↑ Return to Math Team

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

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 http://mathninja.org/number-sense-workbook-errata/


If you prefer to have an invoice sent to you via email, please email  me at mathninjavideos@gmail.com  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.

[spiderpowa-pdf src=”http://mathninja.org/wp-content/uploads/2013/06/sample-book.pdf”]sample-book

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 …

View page »

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 – …

View page »

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 …

View page »


1 ping

Skip to comment form

  1. Pinka

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

    1. anthony gillespey

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

    2. Sarah

      Hope ya do well in state

      1. anthony gillespey

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

  2. Rhythm

    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. anthony gillespey

      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.

  3. Synapse

    Thanks for the videos. My score increased from a 187 to a 382.

  4. Sarah

    I love this amazing website!!! I got a 397!!! SQUEEEEEEEEEEEEE!!!

    1. anthony gillespey

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

    2. Math Rocks

      it’s not possible to get a 397….

      1. FORTNITE

        Thats true

  5. Music to my ears

    Could you please make a video for finding the area of a square with only the diagonal?

    1. anthony gillespey

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

  6. Lightning

    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. anthony gillespey

      Sure there is a video for this https://www.youtube.com/watch?v=_t7Yb3bkh1c

  7. Carol Stringfellow

    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. anthony gillespey

      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.

    2. Math Rocks

      u have to find the number with the higher ones digit

  8. Xavier Piña

    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. anthony gillespey

      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!!!

      1. Xavier Piña

        Today I took a number sense test and I got a 336!!! Thank You!!!

        1. anthony gillespey

          Wow that is a great score. Congrats.

          1. Camille

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


          2. anthony gillespey

            Thanks glad it helps. Great email name : )

          3. Sparkles

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

          4. anthony gillespey

            16 oz = 1 lb.

  9. neon

    Do you happen to have a trick for multiplying by 1998. I know it shows up on a lot of tests.

    1. anthony gillespey

      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.

  10. Math is awesome

    Hello Mr.G

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

    A great fan of yours

    1. anthony gillespey

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

  11. Adhav

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

    1. anthony gillespey

      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. Adhav

        Thank you

    2. anthony gillespey

      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

    3. Math Rocks

      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.

  12. Tony

    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. anthony gillespey

      I plan on making a calculator one some day.

  13. Priyanka

    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. anthony gillespey

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

  14. Math

    Hello Mr. G,
    I purchased one of your number sense workbooks. Do you know when it will come?


    1. anthony gillespey

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

  15. Tom

    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!

    1. Math Rocks

      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………

    2. anthony gillespey

      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

  16. Math Rocks

    Hi mr gillespy, do u think that u could launch a math ninja app

    1. anthony gillespey

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

  17. Tina

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

    1. anthony gillespey

      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.

  18. Shweta

    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. anthony gillespey

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

  19. Jonathan Ye

    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. anthony gillespey

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

      1. Jonathan Ye

        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. anthony gillespey

      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.

  20. lovely unicorn 666

    change from base something to base 10 then change back to what base you want.
    —lovely unicorn 666—

  21. sfd


  22. Lishore

    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. anthony gillespey

      Look up Fermats Little Theorem

  23. balatech

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

    1. anthony gillespey

      The videos are found here on the website.

  24. Super Math Star

    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!

  25. es

    the b/b will be 1
    answer: whatever a was

    it is in mr. gillespey’s new ns book

  26. Aruja Misra

    I think that question number 20 on page 15 is wrong

  27. Jack Graeber

    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

  1. Number Sense Booklet is Up!! | MathNinja.org

    […] Number Sense Video Lessons […]

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

This site uses Akismet to reduce spam. Learn how your comment data is processed.