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Common Core Math for Parents

 

About Common Core

It’s easy to feel upset by Common Core, because it’s new and it uses terms that are not familiar.  But the ideas behind Common Core make sense to me:

  1. Children should be learning roughly the same thing in first grade, whether they’re in Oregon or Ohio (that way, if they move, they’ll know more or less what’s going on.)

  2. Teachers across the country should be using the best, most up-to-date methods. 

With these principles in mind, the Common Core process brought together teachers and parents from around the country over a period of years.  What they came up with is Common Core.

  1. For English Language Arts (ELA), the focus is on thinking critically, thinking about what the text says and how it makes its point.  There’s a focus on nonfiction, as well as fiction. 

  2. For Math, the focus is on flexible thinking – different ways of solving problems and thinking about numbers and quantities.

You can read more about this history, and find links to reliable information on Common Core at www.corestandards.org

This site includes a helpful collection of frequently asked questions. There’s a guide for parents who want to help their children with Common Core homework. And you can read the actual Common Core standards if you want.

As for Math:

Common Core teaches new ideas along with the old methods, not instead of the old methods. The ideas in Common Core make it much easier to do math in your head (mental math) which turns out to be an important skill.  Being able to think flexibly about numbers helps all through school.

Key ideas in addition:  Groups of ones, tens, hundreds.  Place-value shows what it’s a group of (a group of 1s, or a group of 10s, or a group of 100s).  It’s easy to add up 2-digit numbers which end in 0 (just add up the first numerals, and add a 0 to show that you’re adding 10s). Numbers can be broken down and put back together in different order.

For example:  15 + 28 =__

think of this as 1 ten and 5 ones + 2 tens and 8 ones; or (10 + 5) + (20 + 8),

move the parts around to make (10 + 20) + (5+8),

add up the 10s and the 1s separately, to get 30 +13

break up the 13 and move the parts to get (30 +10) + 3,

solve the easy problem 40 + 3 = 43.

Key ideas in subtraction:  Subtraction is the distance between locations on a number line.  Counting forward the way you do when making change at a store.

For example: 45 - 18 = __

Start at 18, add 2 to get up to a nice round number (20)

Add 10’s to get up to a round number that’s close to your goal: 20 + 20 = 40

Add 1’s to get the rest of the way: 40 + 5 = 45

Add up all the bits that you’ve added: 2 + 20 + 5 = 20 + 7 = 27   That’s your answer!

Word problems are big in Common Core Math. 

For example: You’re at a store. You buy some candy that costs $1.56.  You hand the cashier $2.  How much change should you get back?

Start with the price, $1.56.

Add some pennies to get to a round number: $1.56 + 4 cents gets you to $1.60

Add some dimes to get the rest of the way to $2, counting by 10s: 

160 +10 = 170,

170 + 10 = 180

180 + 10 = 190

190 + 10 + 200 —you’ve added 4 dimes, or 40 cents. 

Add up all the bits you’ve added: 40 cents + 4 cents = 44 cents    That’s your answer!

Key ideas in multiplication:  Think of pictures: big rectangles made out of rows of little squares (it helps to have physical cubes to move around).  For small numbers it helps to have some basic facts memorized.  With larger numbers, you can often change these to problems using smaller numbers.

For example: 5 x 7 =___

You might have memorized this fact, but maybe not. 

Think of it as a rectangle with 7 rows, where each row has 5 cubes.

Notice that you can add some space between a couple of the rows, so that you get easy groups.

In this case, you know 5 x 5 = 25 (you memorized it), so you move the top 2 rows up a bit, and now you have 5 x 7 = (5 x 5) + (5 x 2).  You recognize each part, as 25 + 10 = 35.  That’s your answer!

Key ideas in division:  Think of filling up a certain number of buckets, each with the same number of stones (or chocolates). You can count by 1s, or by 5s, or by 10s.

For example: the problem is 105/15 = __

Imagine that you have 105 stones, and you want to fill up 15 buckets.  If you just started adding one stone to each bucket, you’d eventually fill them all up. You could then count the number of stones in each bucket.  This would take a long time.

You could try adding 10 stones at a time to each bucket, but you’d run out of stones before you got to the last bucket.

But, if you added 5 stones at a time, you’d use up 5 x 15 stones.  You do the multiplication: 5 x 15 = 5 x (10 + 5) = 50 + (5 x 5) = 50 + 25 = 75.

You had 105 stones, and you used 75.  How many stones are left? You could count up from 75 to 80 (5 stones), then from 80 to 100 (20 stones), then from 100 to 105 (5 more stones) for a total of 5 + 20 + 5 = 30 stones; or you could just notice that since 70 + 30 = 100, 75 + 30 = 105 (see subtraction above).

So, with 30 stones left, in 15 buckets, you could start adding one stone at a time to each bucket. You’d find that after one round you had used up 15 stones, and after 2 rounds you’d have used up all 30.  Or you might remember that 15 x 2 = 30.  You have to add 2 more stones to each bucket.

How many stones have you added to each bucket? 5 + 2 = 7.  That’s your answer (105/15 = 7)!

This s just one of the clever ways Common Core teaches division; it also teaches the old-fashioned “long division”.  The point is, these are just different ways of thinking about the same problem.  Many kids do better thinking about physical objects (stones in buckets) than about numbers that float around on a page.

 

It isn’t easy to learn new things.  Your children have to do this all the time, of course!  Let them see that you approach the challenge with resolve and good humor.  That’s probably the most important lesson, in the long run.

[this page was last updated by Robert Needlman, on 11-25-2018]