Teaching Decimals with Decimal Squares

The most visual, most fun way to learn decimals is with decimal squares.

We use decimal squares we bought from https://decimalsquares.com  several years ago. 

They show decimals in tenths, hundredths and thousandths, and the equivalencies are obvious. (see below)

The website has fun interactive games, too, but you need to download the Shockwave app to play them.

ACTIVITY ONE – The “I HOPE I GET…” Game

For 2, 3 or 4 children.
Materials Needed: Deck of decimal cards.

To play: Shuffle the deck and lay face down on the table. Player #1 turns over the top card and lays it face up on the table. She looks at the card and says which card she hopes to draw in order to make 1 (For example: if she sees 3 tenths, she says “I hope I get 7 tenths!”). She draws a card. If she can make 1, she tells the other player which cards add up to 1 and takes those cards. If not, she lays her card face up to the table top. Suppose she draws 5 tenths — then she has to lay it on the table.
Player #2 then says which cards he would like to draw in order to make 1 using the cards already on the field. For example, since .3 and .5 are lying on the table, (all cards on the table are shared) he says “I hope I get 7 tenths, or five tenths, or 2 tenths! (considering he could add the .3 and the .5 to make .8, and he would need a .2).  He draws and then either makes 1 or, if not, lays his card on the field and play goes back to Player #1. Combinations of more than two cards are possible and desirable, since the player with the most cards at the end of the game wins.  We like this game because no one says “I hope I get POINT SEVEN”. They can see the 3 tenths in red, so they hope they get 7 tenths (of course, 70 hundredths would be fine, too!)

ALTERNATIVE GAME:  “WAR” Each student gets their own stack of decimal cards,  face down. At the same time, they both turn over one card. The largest decimal wins. Gradually one student’s pile gets bigger and bigger… it’s competitive, but it relies on luck, so students accept defeat when it happens!

ACTIVITY TWO – Number line

In 4 groups, students get 3 or 4 cards (mixed decimal and fraction cards).
The rules only allow one student at a time to tape up a card on their number line. Students take turns putting up one card, then they go to the second round, etc.  They cannot grab someone else’s card.
They usually start with their most obvious cards (1/2, 1/3…) and work from there. And yes, they make mistakes, but they’re thinking. Sometimes we point to 2 or 3 cards (if one of those 3 is wrong) and ask if everyone agrees.

ACTIVITY THREE – Make 21

In groups of 2 or 3, students play the traditional game of Blackjack, but their goal is to make 21 tenths. Suppose a child receives 2 cards from the dealer (we let the dealer play, too), let’s say 5 tenths and 75 hundredths. They usually say “12 and a half tenths” and they usually ask for another card. (“hit me”…:)   If they get 4 tenths (or 400 thousands), they have 16 and a half tenths, and they should hold, but usually they ask for another card and go over. You can play it online, too, at decimalsquares.com

We find we don’t even have to teach any “addition of decimals” rules. These games create a natural understanding of quantity.

Next post: Introducing Decimal Multiplication

 

And Quizzes? How are we doing?

Word doc:   Quiz 3

1. Fractions.

Yay – we’re getting this!  Multiplication plus subtraction with borrowing. Example 3 below is one of the few with a mistake, and its last step is correct, it’s the first step that’s not.

Screen Shot 2019-01-22 at 4.24.08 PM

THIS  problem, however, lead us into the pit of confusion.  Only the last example below is correct, but the others came very close. It tells us what we still need to work on.

Screen Shot 2019-01-22 at 4.26.36 PM.png

2. (Level 2) Multiplication and (Level 3) Different Bases

Multiplication is going well, too. Our students did a lot of area modeling in 4th grade. Exploding Dots helped many students visibly see what it means to borrow and carry within the place value chart.

About 40% of the students tried the Challenge Questions. These challenge questions were useful in clarifying place value relationships for our fastest students who otherwise would say, “just tell me the steps”!

Screen Shot 2019-01-22 at 4.31.05 PM.pngScreen Shot 2019-01-22 at 4.30.55 PM.pngScreen Shot 2019-01-22 at 4.31.27 PM.png

 

Homework: Goals and Structure

Recent Homework assignments:  (mostly available as Word documents)

HW#1       HW#2         HW#3     HW#4     HW#5      HW#6   HW#7   HW#8

Solution Keys:  HW_keys#1to#8

What are our main goals in assigning homework?

  1. Provide thoughtful practice, not drill. Hopefully in an independent setting, without help, so we can see how the learning is going.
  2. To allow for long periods of time (weeks) to repeat the visual representation of important topics. We only do one problem or two per topic. Fractions, multiplication, division, decimals. Here we withhold the algorithm for weeks, until the concept is internalized.

A few notes on our HW problems: Continue reading Homework: Goals and Structure

Experimenting with 3-act Activities

We’ve heard so much about 3-Act activities. Here’s this week’s experiment, with our verdict at the end.

Day 1…

Does $1 million fit in a briefcase?

Show this GIF:

Episode 15 Money GIF - Find & Share on GIPHY

Ask… “Would $1 million fit into a normal briefcase, and if so, could an average adult carry it? Assume the bills are all 100s.

When students asked for more info, we looked up the following  (on the internet):

Continue reading Experimenting with 3-act Activities

Part 2 of “What Does Remediation Look Like?” Michael’s silence. Plus Exploding Dots.

In our last blog, we asked, “How do we humans react to confusion and difficulty?”

  • Amelia claims grumpily “I don’t get the multiply and divide by 10 thing.” She tends to get grumpy when confused.
  • Michael withdraws into silence. “Shall we get the blocks for this, Michael?” Silence. “Which part is confusing?” Silence. Sigh.
  • Tomas minimizes his struggles. “I’m fine now. I was just confused on yesterday’s quiz. I’m good now.”
  • Nicole writes notes to us on her quiz. “I need more instruction in this concept. It makes no sense at all.”

Continue reading Part 2 of “What Does Remediation Look Like?” Michael’s silence. Plus Exploding Dots.

What Does Remediation Look Like? Aka “Bring Your Knitting”

How do we humans react to confusion and difficulty?

  • Amelia claims grumpily “I don’t get the multiply and divide by 10 thing.” She tends to get grumpy when confused.
  • Tomas minimizes his struggles. “I’m fine now. I was just confused on yesterday’s quiz. I’m good now.”
  • Nicole writes notes to us on her quiz. “I need more instruction in this concept. It makes no sense at all.”
  • Michael withdraws into silence. “Shall we get the blocks for this, Michael?” Silence. “Which part is confusing?” Silence. Sigh.

Welcome to what might be the hardest job in the world to do well.

Continue reading What Does Remediation Look Like? Aka “Bring Your Knitting”

Looking at Quizzes- Part 1 … How are we doing?

Quiz #1 as a Word Document:

 

Question 1, Fractions.  It’s Payoff Time! 

We’ve been having students draw  fractions only for weeks now. Weeks! We are gradually increasing the difficulty of the questions, to cover addition, subtraction and multiplication of fractions. We assign about 1 problem a day.  And… drumroll…90% got this problem right now. It involves multiplication and borrowing! Neither of which we’ve taught. We’ve just given students the tools to make sense of fractions. Continue reading Looking at Quizzes- Part 1 … How are we doing?

Group and Independent Practice: Multiplying and Dividing with Powers of Ten

Activity #1: Moving digit cards

There was still confusion after the activity described in our last blog. Normal, but corrigible! We had students draw a Place Value Chart on an 11 x 17 piece of paper. Something like this: Continue reading Group and Independent Practice: Multiplying and Dividing with Powers of Ten