Divvy With Dominoes
Kindergartners Explore Sharing (To Eight)
Nancy Busath
Objective: Use this activity to help your students broaden their understanding of addition.
Core Standards Emphasized: K.OA.1, K.OA.2, K.OA.3: Solve, represent, and record
addition word problems. Decompose numbers less than 10 into pairs in more than one
way.
Contents:
1.
2.
3.
4.
5.
Materials list
Rationale
Activity (procedure)
Black-line masters of double nine dominoes, etc., ready to print and use
Additional resources
Materials:
For each child: One set each of paper double-nine dominoes, paper numbers, + and = (or +//=/≠) signs; one 9” x 12” piece of construction paper
Book, Domino Addition, by Lynette Long, Ph.D
Rationale:
While most students can join sets together given a certain equation, many struggle to interpret
story problems, to determine whether to join or separate number sets, and to represent the
equation with the correct symbols. The following task includes all of those skills. The task is an
open-ended story problem which involves sharing (making partners of a number). I decided to
make the task fit with dominoes because dominoes effectively show how partners go together
to make a whole (all in one).
Procedure:
Day 1 (optional): To introduce dominoes as a means of adding partners together and give
specific practice in making a certain addition equation using number and operation tiles.
Read the book, Domino Addition. It has visuals and models to explain the future task. It
explains how to add the dots on the top and bottom half of each domino to make a total, and it
also gives practice in finding the dominoes that represent the combined total among a group of
dominoes.
Do the activity “Draw to Match,” (see black-line masters) where every child is given two cards
to draw dots to match 4 + 4. Verify childrens’ drawings and send children to illustrate a prewritten problem and solve it, and then glue on number/operation cards to show the number
sentence that matches.
Be prepared to discuss how the picture on the card is one partner and the picture on the other
card is the other partner, and that the two added together make a total number of things. Talk
about how the numbers the children choose must match the amount of objects on the
corresponding cards. Talk about how one part together with the other part shows how many
things in all. This task helps the children prepare for the real-life sharing-with-a-friend situation
that will follow on Day 2. It helps them visualize the sets as individual entities but as part of a
whole that can be shared.
Launch:
(DAY 2):
This activity gives an authentic motivation for finding the answers by involving a
real-life sharing-with-a-friend situation and really gets at what the children understand through
questioning and individual approach. Every child should be able to find an entry point into this
performance task.
Remind students of the previous day’s book, group activity, and individual papers showing how
they joined sets. (Depending on the time of year and your individual group of students you may
want to spend more days developing the use of dominoes as a means of adding sets or sharing
parts of a whole. You could spend a few days connecting numbers to actual dominoes).
Read the following story problem to the children:
“Ricky’s Dad gave him 8
cookies and told him he could share with his friend. Choose
all the dominoes that show the ways Ricky can share with his
friend. Then show the combinations with number tiles and
the plus tile.”
Provide each child with a set of double-nine dominoes and other materials (see black-line
masters). They need to sort out the dominoes that will satisfy the ways Ricky can share with
his friend and separate them from the ones that will not.
You may want to review a pre-generated list of good math strategies such as “Use your fingers
to count,” “Count out loud,” etc. (see additional resources) before you send them off to begin.
You may also want to generate a rubric for the children to evaluate themselves on their effort
in completing the task, explaining that you will be filling it in after the task. The rubric could
include opinion questions about whether they like the activity and if they want to do it again.
After the children sort the dominoes they glue the ones that work onto their paper and add the
number/operation tiles that match. You will need a lot of space for each student to keep
his/her materials contained and organized. Time is also a consideration. When I did this with
my students we had 40 minutes from introduction to near completion, then a break and some
time afterwards to finish up and check their work.
Explore:
You will want to consider what questions to ask the children as you are observing them with
this task. Anticipate what they might be able to do or not be able to do. Think in advance
about what misconceptions they might have. Do they understand that the two halves of an
individual domino are the partners (Ricky shares one part and keeps the other) or do they
simply count to find eight? A child might find all the dominoes with one half an eight and the
other half some other number. Or, he might simply count all the dots on both halves until he
gets to eight. The following questions could be used during the class discussion that follows:
Q. Would Ricky keep eight cookies? If he kept all eight of his cookies would he have any
more to share?
Q. Ricky’s Dad gave him eight cookies and said he could share them. If Ricky kept two
would he still have eight to share with his friend?
Do the children use strategies to help them find the right dominoes or eliminate the ones that
don’t work, such as cardinality, one-to-one correspondence, switching partners, compensation?
(These questions might follow in the discussion phase):
Q. How many did you count on this side? That side? If you count them all together
does that make eight?
Q. What do you know about the partners of eight? What do you know about the
partners of a number?
Q. I see that you have six and two to share. If Ricky keeps one more this time, how
many will his friend get?
Q. Ricky gave away three cookies this time. What if he keeps three cookies next time?
Q. How did you figure out that this domino is like the cookies Ricky can have and share?
Q. Why won’t this domino work for sharing eight cookies?
Do the children select the correct numeral to glue on to represent the dots on the domino?
Q. Count this side. Now that side. Is this the number that you wanted to put here for
five?
With questioning such as this, students who may appear to be Tier 2 students may actually be
able to make the connections they need to in order to complete the task. This kind of
questioning helps keep the task open-ended so that you are not providing the answers but
helping them see what they might have missed. You will want to observe and discover who is
getting the concepts so that you can select certain students to share what they know.
Determine which order to have them share with each other. A child who counted out both
sides together in one, who might not recognize any partners of the number, might go first in
order to demonstrate to the class the cardinality or one-to-one correspondence.
A child who got three out of the five possible dominoes might share next so that you can elicit
from other students which ones he might need to add. (You could try the activity again on
another day.)
The child who got all the possible dominoes might share last so that he can explain the
strategies he used. Maybe that child recognizes that if 7 + 1 is 8 then he can take one away on
one side and add it to the other (compensation) so the total will remain the same (6 + 2 is 8).
Discuss:
When you pull the children together to share their work with each other you will have been
strategic about who will share, what they share, and when. You will connect their various skills
and the strategies they use to the task.
Present the questions you have chosen during the Explore Phase to the students while having
individual students share their work.
You will probably want to do this project again and ask your prepared questions so that those
children who struggled earlier can have more chance to improve their understanding and
succeed in finding all the appropriate dominoes.
For Day 1
From Houghton Mifflin Math, 2007 edition, page 257A
For Day 2
For Day 2
For Day 2
Adapted from Math Expressions, 2009 edition, TRB, M19
For Day 2
Adapted from Math Expressions, 2009 edition, TRB, M35 and M36
For Day 2 (choose this page or the previous page)
Adapted from Math Expressions, 2009 edition, TRB, M35
Additional Resources:
Math Expressions, 2009 ed., Houghton Mifflin Harcourt, p. 302, “Dot Stories.” Children choose
a domino and create a story problem, then show the problem with number tiles and a +/- tile.
(See also Differentiated Instruction Cards, 3-11).
Math Expressions, 2006 ed., Houghton Mifflin Harcourt, p. 302, “Dot Cube Toss.” Student
pairs pick a domino and write comparisons (or matching equations). (See also Differentiated
Instruction Cards, 3-12).
Partner Games (Every Day Counts, Great Source Education Group):
“Memory,” p. 32. Children match number cards and dot cards and rehearse corresponding
number sentences.
“Domino Fill Up,” p. 40. Partners take turns to create number combinations for 5.
“Match the Sum,” p. 46. Children search for cards that make a match of numbers to dominoes.
“Domino Sums,” p. 50. Student partners compare the sums on each of their dominoes to
determine which is more.
Math Strategies:
1. Think before you talk.
2. Talk out loud.
3. Use your fingers.
4. Draw a picture.
5. Look at the number parade.
6. Break things apart.
7. Move objects to count or compare.
8. Ask, “Is it joining or separating?”
9. Help others.
10. Put the big number in your head and count up to the second number.
11. Ask questions.
I had this game prepared for those students who finished early. (Adaptation: On step 3, instead
of adding or subtracting 1, student should add the domino half s/he landed on to the next
domino half after that.)
Taken from Houghton Mifflin Math, 2007 edition, page 276.
I used the following activities with small groups of students who struggled to complete the
domino sharing task (Day 2). They could also be used in centers or at other times:
Taken from First Grade Partner Games, Great Source Education Group
Taken from Math Expressions, Houghton Mifflin Harcourt, Differentiated Instruction Cards
Taken from Math Expressions, Houghton Mifflin Harcourt, Differentiated Instruction Cards