Cover Up
Current California Math Standards
Cover Up
Grade Three Number Sense
3.0 Students understand the relationship between whole numbers, simple fractions, and decimals:
3.1 Compare fractions represented by drawings or concrete materials to show equivalency and to add and
subtract simple fractions in context (e.g., 1/2 of a pizza is the same amount as 2/4 of another pizza that is
the same size; show that 3/8 is larger than 1/4).
3.2 Add and subtract simple fractions (e.g., determine that 1/8 + 3/8 is the same as 1/2).
Grade Four Number Sense
1.0 Students understand the place value of whole numbers and decimals to two decimal places and how whole
numbers and decimals relate to simple fractions. Students use the concepts of negative numbers:
1.5 Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division
of whole numbers by whole numbers; explain equivalence of fractions.
Grade Five Number Sense
2.0 Students perform calculations and solve problems involving addition, subtraction, and simple multiplication
and division of fractions and decimals:
2.3 Solve simple problems, including ones arising in concrete situations, involving the addition and
subtraction of fractions and mixed numbers (like and unlike denominators of 20 or less), and express
answers in the simplest form.
Grade Six Number Sense
1.0 Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve
problems involving fractions, ratios, proportions, and percentages:
1.1 Compare and order positive and negative fractions, decimals, and mixed numbers and place them on
a number line.
2.0 Students calculate and solve problems involving addition, subtraction, multiplication, and division:
2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and
explain why a particular operation was used for a given situation.
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Cover Up
Materials:
Set of fraction strips (1 whole, 1/2, 1/4, 1/8, and 1/16) for each student (see pages 7-11)
Two large sets of fraction strips to use for the demonstration(enlarge the fraction strip masters by 160%)
Fraction dice with faces labeled 1/2, 1/4, 1/8, 1/8, 1/16, and 1/16 for each pair of students (label a blank
wooden cube with the fractions or create with a paper dice template)
One recording sheet per student (see page 6)
Mathematical Practice Standards:
3. Construct viable arguments and critique the reasoning of others.
7. Look for and make use of structure.
Current California Content Standards:
Grade 3 – NS 3.1 and NS 3.2
Grade 4 – NS 1.5
Grade 5 – NS 2.3
Grade 6 – NS 1.1 and NS 2.1
Background Information:
This activity helps students to see how fractions relate to one another. This activity allows students to
practice benchmarking (I still have more/less than half to go to win the game); subtracting (I only need
1/16 to win the game); and making equivalent fractions (I can roll 1/4 and win but I can also roll 1/8
twice and win). Having students make an observation after each turn is an important part of the
learning, so be sure to model this well during your demonstration.
Introduction (5 minutes):
Inform students that they are going to play a game called Cover Up. The object of the game is to be the
first person to use the fraction pieces in the baggie to cover the blue “game board” exactly without
going over. Share with students that when it is their turn to play, each student will receive a baggie of
fraction pieces, and each pair of students will share a die. Explain that the die has faces labeled 1/2, 1/4,
1/8, 1/8, 1/16, and 1/16 to match the fraction pieces that will be used in the game. Each time you roll
the die you get to take the piece that matches the fraction rolled and place it on the blue fraction
labeled with the number one (the game board). Then you need to make an observation about the
progress of the game. Tell them you are going to play a game against one student from the class so
everyone can better understand the game.
Demonstration of how to play Cover Up (15 minutes):
Place the blue “game boards” on the whiteboard. Teacher rolls first to model the process. Let’s say you
have rolled 1/4. You would take the yellow 1/4 piece and place it on the blue game board. Now make a
statement about what you observe. Some possible statements are: “I can see that I have covered 1/4 of
the whole game board or I have covered less than ½ of the whole game board”. Then you say “done”
and the partner now takes a turn (which in this case is the student you have selected from the class).
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The student rolls the die and repeats the process. For example, they may roll 1/8. They can say “I have
covered 1/8 of my game board. You have covered more of your game board. You are winning. Done.”
Continue to play until one person has covered their game board EXACTLY. If a fraction is rolled that
would result in covering more than one whole nothing can be put on the game board and the next
player takes their turn.
1) Once a player makes EXACTLY one whole, both game boards need to have the pieces arranged
from least to greatest (see figure below). This aligns well with the standards of arranging
fractions on a number line from least to greatest.
2) Now demonstrate how to record this information on the student recording sheet (see figure
below).
3) Now look at the game boards to determine how close the opponent was to winning the game.
Model how to complete the game board using only one color (see figure below) so the pieces
will have a common denominator. This shows how far the player was from one whole.
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4) Model how to record the difference on the recording sheet (see figure below). For older
students you can then ask them to find all the other ways to name that fraction.
5) Each student then records some observations about the game which could include things they
noted about: equivalent fractions, the size of the fraction pieces, strategy they employed when
determining which trades to make, the probability of rolling certain fractions versus others
based on the way the die was made, and etc.
Student’s Play the Game (10 minutes): Tell students they are going to do the following:
1) Roll the die to determine who is going to go first (greatest fraction goes first; students may need
to use the game pieces to determine who rolled the largest fraction).
2) Remove the pieces from the baggie.
3) Students take turn rolling the die and placing fraction pieces on the game board.
4) Students must make an observation at the end of each turn.
5) Record the math problems on their papers after the game is done (be sure the fractions are
arranged from least to greatest).
6) Write about their observations.
Closure/Eliciting Student Thinking (15 minutes):
Depending on what grade level standards you are addressing, you can ask students to describe:
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observations they made while playing the game (call on 2 or 3 volunteers; if the conversation heads
in the direction of equivalent fractions or the value of a fraction that is perfect; if not move on to the
next prompts to guide the conversation toward the grade level standards).
a game where someone won quickly (1/2 + 1/2). Why did the game go so quickly?
a game that took a long time (one with lots of pieces). Why did it take so long?
where on the number line these fractions would be found (between what two whole numbers)
what it means when we have a denominator of 16. A denominator of 4. What happens to the size
of the game pieces as the denominator gets bigger? So when we compare 1/16 with 1/4 which
fraction is larger? Ask students to tell you why some students might say 1/16 is bigger than 1/4.
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Extension:
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Have students create a sum of one using a specific number of pieces. Below are just a few
examples:
o 3 pieces 1/2 + 1/4 + 1/4
o 5 pieces 1/4 +1/4 + 1/4 + 1/8 + 1/8;
o 6 pieces 1/2 + 1/8 + 1/8+ 1/8 + 1/8
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COVER UP
Fractions from my board
Fractions from my opponent’s board
Difference between the two game boards
Observations about the game:
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Fraction Strip Masters (1 whole - blue)
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Fraction Strip Masters (1 whole - blue)
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Fraction Strip Masters (1/4 - yellow)
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Fraction Strip Masters (1/8 - red)
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Fraction Strip Masters (1/16 - green)
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