Beacon Lesson Plan Library

Joining Hands

Virginia Spivey
Bay District Schools


Students explore the inverse relationship of addition and subtraction in a "hands-on" activity based on the fact families of ones, twos, and threes.


The student writes notes, comments, and observations that reflect comprehension of content and experiences from a variety of media.

The student understands and explains the effects of addition, subtraction, and multiplication on whole numbers, decimals, and fractions, including mixed numbers, and the effects of division on whole numbers, including the inverse relationship of multiplication and division.


-Thirty 3x5 cards numbered in sets of ten (1,2,3,4,5,6,7,8,9,10; 2,4,6,8,10,12,14,16,18,20; 3,6,9,12,15,18,21,24,27,30).
-Black marker
-Even number of students (If there is an odd number of students, the teacher can participate in the activity.)
-Math journals


1. Use a black marker and number your 3x5 cards according to rows. One set of ten cards will be 1,2,3,4,5,6,7,8,9,10, the second set will be 2,4,6,8,10,12,14,16,18,20, and the third set of cards will be 3,6,9,12,15,18,21,24,27,30.

2. Divide students into three even rows, with no more than 10 students per row.


1. Divide students into three even rows, no more than ten students in each row. (The teacher may participate if needed to build an even row.)

2. Students in row one should number off by ones.

3. Students in row two should number off by twos.

4. Students in row three should number off by threes.

5. The rows should now look like this:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30 (Row 3)
2, 4, 6, 8, 10, 12, 14, 16, 18, 20 (Row 2)
1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (Row 1)

6. Give each student a 3x5 card labeled with his/her appropriate number.

7. Allow each student in row one to add their number with the student in row two. (Students in row one will join hands with the students in row two.) They should equal row three. (It may be necessary to have students stand during this activity if the desks are too far apart between rows.)

8. Allow row three to join hands with row two and subtract their numbers. They should equal row one.

9. Students in row one and two may now change places to demonstrate that they still equal row three when added or subtracted.

10. Students in row three can then change with row one, and subtract to see that they now equal row two.


1. Upon completion of the "Joining Hands" activity, students gather in fact families and list on the back of their 3x5 cards all possible combinations that were found (i.e., The fact family group of 1,2,3 would write on the back of their cards 1+2=3, 3-2=1, 2+1=3, 3-1=2.) Circulate to offer feedback as students work.
CRITERIA: The teacher observes the possible combinations listed by the students to ensure proper understanding of the objective of understanding fact families was reached.

2. The students then write in their math journals what they have learned from this activity and how they would explain it to others. Students share their journal writings with others to explain their findings and understandings of the activity.
CRITERIA: The students' journal writings and conversations should reflect comprehension of the inverse relationship of addition and subtraction. Students may demonstrate an understanding of this relationship by giving examples of related fact families.

Evidence of learning gathered from this formative assessment is used to guide further instructional practices.

NOTE: Since this lesson only assesses part of the benchmark, teachers will need to complete other lessons to address the parts not covered in this lesson.


This lesson can be extended to include higher numbers or additional inverse operations, including multiplication and division.
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