Grade Level: 1st and 2nd
Materials Needed: (9) One large domino set, ~10 small domino sets, domino worm
worksheet (shown below)
Skills Needed: (2) Adding, Counting, Fewest, Most
Objective: When asked to name two numbers with a specific sum,
the students will be able to give several possible answers.
Lead-in: (1,2,3,4,5,6,8,10) For this part of the activity, the teacher and students gather in a circle with the large domino set spread out in the middle of the circle. Placing the domino worm worksheet at his/her feet, the teacher begins the activity by asking "Who can tell me two numbers that have a sum of..." (numbers under ten work best). After receiving a response from one student, the teacher writes the answer down where everyone can see it and then asks the student to show the sum of the two numbers using the dominos to form the worm's body, as shown below.
**Before using the dominoes it is important to explain to the students
that each domino represents one number, not two. (This provides more
adding practice by having the children add not only the dots on the domino
but also adding the dominos together).
This is repeated several more times using different sums.
Teacher-guided practice: (1,3,4,5,11) Reviewing the answers that
he/she wrote down, the teacher goes through each answer, asking the students
to think of two different numbers that have the same sum. For example, if
the first answer given was 5+5=10, then another possible answer could
be 6+4=10. The students show their answers using the dominoes to
form the worm's body.
--This is repeated until all possible solutions have been given for each
original sum, so that the students can see that for each sum, there are
several possibilities. The teacher writes each of the answers down where
all of the students can see them. This helps to make the connection between
the dominoes and the actual equations that they represent. (1)After all
of the possibilities have been written down, the teacher invites deeper
thought by posing the question "What if I had 6+4? Would that be the
same as 4+6?" Thinking about this question, the children are made aware
of the concept of reversibility and can now suggest even more possible addends
of the same sum.
Independent Practice: (1,3,4,5,11) With this new knowledge, the
children are sent to their desks to work in pairs. They are given two worksheets,
one domino worm worksheet and one sum possibility worksheet (seen below).
Directions: (1,15)Find all of the possible pairs of numbers for
each sum. (Don't forget about reversing!)
9 11 6
__+__ __+__ __+__
__+__ __+__ __+__
__+__ __+__ __+__
__+__ __+__ __+__
__+__ __+__ __+__
__+__ __+__ __+__
__+__ __+__ __+__
__+__ __+__
__+__ __+__
__+__ __+__
__+__
__+__
For this part, make the worm's body for each sum using as many dominoes
as you can. Write down all of the numbers you use. (Remember that each domino
is one number)
1).11:___________________________________________________________
2).15:___________________________________________________________
3).8:____________________________________________________________
Now make the worm's body for each sum using the fewest number of dominoes
that you can.
1).11:___________________________________________________________
2).15:___________________________________________________________
3).8:____________________________________________________________
--After the students have completed the worksheet, have different groups share their answers. This will help students to look at their answers in a different way. To further their thoughts, the teacher can ask the class if they used any kind of strategy when making the worm's body using the most dominoes possible. The students may not understand what a strategy is so it may be helpful to explain the meaning. Once they understand what a strategy is, they will be able to share their strategy with the entire class.
**(7,14)I have done this activity with second graders and was amazed at their ability to formulate a strategy for a novel situation. Some students had unique ways of selecting which dominoes to use, such as choosing only those dominoes with even sums. This was an interesting strategy, although not essential to the solution. Other students realized that when making the worm body using the most dominoes possible, it was best to select those dominoes with the lowest sum. When asked why it was better to have dominoes with small sums, they replied "because then it doesn't add up so fast." Conversely, when making the worm body using the fewest dominoes possible, the students found it best to use those dominoes whose sums were large so that they "would add up faster."
(14) Some examples of their answers for the independent practice are:
MOST:
1). 11: (3,0) (1,2) (1,1) (2,0) (0,0) (1,0)-For a total
of six dominoes
2). 15: (4,0) (3,0) (1,2) (1,1) (2,0) (0,0) (1,0)-For a
total of seven dominoes
3). 8: (1,2) (1,1) (2,0) (0,0) (1,0)-For a total of five
dominoes
FEWEST:
1). 11: (5,6) or (5,5)(1,0) or (4,5)(1,1) or (4,5)(2,0) or
(5,3)(3,0) or (5,3)(1,2) or (6,1)(3,1) or (5,2)(2,2) or (3,4)(4,0) etc.
(There are other possible solutions; these are some of the answers that
I received most often.)-For a total of one (the fewest) or two dominoes.
2). 15: (6,6)(3,0) or (6,6)(2,1) or (5,3)(5,2) or (5,3)(3,4)
or (4,4)(6,1) or (4,4)(5,2) etc. (There are other possible solutions;
these are some of the answers that I received most often.)-For a total one
(the fewest) or two dominoes.
3). 8: (6,2) or (4,4) or (5,3)-For a total of one domino.
**It is important to note that for the sums of 11 and 15, answers
using only one domino were rare but did occur.
Follow-up: (12,13)The above activity will probably take the entire
math instruction time to complete; therefore, as a follow up lesson, the
teacher could build on the students' existing knowledge, gained from the
original activity, to deepen their understanding of sum and addends. This
can be done using the same worksheet from the first activity. Passing back
the students' worksheets, the teacher reviews what was learned the day before
(i.e. sums have many addends, addends are reversible, strategies are important
and useful). After reviewing, the teacher invites deeper thought by posing
the question: "Using what you learned yesterday, what kinds of patterns
do you see in the different addends for each sum?" The goal of this
question is to get students to notice that the addends have an ascending/descending
pattern. For example:
For a sum of 5:
0+5=5
1+4=5
2+3=5
3+2=5
4+1=5
5+0=5
--Notice that the numbers on the left increase from 0 to 5, whereas the numbers on the right decrease from 5 to 0. It is also important to note that the range of increase and decrease is governed by the sum number. In this example the sum number is 5, therefore, the range of addends only goes to five, starting with 0.
If the students do not see this pattern, help them by asking "What do you notice about the numbers on the left side? Do they get bigger or smaller?" This should help students to see the pattern on both sides.
**This is a very interesting and fun activity. The children really enjoyed
doing it and learned a lot. I hope you enjoy it too!