Inquiry in K-5 Math Marian Small June 2017

Our focus today What could inquiry in math look like? It could be inquiry into the world using math. It could be purely math inquiry. We will look at both at primary and junior levels.

Inquiry using math People talk about things called giant steps and things called baby steps. How “big” or “long” do you think a giant step or baby step is? How many baby steps would make a giant step?

Mathematically This leads to students realizing that a measurement value is big for one of two reasons (or both). The unit used is small AND/OR the object being measured is big.

Where else does this lead Kids could investigate: Sizes of different animal’s footprints vs pawprints “ratio” of hand size to foot size for people and various animals

Where does this lead The relationships between various measurement units and how knowing about one unit allows you to predict results with another unit

Other measurement ideas What are typical hair lengths (in cm) for various age, cultures? What is long hair in those cultures at those ages?

Other measurement ideas If a traffic jam was reported and it said that 100 cars were at a standstill, what distance would that cover?

That could lead to How long must parking spaces be? How about the width of the “lanes” between them? How wide do streets need to be to allow parking on one side and two-way traffic, parking on both sides and one-way traffic, etc.?

It might be How much paper does a school typically go through in a year? How can you find out?

It might be How big a space (in cubic metres or cubic kilometres) would you need to hold ALL the people in PEI?

It might be How much sand is usually needed to fill a sand area at a public park? How much faster is it to fly than drive to ….?

It might be How many sections are in a typical grapefruit? What is the range?

It might be How big is an Ipad screen compared to a cell phone screen? A TV screen? A laptop screen? What about an Ipad mini?

It might be How many windows does a typical skycraper have? How could you predict without being there and counting every window?

It might be How much slower is traffic during rush hour?

But then there are mathematical inquiries We can pose all kinds of things kids could inquire about in math. Some might come to you as you watch them play, but some will be more deliberately selected to bring some ideas to kids’ attention.

For example Kids in K might be playing on a walk=on number line. You could ask them for different ways to get to, e.g. 10. Or you could pose a problem like this:

A problem You were standing on the number line at 5. You went forward some and then back some and you ended up at 7. How far forward and back MIGHT you have gone?

You could continue What if you did it twice (same forward and back combination twice)? If you started at 5 and ended at 11, what might you have done?

Another investigation You notice kids are playing with square tiles making designs. You could take it to this problem.

problem You made a design that had ALMOST half red tiles. What could it look like? OR

PROBLEM You had some red tiles. You had one more blue tile than red. You had two more greens than blues. How many tiles could you have used? X, x + 1, x + 3 so total is 3x + 4 so min is 7 and numbers go up by 3s

It could be about counting Choose a number of counters, but more than 20. Can you make 3 equal piles with it? Can you make 2 piles, one double the size of the other? Can you make 3 piles, one double the size of another?

Or Students make some structures with linking cubes. You have them put them out and then ask how to rebuild every structure so it is upside down OR so it has only one face the same as it used to look and all the others different.

OR You might investigate what a structure could look like if the top looked like this:

OR You might fold a piece of paper in half or fourths or eighths and hole punch and predict what you will see when you open it.

another situation Kids might be adding and subtracting numbers and you might ask any of these questions:

Addition & subtraction-inquiry 1 You choose two numbers. The answer when you add is twice as much as the answer when you subtract. What could they be? What do you notice?

Addition & subtraction-inquiry 2 You choose two numbers. You add a number to another one. The answer is about triple the smaller number. What numbers might you have added? What do you notice?

Addition & subtraction-inquiry 3 You choose two numbers. The answer when you add is 10 more than the answer when you subtract. What could the numbers be?

You might wonder which is the lie You can add 3 numbers in a row and get the number 74. You can add 4 numbers in a row and get the number 74. You can add 5 numbers in a row and get the number 75.

You might wonder which is the lie 1. It is possible to show the number 534 with 21 base ten blocks. 2. It is possible to show the number 121 with 13 base ten blocks. 3. It is possible to show the number 1048 with 23 base ten blocks.

It might be about multiplication or division You multiply two numbers and the tens digit is 1 more than the ones digit. What numbers might you have multiplied?

Maybe it’s about fractions You might notice that 2/3 > 1/5 and that 2 and 3 are closer together than 1 and 5. So the inquiry focuses on--- If the numerator and denominator are closer together, is the fraction always greater?

OR You might wonder if when you add 5 to a numerator and 5 to a denominator, the fraction gets bigger or smaller or stays the same.

Or You might wonder– can the numerator and denominator of a fraction equivalent to 2/5 be 100 apart? 90 apart?

You might wonder Is it possible to show the same amount of money with 8 coins as with 20 coins? How?

You might wonder If you paid for something with a $20 bill and you get 1 bill and 4 coins back, how much might it have cost?

You might wonder If you cut a rectangle on a line of symmetry and only use half the rectangle, what fraction of the old perimeter can the new perimeter be?

You might wonder A rectangle has a perimeter 3 times its length. What could the length and width be?

3-act math Graham Fletcher examples https://gfletchy.com/paper-cut/ https://gfletchy.com/graham-cracker/

So let’s work together What kind of inquiries can you put together while I’m still here to support you?

Many other examples

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