Math Skills – Number Sense

Number Sense – Understanding Quantity

This starts with the basic concept that there is such a thing as quantity and that it matters. Even animals figure out this one: which bowl has more food in it, which tree has more nuts. Let’s look at how it develops and how we can help

Developmental Sequence

Here’s a typical progression of skills, with approximate ages they may gain the skill.

  • More: A child can understand “more” and “not enough.” If you give them fewer goldfish crackers than they want, they will say “more.” (1 year old)
  • One and two: Can “take one” or “take two”.  Start to see one-to-one correspondence.
  • Can count to 4 sometimes, but they may count some objects twice, skip others. can recite several number words in sequence, but not always in the right order. 1-2-3-4-6-5-7-9  (By end of second year.)
  • Can say the number sequence 1 – 10 reliably. (3 years)
  • Many count up to five items, some can count up to 10, and a few can count to 20. Can say the next number in a sequence: “What numbers comes after 4 – 5 – 6….” (4 to 5 years)
  • Given two numbers between one and 10, can tell which is larger. (5 years)
  • Can count the numbers up to 100, can count 20 objects correctly. May be able to count by twos or tens up to 100. (5 years)
  • Can do basic addition and subtraction in their heads, with answers up to 10. But they find it easier to do math with concrete objects. Can solve basic word problems. (6 years)
  • Fractions: Know that one out of two is half. One out of three is one third. Up to one fifth. Can add or subtract problems with answers in the teens. Can compare fractions like ½ and 1/3 and say what is more; Count by 5’s to 100; some can count by twos to 20. Can read and understand words like equal, greater than, and match them to their symbols. Can estimate number of items in a collection. (6 – 7 years)

Practice / Learn Skills:

These ideas are in order of complexity. Start with the easy ones at the top of the list!!

  • Notice amounts – “you have lots of blueberries, I have a few”
  • Count  – practice saying numbers in order. At first, this is just rote memorization – they don’t really understand the meaning of numbers yet.
  • Sing number songs, like 5 little monkeys or 5 little ducks.  There are LOTS more counting songs at
  • Talk about order – “first we do this”, “we are third in line”
  • Teach one to one correspondence by having them count objects. There’s lots of great tips at, like give child a muffin tin with 6 cups, and six objects – encourage them to put just one in each hole. Then an egg carton and 12 objects. Then set the table, setting out snacks on plates… I also really like the book Old MacDonald’s Farm (Poke-A-Dot!). It’s a counting book with little plastic dots that they “pop” as they count them.
  • Teach them to count on their fingers – check out this great article on how valuable this skill is for math learning: Math at Your Fingertips! Easy Counting Activities Using Number Gestures
  • Read counting books. (I list some favorites here.) Play “what comes next” – so when you’re on the page with five puppies, ask them to guess how many puppies will be on the next page.
  • Don’t always start at one. When you’re on the fifth stair, say five, then six, then seven.
  • Help them realize that two means the same thing whether you’re talking about two dogs, two shoes, two crackers, or two toys.
  • Show how even if you re-arrange things to take up more space, it’s still the same number: Line up 3 toys and count them. Then make a triangle shape and count them. It’s still 3!
  • Show you can count objects in any order and you still get the same sum total objects.
  • When counting, push things aside after you’ve counted them. (Or cross off pictures as you count them.) This teaches a good strategy for counting a large number of objects. (As they get older, you can show how to group into sets of ten as you count.)
  • Counting on – after they’ve counted three blocks, give them two more, and encourage them to say “four, five” rather than starting all over from the beginning.
  • After age 4 or so, play any board game that works on the principle of roll your dice and move your piece that many spaces.
  • Add scoring to any physical play game – when you make a basket, it’s one point. Once they’ve mastered that, then do something like if you get a rock in the blue square it’s 2 points, red square is 5 points, yellow square is 10 points.
  • As they get older, encourage them to estimate first, then count. Estimating is tricky for kids!
  • Adding and subtracting: first work a lot with “more” and “less.” When  you put one more in a pile, you added, and you have more. When you take one away, you subtracted and you have less.
  • Play with number lines. Different combinations of numbers can yield the same sum.
  • By age 5 or 6, start working with place value: 1’s, 10’s, 100’s. Some math manipulables can help with that, such as Unifix Cubes, Base Ten Blocks and Cuisenaire Rods.

Click here to read more about teaching math to kids.

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