Several years ago at my very first math conference, I accidentally walked in to a session for elementary teachers (before learning that they were categorized by grade levels for you). It was on Singaporean Math, where I finally understood what “number sense” meant.
Out of all the epiphanies and eye-openers that I was absolutely amazed to learn, I have some strategies that have been working with my high school students that I’d like to share here.
But first, if you don’t know what the difference between having number sense and counting is, read this following section. If you already do, you can skip on past the next line.
When we add 3+2 in our heads or add 7+3 in our heads, even 6+7, do you actually count out the numbers? Of course not. Most people have developed what is called number sense, which to me, is a type of visualization of the numbers.
What does good number sense look like in:
- young children (kinder-1st)?: If I flash 3 fingers and pull them away immediately, can they identify that it was 3 fingers without having been given time to actually count them? If so, they are developing good number sense.
- early elementary?: Can they add 7+8 in their heads without counting? Can they immediately say what 26-6 is?
- Late elementary: Do they conceptually understand fractions? Fractions inherently require number sense. For example, can they draw and understand 4/3?
So, back to the high school setting. These activities are geared more towards the classes packed with students who lack number sense completely. Classes like pre-Algebra, Algebra support, or if you’re tutoring one-on-one.
#1. Finger Flashes (particularly for those students who count 8+2 on their fingers)
This works best when tutoring a student one-on-one (or for early elem kids).
Flash 1, 2, 3, 4, or 5 fingers on one hand and pull them away immediately and ask them how many fingers you had just held up. They should not have needed any time to count them. They should have just seen them.
After they master seeing up to 5 fingers immediately (usually less than 10 tries), move on to randomly flashing 6, 7, 8, 9, and 10 fingers. It is important that one hand always has the full 5 fingers up (no 4 fingers up on one hand and 3 fingers up on the other for 7). Remember, the whole goal is to get them to see the groupings of 5.
Once they master this, this is when you start asking them, at random, what 5+1, 5+2, 5+3, 5+4, and 5+5 is. Teach them explicitly to visualize the 5 on one hand and the second number on the other.
Then move on to asking them to do 10+1, 10+2, 10+3, etc. Then maybe add in 13-3, 15-5, etc. You get the idea? Always work in groups of 10.
#2. Up/Down (for working in groups of 10 again)
This is a verbal game that you can play with them for about 5 minutes a day. When I call out a number and “UP” or “DOWN”, like “14 UP”, the kids should respond with how many steps it takes UP to the next group of 10. So in this case with “14 UP” the answer would be “six” because it takes 6 steps UP to the next group of 10, which is 20.
To make sure everyone gets a fighting chance, make sure to train your class to only respond after you say “GO”. Threaten them with the fact that you will call them out individually if they do not respond out loud.
I say: “37 UP… GO”
They say: “3”
I say: “28 DOWN… GO”
They say: “8”
I say: “94 UP… GO”
They say: “6”
I say: “42 DOWN… GO”
They say: “2”
Based off of this, with my high schoolers, I’ve actually added a series of saying numbers in the hundreds and still asking how many steps to the next group of TEN. I then graduated them to saying negative numbers with UP/DOWN.
I say: “-37 UP… GO”
They say: “7”
I say: “-28 DOWN… GO”
They say: “2”
I say: “-94 UP… GO”
They say: “4”
I say: “-42 DOWN… GO”
They say: “8”
After playing this in the beginning of the school year while they are working on their times table in their folders, I then add worksheets based off these 2 activities for after they pass all their times tables…
These worksheets are in development and a post on them shall be made one day. In the meantime, I’ve just dropped what I’ve got into the Box widget to the right.
website to generate own worksheets