Camping and Rates Project

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My third grade class is nearing the end of a unit on rates. We’ve been discussing tables and how to use them to record rate information. The students have been given a number of opportunities to fill in missing sections of tables when not all the information is present. They’ve been required to find unit prices of items to comparison shop.  We spent a couple days just on that topic. Whenever money is involved I think the kids are just a tad more interested in the problem. For the most part, students were able to find the unit price of items. It was a bit of a challenge to round items to the nearest cent. I used Fawn’s activity to help student explore this concept.  For example, 32.4 cents per ounce is different than 32 cents per ounce. When to round was also an issue, but I believe some review helped ease this concern. Near mid-week, students were picking up steam in having a better understanding of rates and how to find unit prices to shop for a “better buy” when given two options.

I introduced a camping rates activity on Wednesday. This was the first time that I’ve tried this activity as I have time to use it before the end of the year approaches. Here’s a brief overview: Students are going to be going on a camping trip. The student is responsible for shopping for the food (adding the unit prices), sleeping bags (for the entire family) and tent. They can spend up to $50 for the food and their complete total has to be less than $500.

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Camping file

Students used Amazon to find the items. The most challenging part in this assignment was finding tents and sleeping bags that were the appropriate sizes. The tent had to be at least 100 square feet and each sleeping bag at least 15 square feet. That’s where some problems starting to bloom. Converting the measurements for the tents and sleeping bag took some time. Most sleeping bags were small enough that their measurements were in inches and students needed to record their answers in feet.

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The tent dimensions were in feet so that didn’t cause much of an issue. Students had to figure out which dimension indicated the height and not include that in the square feet. Although, some students thought that was an important piece. Maybe I’ll change this assignment up next year to add a height component. So this took a bit of explaining and guidance, but we worked out the kinks. Students used tables to convert square inches to square feet.

Next week, students will be creating a video of their camping activity. They’ll be taking some screen shots, explaining why they picked each item, (I chose food/this particular tent/sleeping bag because …) explain the unit prices of the food items, describe the process used to find the square feet of the sleeping bag and tent, and how they were able to keep the total cost below $500. I believe they’ll be using Adobe Spark to create this presentation. I need to remember to cap the videos at around three minutes, as some go a bit too long as they might talk more than they needed. I’m looking forward to seeing how this turns out next week.

Thinking About Math Misconceptions

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My students have about one month of school left.  It’s hard to believe that the 2016-17 school year will soon be over.  This year I’ve been attempting to have my kids think more about their mathematical understanding.  Putting aside time to do this hasn’t been easy and there’s been a struggle, but I believe we’re making progress.  One of the most impactful pieces to this has been the inclusion of a more standards-based approach when it comes to student work.

One way in which I’ve had students think more about their thinking is to give students opportunities to redo assignments.  Students are given a second attempt to complete an assignment after they complete a reflection sheet.  The sheet is below.

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The goal is to improve and move from the NY – not yet to a M- Met.  Students are required to analyze their assignment and staple on the NY–>M sheet before turning it back in.  I’ve changed this sheet over the past few months as I started to notice that some students were a lot more successful at redoing their assignments and receiving full credit than others.

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I decided to have a a brief classroom discussion to talk about how analyzing our math work can help us identify where we should target improvement efforts.  I put two slides up on the whiteboard to frame the discussion.

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Indicates what the student wrote and how it impacted the second attempt.

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The class discussed the two slides and the student responses.  I emphasized the need to critically analyze their work before redoing it a second time.  Being specific with the comments also plays a role in how well a student performs again.  I also thought it might be a decent idea to start discussing key misconceptions before the class gets back their assignments.  This already happens, but spending more time discussing prevalent misconceptions beyond “simple errors” might be helpful moving forward.  I’m sure I’ll refine the reflection sheets over the summer, but I like the progress that students are making along their mathematical journey.

 

 

Exploring the Distributive Property

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My fifth grade crew has recently been exploring the distributive property.  What’s interesting is that most of the students have used the property before, but it just wasn’t labeled.  Students mentioned this as I introduced the concept earlier last week.  Although most of the students in the class had background knowledge of how to distribute numbers, the level of that understanding differs depending on the student. The majority of students have mastered many concepts related to number sense, but pre-algebra concepts are fairly new to them. That is one of the reasons that I chose to beef up a lesson related to the distributive property. I have a few specific resources related to teaching the distributive property that I thought might be helpful for this lesson.

The substantive mathematical idea of this month-long instructional unit is to have students experience algebra and use it with geometry/measurement ideas with algebra notation. Later on in the unit students explore the distributive property, apply order of operations, simplify expressions, solve equations, utilize the Pythagorean theorem and use size-change factors. 

The lesson began with an agenda.  The mastery objective for the day was “students will be able to identify and use the distributive property to simply expressions.” I briefly explained and drew an example of the distributive property on the whiteboard. At this point I wanted students to get a quick overview of the distributive property in action. This quick overview seemed to help introduce the concept to students that haven’t seen it before.

Students were then placed in groups to complete an initial distributive property activity. A scenario was given where students were asked to purchase three gifts for three different grandkids. Each grandchild would receive the same items. Students were asked to supply number sentences.  Feel free to download the sheet here.

The groups presented their findings and number sentences. During this time I was able to showcase how the distributive property can be utilized in this scenario. Based on the responses, students were still having trouble identifying and using the distributive property. Also, I was finding that students were adding each individual number instead of using a more efficient distributive property. Seeing that students needed more practice opportunities, I decided to move on to a rectangle method activity.

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Students were then asked to find the area of the above rectangle using two different numbers sentences. I chose this particular assignment because of the math connection opportunities. Students were recently studying measurement concepts during the last unit and it’s still fresh in their minds. So, students were given rectangles that were split into segments and they were asked to show different number sentences find the area of the shaded portion.  I placed the page on the document camera and the class reviewed it together. Students were given time to reflect, make connections and ask questions during this time. I also gave students an opportunity to preview the next few lessons and see how understanding the distributive property will help them as they simplify expressions later in the week.

The distributive property activity contributes to the students’ developmental conceptual understanding of the mathematical idea. Students are asked to create a rectangle, divide it, and then use two different number sentences to showcase the shaded area. Students are using factoring strategies to group numbers in order to find the area. In doing this, students are acknowledging that the distributive property is evident in the combination process.

Screen Shot 2017-04-30 at 4.52.51 PMScreen Shot 2017-04-30 at 4.52.59 PMScreen Shot 2017-04-30 at 4.53.08 PMI believe there were challenges evident when I presented these mathematical ideas to the class. Students often come into class with preconceived notions that parentheses are only used during problems involving the order of operations. I believe that the students’ understanding of the distributive property was strengthened through the use of the rectangle area activity. Although their understanding seemed to improve, some students need to be guided through the activity. They were unsure of how to start the problem and some needed prompts.

I believe that the student work I collected suggests that the next step in my instruction is to expand on being able to use the distributive property and combine it with translating equations into expressions.  The next sequential step is to use equations to solve problems involving integers. Although students have used integers in the past, it may be beneficial to review how negative integers impact the distributive process. Also, as I gave students feedback, I wondered if they would’ve been able to complete the same number sentences, but distribute the numbers from both sides of the parentheses. For example, could they connect that 5(11 – 10) is the same as (11-10)5 ? They’ve only encountered the first example, so this may be something worth investigating for the next time I plan this lesson sequence.  Having practice with these types of problems will benefit students, as they need to have experiences with using signed numbers with expressions.

Modeling Integer Computation

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My third grade class explored integers this week.  Over the past few days students have started to become more comfortable in being able to compare and locate integers on vertical/horizontal numbers lines.  The next sequence is integer computation.  I find this to be more of a challenge for students.  Specifically, some students find the concept of subtracting a negative integer to be confusing.  Most students have encountered computation at this stage as either addition, subtraction, multiplication, or division.  The idea of subtracting a negative isn’t something that they’ve experienced and can cause students to question their own understanding.

This topic was discussed at #msmathchat last Monday night.  The consensus was that students need to experience different models to gain a better understanding of how to put together and take apart integers.

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Manipulatives, such as counters and the such are always important.  I believe most teachers use some type of manipulative to showcase integer computation.  Sometimes they’re taken away too early.

The problem that sometimes comes up with this, is that students want to move towards only following a rule/process to find the solution.   This “answer getting” mentality can lead to a lack of understanding and isn’t beneficial long-term.  Wording also plays a role with integers.  Getting caught up with “add” and “subtract” can limit what students perceive.  How about find the “difference” between x and y?

Changing the wording and using a number line can make a huge difference and can empower students to rely on their own understanding of computation and integers.

I kept this chat in mind as my third grade crew finished up a lesson on integer computation.  Near the end of one lessons I gave each student a blank number line and asked them to find the difference between two integers.  The instructions are below.

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Students were given dice and headed to work.  Students ended up rolling the dice and then created their number lines.  They were required to show a number model, the number line and any type of work that was used to find the solution.  The number line was initially blank and they had to fill it in with the numbers related to their problem. There were initial questions, but it seemed as though the multiple models/strategies were beneficial.

I believe students are making progress in better understanding how to put together and take apart integers.  There’s more work ahead of us, but I’m excited about the growth so far.  Next week, the third grade class is scheduled to use a number line to show multiplication and division.  I’m thinking of using a similar model for those lessons.

Improving How Students Analyze Their Work

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One of my goals this year was to have students analyze their own work, make observations and improve. These observations have improved this year by a light margin. For example, students get back their graded paper and look over how they did. Most students look at the top for their points or some type of feedback. Some look for where something was marked incorrectly, while others look for a place in their binder to place the paper. The good news is that students are looking at their graded papers with a more critical eye. That’s a win in my book. Students are starting to observe where they needed to elaborate or change a procedure. That’s good, but the time spent looking at what to change is still minimal.

This year I introduced the NY/M model. Students were a bit hesitant at first, but I’m finding some pockets of success. Those pockets are not just related to the new model, but also a whole range of opportunities that have been put in place for students to understand where a mistake might’ve occurred. Ideally, I’d like to have students identify how the mistake or error happened and to curb that action in the future. Don’t get me wrong, I’m all for making mistakes in order to learn, but some errors impact an entire answer and I’d like students to be able to identify where that’s happening. Being able to self-reflect in order to improve is a beneficial skill.

In an attempt to provide multiple opportunities for error analysis, I’ve intentionally planned for students to identify their own math misconceptions. This has taken many different forms. I believe that students that can identify math misconceptions may be better able to proceed without making them in the future. Three tools/strategies that have been helpful in this endeavor are found below.

  • Nearpod has been a useful too this year. Specifically, having students show their work using the draw tool has helped other students identify misconceptions within their own understanding. Displaying the work on the whiteboard without a name has been especially helpful, as a student might not be embarrassed, yet the class can still learn from that particular person. I’ve used this as an opportunity to look at positive elements of student work and also look for areas that need some bolstering.
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What do you notice?

 

  • Lately I’ve been giving feedback on student papers and incorporating that into my agendas. Before passing back the papers I review the misconception list and answer questions then. I then pass out the papers and students complete the NY/M process. Generally, students make very similar errors and I attempt to address this while reviewing the agenda. This has decreased the amount of questions that students ask related to why/how to improve their answer to receive a M.

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  • On the paper I’m making a renewed effort to write feedback on homework and projects. The feedback takes many different forms and isn’t necessarily in a narrative form. Sometimes I ask question and other times I might circle/underline a specific portion that needs strengthening. This method often elicits student questions as it’s not as clear-cut as other methods. Regardless, it’s another way for students to analyze their work, make changes and turn it back in a second time.

Why is this important to me? Well, I believe that students should be provided additional opportunities to showcase their understanding. At times, I feel as though there’s a gap between what math work they show and what they’re capable of showing. Giving feedback, along with another opportunity to improve, tends to help my students show a real-time understanding of a particular concept. Ideally, this would seamlessly work and all students would move from an NYàM. It’s not all roses though. I’d say at least 50% of the students improve on their second attempt, but I’d like to see more. I believe we’re making progress and have more to go, but I believe we’re on the right track. I’m encouraged to see that this model is slowly and slightly changing the review, redo and improve cycle. This has me thinking of how to expand on it for next year. Stay tuned!

Proportions and Action Figures

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My fifth graders are in the middle of a unit on ratios and proportions.  Two weeks ago the fifth grade kids worked through a detective mystery.  It was a good start and a decent opportunity for students to explore proportions.  This week my students came back from spring break.  It took a while to get back to our regular schedule after a week off. We had to complete some review on Monday and started a new project today.  I was meaning to start it before break but we ran out of time.  I researched a few different sites (1,2,3) and decided to modified my original project.

The class began by talking about proportions and scale models.  The discussion lasted around five minutes and then we reviewed the concept and vocabulary with a Kahoot  The majority of kids were able to answer the questions using estimation, but many were challenging, which was good because we were able to stop and use different strategies.  Most students wanted to cross-multiply for everything, but by the end of the activity students were starting to see the value in diversifying their strategies.  I felt like spending time on this was worthwhile.  This experience reminded me of a Tweet from #msmathchat from last night.

Afterwards, I introduced the action figure project to the students.  Students measured the dimensions of the action figures.  They measured the figure in millimeters, converted it to centimeters and eventually to inches.

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They then measured their own dimensions with a partner and compared them to the action figure.

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Many of the students were able to use proportions as a tool to find a solution.  Some students had a bit of trouble tackling the issue of converting the units.  Overall though, students are becoming better and using different strategies to solve proportion problems – an #eduwin in my book.  You can access the files that I used for this project here.

 

Math BreakoutEdu

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Today is the last day before my school’s Spring Break. Generally, my classes end up finishing up a particular unit before a large break. This time is different. Both my fourth and fifth grade classes are in the middle of a unit.   I’m also finding that both classes are due for some review. Foundational pieces involving place value and order of operations are tripping up some of the students. While looking around for resources, I came across a BreakoutEdu that corresponds with March Madness. I need to give a huge shoutout to Rita for creating this game. I’ve used Breakout in my class before, but am still in the rookie stage. I printed out the files and started to compile them last week. I figured out which locks where needed and started to compile a few different ideas on how it would work.

What’s great is that my school’s media specialist, the fantastic @mrsread, has a teacher BreakoutEdu box that’s available for checkout. I was able to checkout the box and fiddle with the locks earlier this week. I was able to get most of the locks figured out and reset to the codes needed for the activity.  I say most and not all because the multi-lock is still giving me issues. After checking on the forums it seems like this tends to happen more frequently than I originally thought.

After becoming a bit more confident in how to use the set in my own classroom, I decided to use the Breakout with a fourth grade math class this past Thursday. Since I couldn’t use the multi-lock, I decided to use a combination lock that I had at home. I put together a small Google form that coordinated with that particular lock. The next day I spent my planning period organizing the materials. I decided to go with manila envelopes to store the papers and deviously hid them around the classroom. I introduced the game with the slide show in the file at the bottom of this post.

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From the March Madness Breakout PowerPoint

The kids were excited as they already completed a Breakout a few months ago. I told the students that four manila folders were in the room and they had to find them to locate the clues to open the box. I then started the timer and they were off.

Observations

The class of 21 split themselves fairly evenly and started working on the tasks. It just so happened the Google form was completed quickly and one of the locks was open in less than five minutes. That wasn’t my intention.  I was hoping it would be a bit more challenging.   The other tasks, especially the order of operations, took more than 20 minutes to complete. I noticed that around 4-5 students would be working on the sheet while others congregated and tried to find more clues. Some of the kids were making simple errors with the order of operations. The bracket challenge was also tricky, as some students didn’t understand how a bracket worked. Students would complete the bracket and not understand that the larger number would move on to the next section. I could tell that students were getting frustrated as time ticked away.   I didn’t interject although I wanted to help. Eventually, students had to use a hint card, but they prevailed. We had a great conversation afterwards using the Breakout reflection cards. This was also great for me to hear, as students gave feedback about which particular tasks were the most difficult and how they contributed to their team.

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The Breakout worked so well that I decided to use it with my fifth graders the next day. I changed up the Google form piece and made it more aligned to what we’ve been learning over the past few months. I even added a question where students had to translate a problem from German to English. I may or may not have had a ton of fun helping create questions for the game.

Overall, the game went just as well with the fifth grade group, although they had more trouble with the locks. They were a bit confused with the combination lock. Once they figured out at that skill the class opened up the final locks with about 15 minutes or so to spare. The class didn’t have time to review the reflection cards. I’m hoping we can take those out after spring break is over.

Rita’s files for this Breakout can be accessed here. Feel free to use the Google forms (1) (2) that can be copied and used as well.