Division and fraction for beginners

A script of our game: dividing

Stage 1

Me: "Let's start with a number. Hmmm, which one?"
Eldest: "12!"
Me: (Oh good one!) "Okay, can you share 12 crayons with 3 people. Make sure everyone gets the same amount of crayons."
Eldest: Starts to separate them all by ones.
Me: "That's a lot of people. How many people were we sharing with?"
Eldest: "Oh." Starts to make groups with 2 in each.
Me: "How many do I get?"
Eldest: "Two"
Me: "What about your sister?"
Eldest: "Two"
Me: "What about you?"
Eldest: "Two"
Me: "But that leaves a bunch of crayons. Why don't we start by giving one to each person and then do it again until we have no more crayons?"
Eldest: "Okay." Starts handing them out. Fights ensue over which colour each gets. Finally...
Me: "So how many do we each get?"
Eldest: Counts "Four."
Me: "So what is 12 divided by 3?"
Eldest: Thinks a minute to figure out why I changed the words from share to divide. "Um..."
Me: "How many is in each group of crayons."
Eldest: "Four"
Me: "So what is 12 divided by 3?"
Eldest: "Oh. Four."


Stage 2

Me: "Do you remember when we divided 12 crayons?"
Eldest: "Can I draw?"
Me: "Yes, can you draw 4 circles, make them big because we are going to divide some numbers into 4 groups."
Eldest: "Okay."
Me: Takes out 4 counters. Writes 4 divided 4 on a slip of paper. "Can you divide these 4 counters into these 4 circles?"
Eldest: Hesitates. "Like this?" Puts all four in one.
Me: "No. You want to make sure that each circle gets the same amount. Divide the counters into 4 circles. Divide by 4."
Eldest: Puts one counter in each circle.
Me: "Tell me how many is in each circle. What is 4 divided by 4?"
Eldest: "One."
Me: "Good! Let's try it with a bigger number. Let's divide 8 by 4."

This game continues with different circles and different amounts of counters until the words 'share' 'same in each circle' etc.. are entirely dropped and only divided by and equals are used. It can also be done with blocks making evenly sized towers. This is great for making sure that you have divided evenly - all the towers are the same height.

Of course, if your child gets bored, it is good back to concrete examples such as plates and raisons. In fact, in order to use math effectively, concrete examples should never be abandoned entirely. This ensures that instead of word problems being difficult, they are easy, maybe even easier initially.


The Script: Starting with Fractions

Me: "Who wants to make a pie?"
Eldest, youngest: "Me, me, strawberry!"
Me: "Okay, I'm drawing a big pie. Youngest, how many pies is that?"
Youngest: "One."
Me: "Okay, I'm going to divide the pie. Do you all want a piece?"
Eldest, youngest: "Yes."
Me: "How many of us are there?"
Eldest, youngest: Counting overtop each other. Somehow the number "Three" appears.
Me: "Okay, I'm dividing our pie by three." Cuts up pie with scissors. "One, two, three pieces. How many pies do we have?"
Youngest: "Three."
Me: "Really? We started with one. I'm going to put it together again. How many pies is that?"
Youngest: "One."
Oldest: "Just one."
Me: "Yup, but we all get a piece." Drawing on each piece, I put the fraction 1/3 and say "One piece out of three. That's one out of three. One divided by three. We divided our pie three ways. Wait. Oh no!"
Eldest, youngest: giggles.
Me: "I see a mouse. Do you see it? It's over there." Points. They both look (we hope). I take away a piece. "Hey, that mouse wasn't over there. It was over here. A piece of our pie is missing! How many pieces do we have now?"
Eldest: "Aw. We have two."
Me: "Sigh. Two. Two out of what? What did we start with?"
Eldest: "Three."
Me: "Can you say all of that so I can write it down."
Eldest: "Three. Um"
Me: "What do we have left?"
Eldest: "Two."
Me: "Two out of ?" I write two with the fraction line
Eldest: "Three."
Me: "Which is?"
Eldest: "Two out of three."
Me: Write the three on the bottom. "Wait, there's that mouse again." Point. "Hey, it's not two out of three anymore!"

Continue.

Later on,

Me: "Let's make a pie with 8 pieces: one for ..., one for ..., one for ... How many pieces do we have all together?"
Eldest: Counts
Me: As she counts, put a cherry sticker or counter on each piece.
Eldest: "Eight."
Me: "So what should we put on the bottom?"
Eldest: "Eight."
Me: "Did the mouse eat any? Did YOU eat any?"
Eldest: giggling "No."
me: "What number should we put on the top then? Are they all there? All ..."
Eldest: "Eight?"
Me: "Okay." Makes fraction. "Does that look right? Eight out of eight pieces of the pie."
Eldest: nods.
Me: "Did you know that this line also means divided by?" Put dots on either side of the fraction line so it looks like a divided by symbol. "What does this say?"
Eldest: "Eight" Looks at me.
Me: "Right. Go on."
Eldest: "Eight divided by eight."
Me: "You got it. What is eight divided by eight?"
Eldest: "Um... one?" (This only works if they have learned about numbers dividing by themselves in the first place obvioulsy)
Me: "Hey one is how many pies we have. How did you know that?"
Eldest: "We only drew one pie."

This game can be extended to look at adding and subtracting pies with the same number of pieces, as well as in the mouse ate two pieces so 4/4-2/4 = 4-2/4 = 2 and adding as you unevenly share pieces so that daddy gets 2/4 and kids only get 1/4 each which still adds up to 2+1+1/4. If you use two pies, you can practice converting fractions like 8/4 into 8 divided by 4 or 2 (pies).


Enjoy and let me know how it went with your kids!