’ve done in the number sense area. Your work has helped me greatly.


          1. Thanks glad it helps. Great email name : )

            • Sparkles on November 25, 2015 at 1:17 am

            Do you know how to remember conversions such as oz-lb

          2. 16 oz = 1 lb.

    • neon on July 2, 2015 at 7:55 pm
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    Do you happen to have a trick for multiplying by 1998. I know it shows up on a lot of tests.

    1. The best you could do it think of it as 2000 – 2 and distribute the number
      example : 8 x 1998 = 8 ( 2000-2) = 1600 – 16= 1584 which is all easy math.

    • Math is awesome on October 4, 2015 at 2:46 am
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    Hello Mr.G

    I purchased one of your books this afternoon, do you know when it will arrive?

    A great fan of yours

    1. Ill send it out today. You should get it by Thursday.

  1. Is there an easy way or shortcut to multiply 3 numbers by another 3 numbers
    Thank you

    1. The best you can do in general is FOIL it. In this specific case I would do (250-4)x 556) which is a variation on the 25’s trick. But that is some hard math to do in your head.

      1. Thank you

    2. Once again if this is an estimator on the test then dont worry about the exact answer. Round it. call this problem 250 * 560(round one up and one down) then use the 25’s trick. 140000

      • Math Rocks on April 27, 2016 at 12:15 am
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      I would do it a different way. Since 556 is close to 555, I can “trade” that in for 5/9, and round 247 to 243, which is a multiple of 9 ( I can tell because of the divisibility trick Mr. G put up) and then divide 243 by 9, yielding 27. Then I would multiply 27 by 5, resulting in 135. (BTW, I’ve always found it easier to divide first than multiply first!) Then, I would add back the three zeros I lost when changing 555 to 5/9, yielding 135000, which fits smug in the 5% range of (in this case) 137332.

    • Tony on November 19, 2015 at 12:36 am
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    Your book really helped my scores went from a 283 to a 391 in only 1 competition. I hope you are making a calculator book or a science book because i would definitely buy it!

    1. I plan on making a calculator one some day.

    • Priyanka on November 23, 2015 at 2:45 am
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    Hello Mr.G,

    I have learned a lot from your awesome number sense workbook so far, but I found an error in the answer key. The key states that on page 9, the answer to number 13 is 13, but that cannot be true because 75*88 (number 13 on page 9) is 6600. Thanks for this great workbook! Hopefully you will write a new book, since I really like this one.


    1. Thanks. I will get fixed. I am going to start working on a second book for Calculator but it takes a lot of time.

    • Math on December 10, 2015 at 12:31 am
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    Hello Mr. G,
    I purchased one of your number sense workbooks. Do you know when it will come?


    1. Put it in the mail this morning. You should have it by Saturday or Monday.

    • Tom on April 15, 2016 at 1:56 pm
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    Dear Mr. G,
    Thank you creating such wonderful resources for the number sense tests. My score has tremendously improved over the past year.
    By any chance do you have any trick for 4^3 times 5^5 or 2^5 times 5^3? (Two different questions)
    Thank you once more for the helpful tricks!

      • Math Rocks on April 27, 2016 at 12:06 am
      • Reply

      2 to the 5th power times 5 to the third is pretty easy. I didnt know it, but now i do. first you find by how much the exponent is greater than the other exponent. The 5 ( in two to the fifth power) is greater than the 3 (in 5 to the third power) by 2, so you do 2 to the second power. That’s 4, and now you are solving a problem that states 2 to the THIRD power times 5 to the third. Since these have the same “exponent base” you can multiply 2 and 5 to get 10, and do 10 to the third power, which is 1000. now you do the 4 and multiply by 1000, which is 4000. you can use this trick for the other problem u mentioned, and basically all of them. But you’ll usually see 2^x times 5^y ( in 2/5 format) because 2 x 5 is ten, and ten is an easy number to work with, especially in multiplication! Sadly our luck is running out because TMSCA is making the tests harder than ever. Oh yeah, and you might be wondering, “WHO IS THIS GUY?! He’s like on every other comment!” WELL…. If that’s what you’re thinking, I’ll reply to you right now. I’m just trying to help people! I mean no offense to you if you’re NOT thinking that. Just saying………

    1. Think of 4^3 as 2^6, now every 2 time 5 makes 10. How many tens can you make.? You can make five tens. So what’s left? One 2. So it’s 2*10*10*10*10*10=200000

    • Math Rocks on August 3, 2016 at 4:26 pm
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    Hi mr gillespy, do u think that u could launch a math ninja app

    1. I would really like to do that but I have never looked into it yet.

  2. Before I purchase any of the workbooks, I was curious to find out if these were appropriate for 5th Grade Number Sense.

    1. Absolutely, my own daughter is in 5th grade and she is starting on the book. It takes a long time to get good at number sense. The more time the better. The important thing is that they have a firm grasp of multiplication before working with the book.

    • Shweta on December 5, 2016 at 12:11 am
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    My daughter has joined math club in 5th gr and my son is in 8thgr they love math. I am just surprised why I never got this book before and never knew about this site before. It’s so much fun and exciting and we have great love and respect for all the teachers for their hard work. Thank you so much! As a woman who loves math and science more than anything else it is great pleasure to see there are people like us who respect teachers and knowledge and school, which other people label boring.
    Thank you,

    1. Thank you for the kind words. I’m glad my site is helping others.

    • Jonathan Ye on January 4, 2018 at 4:14 am
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    Hi Anthony. I’m trying to find a trick for a specific type of question I’ve come across while going through some number sense test. An example is question 61 from the 2007-2008 State Number Sense test. It requires you to directly convert from a non-10 base to another non-10 base. I’ve tried combining the tricks going from a non-10 base to base 10, then base 10 to a non-10 base, but I found it extremely difficult and it took too long, long enough that it’d be faster to skip that problem. Do you have any tricks for this kind of problem?



    1. Was it base 2 to 4 or 8. Or maybe base 3 to 9? If there is a trick.

        • Jonathan Ye on February 11, 2018 at 2:35 am
        • Reply

        Sorry, I thought I’d get an email if I ever got a reply. I showed the problem to a friend and he recommended a trick to me, but never got to teaching me it. They are probably the specific bases tricks you are thinking of. What are the tricks?

    2. Does this trick ask about base 2 to 4 or base 2 to 8 or perhaps base 3 to 9? If so they have a fun way to do them. Its quite complicated but I might be able to put a video together of it.

    • lovely unicorn 666 on February 8, 2018 at 3:01 am
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    change from base something to base 10 then change back to what base you want.
    —lovely unicorn 666—

    • sfd on December 10, 2018 at 12:36 am
    • Reply


    • Lishore on April 22, 2019 at 4:07 am
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    Hi Mr. Gillespy,
    Do you have a trick for a^b/b
    for example, 3^8 / 8
    Also do you have tricks for the other variations
    For example: 3^8 / 9

    1. Look up Fermats Little Theorem

  3. S,I ordered the number sense workbook.Then how do I access the number sense videos?

    1. The videos are found here on the website.

    • Super Math Star on September 3, 2019 at 11:39 pm
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    Thanks for the great Number Sense books Mr. Gillespy! I recently also took your number sense lesson during the summer and it helped a LOT. Around a few days ago, i ordered your number sense 2nd book and I hope that it will also be filled with great tips and tricks!

    • es on November 14, 2019 at 2:23 am
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    the b/b will be 1
    answer: whatever a was

    it is in mr. gillespey’s new ns book

    • Aruja Misra on January 23, 2020 at 3:06 am
    • Reply

    I think that question number 20 on page 15 is wrong

    • Jack Graeber on March 9, 2020 at 7:08 pm
    • Reply

    hey i found a mistake on example 3 of “multiplying by 125”

    you used the multiply by 75 trick and divided by 4 instead of 8

    just wanted to point that out

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