ACTIVITY 1: Combining Integers – A Hands-On Lesson!
Have students clear off their desks except for a pencil.
Hand out 1 set of beans (bag of red & bag of white) to each student.
** Alternative ** Have students work in pairs. One person is actively manipulating while the
other is the recorder. Have them switch roles after each problem.
**NOTE** from personal experience: Prior to handing out the beans, set rules regarding them
(ex. Leave them in the bag; do not play with them, etc. until instructed to do so).
Hand out Combining Integers (with Beans) WS (have an overhead copy of the worksheet for
use in front of the class).
Section 1: Combining Positive Integers
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Have students take out the positive (white) beans and put them on their desk.
Demonstrate on the overhead 1 or 2 examples, having students duplicate with the beans
on their desk.
Have students complete the rest of the examples at their desk using the beans.
o EXAMPLE: 2+3
Set out 2 positive (white) beans and 3 positive (white) beans.
Now “combine” them into 1 “pile.”
Ask, “How many beans are there?” (Answer: 5 beans)
Ask, “What ‘kind’ of beans are they?” (Answer: positive)
Say, “So when we combine positive 2 and positive 3 we get what?”
(Answer: positive 5).
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After doing 2 or 3 examples like this, introduce doing a “representational drawing” for
the beans (because they can’t take your beans home with them!)
●
o Use
to represent 1 positive.
o EXAMPLE: 2+3
Have students (and demonstrate on overhead) the following drawing:
●● + ●●●
Ask them to combine the dots.
●●●●●
“How many are dots are there?” (Answer: 5)
“What kind of dots are they?” (Answer: positive)
“So what does positive 2 plus positive 3 equal?” (Answer: positive 5)
o Have students complete the rest of the examples in this section using the “dot”
representations.
o Have students compare their results with partner/neighbor.
o Go over results as a class prior to moving on.
Section 2: Combining Negative Integers
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Now have students take out the negative (red) beans and put them on their desk. (Have
them leave the white ones out – we’ll be using them again soon).
Demonstrate on the overhead 1 or 2 examples, having students duplicate with the beans
on their desk.
Have students complete the rest of the examples at their desk using the beans.
o EXAMPLE: (-2)+(-3)
Set out 2 negative (red) beans and 3 negative (red) beans.
Now “combine” them into 1 “pile.”
Ask, “How many beans are there?” (Answer: 5 beans)
Ask, “What ‘kind’ of beans are they?” (Answer: negative)
Say, “So when we combine negative 2 and negative 3 we get what?”
(Answer: negative 5).

After doing 2 or 3 examples like this, introduce doing a “representational drawing” for
the beans (because they can’t take your beans home with them!)
○
o Use
to represent 1 negative.
o EXAMPLE: (-2)+(-3)
Have students (and demonstrate on overhead) the following drawing:
○○ + ○○○
Ask them to combine the dots.
○○○○○
“How many are dots are there?” (Answer: 5)
“What kind of dots are they?” (Answer: negative)
“So what does negative 2 plus negative 3 equal?” (Answer: negative 5)
Section 1: Combining Positive & Negative Integers
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Now students should have 2 piles of beans (one red & one white)
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Review the concept of zero pair (1 positive & 1 negative combined equal zero)
Demonstrate on the overhead 3 or 4 examples, having students duplicate with the beans
on their desk. (Make sure the examples you do demonstrate problems that result in both
positive & negative numbers.)
Have students complete the rest of the examples at their desk using the beans.
o EXAMPLE:
2 + (-3)
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Set out 2 positive (white) beans and 3 negative (red) beans.
Now “combine” them into 1 “pile.”
Ask, “Are there any “zero pairs”? (Answer: yes, 2 of them)
Ask, “What do we do with zero pairs”? (Answer: get rid of them)
Get rid of the zero pairs.
Ask, “How many beans are remaining?” (Answer: 1 bean)
Ask, “What ‘kind’ of beans are they?” (Answer: negative)
Say, “So when we combine positive 2 and negative 3 we get what?”
(Answer: negative 1).
o EXAMPLE:
(-2) + 3
Set out 2 negative (red) beans and 3 positive (white) beans.
Now “combine” them into 1 “pile.”
Ask, “Are there any “zero pairs”? (Answer: yes, 2 of them)
Ask, “What do we do with zero pairs”? (Answer: get rid of them)
Get rid of the zero pairs.
Ask, “How many beans are remaining?” (Answer: 1 bean)
Ask, “What ‘kind’ of beans are they?” (Answer: positive)
Say, “So when we combine negative 2 and positive 3 we get what?”
(Answer: positive 1).

After doing 3 or 4 examples like this, introduce doing a “representational drawing” for
the beans (because they can’t take your beans home with them!)
○
o Use
to represent 1 negative and
o EXAMPLE:
2+(-3)
● to represent 1 positive.
Have students (and demonstrate on overhead) the following drawing:
○
** Students should be drawing the positive 2 dots and then drawing
(circling) those with the 3 negative dots (leaving 1 negative dot all by
itself).
Ask them to eliminate the “zero pairs” (any of the solid/open dots
combined)
○
“How many are dots are remaining?” (Answer: 1)
“What kind of dots are they?” (Answer: negative)
“So what does positive 2 plus negative 3 equal?” (Answer: negative 1)
o EXAMPLE:
(-2)+3
Have students (and demonstrate on overhead) the following drawing:
●
** Students should be drawing the negative 2 dots and then drawing
(filling in) those with the positive 3 dots, (drawing 1 positive dot all by
itself).
Ask them to eliminate the “zero pairs” (any of the solid/open dots
combined)
●
“How many are dots are remaining?” (Answer: 1)
“What kind of dots are they?” (Answer: positive)
“So what does negative 2 plus positive 3 equal?” (Answer: positive 1)
o EXAMPLE:
-3 - 7
Talk with class about recognizing (and circling) the different terms. Make
special note that the number’s sign is based on the “symbol” that is
directly in front of it (+ positive and – negative).
-3 – 7
Set out 3 negative (red) beans and 7 negative (red) beans.
Now “combine” them into 1 “pile.”
Ask, “Are there any “zero pairs”? (Answer: no, they are all negative)
Ask, “How many beans are there?” (Answer: 10 beans)
Ask, “What ‘kind’ of beans are they?” (Answer: negative)
Say, “So when we combine negative 3 and negative 7 we get what?”
(Answer: negative 10).
o EXAMPLE:
6 - 15
Talk with class about recognizing (and circling) the different terms. Make
special note that the number’s sign is based on the “symbol” that is
directly in front of it (+ positive and – negative).
6 - 15
Set out 6 positive (white) beans and 15 negative (red) beans.
Now “combine” them into 1 “pile.”
Ask, “Are there any “zero pairs”? (Answer: yes, 9 of them)
Ask, “What do we do with zero pairs”? (Answer: get rid of them)
Get rid of the zero pairs.
Ask, “How many beans are remaining?” (Answer: 9)
Ask, “What ‘kind’ of beans are they?” (Answer: negative)
Say, “So when we combine positive 6and negative 15 we get what?”
(Answer: negative 9).
o EXAMPLE:
7-5+(-5)+2-(-2)
**NOTE** Teach/Remind students that before they start this problem then need
to make the “double negative” a positive. Hints that could be used to remember
this are:
 “Draw a line, change the sign”. (Draw a vertical line through the
subtraction symbol which makes it into addition and change the negative
sign to a positive sign)
-(-2

Connect the “negatives” through the parenthesis. (This makes what
looks like a large + sign to show that it is now adding a positive number.)
-(-2
7 -5 + (-5) + 2 + 2
Allow students to approach this problem themselves…what do
they do?
Do they set out the positive 7, then the negative 5, then another
negative 5, etc. or
Do they combine all the positive #’s and set out that many
positives & then combine all the negative #’s and set out that many
negatives?
Discussion question: Is there more than one way to determine the
correct answer?
ANSWER: 1 (positive)
** Remind students that they can use the beans or the dots if
necessary to assist them on these problems.
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Class Discussion
o Some of these examples had 1 positive number and 1 negative number. Why did
some of them result in a positive answer and the others result in a negative
answer?
o Can you determine a pattern (or rule) that you could follow for this type of
problem?
o Possible HINT: Think of absolute values of the numbers.
o Common (yet incorrect) answer: Whichever number is bigger uses that sign for
the answer. To which the teacher can remind students (or ask) about how
negative numbers are never “bigger” than positives. At this point, bring into the
discussion a review of the concept of Absolute Value (use the sign from the
number that has the larger Absolute Value).
FOLLOWUP/ASSESSMENTS:
o Combining Integers Worksheet #1
o Combining Integers Worksheet #2
o Combining Integers Worksheet #3
o Combining Integers Worksheet #4
o Combining Integers Test