How to Teach Decimal Addition and Subtraction
How do you teach adding and subtracting decimals in upper elementary or middle school math?
In 6th grade, my math students have typically come to me knowing the 'rules' for adding and subtracting decimals.
However, when the number of digits in the numbers they're adding or subtracting aren't the same, they don't necessarily line the numbers up the way they need to...even though they 'know' the rules. Why is this?
I believe it's because they really don't understand the point of 'lining up the decimal points.'
My belief is reinforced by student comments I collected one year as we began our decimal operations unit.
I asked my 6th grade math students to solve 35.2 + 7.489 and then explain why their answer made sense. These are a few of their responses:
Of the 120 students in my classes, only 8 said the answer made sense because "35 + 7 is 42" or because "I estimated" or "when we're doing addition, we know we end up with a bigger number."
I don't want to assume that students who didn't write this didn't think about those things at all, but to the majority of students, their answers "made sense" when they followed the rules - even if they didn't remember the rules correctly.
What's the Point?
What's the purpose of lining up the decimal points?
Lining up the decimal points helps us line up the place values so that place values are added with or subtracted from 'like' place values.
If students don't understand the point of lining up the decimal points when adding and subtracting decimals, then somehow they've missed the idea of place value.
And what do we do if they numbers don't even HAVE a decimal point?? (Some students get pretty lost when that happens.)
Start With Estimating When Adding or Subtracting Decimals
Because I believe students don't understand the point of lining up the decimal point, I teach them to add and subtract decimals by doing the following:
Tools for Teaching Decimal Addition and Subtraction
One of my favorite ways to teach the addition and subtraction process is to use notes that emphasize estimating.
I include this in my unit notes and practice, and I also use math wheels for note-taking.
The math wheels break the processes into steps and allow room for examples and practice. They also give students a chance to color-code, doodle, color, and add memory triggers to their notes. Then they can keep them in the notebooks all year for reference.
Adding Decimals Wheel
Subtracting Decimals Wheel
A couple practice decimal activities:
There are a couple free decimal activities found in the blog posts linked below that I've used to give my students some additional decimal operations practice.
Decimal Operations Problem Solving
Decimal Practice with Number Puzzles
What are your tried and true methods for teaching adding and subtracting decimals?
Resources to Practice Adding and Subtracting Decimals:
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With a Peer Teaching Component
An Alternative to Daily Oral Language
I'm really excited to share my version of daily language review! I've used this method in 4th, 5th, and 6th grade language arts classes.
This daily language review incorporates peer teaching and was many years in the making:-) I published 24 weeks of this daily language review for 6th grade a few years ago, but didn't share much about it at that time!
So, here's the story:-)
About 20 years ago, after using Daily Oral Language in a variety of ways in my classroom, I decided that each student needed to become more engaged in our daily language instruction.
Many were already engaged...students took turns coming to the board to make corrections and identify parts of speech, but typically, only one student had a turn at any one time.
At that time, my goal was to make sure students understood the reasons for the corrections they were making. Unfortunately, if they tuned out for even a little bit, they missed some information.
So, using the Daily Oral Language sentences, I created a peer teaching method for our daily language, which I'll explain below.
** Note: this daily language review is not the only method I use to teach grammar, punctuation, spelling, etc, but it has been a fantastic supplement to provide continual reinforcement throughout the year.
Results of Using Peer Teaching in Daily Language Review
After using daily language with peer teaching for the first year, I observed that my students absolutely understood the content better than students in the past. This was evident in their assessment results and especially in their daily practice. So I continued to use it on a regular basis for about 15 years.
I love this version of daily language review, because I've seen my students develop a greater understanding of spelling, grammar, punctuation and parts of speech.
The students like it more than previous methods because they are ALL able to be active and part of the discussions. I've wanted to share this idea in the past, but couldn't use the "DOL" sentences to do so; so, I finally took the time to create my own sentences for my 6th Grade language arts class, and decided what grammar, spelling, and punctuation I wanted each particular week to focus on.
Daily Language Review Using Peer Teaching Method
Here's how my "Partner" Daily Language Review works. It may sound complex to start, but a little modeling makes it easy to understand:-)
1) Each student receives a sheet of paper, labeled Partner A or Partner B.
On the paper are two sentences.
5) Each partner writes the correct editing marks, reasons, and parts of speech for his/her own sentence. The sheets are then the students' study guides for quiz time.
Modeling Daily Language Review
When I first introduce this procedure to the students, I give each student a sheet, and we discuss the set-up of the sheet and the way the corrections and reasons are numbered.
Try Daily Language Review Using Peer Teaching
If you'd like to give this method a try, you can try Week 1 for free - just select the button below.
The sentences in this week are pretty easy, to help students focus more on the learning the process of this peer teaching method.
If you give this daily language method a try, I'd love to hear how you like it!
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Six Tips to Make the Grading Process Faster
Grading Papers Quickly and Efficiently
How often have you wished you could just snap your fingers and have all the grading finished??
I don't know about you, but grading papers is definitely an area where I needed to find some ways to make the process faster. Over the years, I found a few little ways to get my grading done more quickly and efficiently.
These days, the use of digital assessments can make some grading faster; however, you may not be able to (or want to) use digital assessments all the time.
So, for those cases when you're working with paper assessments, I've got six tips for you!
Grading Tip #1: Answer Sheets
1) If you're grading multiple choice/true or false (and aren't planning to do any partial credit), design your assessment so students will put their letter answer in a left-hand column.
Or, give them a separate answer sheet with answer spaces in a column.
This way, all the letters are in an organized column for you and you can quickly go down the column, comparing the answers to the answer key.
Grading Tip #2: One Page at a Time
2) If you have a 2-page (or more) assessment that's multiple choice/true or false, do all of page 1 first, then all of page 2, 3, etc. It's a small thing, but it:
Grading Tip #3: One Question at a time
3) When you're grading essays or open-ended questions, grade all of the same question before moving on to the next. In other words, grade all of question #1 first, then all of question #2, etc.
Switching from one question to the next on each paper is really a form of 'task switching,' which has proven to be less effective in getting things done quickly.
When your mind gets 'into' the first question and then has to adjust to question 2, 3, etc., and then do the whole thing over again, it slows you down.
Grading Tip #4: Grade when students are testing
4) Grade papers as students are finishing their assessments. There are always students who are done first, and you can easily grade any multiple choice questions on their assessments while other students are finishing up.
I always circulated when students were taking an assessment, so I'd carry a clipboard around the room with my key. As students finished, I'd grade the parts of the tests that weren't open-ended or wouldn't get partial credit.
Grading Tip #5: Don't grade the entire activity
5) If you don't need to grade the entire activity, don't! Choose a few questions and just grade those.
When I taught writing, I'd give students "quick writes" several days a week and then choose just one of them to grade. These were short samples that gave students great practice and gave me a good snapshot of their writing without spending too much time in the grading process.
Grading Tip #6: Alphabetical order
If you prefer to wait until all students finish an assessment to collect it, take a little time to collect the assessments in alphabetical order (or number order).
This doesn't make the grading part of the process go faster, but it can make recording the grades go a little faster. When assessments are in order, you don't need to look through your grade book list for each name as you come to that student's paper; instead you can go right down the student list and record, being careful to make sure absent students don't get another student's grade:-)
Your Grading Tips?
What are your best tips for how to make grading papers go more quickly? If you have some, I'd love for you to share them in the comments below.
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End of Class Routines
What are your end of class routines in middle school?
Do you have specific routines?
A few weeks ago I wrote about routines to begin class; today I'll touch on routines to end class in middle school.
I have to admit, my end-of-class routines often didn't go as smoothly as my beginning-of-class routines:-)
Best laid plans, you know....
When it went well, my routine at the end of class would include:
1) Writing homework on the board so students could add it to their assignment books.
I did accomplish this nearly every day:-) Writing the homework was critical. Our team teachers made a point of doing a quick check at the end of class every day, to be sure students were writing their homework down (for some students, this was an accommodation we had to meet - checking the homework book. So, why not quickly scan/check all students' books?)
2) Asking an 'exit' question.
I had a "ticket out the door' poster in the classroom that I numbered 1-30. Each student had a class number, so they'd answer the question on a post-it and then put the post-it on their number on the way out of class. I loved this method because:
As I admitted at the beginning of the post, end-of-class didn't always work this way. I would often try to squeeze in one more example or complete one more practice problem with students and the exit ticket would get skipped.
But, the students learned and understood the routine so that when it went as planned, they'd know exactly what to do.
Other Routine Ideas for Ending Class
I'm always looking for new ideas for quick end-of-class activities, since my classes are only 40 minutes and there's so much to do! Here are a few ideas that can be used to wrap up quickly.
Have students jot a quick reflection on a post-it. This reflection can be a variety of question types or statements, like:
3) Vocabulary or Fast Facts
What are your favorite routines for the end of class? Feel free to share in the comments!
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Graphing Functions Practice with Footloose Task Cards (free download)
This Graphing Linear Functions post is from my old blog, written in May, 2015, but updated here:-)
Graphing functions hit us in May of this school year. Our state testing had wrapped up and we started working with function tables and graphing function equations, on a pretty basic level.
This post is my summary of how I approached practicing the basic idea of graphing linear functions with my 6th grade math students:-) Included is a description of the task card activity I used, which you can download for free at the end of the post.
Our Graphing Functions Practice
As my 6th grade math students started graphing functions, we used some practice from our textbook, and the students created functions for each other to graph, but I felt that it just wasn't enough practice.
I couldn't find any functions activities to suit my needs "exactly," so I decided to make a shorter Footloose task card activity to give the students some extra practice (and some movement that Footloose provides...movement helps keep the students engaged...especially in May!).
I created 15 Footloose task cards for graphing functions. The cards all have the same directions ("Choose x-values to complete a function table for:_____" and "Graph the function."), but they have different functions to graph.
For example, Card 1 says:
1) Choose x-values to complete a function table for: y = x + 5
2)Graph the function.
The answer grid for this graphing functions activity is actually two pages:
Graphing Functions Task Cards Extra Instructions
Before students began choosing x-values for their tables, we discussed the fact that the axes on the coordinate planes only go to 10, in both the positive and negative directions.
Knowing this, they needed to be careful to choose x-values that would result in y-values that were less than 10.
As the students worked, it was interesting to see which students purposely chose negative x-values, to challenge themselves to work with negative numbers (we hadn't officially studied operations with negative integers), while others stayed with the comfortable positives.
The students really enjoyed this one!
Feel free to download and use it with your students:-)
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Pi Day Ideas for Middle School Math
March 14, also known as Pi Day, is coming soon!
Do you have exciting plans for Pi Day activities in your math class?
Maybe you have some tried and true favorites, or maybe you're looking for something new.
Whether you teach 5th or 6th grade math, elementary math or higher levels of math, Pi Day is a day that can be celebrated and used to explore the concept of Pi - in so many different ways!
Pi Day Activity
Have you tried using donuts to have students discover the Pi relationship between the diameter and the circumference? Or maybe cookies?
I tried it with donuts recently.....can be a little messy, but fun!
In my pictures, you'll notice I had some donuts with icing and sprinkles....I'd suggest NOT using those if you want to minimize mess:-)
Materials for Pi Day activity:
2) Licorice 'strings' for measuring (if you have tape measures that would be best, but I never had those in my classroom, so I went with the string idea)
Steps for Discovering Pi Using Donuts
1) Measure the circumference of the donut using a string of licorice (regular string will work just as well....maybe better, depending on the size of the donuts. I had to use 2 pieces of licorice on my donut, which could result in less accuracy.)
Once students mark the circumference on the string or the licorice, they measure that length.
2) Measure the diameter of the donut in the same way.
3) Divide the circumference by the diameter.
Discussing the Results
Chances are that students won't get exactly 3.14 when they divide their circumference by the diameter. But they should get close if they've measured carefully (and if the donuts are close to being perfect circles).
Take some time to compare students' results and help them analyze the data by discussing questions like:
How close are students' results to each other?
What could cause students' calculations to be less accurate than others'?
Once the discussion is done, students can enjoy the donut treat!
Pi Day Activity Posts
There are some awesome ideas on other blogs, so I thought I'd link a few for you here:-)
From The Colorado Classroom:
Pi Day Fun
Pi Day - Not Just Another Day
From Math Giraffe:
Unique Ideas for Pi Day
From We Are Teachers:
31.4 Mathtastic Pi Day Activities for the Classroom
What are your favorite ways to celebrate Pi Day and teach about Pi?
Resources to learn about and practice with circle concepts:
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Beginning of Class Routines
What do the beginning of class routines look like in your middle school classes?
Do your students enter the classroom and know exactly what to do? Or, in this age of virtual learning, do they know exactly what to do when they log on....or even before they log on?
For a few of my first years of teaching, I didn't have specific classroom routines. Then I read The First Days of School and everything changed...I started incorporating specific tasks and routines for students to do/follow when they arrived in class.
For several of my middle school teaching years, my homeroom students were my first period class, which made getting 'into' class really easy - the routine for those homeroom students was to begin specific tasks as soon as they had completed their homeroom routines.
Beginning of Class Routines for ELA
What did my students actually do as part of the routine at the beginning of class?
When I taught ELA, my students worked on their 'partner daily language' which was my spin on the 'Daily Oral Language' we used when I first started teaching.
This routine involved:
While students completed this routine, I'd take care of any miscellaneous items and then circulate, answer questions, and listen to the students' discussion.
When all students were finished, we'd review any daily language questions or I'd throw in a little mini-lesson, and we'd move on to that day's lesson.
Beginning of Class Routines for Math
In math classes, the beginning of class routine started with what I called M.G. (for Mental Gymnastics), which was our daily math. I used a variety of daily math books over the years, but then created my own daily math, to spiral and review the concepts I knew my 6th graders consistently struggled with over the years.
The beginning of class routine looked like this:
1) Students took out the daily math immediately and worked on that day's problems (students kept the daily math in their binders so nothing needed to be passed out or retrieved at the start of class).
3) I'd answer any MG or homework questions.
Then, on to the lesson!
All in all, the spiral review problems/discussion and homework checking took about 7-10 minutes (yes, sometimes I'd take a little longer answering questions that came up:-)
Other Ideas for Beginning of Class Routines
While using the daily language and daily math worked well for me, maybe you'd like some other routines to begin class.
Here are a few alternatives:
1) Entrance tickets:
These are a quick way to assess where students are with your topic for the day. I think these would be easier to incorporate if you have a class period longer than 40 minutes.
These could be
2) Problem Solving:
Have a problem ready to go so students can begin as soon as they enter the room. It could be projected, could be in Google Forms, or could be a printed sheet.
When I taught 5th grade and had longer math periods, I often began class with a problem to solve, so we could work on problem solving strategies. There was a structure to this, so students knew what was expected (the routine!) when they entered the classroom and saw a problem posted.
3) Homework Review/Discussion
As a routine, this would look like: students enter the room, automatically take out their homework, and check answers with a partner or the classmates that sit in their group (or near them).
I used this if our class time was cut shorter for some reason.
What are your favorite classroom routines?
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Hey there! I'm Ellie - here to share math fun, best practices, and engaging, challenging, easy-prep activities ideas!