We played more Domino War this week, but added a recording sheet that prompted us to think about equations and equivalencies, and greater than/less than notation. Please play this game at home; it is surprisingly fun and offers lots of opportunities to talk about numerical relationships. If you draw a 5/6 tile, you can verbalize how you could see it as 5+5+1, or "I know 5+5=10 so 5+6 should me one more than 10". Share how you think about the sums and ask your child on every turn how they found the sum. They might say that they have that one memorized which is great, but push a little and ask them how someone who didn't just know it could figure it out.
We also started being more metacognitive about addition strategies. We discussed:
using facts we know to figure out the ones we don't know
just knowing from memory
Most kids in the class are using a variety of these strategies for different problems and we will introduce more addition strategies as their repertoire of memorized facts becomes more robust. One of our goals this year is to move everyone out of counting strategies into additive thinking.
This week we did more visual estimating with beans, worked on place value understanding, and +/-10s. For example, 67 + 20. Being able to +/- 10s is important to the more sophisticated adding and subtracting strategies we will develop this year.
We started a brief metric measurement unit this week that also allows us to explore scaling up and down my powers of 10. This is an inroad to multi-digit multiplication. Please be clear when you talk to your kids about multiplying by 10, often kids are told that x10 means you add a zero. First, x10 does not mean the same as +0; and that rule does not work for fractions and decimals multiplied by 10. When we give kids tricks and rules that are not transparent or generalizable, we imply that math is rules to follow and it is not something that should make sense. It is more accurate to talk about x10 as shifting the digits to the left by one place value because each place to the left is 10 times bigger. I used to make the mistake of talking about shifting the decimal point to the right, but that doesn't make sense - shift the numbers to the left.
We explored clock fractions this week. Money and clock fractions give us handy common denominators we can readily use because we carry the equivalencies in our heads. For example, 1/15 + 1/2 is like 4 minutes + 30 minutes, or 4/60 + 30/60 = 34/60.
We worked more with arrow string notation this week. The homework is pages 10-11. We also worked on a rich task about the price of off-the-menu items at In-and-Out Burger. Ask your child about it. It is optional to find the price of a 5x5 cheeseburger. We will find the price of a 100x100 next week.