Number and Operations

  • Number Properties and Operations  


    Different ways to teach the four operations  

    CiderSites Multiplication

    Cool math 4 kids .com - Lattice Multiplication

    Everyday Math



           Number Sense Activities by Grade Level       
    Grade Three

    Grade Four

    Grade Five  

    Grade Six

    Grade Seven

    Grade Eight

    High School

    Four Operation Practice

    Touch Math
    TouchMath - Free materials


    Multiples and Factors
    Students seem to have a hard time remembering the difference between multiples and factors.  This chant helps them.  "Multiples, raise them up.  Factors, break them down."  Make the raising the roof gesture for multiples and roll your arms down around your knees to one side for factors. 

    Illuminations: Factor Game

    Chant for subtraction
    More on top?
    No need to stop!

    More on the floor?
    Go next door and get ten more!

    Numbers the same?
    Zero's the game!

    Tile Cards- There is a template for the tiles 0-9 on this page.  You will also find four activities for each number starting at five.  These are self-checking activities.  Students love these.  They work best if you have the tiles in baggies for the children in your room.

    Math - Times Tables

    Number Op Activities

    Place Value Game
    Place Value Activity


    What is Number Sense?
      Number Sense has been described as the common sense of numbers, a kind of mathematical literacy.  A person with number sense knows what numbers mean and understand how to use them.  Developing this kind of mathematical literacy is at the heart of the National Council of Teachers of Mathematics. 

         Children with Number Sense"

    • Understand numbr meanings.  Students who understand numbers know them by different names or representations.  They know that 17 is 1 more than 16, or 10 + 7, or 3 less than 20.  That know that 2/3 is 2 of 3 equal parts, more than 1/2 and less than 1.
    • Have developed multiple relationships among numbers.  Students who recognize number relationships can realize the effect of patterns, see what happens when numbers are doubled, halved, or otherwise reconfigures.  Number patterns can also help children see if numbers are less than, greater than or between two numbers.  For example 58 is 50 + 8, so less than 59.  It's between 50 & 60.
    • Recognize the relative magniture of numbers.  Magnitude often involves both number meaning and number relationships.  Students who have this skill understand, for example, that 15. x 2 and 15 x 10 is less than 200 AND 1/4 is less than 1/3 so 1/4 is less than 3/8.
    • Have developed references for measures of common objects and situations in their environment.  With this knowledge they know that about 8 people can fit around the dinner table, or that a million people cannot fit into the average baseball stadium.  The realize they cannot walk 10 miles in one hour, but can walk 1 mile in one hour. 


    Common Misconceptions

    A number with three digits is always bigger than one with two. Some children think that 3.24 is bigger than 4.6 because it's got more digits.  Why?  Because the first few years of learning, they only came across whole numbers where the rule does work.
    When you multiply two numbers together, the answer is always larger than the original number. Another  rule that has always worked with whole numbers in the early years, but falls to pieces later on.  Remember, instead of times we can  substitute the word "of".  So, 1/2 times 1/4 is the same as half of a quarter.  That demolishes the expectation that the product is going to be larger than the original numbers.
    Which fraction is larger 1/3 or 1/6? Many students will say 1/6 because the denominator of 6 is larger than 3.  Practical work, such as cutting pre-divided circles into thirds and sixths, and comparing the shapes, helps cement understanding of fractions.
    Common regular shapes aren't recognized for what they are unless they are sitting upright. Teachers can draw them occasionally facing in different directions or just tilted over to force pupils to look for different properties.  A triangle does not always sit on its base.