Subtracting Integers Using Zero Pairs

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SWBAT use zero pairs to apply and extend previous understandings of addition and subtraction to add integers.

Big Idea

Zero pairs! These are a fun and rigorous way to help kids understand integers.

Bell Ringer

20 minutes

Bell RingerGive each student the same problem to persevere through.  I like to pair my students up so that they may have another partner to help talk through the process of solving the problem.  This will lend itself to MP1 and MP3.   The students should be able to use the two colored counters to model the process of the setup, how to solve by adding zero pairs to create the number needed to subtract, and the final answer.  An example is provided for you in the direct instruction section.  You may opt to use this example with your students or create another example that better suits the needs of your students.  For the example below use (-) symbols for negative numbers and (+) symbols for positive numbers. Discuss the strategies used by several partners. 

-5 – 2 

Teacher Guided Notes

1 minutes

CCSS: 7.NS.1d

Teacher Guided Notes:

This lesson calls for two-colored counters, if you do not have two colored counters you may have students use (+)symbol for positive numbers and (-) symbol for negative numbers.  This is an extension lesson from the Adding Integers using Zero Pair lesson.   Students will now use the zero pair method to subtract integers. 

Students will be able to discuss from the addition of integer lesson that when adding integers you will write the number of positives in the equations, then write the number of negatives in the equation, group zero pairs, get rid of the zero pairs, what is left is your sum.  With subtraction students will need to understand that they will need to add zero pairs to a group in order to have enough of the number to subtract it.  Students will need time formulating the relationships. Use the bell ringer to have students persevere through an example problem.  This has proven to be a difficult transition from adding to subtracting using zero pairs.  An important role for you will be to guide students to formalize the relationships. And to use the concepts from adding integers using zero pairs to create starting points to help the students grapple with what can be a difficult concept.  

Direct Instruction

15 minutes

Direct Instruction Notes: Have students use their Interactive Math Journals to take notes during the Direct Instruction.   Using the example -6 – 3, the first thing that I ask of my students is…… What is being subtracted?  Many students have a hard time with just that question. They should be able to tell you that 3 is being subtracted from (-6).  My next question will be to ask, Do we have 3 positives to subtract from (-6)?  Students should be able to recognize that (-6) is less than 3.  A mini lesson over comparing integers would be a great review for lower level learners.  Once students understand that you cannot take positives from a negative number, this is where you discuss step 1 of the process. 

Step 1 in solving this problem calls for the students to set up the first number of the problem.  The first number is (-6) therefor the students should write 6 negative symbols.  Now, the question is more apparent here.  Are there 3 positives to subtract?  Students will collectively say no.  Ask students to ponder what should be done.  Many students will tell you to write 3 positives and take away 3 zero pairs.  Do not shy away from showing students why this will not work.  Use their previous learning over addition of integers to help prove that scenario incorrect.  This is a common mistake that many students will make.   Use the inverse of the expression and solve for the sum.  Compare the sum and the difference.  Students will see that their thinking needs to continue.  Once students have had time to grapple with that, explain that when you do not have enough of what needs to be subtracted you must add zero pairs to create what needs to be subtracted.  This is one of the major differences between adding integers with zero pairs and subtracting integers with zero pairs.   Students will be tempted to group zero pairs and take them away, because of their comfort level with addition of integers using zero pairs.  Allow students to do this, they will see that they end up with the minuend or the first number in the expression.  Ask students:

What is the expression asking us to do?  Students should respond with subtract 3 positives.  Tell students to subtract 3 positives.

What is left? 

Do you have zero pairs to subtract? 

What happened with addition when you did not have zero pairs left?  Students should recognize that (-9) is the correct response.  Using the additive inverse to check responses is a great way to tie in 7.NS. 1c into the lesson. 

Step 1   Step 2        Step 3                      Step 4

-               -   +          Take away                What is the answer?

-               -   +          the 3 positives.

-               -   +






-6 -3    Many of my student struggle seeing the 3 as a positive being subtracted and visually see negative 3.  One visual cue that I give students is for them to box each part of the expression.  The correct terminology of these parts are the minuend, subtrahend, and difference.  I choose to tell my students, the first number, the sign, and the second number.  If they box each part of the expression they will then see clearly whether the subtrahend is positive or negative. 


Activity/Exit Ticket

20 minutes

Activity:  Subtracting Integers lab sheet

Give each student a lab sheet to complete Part A of the lab individually.  Allow students to use the notes taken during direct instruction to help them solve the problems in the lab.  Allow students 5 minutes to get through part A. MP1 will be the focal practice in part A of the activity.

Direct students to partner up with who they partnered with during the bell ringer for part B of the lab.  Students will take 10 minutes to complete Part B of the lab. This will lend itself to MP1, and MP3.

Use Part C as the Exit Ticket for the day.