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

Continue reading Teaching Decimals with Decimal Squares

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