Day 47: negative exponents can create complex fractions

I was concerned my pre-algebra students had absolutely no idea what this means.

negative exponents  They understood the rule, could apply it using numbers and variables, but I truly felt they had no idea that this problem represents a whole number divided by a fraction.

complex fraction

dividing exponents

They also had no idea that this problem was a fraction divided by a fraction.

complex fraction2

So I created a silent screencast for them to study. I didn’t narrate because I wanted the students to focus on what I was trying to convey without words. I used “pen gestures” such as circling words, the pen moving back and forth, etc.

I also created a quick and dirty handout for them to turn the problem into a complex fraction, solve it, then solve using the quotient rule.

student exponent

student exponent2

student exponent3

They realized that one third is equivalent to 3^-1.

Now I have to figure out a way to incorporate interpretative dance!


Day 46: slowing down the pace for negative decimals

About half of today’s standard class is still struggling with negative decimal addition. Students completed 6 problems and I did a quick sort to decide who to catch and who to release. Those who were released worked on pattern problems–writing an expression to find the nth term. Those who I caught worked with me. Lots of confusion when the signs are different.

Day 45: assessment corrections on exponents

The Pre-algebra students rocked multiplying and dividing exponents, but I wasn’t satisfied with their performance on zero and negative exponents. Over the weekend I graded the assessments and it was clear I shouldn’t take the negative exponents for a grade. We’ll spend more time practicing and reviewing and I’ll reassess next week. The quarter ends tomorrow so the assessment will be entered in the second quarter grade book.

As we  took a closer look at the assessment students shared their problems on the board. When it came time for this problem:


I mentioned I didn’t see anyone simplify like this:

exponents simplify

There were about 15 minutes left in the block when we had an unannounced fire alarm. By the time we got back to the room there were only a few minutes left in class.

The standard kids today were treated to the think aloud I did yesterday. Lots of struggle, but several students caught on rather quickly to adding negative decimals.

Days 42 and 43: Careless mistakes with decimals; exponent reflection

We’re heading into decimals as integers. I want to make sure the students know place value so I gave the standard classes a pre-test on adding and subtracting positive decimals. Before the pre-test, I talked about attending to precision and I specifically asked the students to rewrite the problem vertically to avoid careless mistakes.

Students shared their work on the whiteboard and we talked about each problem.  Of course I had a few who did not take my suggestion to heart. I didn’t have my smartphone handy to capture the actual student work, but below is a recreation of a mistake one student made with the first problem.

decimal mistake

This was a great mistake because it generated a conversation about place value, but I was soooo disappointed the student didn’t rewrite the problem to solve. Perhaps the problem was too easy so they didn’t feel it was necessary to rewrite it. But what’s going to happen when they encounter decimals as integers.

decimals as integers

At the end of the period one of the students I had last year came up to me and said, “I’m not being challenged by this, Mrs. Dooms.”

I said, “I understand, Mark.” I walked over to the white board and showed him a problem like the one above. “I want to make sure you remember how to add decimals because next week we’ll be doing that.” He stared at the problem, grabbed the dry erase marker, took off the cap, but made no attempt.

“Ok. I’ll be challenged next week.”

Pre-algebra reflection

On Thursday, the pre-algebra students were assessed on the exponent rules they’ve learned thus far. It ended up taking longer than expected for some so they finished up on Friday. As students turned in their assessment they stapled practice the problems I assigned as optional homework. It led to an interesting exchange with one student who chose not to do it.

“You left some problems blank.”

“I know. I don’t know how to do them.”

“We’ve done them before and they’re just like the practice problems I gave to help you get ready for the test.”

“It was optional so I didn’t do them.”

At first I’m thinking this is a good lesson for him to learn. On the other hand where’s the hole in my teaching? Why didn’t I catch that? Looking back to when the original lessons unfolded, he was showing me he grasped the concepts during individual whiteboard work. We even spent the entire block reviewing for the test. I was a hawk catching mistakes when the students practiced in pairs with the “Around the World” activity. The next time I see him I’m going to ask if he pushed the Expo marker or did his rotating partners do the work.

I need to reintroduce exit slips.

Day 41: Order of operations

I remediated most of my standard students today with more integer review of multiplication and division. Since there were five in the class who already mastered the topic, I had them review order of operations while I worked with the rest of the class on integers. Of those five, only one needed remediation and it was minor. I then cast them into the hall to practice some advanced order of operations problems.

About twenty minutes later the rest of the class worked on order of operations. A few students remembered the rules so they moved quickly to independent practice. The rest of the class worked with me. I used worksheets generated from this website.

The common core standard is listed as 6.EE, but the seventh graders needed the practice.

Day 40: review day for both classes

Today was a good day. Only a handful of my standard students need to reassess multiplying and dividing integers. I could let the students who demonstrated a level of proficiency of  2.5 (equivalent of 80%) off the hook and not reassess, but I want all of the kids to meet the standard.

“But I’m happy with an 80%.”

“Your parents and I want you to reach your full potential.”

“What if 80% is my full potential?”

“Then the retake will confirm that.”


After reviewing the first assessment the students who earned a level 3 or higher were given enrichment problems and used the doceri app on the iPad. The rest of the class reviewed problems using the the white boards.  As the rest of the class “got it” I let them pair up with the iPads. With about 25 minutes left in the block the entire class was sharing iPads. What a treat for them!


The pre-algebra students spent most of the block reviewing the exponent rules they’ve learned thus far. They like doing around the world. They pair up and they’re stationed at either a jumbo whiteboard or a wall mounted whiteboard. They number their station and every two problems one person rotates, creating new partners.

The assessment is on Thursday.