This is a repost from 2013, transferred from my previous blog:-)
Some students finally got to play Fraction War today!
We again worked on the group problem solving that we started last week (comparing and ordering fractions), and continued with Footloose...also comparing and ordering fractions (click for description of Footloose game). Students finish Footloose at all different times, so the few that did finish today had the opportunity to play Fraction War with the fraction card decks I've made.
I am loving these fraction cards! I made them during the summer, just with the idea of playing "Go Fish," but I also used them for an equivalent fraction sorting activity, and now they are great for playing "War." The kids who played today did a great job deciding which fraction was larger....I asked them to write their work on paper, so I could be sure they weren't guessing, but after a few turns, I could hear them discussing as they found common denominators and made equivalent fraction to compare, or reduced the fractions to compare. They were definitely thinking!
I'm finding that the use of these cards is really helping students' mental math abilities as well as the math conversations that they are having.
Only a few students got to play today, but several of them asked to play during 9th period today (homework/activity period). I'm looking forward to more students playing tomorrow, as the rest of them finish up their Footloose!
Grab this free fraction operations math wheel!
Using Graphic Organizers in Math Class
We know that graphic organizers are not only helpful for organizing information, but they can also be helpful in creating visual cues that help students remember specific information. Using color patterns and graphics also increases student engagement:-)
This math wheel focuses on the topic of rounding decimals. When I have reviewed rounding decimals with my students in the past, they often remember whatever trick or saying they've been taught, but they often can't explain the math reasoning (therefore, I always save any sayings/tricks until after the math concept is understood, if I use them at all).
When using this math wheel, I start with the number lines - looking at the distance between 1 and 2, where 1.5 is, and visually draw attention to the fact that 1.6-1.9 are closer to 2 and 1.1-1.4 are closer to 1. The students write in the labels and then there's space for you, the teacher, to add several examples of your choosing.
Then I move to the benchmarks. You'll see on the completed version, I drew a small number line to create the visual of the space between 1 and 1.1, labeling 1.05 as the half-way point. The same thing could be done for the others, or examples of rounding can be added (like the one below 0.0005).
Students can then do the practice problems all around the page. Above each number is a T, H, or TH, to indicate the place to round to (tenth, hundredth, thousandth).
I have the students color their problems/answers according to numbers that rounded up (my example uses green) and numbers that rounded down (pink), which gives a quick, easy visual to see that they knew which way to round. A closer check will then tell me if their answers are actually correct:-)
(You can always let them just color the background later, for fun!)
Last, I'll have them add a rule/saying to help them remember.....one that each student creates him/herself would be best.
I hope you're able to use this math wheel! Let me know if you have any questions:-)
Rumors is another great lesson from Mathline! This lesson allows students to explore exponential growth, in the context of spreading a rumor. In addition to the focus on math concepts, this lesson can also help students to understand how quickly rumors can actually spread....an important idea for middle schoolers to consider.
To begin the lesson, students are presented with the following scenario:
"Two students who were both born on December 21st, the date of the winter solstice, decide that it would be great not to have to attend school on that day. Therefore, they start a rumor that schools will be closed to celebrate the winter solstice. So, on December 1st, one of the students told two of her friends that school would be closed. On the next day, each of these students tells 2 students and on consecutive days, each of the new students tells 2 more students and so on. If there are 8,000 students in the school district, the question arises as to whether the rumor was started early enough for everyone to have heard it?"
Students can act out this scenario by having students form a human triangle, with Student A first, then the two students she told (students B and C), then four students representing the two that Student B told and the two that Student C told, etc (as far as possible, depending on how many students in the class). This will help students visualize the problem and understand how this rumor is being spread. The triangle also help students to understand the growth pattern.
The human triangle will only go so far, so students will then need to use their calculators or paper and pencil to find how many days it will take for the rumor to reach 8,000 people. I would recommend providing the students with a blank chart to give some structure to the students' work after they try the human triangle.
The chart below includes the first several days (the numbers for the entire chart can be found in the lesson).
In addition to understanding more about exponential growth, students can be asked to determine the algebraic expression to describe the number of new people to hear the rumor each day (2n), as well as the
expression for the total number of people (2n+1-1).
To read the full lesson and the possible extensions, check out the lesson here.
Do you use the ladder method in middle school or elementary math, to find GCF, LCM, or for any other math concepts?
If you haven't had the chance to use the ladder method (or the upside down birthday cake method, as some call it), I highly recommend it.
Uses of the Ladder Method
As you can see in the anchor chart, math students can use the ladder method to find greatest common factor (GCF), least common multiple (LCM), for factoring, reducing fractions, finding prime factorization, and for finding the least common denominator (not pictured)! So many uses! And what I really like about this method is that the process is the same for each use; the outside numbers are just used differently. I like the fact that the continued use of the ladder method (for various concepts) leads students to make greater connections between numbers.....and finding factors seems to come more easily.
Benefits of Using the Ladder Method
In addition to helping math students find GCF and LCM, using the ladder method helps students see the relationships between numbers a little more clearly. It's very easy to see what factors different numbers have in common and how those factors 'contribute' to the LCM or GCF. When I used the ladder method for factoring, students picked up the factoring concept MUCH more quickly than when I hadn't used it. The short video below demonstrates how to factor a simple expression.
Ladder Method Resources
A while back, I wrote a guest post about the ladder method on Rachel Lynette's blog, so if you're interested in reading more, check it out here. I shared a ladder method fold-it-up in my guest post, but you can also click on the image here, if you'd like to download it.
I've also created a fun Doodle Notes page to help students with the Ladder Method!
Click on the image, to see it on TPT.
If you haven't used the ladder method before, I hope you'll give it a try! If you have, I'm sure you understand why I love it:-)
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