Tree
Diagrams
✹ permutation ✹ factorial ✹ co mbination ✹ sampling ✹ fre quency ✹ statistics
Clothes Combos
How many outfits can students make from a pile of clothes?
With tree diagrams, they’ll always dress for success!
LEARNING OBJECTIVE
Directions
Students draw tree diagrams to
count possible outcomes.
1. Duplicate the reproducible for each student.
2. At the start of class, bring out your items of clothing. Make sure the
different types of items are all mixed together. Ask volunteers to
come up and make as many different outfits as possible using one
hat, one shirt, and one pair of pants for each outfit. Choose another
volunteer to record all the different outfits on the board.
GROUPING
Whole class/Individual
3. When students are confident they have come up with every
possibility, distribute the reproducible. Let students complete it on
their own.
MATERIALS
4. After students have finished, have them compare answers.
✹ Clothes Combos reproducible
(p. 194)
5. Ask volunteers to draw tree diagrams on the board showing how
many outfits can be made with the items of clothing they looked at
earlier. Students may draw each item or describe it in words. When
the volunteers are finished, determine whether they have come up
with the same number of outfits as before.
✹ a number of different items of
clothing: hats, shirts, and
pants, for example (These may
be funny/silly items if you
want.)
6. Ask students to describe the benefits of using a tree diagram versus
making a list. In this case, a tree diagram makes it easier to keep
track of every possible outcome, and every outcome is clearly shown
in order.
Taking It Further
Repeat the activity several times using new groups of clothes. You may
also ask students to make a list of several of their favorite clothing items
and draw tree diagrams to count how many outfits they can make.
Assessing Skills
Answers
Page 194:
1. 6 2. 2 3. 3
Check students’ completed tree
diagrams. Outcomes: PLSN, PLSa
PShSn, PShSa, StLSn, StLSa,
StShSn, StShSa
4. 4 5. 4 6. 4
Observe whether students are able to correctly describe all the outcomes
from their tree diagrams. If they are having difficulty, try having them
trace the “limbs” of a tree diagram with their finger. For example, they
may start at “green hat,” and follow the branch to “yellow shirt” and
then “blue pants.”
The Great BIG Book of Funtastic Math © Scholastic Teaching Resources
193
Name
Date
Clothes Combos
How many combinations can you make with your favorite clothes? A tree diagram can show
you. For example, Doug has one baseball cap, three shirts, and two pairs of pants. If he chooses
one hat, one shirt and one pair of pants for each outfit, how many outfits can he make?
HAT
SHIRT
PANTS
OUTCOME
white shirt
(W)
cap
(C)
black shirt
(B)
polka-dot shirt
(P)
jeans (J)
CWJ
sweatpants (S)
CWS
jeans
CBJ
sweatpants
CBS
jeans
CPJ
sweatpants
CPS
1. How many of Doug’s outfits include a baseball cap?
2. How many outfits include a white shirt?
3. How many outfits include jeans?
Fill in this tree diagram to find out which different outfits Stella can make with her clothes.
She can pick one shirt, one skirt, and one pair of shoes for each outfit. Here’s what she’s got:
polka-dot shirt, striped shirt, long skirt, short skirt, sneakers, and sandals.
SHIRT
SKIRT
SHOES
OUTCOME
sandals (Sa)
PLSa
long skirt (L)
polka-dot
shirt
(P)
striped
shirt
(St)
sneakers (Sn)
sneakers
short skirt (Sh)
4. How many of Stella’s outfits include a striped shirt?
5. How many outfits include a long skirt?
6. How many outfits include sneakers?
194
The Great BIG Book of Funtastic Math © Scholastic Teaching Resources
StShSn