Teaching Number Concepts
I am trying to teach my son a concept of positive whole numbers being made up of other, smaller, positive whole numbers. This has been a tough going so far, full of unexpected obstacles. There was, for example, the part where I tried to explain and show that although a larger number can be made up of smaller numbers, it doesn’t work in reverse and a smaller number cannot be made up of larger numbers.
An even more formidable obstacle was (and still is) showing that a larger number can be made out of various combinations of smaller numbers. Say, 5=2+3, but also =4+1 and even 1+2+2. And by showing I mean proving. And by proving, I mean having my son test the rule and prove (or disprove) it to himself.
That’s why I was very happy when I got a hold of Oleg Gleizer’s book Modern Math for Elementary School. By the way, the book is free to download and use. We’ve been building and drawing multi-story buildings (mostly Jedi academies with x number of training rooms) ever since. If this sounds cryptic, I urge you to download the book and go straight to page 12, Addition, Subtraction and Young Diagrams.
And just yesterday I found this very simple activity on Mrs. T’s First Grade Class blog, via Love2Learn2Day‘s Pinterest board. All you need for it is a Ziploc bag, draw a line across the middle with a permanent marker, then add x number of manipulatives. Took me like 2 minutes to put it together, mostly because I had to hunt for my permanent marker.
The way we played with it was I gave the bag to my son and asked him how many items were in the bag. He counted 8. I showed him that the bag was closed tight, so nothing could fall out of it or be added to it. I also put a card with a large 8 on it in front of him as a reminder. At this point all 8 items were on one side of the line. I showed him how to move items across the line and let him play. As he was moving the manipulatives, I would simply provide the narrative:
Ok, so you took 2 of these and moved them across to the other side. Now you have 2 on the left and how many on the right? Yes, six (after him counting). Two here and six here. Two plus six. And how many items do we have in this bag? Good remembering, there are 8. So two plus six is 8. Want to move a few more over?
It went on like this for a few minutes until he got bored with it. Overall, I thought it was a good way of teaching, especially for children who do not like or can’t draw very well yet. Plus upping the complexity is really easy – draw more than one line on the bag and create opportunities for discovering that a number can be made of more than two smaller numbers.
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Just a Little Beautiful Math Thing
One of us, Maria, recently posted this on our Facebook page:
This is what I call “lap-ware”: a little beautiful thing you show a toddler who climbs into your lap as you work on your computer. Even someone who knows nothing about math can change, say, 2 to 3 in the formula and observe the (beautiful) results. Math experimentation for the w
And the other one of us, Yelena, tried it with her son. The results where exciting and unexpected.
The first thing that my almost 5-year old boy said when he saw the original graphics was “Wow! Can I see it again?!“. That sounded promising. So I told him that not only could he watch it, but he could control it and change it HIMSELF! Immediately he was eager to try his hand at manipulating the graphics. I showed him the formula and explained that it was a coded command, called a function, that he could control by changing one, two or three parameters and put his own numbers where the original 2, 2 and 0.7 were.
First, he replaced the first two numbers only and kept the third one, 0.7, the same. He tried 1, 3, then 7. Then, as he was about to try plugging in 4, I asked him what he thought the result was going to be. Was it going to be flat, similar to what he got when he put 1 into the equation. Or was it going to be all scrunched up and spiky like when he used 7. After a bit of thinking, he predicted that, although the result wouldn’t be flat, it wouldn’t be as “wrinkled” as the result he got with 7. Even though his prediction turned out to be accurate, he was more thrilled with the ability to check his prediction than with the accuracy of the prediction.
Next, he wanted to plug in more different numbers. So we tried ages of all the family members, including our cat. In the process, I noticed that some of us were squares and others – triangles (depending on whether our age was an odd or an even number). This led to lots of giggles as we were trying to figure out who was who in our family.
As we plugged the number 100 into the formula (the age of a tree outside), something wonderful happened. My son looked at the graphics and exclaimed “Look, Mom, it’s also symmetrical!” And sure thing, it was.
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Mini Math Quest #1 – Symmetry Seekers
Ask a child to be a line of symmetry for an object or an arrangement. Children are natural symmetry seekers whether they are building with blocks, drawing with crayons, or mimicking your gestures. Help your child explore the concept of symmetry this week.
Go on a quick (just a couple of minutes) symmetry scavenger hunt around the house or outdoors. Make your own symmetrical art. Arrange toys symmetrically. Identify and clearly mark lines of symmetry. Keep your camera ready because symmetry is beautiful. Take a picture and send it to us. Don’t forget to include your child’s name (or first initial) and age.
Note: If you have privacy concerns, don’t let them stop you from participating in this Challenge. Your child’s face does not have to be in the picture. In fact, why not take a picture of your child’s shadow or a bird’s eye view (so just the top of the head is visible). The possibilities are endless!
Submissions close January 22, 2012 at 10pm EST
Send submissions to yelena@moebiusnoodles.com
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Playing Math Every Day – December 12 – 18
Math games can be played any time anywhere. Here are some ideas for each day of the week. These games require very little, if any, advance prep. Give them and feel free to change them to make math more interesting for your children.
December 12 – More Evergreen Fun
Remember our Evergreen Fun gradients game from last week? If you don’t have a tree farm nearby, you can still play it. Simply cut isosceles triangles of various sizes out of green paper or felt and let your child create her own trees.
December 13 – Magnetic Pompoms and Patterns
Have you ever tried magnetic pompoms? These are just regular pompoms, but with little magnets hot-glued to them. There are countless games that can be played with these pompoms. One of the games is making patterns and designs with them on a fridge, a cookie sheet, etc. Another absorbing game is making little pompom sculptures and figuring out in the process the difference between odd and even numbers.
December 14 – South Pole Day
On this day in 1911 the Norwegian explorer Roald Amundsen and his dogsled expedition reached the South Pole. How can it help learn math? Remember the real multiplication tables game? If one of the Amundsen’s dogs were to need warm booties, how many would it need? What if two dogs needed warm booties? Three dogs?
December 15 – Puzzles Day
Do you have a Pentomino puzzle? If not, it’s easy to make out of craft foam, cardboard or construction paper. If you have building blocks to spare, then you can use those too, just hot glue them together. Younger children might be more interesting in creating their own designs than solving actual puzzles. Still, Pentomino teachs such important mathematical concepts as rotational and reflection symmetry, chirality, and tessellation or tiling.
December 16 – Math That Is Hands (and Feet) On
Let’s continue learning about chirality by turning it into a mix of a scavenger hunt and an art project. First, let’s make some hand and foot prints. Are these symmetrical? Are these chiral? If your child needs a bit more help figuring out the answer, you can help by cutting out one of the hand prints and suggesting he superimposes it over the other print. Repeat it with foot prints. What about other objects around the house, such as blocks, LEGO pieces, sliced fruits and veggies, letters of the alphabet…
December 17 – Live Sculptures Fun
Let’s make live sculptures. The trick is your sculpture must be symmetrical to your child’s creation. But guess what… live sculptures sometimes move. Can you keep up and maintain the symmetry?
December 18 – Crazy Gumball Machine
How would your child like having a gumball machine in the family room? Well, what if this gumball machine had a mind of its own? A regular well-functioning gumball machine follows a simple rule: one quarter goes in, one gumball comes out. This machine is different. What kind of crazy wacky rule can it follow? Would it give 2 gumballs at a time? Red gumballs only? How about red gumballs for a quarter and green ones for a dime? Let your child figure out the gumball machine’s rule. Then let him take a turn controlling the machine.
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