# Teaching Positive and Negative Integers in Special Education

Do your students struggle with adding or subtracting positive and negative integers? This can be a mind-blowing concept for some students when first introduced, but it doesn’t need to be. Here are 4 ways to teach this so all students understand:

I introduce the topic of negatives by having a discussion about where they might have seen negative numbers. Someone might talk about temperature, particularly if this lesson happens to be during winter, if I’m lucky, a student might bring up coordinate places (cue perfect segway into the number line approach!), but invariably someone always mentions owing money. We have a classroom economy system, and it sometimes happens that a student might go into debt, so they’ve seen negative amounts of money. We just call it “debt” or “money owed.” Now though, we can discuss it as negatives.

Discuss what happens when money is earned or money is lost; this is adding and subtracting with negatives! Pull out the play money and an account register like this one I made here. Let the students have some hands on practice adding and subtracting dollars by giving them different real-world scenarios.

The Number Line/Coordinate Plane

If it happens that your students have already worked with 4 quadrant coordinate planes, then this method will be easy to help your students visualize adding and subtracting with negatives. I prefer the x and y axis plane, because you have both the horizontal and vertical number lines, but if it hasn’t been introduced to your students yet, just use whatever number line is familiar to your students.

Number lines allow students to not only compare integers, but to begin to view positive and negative numbers as opposites. To encourage this, I have students draw on transparency and label the x and y number lines on their papers using rulers to ensure spacing is even and exact. e fold the lines in half and discuss how the numbers are the same unit value (absolute value review here!), but negative is the opposite of positive, meaning it’s been removed. Put together, two opposite integers of the same value cancel each other out, giving a value of zero. This step is important for students to grasp for when we eventually get into equations with integers, but it is also helpful in understanding subtracting or adding negatives.

No Such Thing as Subtracting

After teaching these methods,  I then prep my students for a mind bender. I tell them there is no such thing as subtraction. It doesn’t exist; subtraction is just adding a negative! There is a great video clip of a PBS Math Club debate on this topic that you can watch here:

We then do some practice problems to drive the point home. I box the signs with the number it is attached to to help the students visualize how the subtraction sign is acting as an added negative.
Commutative Property

This one is short and sweet. I do a quick reteach of the commutative property. We’ve now looked at how the subtraction sign can be attached to a number to become an added negative. Commutative property helps students put this understanding to work by switching around different expressions. 4 – 7 is the same as -7 + 4. This helps students see how the minus/negative sign is attached to the number “behind” it. It also gives students the “permission” to move around the numbers into whatever order is easier for them to solve and adds some extra perspective into their practice.
Integer Song – Summary Activity

Finally, I give students the rules of adding and “subtracting” positive and negative numbers. My notes for them are brief and given only after teh previous discover activites.

1. If both numbers have the same sign add the values. Keep the sign the same.
2. If each number has a different sign, subtract the values. Give the answer the sign of the larger number
3. If there is a minus next to a negative, the 2 signs combine to become a positive(relate this to taking away debt). Then follow the above rules.

I type these notes up to give students a printed handout which they keep in a sheet protector in their math binders. Get your copy of my Integer Operations Rules Handout on my Teachers Pay Teachers Store.

We end this intro unit by singing a song to the tune of “Row, Row, Row Your Boat.”

Different signs, subtract!

Keep the sign of the bigger number,

and it will be exact.

Once we’ve finished all these activities, it’s time for some assessment to see where students are. This Formative Benchmark Negative Operations Quiz is great to get a good idea of where, or even if, students are still tripping up.

Bonus Strategy – Bird Beak

This year, one of my students came up with her own method of remembering rule 3: a minus sign next to a negative sign becomes a plus/positive sign. She drew this:

She thought it looks like a bird eating. Any time she sees the “eyes,” she knows to draw the beak and a the plus sign underneath.

# Back to School!

Hello, Everyone! I hope you have all had a great summer. It has been a while since I’ve been in one place long enough to sit down and write a blog post. I’m itinerant with my Extended School Year students in the summer, and then I was lucky enough to go on an awesome road trip around the Midwest during which I had pretty much zero internet access.

But school started back yesterday, and I’m on my second day with students! We have an a blessedly smooth start to the year. All but 3 of my 11 students had already had me for at least 1 year. I kept all of my rules and most of my procedures exactly the same, so there would be no confusion of the old way vs. the new way that caused a problem at the start of my last school year.

The students stepped smoothly into back academic mode and gave only cursory complaints at having to go back to waking up “so so very early.” (I was right there with them, even if I didn’t let on.) I did institute an addition to my classroom behavior plan (more about that later) that may have helped reduce complaints and encourage on task behavior.

I intend to give you a full debriefing about our first week back to school after Friday has wrapped up, but I did want to catch all of you up on that Summer Teacher Bucket List I mentioned in this post. Here is the list again with commentary.

Teacher-y Bucket List

• 40 hours itinerant Extended School Year I managed to fit in all 40 hours of service before the last week of July, which is the earliest I have ever finished summer schooling. My students and I were equally thrilled, because it gave us a sold 3.5 weeks (2.5 for me since teachers started back a week earlier) of summer before the 15-16 school year started up.
• Summer Academy PD workshops  This was semi-helpful. The Stetson courses gave tips on differentiating, but many of them were pretty common sense to special education teachers who are used to having multiple ages, grades, and abilities in one room. I did manage to pull out a couple of helpful pointers and I was reminded of some activities I had forgotten about, so that was good. I did attend an excellent training on the SRA curriculum. I have used the curriculum for years, but had never actually been trained on it. This was incredibly beneficial, and really helped explain what was being done wrong to cause some of the problems I had previously encountered. Do any of you use SRA? If so which courses? I would love to hear how you incorporate it into your class.
• teach parent and student ASL classes I did teach student ASL classes all through the summer. None of my parents attended more than one class though. It’s a good bit more to it than in Cued Speech, so I think they may have been overwhelmed. The kids stuck it out though, and we made great progress!
• plan daily math centers with independent, hands-on activities I’m to say I never really got around to this. I sat down several times, and I just could not figure out a way that would allow the students to be completely independent in the center from beginning to end when they can’t read. Any tips? I don’t have BoardMaker, or any software like that, and reading/explaining the directions to them defeats the intention between my wanting to set up these center. The goal was for me to let them work, so they could let me work with my resource students without interruption. Reading to them would require I leave my resource kids in the middle of the lesson when my math kids come in.
• select class novel and write reading guide and lesson plans I selected Our Strange, New Land: Elizabeth’s Diary by Patricia Hermes. It has a Lexile level of only 350 according to one calculator, so I am hoping it will be an appropriate read for even my lowest student if we preteach vocabulary and time the novel to read it after we’ve finished our Colonial American unit in social studies. It will be a good opportunity to do cross curricular activities with history, ELA, geography, math, and art. I’m really looking forward to it.
• get TESOL certification This did not happen. I did look into a program, but they offer guaranteed job placement that you must use within one year. I’m not quite ready to make that change just yet, so I’m putting this off for at least another year.
• improve Cued Speech fluency I did practice. My students still complain I’m too slow and make mistakes, but hopefully there’s been some improvement. Perhaps they just forgot how poor my fluency was at the end of last year. Yikes! I think I’m a little better than I was then.
• develop way to integrate Cued Speech reading instruction Integration did not happen, but I did manage to get a transliterator to agree to offer classes to my seventh graders during their resource period, so that’s something.
• make conversation sentence stem cards to help with language samples and class discussions I have started this, but it’s not quite finished yet. Stay tuned!

Non-Teacher-y Bucket List

• Italy trip Check!
• visit college friends (Atlanta, Virginia, Nashville) Check on 2 of the 3. I never made it up to Virginia. We have an overdue Skype date set for tomorrow though!
• sew travel kit accessories Check!
• sew placemats This one hasn’t happened yet, but I did get the materials, so perhaps sometime soon.
• knit sheep baby blanket I’m about 4 inches deep into this blanket, but I did double the width since it seemed a little small. It’s coming along nicely.
• finish mug storage Check! Just need to hang it on a wall now…

I was not quite as good about following though on my Reading Bucket List. I’ve only read 2 of the 5, Building Academic Language and The Lady in Gold, partly because I joined a book club at the start of the summer and ended up reading a ton of really enthralling novels.

• I Can Hear You Whisper: An Intimate Journey Through the Science of Sound and Language  by Lydia Denworth
• Talking Hands by Margalit Fox
• When the Brain Can’t Hear: Unraveling the Mystery of Auditory Processing Disorder by Dr. Teri James Bellis, Ph.D.
• Building Academic Language: Essential Practices for Content Classrooms Excellent read! Very informative, and it helped to kick-start my sentence stem prompts I’m still working on. I highly recommend this. Be on the look out for a book review here soon.
• The Lady in Gold Not as great as I expected but there was a solid middle section that was very historically illuminating, and I do enjoy my history! (as my students tell you with a moan)

That was it. Check back Saturday for a window into our first week of school!