This lesson contains many student activities to help students master addition and subtraction skills.
For every group of three
- Two dice (One marked
with the numerals 4, 5,
6, 7, 8, 9; the other
marked with one dot,
two dots, three dots in
the formation of regular
dice dots.) If blank dice
are not available, use 3"
x 5" cards to make two
sets of the numeral
cards and four sets of
the dot cards. Place the
numeral cards in one
pile and the dot cards in
- Count the Dots worksheet (pdf)
Doubles and Doubles +1: Slap It Fast
Combinations of 10
- Egg cartons cut into
- Ten-frames (pdf)
- Two-sided counters
- Unifix cubes
- Playing cards or number
Combinations of 10: Fishing for Tens
- Egg carton cut into tenframes
- Pipe cleaners
- Mission: Addition, by Loreen Leedy; ISBN 0-8234-1307-1
- Subtraction Action, by Loreen Leedy; ISBN 0-8234-1454-X
- Counting Crocodiles, by Judy Sierra; ISBN 0-1520-0192-1
- Domino Addition, by Lynette Long; ISBN 0-590-33027-6
- Ten Sly Piranhas, by William Wise; ISBN 0-8037-1200-6
- Elevator Magic, by Stuart Murphy; ISBN 0-0644-6709-0
- Two of Everything, by Lily Toy Hong; ISBN 0-8075-8157-7
- Double the Ducks, by Stuart Murphy; ISBN 0-0644-6249-8
- 10 For Dinner, by Jo Ellen Bogart; ISBN 0590731734
- Ten Dirty Pigs, by Carol Roth; ISBN 0-7358-1569-0
Background for Teachers
There is an order of teaching addition strategies that is beneficial to
helping children understand and learn the basic facts. It is:
- counting on
- combinations of 10
- doubles +1
- bridging 10
These same strategies work for subtraction, with the addition of the
counting back strategy and fact families.
These strategies should be taught and retaught using many different
methods and manipulatives. Herein is not a single lesson, but a
compilation of activities for several of the strategies that can be used
throughout the year.
Intended Learning Outcomes
1. Demonstrate a positive learning attitude.
5. Understand and use basic concepts and skills.
6. Communicate clearly in oral, artistic, written, and nonverbal form.
Invitation to Learn
Literature is always an enticing way to introduce math concepts. We
are fortunate to have an abundance of quality math literature to choose
from. Here are a few suggestions of how to introduce these fact
Concept of Addition and Subtraction
Mission: Addition, by Loreen Leedy
Subtraction Action, by Loreen Leedy
Counting Crocodiles by Judy Sierra
Domino Addition, by Lynette Long
Ten Sly Piranhas, by William Wise
Elevator Magic, by Stuart Murphy
Two of Everything, by Lily Toy Hong
Double the Ducks, by Stuart Murphy
10 For Dinner, by Jo Ellen Bogart
Ten Dirty Pigs, by Carol Roth
Counting On--Count the Dots
Counting on is the first and simplest addition strategy. Children
learn to start at one of the addends, which may be a number other than
one, and count on from there. Eventually they are able to see the
advantage of starting with the largest number and counting on from
there. This strategy is most effective when the addends are small: 1, 2,
or 3. It can be used with larger numbers, but is not as efficient.
- Before playing the game, children need to spend some time just
rolling the dice (explained in Materials) and counting on, starting
with the die marked with the numeral, and counting on with the
die with the dots. After some experience, ask the class to
determine the smallest and largest number that can be rolled with
these dice. Then ask them to predict which total they think will
come up most often if they roll the dice 30 times. Have them
explain their thinking.
- Give each group one set of dice and one Count the Dots worksheet.
- One child rolls the dice, another determines the amount, and the
third marks the tally by the appropriate number and records the
roll. After ten rolls, the children rotate duties so that by the end
of 30 rolls each child has participated in each task.
- After 30 rolls, the children count the tallies for each number and
record on the bar graph at the bottom of the worksheet.
- Record each team's totals on a class graph. Discuss if any team
predicted correctly which total would come up most often.
Discuss why the graph looks the way it does. Does the class
graph look like the individual team graphs? Would it look the
same if we played the game again?
Doubles are facts in which both addends are the same. Children find
the double facts easy to remember. This is an important strategy because
the doubles can work as landmark or benchmark facts that can help
children to find answers to other related facts, such as doubles + 1 and inbetweens.
Doubles + 1 are facts in which one addend is one more than
the other (3 + 4, 7 + 8). In-betweens are facts in which one addend is
two more than the other; the number in between them is doubled to find
the sum (6 + 8 = 7 + 7)
Any game that uses dice can be adapted so that it involves doubles.
Simply use one die doubled instead of two.
- Mirrors and counters can be used to write equations for
doubles. Partners put counters in front of a mirror so that both
the objects and their reflections are visible. Then they write an
equation for what they see.
- Double dominos can also be used for writing doubles equations.
- The activity from the 2nd Grade 2003 Elementary CORE
Academy Handbook entitled "Our Class and the Magic Pot" is an
excellent way to discover doubles. This activity uses the book Two of Everything.
Doubles and Doubles +1: Slap It Fast
- Spread Slap It Fast Number Cards (p. 8-11) in random
order, in a pocket chart, or attached to white board.
- Divide class into two teams. One person from each team
comes to the front with a paddle.
- Caller says a number. Players mentally double the number,
find it on the Slap It Fast Team Board (p. 8-18) and slap it
with the paddle. The first player to slap the number gets a
point for his/her team.
- This activity can be extended to doubles + 1. Players
mentally double the number and add 1.
For groups of three
For this game, it is a good idea to match children by ability.
- Two children have mini-paddles, one calls the number.
- Use the Slap it Fast Team Boards.
Combinations of 10
Combinations of ten are any facts that have a sum of 10. These are
also landmark facts that can help children find related facts.
(If 7 + 3 = 10, then 7 + 4 = 11)
- Egg cartons cut into a ten-frames are helpful in finding
combinations of ten when used with two-sided counters (see Tenframes). A counter can be placed in each compartment
with the same color showing. Record the equation 10 + 0 = 10.
Turn counter in bottom right-hand corner over. Record equation 9
+ 1 = 10. Continue turning one counter at a time and recording
until all counters have been turned. Ask children if they have
found all combinations of ten.
- The activity above can also be done with 20 Unifix cubes in two
colors of ten each. Start with a train of ten in one color and
record equation. Trade one cube for a different color and record
again. Continue until train is completely the other color.
- Play concentration with playing cards, using the ace through nine,
or number cards zero through ten. Place in a 4 x 4 array.
Children take turns turning over two cards at a time. If the sum
of the cards is ten, it is a match and the child keeps the cards.
The empty spaces are filled with two cards from the draw pile.
Play continues until all cards have been matched.
- Use ten-frame flashcards. Flash a card for three seconds. Use the
card in any of these ways:
- Have students tell you how they "saw" the number.
- Have students tell you the missing number.
- Flash two cards. Have students tell you how they recombined
the numbers to get the total.
Combinations of 10: Fishing for Tens
- Players are each dealt five Fishing For Tens Number Cards. The rest of the cards are spread out into a "pond."
Any pairs that total ten are immediately matched and replaced
with cards from the "pond." The matched pairs are placed in
front of the player to be counted at the end of the game.
- Players take turns asking each other for a card that will help
them make a ten. If the player asked has the card, the player
whose turn it is gets another turn. If not, s/he must take a card
from the pond.
- If a card drawn from the pond is the card originally asked for the
player gets another turn. If the card makes a ten with another
card in the hand, it can be placed in the pile with the other
matches but play moves on to the next player.
- Play continues until all cards have been matched. The player with
the most matches is the winner.
- Each player must then record all their matches in the form of
equations on the Fishing For Tens worksheet.
The facts assisted by this strategy are those in which one addend is
close to ten (7, 8, 9). In this strategy, the child mentally moves partial
value from one addend to the other to make a ten, thus making the fact
easier to solve (5 + 9 = 4 + 10).
- The egg carton as a ten-frame can also be used effectively for
this strategy. Children can build the fact with counters by putting the larger
number in the ten-frame and the smaller number outside of it.
Then they rebuild the fact by taking counters from the outside
number and filling the ten-frame to make a ten.
- Build a bridging ten tool by stringing ten beads of one color and
then ten beads of another color onto a pipe cleaner. Turn up and
twist the ends so the beads don't come off. Start with the largest
addend and show it with beads. Leave a space and count out the
smaller addend. Move the beads of the first color together to
show a new fact using ten.
This strategy helps children to see the commutative property of
addition as well as the inverse operation of subtraction. Children begin
to see the relationship between addition and subtraction. The more
exposure children have to the two or three numbers involved in each
fact family, the more comfortable they become with facts, particularly
- Dominos, 12-sided dice, and Unifix cubes are all good
manipulatives for exploring fact families. Dice Fact Families, Domino Fact Families, and Unifix Cube Families worksheets are good practice for each of these
- Triangular flash cards are also helpful in reinforcing fact families.
Each number in the family is written in one of the vertices of the
triangle, with the two smaller numbers written in black and the
larger number written in red. These may be used in several ways.
At first, the children may use them to write 4 equations for the
family represented by the card. Later, they can be used to find the
missing number by covering any of the vertices.
- Using two sets of cards numbered from zero to ten, children can
work in pairs to draw two cards and fill in the Fact Families worksheet. This activity can also be done with dominos,
using each side of the domino as an addend.
- Use children's names, spelling words, vocabulary words, or
special unit words to make fact families--# of vowels, # of
consonants, total # of letters.
Strategies for Diverse Learners
For Learners with Special Needs
- Give instructions for games, individually, one step at a time.
- When appropriate, use smaller numbers and gradually increase.
- In Fishing for Tens activity, give a “cheat’ sheet with
combinations of ten.
Math Journals Entries
- Write the rules to one of the games you have learned.
- Write about and describe a favorite strategy for adding and
why it works for you.
- For the Counting Crocodiles book: How many crocodiles did
the monkey trick? Use words, pictures, and numbers to
- Two of Everything—I put ____ in the magic pot and I took out
- Elevator Magic—I’m on Floor____and I want to go down to
Floor _____. On that Floor I found______.
- Teach games to family.
- Teach strategies to family.
- Make a fact family using family members (# of girls, # of boys, total # in family).
- Observation of children while participating in any of the
- Journal entries from Possible Extensions/Adaptations/Integration.