What type of math activity do you most like to have your middle school math students work on?
For me, it's almost always been problem solving. This could include word problems that apply specific math concepts, word problems that incorporate a variety of math concepts, logic puzzles, or word problems that focus on problem solving strategies (create a table, make an organized list, find a pattern, work backwards, draw a picture, etc). I love using problems that have more than one correct solution, so students can share the thinking that leads to different answers.
When we work on problem solving activities, I often have students work together, so they can model for each other and share/listen to each others' thinking and reasoning.
I wrote the "Party Planning" problem to give students practice with decimal operations and with solving problems with multiple solutions. To solve the problem, students worked with one or two partners to come up with combinations of foods that Reggie could buy for a party. To find their solutions, students needed to add decimals; multiply if they were going to include several of one item; and possibly subtract, if their total was over $50.
Student Conversation and Feedback
I loved listening to the kids' conversations as they worked on this problem. I heard comments like, "No one eats pretzels," or, "I'd choose candy and chips over pretzels," and so on.
The students had a few important questions for me, as they were pretty serious about this planning.
"Is this a "regular" party or like a sleep-over party, because the kind of food would depend on how long the party is."
"How big is the container of ice cream?"
"How big is the bag of candy?"
Could you use a quick math activity to help your students practice identifying decimals in standard and word form? How about some comparing and ordering of decimals? I've got an activity that covers all of those for you:-)
When I created this one, we were just beginning our work with decimals (in grade 6), and my students had done a little bit of work with writing decimal numbers in word form. They had also worked on comparing decimals several times during the year, in our Daily Warm Ups book.
Using the Decimal Matching Activity
The first step in the activity is to match each card with a decimal number in standard form to the card with the correct word form. I allowed students to work alone or with one partner, and the matching didn't really take that long. I did have similar numbers (like 9.68, 9.068, 9.0068 etc), so that the students had to read carefully and take some time to compare those similar numbers.
Finding the Lowest Common Denominator with the
What's the most challenging math topic to teach/most difficult for your students to ‘get'?
This was my question in a recent Instagram survey. I got a variety of responses, but the one that came up most often was fractions – remembering the ‘rules;’ students finding common denominators when they were multiplying; students (older students) not being able to find a common denominator; and so on.
So, today, I’m going to share how to use the ladder method to find the lowest (least) common denominator, and hopefully, if your students have struggled with this, it will help them (and you!). Before I explain how it works, I want to share that I've used the ladder method for several years, after many years of teaching GCF and LCM the ‘traditional’ way - the way I’d been taught! And during those years, I’d often get frustrated by the fact that students would miss the GCF because they missed factors, or they couldn’t find the LCD because the numbers got too big so they just multiplied the denominators…..or they listed out the multiples, but made a mistake in one list, and so they never found an LCM/LCD. I'm sure you know what I mean!
The ladder method took these issues away, and it also added something I didn’t initially expect – it appeared to improve number sense for many students who struggled with their multiplication facts or with the idea of finding factors and multiples. It helped them understand HOW numbers were related to each other by making the breakdown of the #s more visual (using prime factorization does this as well, but the ladder method provides a little more organization to the process, and I think that’s helpful).
I used this week's problem in class today (6th grade), for early finishers. Because we haven't gotten too "into" a particular topic, I made the problem a mix of operations - mostly division and multiplication, but I saw students using addition as well.
I really enjoy talking with my students about what they are thinking when they try to solve problems, for a few reasons - because 1) they think about problems in a different way than I do; 2) it makes me rethink the wording of the questions I ask (which makes me improve); and 3) I learn that there will be several ideas to share with class.
I noticed a few different things when the students were solving the different parts of this week's problem:
For part A, I multiplied 85 times 3 to get the total number of cookies and then divided by 24 (when I wrote the problem, I wanted the students to have to interpret the quotient, so I approached it with a desire to use division). And most students did the same thing (except for the few that multiplied 24 x 3 - that gave me some good info: -), but one student was just sitting and thinking, so I asked him what he was thinking. He started to say he divided 24 by 3 and then paused - I almost interrupted his thinking to redirect him to my way, but I successfully restrained myself, and asked why. He said he was thinking about how many baggies could be filled with one batch, and since the numbers worked nicely, he could definitely say that one batch would fill 8 baggies. I really liked his thinking process, because it hadn't occurred to me to do it that way. Now, if the numbers hadn't worked out evenly, it might not have been the best approach, but we can expand our class discussion to explore that. After deciding he could fill 8 baggies per batch, he added on sets of 8 until he reached the correct number of batches.
As some students worked on part C (below), I started to think that I should adjust the wording of the problem. When I wrote the problem, I thought it would be clear that the number of cookies for part C was the same as part A, but some students thought of the part C as using 85 baggies of 2 cookies (same number of baggies), instead of using the same number of cookies. As more students worked on it though, other students seemed to understand that the number of cookies should be the same as the original number they were working with, so I haven't changed it yet. If you use the problem, please let me know what you think.
Again, a few students approached this part in a different way than I did - they said that in both cases, the cookies cost 25 cents each. Using this reasoning, some students said the cost was the same, while others did not - again, a great opportunity for discussion, both in small groups and as a whole class.
To see and/or use the entire problem and answer key, click on the link below the picture.
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Have a great week!
Early last week, I was trying to think of a different kind of activity to help my middle school math students who needed more reinforcement with order of operations, and I decided to make a sequencing activity. I hadn't tried this before, so I wasn't sure about the best way to design it, but the activity ended up working quite well. Here's how I put this math activity together and used it with my 6th grade math classes:
Order of Operations Activity Design
For this math activity, I created 8 different
expressions, and then typed out the steps to simplify each expression. I copied the expressions and steps onto different colored papers, so that two expressions would be on the same color. I cut the steps apart into strips, and then put two expressions and their steps (of the same colored paper) into a baggie...I figured if I put only one equation in a baggie, the activity would be too simple. If I put two expressions of two different colors, it would be too easy. So I went with two expressions in the same color. That way they'd have to do some sorting of the expressions.:-)
Using the Order of Operations Activity
I put 3 baggies (6 different expressions and their steps) into a manila envelope for each group. Groups were mostly just partners, with an occasional group of 3.
I typed directions to include in the envelopes, and asked students to do their best to follow those directions before asking for clarification (some of the students worked on this activity, while others completed different activities, so I needed them to try to work through the directions themselves before I got to each group to discuss with them). Some students needed additional instruction, while others did not.
After students put the steps into the correct sequence (shown in the image above), they had to write those steps onto a recording sheet, pictured below.
In each of my math classes, students worked on this activity for about 15-20 minutes. Some groups completed all 6 expressions, while others completed only 2-3. A few more minutes would have been helpful for those students who didn't complete as many expressions, but I can revisit the activity with those students this week.
I will definitely use this again next year:)
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