When I tutor children in math, the first thing I do during
their assessment is to find out where their number sense falls away. Can they subitize the number 4? 7?
Subitize means to look at an amount of something (like four
blocks, or two forks) and know how much it is without counting.
I need to distinguish between number and numerals. Number is an amount. Numerals are the written representation of
that amount. 1, 2, 3, 4 are
numerals. While recognizing and writing numerals is important, it doesn't necessarily mean that a child has a strong number sense.
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| This cutie is demonstrating the equation 1 - 1 = 0. Genius little cousin of mine Peekaboo! |
My general rule of thumb for children aged one through five is
that the amount a child can subitize directly corresponds to their age. So, a three year old can usually understand
the amount of three, but the number four is a little trickier.
You may be thinking that a one year old can’t
understand the number one. But they
do. When they play Peekaboo, they see
one thing (like your face) and then it goes away (behind a blanket). The equation 1-1=0 is hysterical to
them. Even though your one year old
probably will not recognize the numeral 1, he or she CAN understand the amount
of one. Your baby is a genius!
Playing some simple games with your three to five year old will help them develop a better Number Sense. This process is also VERY helpful for early elementary students who struggle to understand number concepts. (I ALWAYS assign these games to my struggling math students.)
Many of the games I will
present today come from the book Developing Number Concepts Using Unifix Cubes by Cathy Richardson. Sadly, this book is
out of print, but it is worth tracking down a used copy. Amazon and Ebay usually have several inexpensive
copies available. This book has
activities that strengthen skills in addition, subtraction, multiplication,
division, patterns, and so much more. I
think it is worth every penny.
You don’t need fancy schmancy math manipulatives to help
children develop a Number Sense. One of the first things I do with my young
learners is to find an age appropriate small toy that they like to play with to use as counters.
Shopkins are popular for girls. Or you could use Lego Mini figures for boys, or
just some plain Legos. Beans are cheap,
but not as motivating. M&Ms are just
a little too tempting for my taste. If you have Unifix cubes, this is a great
way to use them. Get a butter container
or a plastic cup- anything that is not see through and that is large enough to fit all the counters inside.
We are going to focus first on the number (amount) as opposed
to the written numeral. We’ll get to
numerals eventually.
Game 1 : How many are in the tub?
Secretly put a number of counters under a plastic cup. Have the child peek under the cup and quickly
subitize (know the amount without counting) the answer. Repeat with another amount.
Game 2: Matching Number and Numeral Correspondence
Put one counter under the first cup, two counters under another
cup, three under a third cup, four under another cup, and five counters under
the last cup. Mix them up. Make a numeral card for each of the number
amounts used. Turn them over and mix
them up. Take turns looking under the
cup to subitize the amount, and turning over a numeral card. Try to match the amount with the numeral
card.
Game 3: Making Equations
Step 1: Start with one less toy than your child’s age. My son is 5, so I’m going to start with four
Lego Mini figures. Show your child all of
the toys. Then secretly put one of the
counters under the butter tub. Put the
remaining toys on top. Ask the child how
many are under the cup. Most children
should be able to know how many are in the cup. If the child has no idea, start
with a smaller amount. If this seems a
little two easy, you can increase the beginning amount by one.
Step 2: Repeat Step 1, but put two counters under the cup
instead of one. Then three, etc. Do not
go on to a higher beginning amount until you have completed at least steps 1-5.
Step 3: When you feel like your child has an understanding
of how many are in the cup, start using some math language. “There are 3 on top of the cup. How many are inside the cup?” “One” “Yes. One counter is inside the cup because one
plus three equals four.” And “I have four counters. I’m going to put some inside and 2 on top.
How many are inside?” “Two” “Yes, because four minus two equals two.”
Step 4: Now each
time you play the game, show the child the written equation. 1 + 3 = 4.
2 + 2 = 4. 3 + 1 = 4. This is also subtraction . 4 – 1 =3. 4 – 2 = 2.
Step 5: Feeling daring?
Did you know this game is really ALGEBRA? Your four year old is a smartypants. Use the term “unknown.” Say this: “I’m going to start with four
counters. I’m going to put an unknown
amount under this cup. There are 3 on
top of the cup. What is my unknown
amount?” After the child answers, show your child this equation. x + 3 = 4. (This step is not from Developing Number Concepts. It's just from me. I learned the value of exposing Algebra to young children from the Life of Fred Books. You can read my LoF review here.)
This game can take just five minutes each day. You could start with the first two steps,
then add a step each day. After a week, increase your beginning number of
counters by one, and follow the steps.
Step 6: Eventually you can have your child copy the
equations on a marker board or a piece of paper.
Step 7: See if they
can write the equation on a piece of paper without any prompts. There are three different ways to write any
representation. 1+3 = 4. 4-1=3. x
+3 = 4 are all the same thing. You could also have them practice writing
them vertically.
These are just a few of the games found in Developing Number
Concepts Using Unifix Cubes that I use with so many of my students. Whether your child is in PreK or Kindergarten
or is struggling to retain math facts in elementary school, these games are sure
to help your child succeed in math.
Need more help? I love tutoring elementary children in Math! Let me know how I can help your child.
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