Many of my pre-algebra kids continually seek context, so I thought I’d head them off at the pass by introducing graphing systems of equations as an exploratory activity using a couple of word problems. Here’s one of…]]>

I’ve run out of gas with my daily postings. Here’s what we did in pre-algebra on Friday.

Many of my pre-algebra kids continually seek context, so I thought I’d head them off at the pass by introducing graphing systems of equations as an exploratory activity using a couple of word problems. Here’s one of them:

We’ve been graphing linear equations for a while so I purposefully added the “How could graphing each equation help you?” question to guide their thinking.

I came to learn that some students would rather not have the context and just be given the systems to graph–it’s a lot easier. “I hate word problems,” said several students.

That’s my fault. I need to do a better job of applying these skills in context. After we talked about context it was time for some graphing practice. As I checked their work I was reminded that a few haven’t improved their “number sense” when it comes to graphing. I wish I had snapped a photo of one student’s work, but I’ve recreated it below.

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Yesterday Algebra’s Friend introduced me to a new professional development blog Read…Chat…Reflect…Learn! While I enjoy reading blogs for lesson ideas, I also love reading journal and magazine articles, books, research studies, etc. as another way to stay…]]>

I’ve lost track of the days, but here’s what I did today.

Yesterday Algebra’s Friend introduced me to a new professional development blog Read…Chat…Reflect…Learn! While I enjoy reading blogs for lesson ideas, I also love reading journal and magazine articles, books, research studies, etc. as another way to stay current. I’m glad I found this blog and I’m thrilled to see that it’s in its infancy, only because it makes me feel that I haven’t missed out on too much!

The current topic is feedback. The article for discussion was How Am I Doing? It offered a good overview, but what was missing was how to provide feedback using a growth mindset. This excerpt, Types of Feedback and Their Purposes, gives clear examples. One type of feedback I tend to focus on is descriptive as opposed to judgmental feedback.

When examining student work for feedback I’ve collected their work in progress, and provided descriptive feedback. I won’t kid you. It’s time consuming. But…

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Most of my energy has been depleted by reteaching a small group of at-grade-level students. This group cannot remember integer rules and the numerous steps involved with multi-step equations. I thought continual practice would help, but for these students something else is blocking their progress. Earlier in the week I spoke with our school psychologist who said, “They’re just not ready for the concepts. Have them make note cards, or use their notes.” So on Friday they made color coded note cards.

We’ve moved on to inequalities, but the group that needs to reassess two step equations will be using their note cards when they reassess.

The kids have been learning slope. I used a couple of Dan’s Graphing Stories to pique interest and launch the unit. They’ll be assessing this week.

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Here, one student combines like terms, then combines unlike terms, then maybe divides by 10? However the work from that point on is unclear.

I thought I had been breaking down the lessons into manageable parts, but something’s amiss.

I’m hoping my other standard class will have a better conceptual understanding.

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After I returned the assessments I sent the 6 enrichment students out in the hall to work on a set of problems from our pre-algebra series. The rest of the class stayed with me for another mini-lesson. I chose to begin with the distributive property because all of those students needed to see it again. Plus, those who already got one-step shouldn’t have to sit in on another one step mini-lesson. After reviewing the distributive property, those six students received additional practice problems I made using Kuta software. They stayed in the classroom and periodically checked their answers against some keys I had posted in the room. As they finished they worked on the enrichment.

The final 10 were with me as I once again walked through adding and subtracting one-step equations. I got them going on their one step worksheets (again Kuta software generated) and had keys posted for them as well. As they finished, they moved on to practicing the distributive property.

This took about 40 minutes. Four of the 10 students who had the most remediation came to see me in math lab today. The rest is homework.

The rest of the block was devoted to multiplying and dividing one step equations.

My “B” day standard class will experience the same lesson format tomorrow. Though fewer students will need remediation.

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I created a SMART board lesson and walked them through this problem:

I then gave them four problems as a handout and guided them through the first problem.

Some were still confused by which coordinates to use so I added a table with headers for them to keep track.

By the last problem the kids were sailing on their own, without the aid of the coordinate plane. Their ticket out the door was to find the distance of (1, 3) (5, 8). Only one student struggled.

The standard classes today reviewed their one step equations (add/subtract) assessment. I was pleased with the results for most of the students, but I want to add more problems with simplifying and solving. I’m looking forward to next week where we’ll be doing more complex problems.

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My standard classes on Wednesday and Thursday had an assessment on one-step equations. In pre-algebra students students explored the distance formula using this resource along with help from portions of this video. The students had some difficulty getting started so I showed the first few minutes to get them thinking about using x coordinates to find the length of the parallel line segment along the x axis.

When I gave them snippets from the video, it was just enough to get them going. Then they would get stuck. I showed a bit more of the video and they would be able to continue. We’ll keep working at it.

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After the long weekend, students needed a refresher on combining like terms. Actually they needed more instruction on applying integer rules. I was hoping to give an assessment this week on writing expressions, the distributive property, and simplifying expressions but they needed more practice.

We explored the Pythagorean Theorem. I wanted to try something different so I followed this lesson idea from the Teaching Channel. I really liked it. The kids loved it. Part of the lesson included a scavenger hunt and unscrambling anagram clues to solve a Who Done It. Instead of using technology to get the clues after solving each problem I substituted it for human contact. They had to see me to get a strip of paper for each clue. The write up is on the Curiouser and Curiouser blog.

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Writing expressions, identifying constants, coefficients, like terms and combining like terms.

An assessment on multi-step equations, variables on both sides, and special cases. When we go over the assessment, I’m continuing the practice of students first meeting in small groups to discuss answers. I then hand out copies of the key for further discussion. I’ll then take specific questions from the class. I’m finding this approach allows for much more mathematical conversation, gives students more time to carefully review their work and identify their own mistakes instead of me pointing them out to them.

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I introduced writing expressions and equations using a warm-up. I handed out four expressions.

Students shared their answers under the document camera. This led to the mini-lesson which included using a term with a coefficient instead of the multiplication symbol x and interpreting the division symbol as a fraction bar. (And the kids thought they we were done with fractions!) For the rest of the period the students worked in pairs completing this puzzle:

They didn’t have enough time to finish the puzzle, so we’ll pick it up again next week. When we debrief we’ll reflect on both strategies examine the *translations*. As I checked on the pairs I heard one student say, “Look for ‘equals 12’ to see if it matches” Another said, “Subtract means minus. Where are all the minuses?” Even though those strategies help the student complete the puzzle, the point of the puzzle is to analyze the translations. I can’t overlook that when we debrief.

Students entered the class with this warm-up:

Most chose to solve by using their newly discovered method of clearing fractions. One student chose to solve it by keeping the fractions.

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