## WHAT IS A SANDWICH UNIT?

We teach 5th grade fractions using a “Sandwich” strategy.

## Review Lesson: Fractions, Word Problems and Patterns.

These 4 problems actually took a whole period! Problem-solving takes time.

CW review

We did this review in groups of 3, with some students rotating after each problem, but the rotation is not necessary. (See Alpha Beta Gamma post from Sept) Rotation breaks up the period with a little movement, and decreases group competition.

### Problem #1: Claire has 4 cookies more than Max. Max has 3 times as many cookies as Oliver. Altogether they have 81 cookies. How many does Claire have?

VERDICT: The kids have got it now.

## Starting the Multiplication Unit

We believe there are 3 non-negotiable skills for fifth graders moving on to sixth grade:

• Fractions
• Multiplication
• Division

Accordingly, we spend more time on these 3 units than most schools do, although we work in a handful of additional topics as well. The payoff comes later —  middle school (and high school!) teachers don’t have to reteach these topics. A goal in itself!

## Multiply and Divide by Powers of Ten

Interestingly, this was one of the most difficult lessons we’ve taught this year, both for teachers and students. There are several possible reasons:

## 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:

## Galaxies, Pennies and Grains of Rice

Learning is an emotional pursuit. A teacher’s most powerful ally is success. Students who can see (“feel”!) their own progress will bring up the perseverance needed to master each new concept.

However, there are times when math should just be fascinating. When we should all step back and say “Wow”.

## 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.

## Looking at Quizzes- Part 2 … How are we doing?

Quiz 2, Trimester 2, as a Word Document:

Question #1: Fractions.  Everyone was able to solve this problem correctly!  This is huge. Fractions matter.

## 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.