Comparing Fractions using Creature Capture
Patterns in Fractions
Lesson time: 25-45 Minutes
Lesson Overview
Students will explore the nature of fractions through playing the game: Creature Capture. They
will need to analyze both the properties of the numerator and denominator when comparing to
other fractions. In addition, they will need to create strategies related to the cards to be played
and where to place them on the board.
Lesson Objectives
Students will:
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Determine if given fractions are relatively larger or smaller than other fractions
Determine if given fractions are closer to the benchmark of ½ when compared to other
fractions
Compare fractions through modeling (drawing)
Explain the effect of the numerator and the denominator on the size of the fraction
Estimate the relative size of two fractions added together
Estimate the relative size of two fractions multiplied together
Convert fractions to have a common denominator [Challenge]
Anchor Standard
Common Core Math Standards
3.NF.3d
4.NF.2
Compare two fractions with the same numerator or the same denominator by
reasoning about their size. Recognize that comparisons are valid only when the two
fractions refer to the same whole. Record the results of comparisons with the symbols ,
=, or
Compare two fractions with different numerators and different denominators, e.g., by
creating common denominators or numerators, or by comparing to a benchmark
fraction such as 1/2. Recognize that comparisons are valid only when the two fractions
refer to the same whole. Record the results of comparisons with symbols , =, or
Lesson Plan Summary
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Introduction (1-5 minutes)
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Game Play (15-25 minutes)
Reflection (10-15 minutes)
Materials, Resources, and Prep
For the Student
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At least one computer for every two students
Any handouts desired for the reflection activity
For the Teacher
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Ensure you can load the game from your classroom:
http://play.centerforgamescience.org/creaturecapture/
Decide if, and how, you want to activate prior knowledge before the game
Decide how the vocabulary will be incorporated into the lesson
Decide if the class will use power cards and what characteristics of them you will explore
(i.e. keep it simple. A fraction + fraction results in a bigger fraction OR make it harder.
What is the exact result of ¼ + 2/3 ?)
Prepare at least one reflective activity for the class
Lesson Plan Details
Vocabulary
This lesson has a number of words that can be incorporated. These should not necessarily be
introduced at the beginning but the teacher should try to use as many as appropriate and assess
understanding of the chosen words upon completion:
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Fraction: A number which represents equal parts of a whole.
Numerator: The top number in a fraction which tells how many parts of the whole. A
larger numerator means more a larger number (more parts shaded).
Denominator: The bottom number in a fraction which tells how many equal pieces the
whole was broken into. A larger denominator means smaller pieces (the whole has been
broken into more parts)
Benchmark(optional): A number we use to help us compare other numbers. “1” is a
good benchmark. We know a fraction is greater than one if the denominator is less than
the numerator (such as 4/3). “½” is another benchmark we often use. Fractions whose
numerator is less than half of its denominator are below ½ (such as 3/8 is less than ½
since 3 is less than half of 8).
Introduction
Students will come into this lesson with varying experience of fractions. In general, less talk at
the start is better but activating some prior knowledge (especially student-to-student) may be
helpful. Here are a few questions that might be worth discussing before (and definitely after)
some game play.
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How can I fairly cut this pie (circle) or cake (rectangle) to share among 3 people? 4
people?
How can I share 2 candy bars (strips) among 3 people?
Which is bigger 1/3 or ¼? Why? [a third is a bigger slice than a fourth]
Which is bigger 3/5 or 4/5? Why?[four somethings is bigger than the 3 of the same
somethings]
Which is bigger 5/6 or 7/8? Why?[7/8 because taking away an eighth from a whole will
leave you with more than if you took away a sixth from a whole]
Which is bigger 1/3 or 3/4? Why? [3/4 because we see these fractions every day!]
Which is bigger 3/7 or 4/5? Why? [Hard to say. Maybe I recognize that 3/7 is less than
1/2 and 4/5 is not. Maybe I know how to get common denominators. Maybe I draw
them out and color them and see that 4/5 is bigger]
Is there a general rule (or set of rules) for telling if a fraction is bigger?
TIP: Interrupting the students after 10 minutes of game play to re-focus on these questions
as well as allowing them to share discoveries and strategies is recommended.
Activity: Creature Capture Online Fraction Game
The standard version of Creature Capture that is posted on the Center for Game Science web site
allows the student to begin at any level. Ideally they will start from Level Pack 1 level 1 and
work their way through. A detailed breakdown of the levels and other considerations are at the
end of this lesson plan.
Suggested In-Game Activity:
When confronting fractions of unknown size,
draw the two fractions either as number lines
or as pie charts (with the numerator part
shaded). To help in this effort, fractions in the
players hand will usually reveal either a
number line or pie representation by hovering
over the card. Even a student who knows the
fractions might be encouraged to draw four
sets of comparisons: Two sets as number line
and two sets as pie representations. For thirds
and sixths, some younger students may need
help drawing these.
If students are sharing a computer, they should alternate who is controlling the mouse on each
level. The person without the mouse should be the decider and select which cards to play and
where to play them. A goal would be to have all students be able to correctly know if a
particular match-up of cards would win AND to be able to explain their thinking.
Reflection & Wrap-up
Research has shown critical that some form of debriefing takes place after any game in the
class room for the learning benefits to be realized. Reflection is where the students transfer
the play into learning outcomes. Based on your adaptation of this lesson, please choose at
least one to implement in the classroom.
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Come up with a set of SIMPLE rules (or examples) for adding with power cards (for
instance, if both are less than ½ then the result will be less than 1). Display these using
combined pie charts.
Come up with a set of SIMPLE rules (or examples) for multiplying by power cards (for
instance, if multiplying by a number more than 1 the result is bigger whereas if the
multiplying by a number less than 1 the result is smaller). Display these using crosshatched grids.
Have students play the candy cut game (similar to Create Capture). See
http://games.cs.washington.edu/fv/resources/BeginningFractionsGame%28CutCandyCar
ds%29.pdf . There is a lot of information here including many variations of this game.
Note that the game includes coloring a lot of pre-made fraction cards.
Revisit the discussion questions. Have the students verbalize (and write if appropriate)
the answers to two of these questions.
Give the students 3 comparisons using pie charts, 3 with number lines, and 3 with
numbers only. Have them circle the one that would win a fire battle (larger). Have them
star the one that would win a grass battle (closest to ½ )
Have them determine which fraction goes between the other two. See
http://www.commoncoresheets.com/Math/Fractions/Dividing%20Unit%20Fractions%20
Visual/English/1.pdf
To further explore relative size compared to the benchmark ½, discuss strategies for
deciding if the same as ½ (or less than) and then attempt the following:
http://www.commoncoresheets.com/Math/Fractions/Relative%20Value%20E/English/1.pdf (or
easier version:
http://www.commoncoresheets.com/Math/Fractions/Relative%20Value%20%28Visual%29/Engl
ish/1.pdf )
END OF LESSON PLAN. MATERIAL BELOW THIS POINT FOR
REFERENCE ONLY. NO NEED TO PRINT (OR READ UNLESS CURIOUS).
Additional Common Core Math Standards which are connected to this lesson
3.NF.1
3.NF.3d
4.NF.2
4.NF.3a
4.NF.3b
4.NF.3c
5.NF.1
5.NF.2
5.NF.4a
5.NF.5a
5.NF.5b
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned
into b equal parts; understand a fraction a/b as the quantity formed by a parts of size
1/b.
Compare two fractions with the same numerator or the same denominator by
reasoning about their size. Recognize that comparisons are valid only when the two
fractions refer to the same whole. Record the results of comparisons with the symbols ,
=, or
Compare two fractions with different numerators and different denominators, e.g., by
creating common denominators or numerators, or by comparing to a benchmark
fraction such as 1/2. Recognize that comparisons are valid only when the two fractions
refer to the same whole. Record the results of comparisons with symbols , =, or
Understand addition and subtraction of fractions as joining and separating parts
referring to the same whole.
Decompose a fraction into a sum of fractions with the same denominator in more than
one way, recording each decomposition by an equation. Justify decompositions, e.g., by
using a visual fraction model.
Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed
number with an equivalent fraction, and/or by using properties of operations and the
relationship between addition and subtraction.
Add and subtract fractions with unlike denominators (including mixed numbers) by
replacing given fractions with equivalent fractions in such a way as to produce an
equivalent sum or difference of fractions with like denominators.
Solve word problems involving addition and subtraction of fractions referring to the
same whole, including cases of unlike denominators, e.g., by using visual fraction
models or equations to represent the problem. Use benchmark fractions and number
sense of fractions to estimate mentally and assess the reasonableness of answers.
Interpret the product (a/b) × q as a parts of a partition of q into b equal parts;
equivalently, as the result of a sequence of operations a × q ÷ b.
Comparing the size of a product to the size of one factor on the basis of the size of the
other factor, without performing the indicated multiplication.
Explaining why multiplying a given number by a fraction greater than 1 results in a
product greater than the given number (recognizing multiplication by whole numbers
greater than 1 as a familiar case); explaining why multiplying a given number by a
fraction less than 1 results in a product smaller than the given number; and relating the
principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
GAME AND PROGRESSION NOTES:
For the basic level of this lesson plan, only the first Level Pack (1-12) needs to be played. The
levels after this all involve Power Cards and you will need to decide on how you wish the class
to address these. See the Power Card notes at the end of this section.
GOALS STUDENTS SHOULD HAVE:
1) To be able to recognize the outcome of any battle before the card is played and be
able to explain their thought process to someone.
2) To watch the animations during the battles and to use the mouse over animations to
explore their cards if they are unsure as to their size. This exploration will improve their
understanding of fractions and the game.
3) IF YOU ARE USING POWER CARDS, encourage the students to try to use the Power
Cards on each turn. It is possible to win without them but using them will expose
additional patterns related to multiplication and addition with fractions. Encourage them
to risk a mistake by using the Power Cards rather than going for the sure win without
using them.
A brief outline of the levels and their contents is below.
Students are given the choice of where they start.
Ideally they should start at Level 1. From the
Level Menu, you can tell if a level has been
finished by a star (see level 5 on right) .
Level 1: Provides a board where the student
cannot lose. This is simply teaching them to place
tiles and that water battles are looking for the
smallest number.
Level 2: The real challenge begins. Fire Battles
are looking for what is largest. The simplest
concept of “winning” at this level is flipping a
card to your color. In the example provided, the
only “mistake” a student can make is by placing
one of the cards on a tile that is not adjacent to
the ½.
Level 3: A mix of fire and water battles. In
addition to understanding the relative size of a
fraction, the student must be aware of which type
of battle is being fought. Here the student can
make a mistake if they do not recognize the
water battle next to the ¾. The ½ and 2/3 will
win but the ¾ and 5/6 will not.
The advanced student may be looking ahead one
move to see if their “win” will be short-lived (for
instance, placing a 1 on a fire battle will likely
win that turn, but if a water battle is adjacent to
this, the rival will almost certainly take this card
back on the next turn.’
On this level, the cards you see are all you will receive. Some students may notice that the cards
are in order from smallest to largest.
Level 4: Only one “correct” first move. ¼ on
water next to ½ .
Level 5: Grass Battles indicates closest to ½
wins. Rival also gets to go first. A strategic best
move MIGHT BE to play the ½ next to the ¾ as it
cannot be flipped back once placed.
Level 6: Mix of all battles. Student fraction cards are ¼, ½, ½, and 1.
Level 7: Mix of all battles. Student fraction cards are ¼, 1/3, ½, and 1.
Level 8: Fractions no longer perfectly ordered. Student fraction cards are ¼, 1/3, 1/2, 1 and 2/3.
Level 9: Fractions no longer perfectly ordered. Student fraction cards are ¼, 1/3, 1/2, 1 and 3/4.
Level 10: Begin drawing fractions. Player
only gets one card at start. A new fraction
card is drawn after each turn. They appear
in this order: ¼, 2/3, ¾. At this level,
students may opt to skip animations that
appear during battles.
Level 11: Start with 5 cards but draw after
each one. Initial cards: 1,2/3, ½, 1/3, ¼
(always in reverse order like this). First
card drawn is 1/6. Varies after that.
Level 12: Repeat of Level 11 except board is different shape and distribution of battles. This
level may require slightly more strategic thinking to win the level.
POWER CARDS
Levels 13 – 24.
Power Cards are cards that can add or multiply an
existing card OR a future card. In the example,
shown (Level 13), I might place the (x ½) card on
the existing 1 on the board so it is smaller. Then
placing the 1 (or ¾) on the fire battle will win
(because the newly established ½ loses to ¾ in a
fire battle). Note that the power card disappears
after the battle and the card returns to its previous
value.
Level 13. One turn. Cards: 1, ¾. Power Card: (x2)
Should use both power card and a number card. Note the should. They are not required to use
the power card but this particular level is impossible to win without its use.
Level 14: 4 turns . Cards: 1,1/3,2/3,1/4. Power
Card: (x2/3),(x1/3). At this point the students do
not have to know the exact value of the
multiplication but they should understand when
multiplying by a number less than 1, the resulting
number is smaller than the original. Thus
2/3(x1/3) will be less than 2/3.
Level 15: 5 turns . 5 cards: Random. No 5/6 or
1. Power Card: (x2/3),(x1/2)(x3/4).
Level 16: Perfect Puzzle Level. Take all 4 at
once. Note these are addition power cards.
Level 17: 3 turns . 4 cards: Unit fractions: ½, ¼, 1/3, 1/6. Power Card: (+1/2),(+1/3).
Level 18: 4 turns . 5 cards: ½,3/4,2/3,1/3,1/5. 3 Random Power Cards selected from (+1/3),
(+1/4), (+1/2)(+2/3)(+3/4)(+1),(+4/3) (x1/3)
Level 19: 6 turns . 5 cards: ¾,5/6,2/3,1/6,1. Power Card: (x1/2)(+1/2). Draw additional number
cards on each turn BUT NO ADDITIONAL POWER CARDS.
Level 20: 3 turns. 3 cards: ½, 1/6, 2/3, 1/3. Power Cards: (+3/4)(+1/2)(+1/3)
Level 21: 4 turns. 5 cards: Random All. 2 Power Cards: Random All. Draw additional number
AND POWER cards after each turn.
Level 22: 5 turns. 5 cards: Random All. 3 Power Cards: Random All. More “intelligent” rival.
This level will be challenging to win.
Level 23: 6 turns. 5 cards: Random All. 2 Power Cards: Random All. More “intelligent” rival.
Level 24: 8 turns. 5 cards: Random All. 2 Power Cards: Random All. More “intelligent” rival.
From this point on, it is essentially more practice with various board configurations and number
of turns. Levels 25 and 26 have a slightly easier rival again but from level 27 – 60 the rival is
similar to playing a fairly smart human opponent.
MORE NOTES ABOUT THE PROGRESSION:
All students should play levels 1-1 to 1-5 to familiarize themselves with the game and the three
battle types. If you want students to play using power cards, you might have them jump to level
13 AFTER FAMILIARIZING THEMSELVES WITH THE GAME.
MORE IDEAS ON CLASSROOM MONITORING:
It is possible for students to skip levels or accidently repeat the same level over and over
again. When monitoring students look for the following:
 For any given card placement, can they explain what will happen and who will win? If
not, here are possible forms of remediation:
o Q: Can they explain the differences in the three battle types?
o Q: Do they know the objective of a single turn?
o Q: Can they explain who would win a fire battle between ½ and ¼?
 Inability to answer the first two sub-questions above might require them to go back and
repeat earlier levels. It may be that they have skipped levels. From the main menu only
completed levels will have stars.
 Difficulty with the last sub-question above might be address through a mini-lesson or
having them repeat levels but paying closer attention to the animation and the card
animations (received when hovering mouse over unplayed card).
 If students seem very far behind, it may be they continue to repeat the same level. They
may be hitting the Replay Button at the bottom of the screen instead of Next Level button
at the bottom right.
 If the main menu makes it appear that they have solved far more levels than you think
possible, it’s likely a cache issue. The cache is the memory that the browser keeps for
the game. If another player from a previous class has been playing on the same
computer, it may be that the computer is remembering this first player’s history. You can
simply ignore it, open an anonymous version of the browser (which will not have a cache
and all stars from completed levels will be removed), or clear the cache (this process will
vary by browser).
More On Using Power Cards: Power Cards do not have to be played. A student may
completely ignore them. You must encourage their use. One way to do this, is for a student to
“get a witness” when they think they are using one correctly. They should write down what the
play is (for instance, rival 1 (x1/2) fire battle vs. my ¾. I win because ½ < ¾ ). The witness
should initial the statement if it played out as described. If they lose the battle, they can still get
a point if the player and the witness can describe what actually happened.