Do you teach divisibility rules in your math class?
I've always enjoyed teaching divisibility rules and my 6th grade math students have always seemed to have fun using them!
I've read different opinions about whether or not teaching divisibility rules should be a focus in math class, because they may be viewed as 'tricks.'
However, I think understanding and using them in middle school helps students develop number sense and number fluency.
Rather than being taught as a 'unit,' I think divisibility rules should be introduced and then referred to again and again in any applicable situation throughout the year. To make the continuous revisiting easier for students, I've always liked to have a resource for them to refer to throughout the year. We used to create fold-it-ups, but then I moved to using a Doodle Notes resource or a Math Wheel.
Any reference sheet is helpful so that when you ask a divisibility question, students can grab it (or look at it on a wall) to quickly refresh their memories, if needed.
Where can students apply divisibility rules?
There are several math concepts where students can apply the divisibility rules:
1) Working with division facts that are beyond the 'basics.' Like 51 divided by 3, for example. Students so often believe 51 is prime, but if they take a second to test the rule for 3, they can quickly see that 51 is in fact a composite number.
2) Prime factorization. When determining the prime factorization of a number like 51, 57 or 87, using the divisibility rules can be very helpful!
3) GCF. To find GCF, students need to determine what each number can be divided by, so the divisibility rules are quite helpful here.
4) FACTORING. If you teach divisibility rules in elementary school, you might not be thinking of this eventual application. However, the more frequently math students work with divisibility rules, the more their number fluency improves, and the easier factoring will be for them.
Finding the sum for checking 3 and 9 sometimes led some students to start adding the digits to check for every number. I found the use of visuals with the Doodle Notes or the Math Wheel reduced this tendency, as compared to when we used the fold-it ups.
What's your favorite way to teach (or use) divisibility rules?
To Read Next
You walk around the classroom, looking at students' math work, listening to students' conversations, chatting with students about their math work, correcting possible misunderstandings, and reinforcing correct thinking. This is a big part of your 'normal' teaching day, right?
But this probably won't be the scenario for your fall 2020 math class. Whether you're totally online, in a hybrid model, or face-to-face but need to social distance, providing feedback will look different.
Providing feedback in distance learning
Feedback is so important. When a student completes a task - a practice problem, responding to a reading passage, reading aloud, writing an essay - whatever they're learning - they need to know if they did it right or they need to know what to do differently. Then they can repeat and practice correctly.
When you're with your students, giving feedback is relatively easy. You can nod, give a thumbs up, give verbal feedback, etc. But when the learning is virtual, or you need to social distance, it's not so easy! You can't walk among the students, look at their work, and take the quick moment to correct a little misunderstanding. So providing feedback becomes even more critical with distance learning, when you can't see students' body language, facial expressions, etc, that indicate they don't fully understand the concept. Even on a Zoom call or Google hangout, it's tough to just see everyone, let alone notice everyone's cues!
How can you provide feedback to students in this situation? Or in a situation where you're in the classroom, but can't be close enough to students to check their math work in the same way? Self-correcting digital activities are one great way to provide that feedback.
Benefits of Self-checking Digital Resources
How are self-checking resources beneficial? Obviously they aren't the same as being next to your students, checking their work yourself, and giving them verbal feedback. But, they're so much more beneficial than assigning an activity that gives students no indication of whether they 'get it' or not. The self-checking element is a step toward avoiding a lot of incorrect practice.
1) Self-checking resources provide immediate feedback
One benefit of self-checking math activities is that they provide immediate feedback - research has shown that feedback is most effective when it's given immediately. While you may not be able to give very detailed feedback all the time in a distance learning situation, it's helpful for students to at least know if they're correct or incorrect when they're practicing math concepts.
2) Self-checking activities give students more independence
Self-checking, digital math activities, especially non-graded activities, allow students to feel independent and more responsible for their work. The benefits here are that students may take more time to retry a question they answered incorrectly, or retry the entire activity because they aren't being monitored. Since they aren't being watched as they're practicing, they can try again without feeling self-conscious about it.
I remember doing math homework back in high school and loving when the answers were in the back of the math book - not because I wanted to cheat, but because i wanted to check myself! If my answer was wrong, I'd redo the problem until I got it right.
Three types of self-checking digital activities
So far, I've created three types of self-checking activities.
1) My favorite are the Truth or Dare games:-)
These are in Google Slides (and on my digital math activities site) and do require a good amount of navigation. This is a quick overview of the steps (video demo below).
2) The next favorite are the self-checking task cards in Google slides (video on the left, below). These are multiple choice questions. Selecting an answer takes students to a 'correct' or 'incorrect' answer slide. If the answer was incorrect, there's a Back button they can select so they can try again.
3) I also love the pixel art color by answer activities in Google Sheets (right, below). These offer more 'fun' feedback because students see the colors appear if they get the answer correct. They can try again on these as well, by deleting the incorrect answer and entering a new one.
I'll be continuing to brainstorm to find other activities that can provide feedback, instructional when possible.
What other ways do you use to provide feedback during distance learning or social distancing?
To Read Next
Do your math students love using technology? Playing math games?
Do you love math resources that are easy to use? AND great quality?
The digital math activities on my site are perfect for those who answered yes to these questions!
As more and more teachers and students are using the digital games on my site, I've received a few commonly asked questions, so I'm taking some time to answer them here, for anyone who has the same questions, but hasn't asked:-)
Evolution of the Digital Math Activities:
The digital math activities page of this site has been active since August 2019. It started out with 14 Truth or Dare math games for only members to use. Over the past year, I've added seven free activities for anyone to play, as well as several new member activities (member activities are up to 28 and I'm adding more as quickly as I can).
I've migrated the activities to a stand-alone math activities site, called cognitivecardiomiddleschoolmathdigitalactivities.com (I'm still adding/updating new activities there.) On that site, I added 'upgraded' versions of the free activities to the member section - I added question banks and more exercises to them, so students don't get the same questions each time. So, while you may see the 'same' activity on both the Free and Member pages, the activities aren't quite the same.
On to the FAQs...
Q: How do I know what content is in the activities?
A: This document gives an overview of the current activities - content covered, types of questions, number of questions in the question banks. (Plus, there's a free trial week July 22 - 28 so you can check out all the activities - you can sign up at the bottom of this post.)
Question: Do students get the same math questions every time they do an activity?
For the Truth or Dare games: yes. The logic in designing the Truth or Dares was pretty intense and can't be quickly changed to offer different questions each time; however, I will explore making versions that will allow for that.
For all other member activities: NO. All the other member activities will pull from question banks, so while a student may get one or two repeat questions when they play multiple times, the entire set of questions they see will be a bit different each time.
For free activities: yes
Question: How many students can log in at once?
A: As many students as you want. Students use a password to access each activity and there's no limit to the number of students who can access at the same time. None of the teachers who've used the site have reported issues with using the password/logging in.
Q: Can I assign an activity in Google Classroom?
A: Yes! Each activity has its own link, so you can assign an activity by adding the link to your assignment in Google Classroom. In the left image below, I circled the instructions I might write for students; and I circled the 'Link' section under 'Add.' This is where you'll add the link to the activity you want to assign. In the right image, you can see the way the link appears for students (since the page is password protected, that does show in the assignment.)
Q: How do I see students' results?
A: All of the math activities show results in some form. For example, the Truth or Dare games have an "Answer Sheet" (shown below). Many of the other activities show students' points on the main screen; some show the point totals on an ending results screen. Others show results by color, like the absolute value activity shown below (green for correct, red for incorrect).
Regardless of where the results are shown in the activity, students need to take a screenshot of their results page to send to you (or upload into Google Classroom, or another LMS you may be using.) Unfortunately, the software I use can't be programmed to report scores to all the different LMSs classes are using.
The image below shows the student side of Google Classroom, with the screenshot of the results page.
* The Truth or Dare games do have a Print button on the Answer Sheet, so if you're in the classroom and students can access a printer, they could print their results.
Q: How are teachers using the digital math activities?
A: Teachers are using the activities for:
Q: How are parents and tutors using the activities?
A: Both parents and tutors have been using the digital math activities to provide extra practice/reinforcement for students at home.
Q: Where can I find pricing/membership information?
A: Membership Information is listed on Teachers Pay Teachers.
If you have any questions, please feel free to get in touch - firstname.lastname@example.org
To Read Next:
Color by number math activities and distance learning? You bet!
Digital color by numbers? Nope, not for me:-) I like the paper and pencil!
A Little Distance Learning History
As we know, distance learning and digital learning are not synonymous. Distance learning has existed for a looonng time. Early on, it was called 'correspondence education' or 'correspondence learning.' Students received assignments in the mail, completed them, and mailed their work back to their educational institution.
A few examples of early distance learning include:
Check out this infographic for more detail about distance learning history.
Distance Learning Doesn't Have to Mean Digital Learning
Why consider this history? With schools moving to distance learning in light of the COVID-19 pandemic, I think it's important to remember that even though we have the technology to provide digital learning experiences, distance learning doesn't have to mean just digital learning. Paper and pencil activities have their place in distance learning; in some cases, such activities can provide greater benefits than digital activities.
Color by Number Activities Help Children (and Adults)
Why are color by number activities an important part of the current distance learning needs? Because of the many benefits coloring provides!
During this difficult time, the benefits of coloring are so helpful to our students and our own children (and to us). Here are just a few:
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?"
Tip #1: Establish a morning routine - for YOU
Establish a morning routine - not just in your classroom, but as part of your 'personal' morning. Some of us are morning people, and we like to get up extra early, do our workouts, read, walk the dog, make a big breakfast, read to the kids, etc, before we head off to work early, to prep at little at school and then share our day with the students in the classroom.
But others of us are NOT morning people, hit the snooze button five times before slowly rolling out of bed, getting ready as fast as physically possible, getting our kids ready, grabbing our morning coffee (and maybe a bagel or something), and getting into the classroom right on time....about 5 minutes before the kids arrive.
Which one of these scenarios sounds like you?
USING SLIDE MASTERS
Does This Sound Familiar?
You're close to finishing a resource for your classroom, or for TPT, and then you decide you want to rearrange/move elements, add/change the clip art, or change the font.
That may not be a huge deal if your pages are all designed differently, have no repeated elements, or there aren't many pages; but if you're creating task cards or multiple pages with the same elements over and over on all the slides, making those changes can be a pain!
Slide Masters Can Help!
All those little changes can be made more quickly and easily if you create your resources using slide masters (in PPT or in Google Slides). Slide masters make some parts of resource creation a bit faster - using them can definitely save you time! Before we look more closely at how they work, check out a few benefits of using the slide masters:
What Exactly Are Slide Masters?
According to the PPT description, “Slide Masters control the look of your entire presentation, including colors, fonts, backgrounds, effects, and just about everything else. You can insert a shape or a logo on a slide master, for example, and it will show up on all your slides automatically.”
So, slide masters are basically a way to control the elements on your slides.
Hey there! I'm Ellie - here to share math fun, best practices, and engaging, challenging, easy-prep activities ideas!