In-Class Reference Sheet
Big Idea 2: Fractions with like denominators (same size parts) are numbers that can be easily added or
subtracted because the size of the parts in each of the wholes is the same.
Topic 3: Missing Parts
Key Concept: Inverse relationships that occur in whole numbers also occur with fractions.
Prior Knowledge:
1. Writes and models fractions less than 1 whole.
2. Illustrates addition and subtraction of like fractions using a variety of models.
3. Addition and subtraction of whole numbers including solving for unknowns.
4. Understands that addition and subtraction are inverse operations.
5. Addition and subtraction of like fractions.
Activity 1: Missing Addends
Description
Student determines the value of a
missing addend.
Vocabulary
Content: addend, unknown
Process: model, unknown
Preparation for
Learning
Open the Addition with Common Denominators tool and create an equation. Define and
use the term addend.
Cover one of the addends with a large piece of paper.
• Give students three possible options for what the missing addend could be. Have
students discuss and justify their thinking.
• Using the model, show students how to drag the shown addend over the model of
the sum to assist in determining the missing addend.
• Explain that they can subtract the known addend from the sum to find the missing
addend. Reveal the answer.
• Without showing your work, create another example and cover one addend.
• Have students generate possible numbers for the missing addend.
Ask them questions such as, “What would the denominator be?” or “Would the addend
be greater than or less than one half?”
Teacher/Student
Dialogue
While students are working in the software, be sure to circulate and ask:
• How many more parts of the whole do you need to have in order to have the
same amount of parts as the sum?
• How did you determine ___ is the missing addend?
• How did you use subtraction to solve for the missing addend?
Indicators of
Understanding*
•
•
Determines the value of a missing addend by using subtraction.
Verbalizes, using effective reasoning and mathematical terms, the process by
which the value of the missing addend was determined.
* Indicators of Understanding are in addition to the formative assessment at the end of each activity.
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© 2010 Conceptua Math LLC
1
In-Class Reference Sheet
Big Idea 2: Fractions with like denominators (same size parts) are numbers that can be easily added or
subtracted because the size of the parts in each of the wholes is the same.
Topic 3: Missing Parts
Key Concept: Inverse relationships that occur in whole numbers also occur with fractions.
Prior Knowledge:
1. Writes and models fractions less than 1 whole.
2. Illustrates addition and subtraction of like fractions using a variety of models.
3. Addition and subtraction of whole numbers including solving for unknowns.
4. Understands that addition and subtraction are inverse operations.
5. Addition and subtraction of like fractions.
Activity 2: Missing Minuend or Subtrahend
Description
Student determines the missing
minuend or subtrahend using known
information and models.
Vocabulary
Content: minuend, subtrahend
Process: unknown, model
Preparation for
Learning
Open the Subtraction with Common Denominators tool.
• Review Activity 1 and define and use the terms minuend and subtrahends
while modeling an example.
• Have students work with a partner to develop an equation. Have one student
cover either the minuend or the subtrahend using a folded piece of paper with
the word minuend or subtrahend. Have the partner solve the equation.
Model some of the student examples.
• Remind students that they can drag the shown part of the equation over the
model of the difference to assist in determining the unknown.
• Ask students to explain their thinking. If students are not effectively
verbalizing their thinking, take on the role of a student and model your
thinking aloud as you work through the process.
Teacher/Student
Dialogue
While students are working in the software, be sure to circulate and ask:
• How did you come to the conclusion that ___ is the missing minuend or
subtrahend?
• How did you use subtraction to solve for the unknown?
• How are the models assisting you in solving for the unknown?
Indicators of
Understanding*
•
•
Solves for the missing minuend or subtrahend in a subtraction equation.
Manipulates models to demonstrate a correct subtraction equation.
* Indicators of Understanding are in addition to the formative assessment at the end of each activity.
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© 2010 Conceptua Math LLC
2
In-Class Reference Sheet
Big Idea 2: Fractions with like denominators (same size parts) are numbers that can be easily added or
subtracted because the size of the parts in each of the wholes is the same.
Topic 3: Missing Parts
Key Concept: Inverse relationships that occur in whole numbers also occur with fractions.
Prior Knowledge:
1. Writes and models fractions less than 1 whole.
2. Illustrates addition and subtraction of like fractions using a variety of models.
3. Addition and subtraction of whole numbers, including solving for unknowns.
4. Understands that addition and subtraction are inverse operations.
5. Addition and subtraction of like fractions.
Activity 3: Addition and Subtraction: Missing Unknowns
Description
Students use mathematical strategies
and models to solve for the unknown
addend, minuend, or subtrahend in an
addition or subtraction equation with
two like fractions.
Vocabulary
Preparation for
Learning
Content: difference
Process: unknown
Review strategies to find a missing addend, minuend, or subtrahend using the Adding
Fractions with Common Denominator and Subtracting Fractions with Common
Denominators tools.
• Write strategies on chart paper noting similarities and differences.
• Use math terminology while modeling.
• Require students to us correct mathematical terminology when discussing
their processes. You can assist students in this by having key mathematical
terms written on placards or by giving students key word lists.
• Prepare students for the activity through modeling examples.
Teacher/Student
Dialogue
While students are working in the software, be sure to circulate and ask:
• How is the process different when you solve for a missing addend versus
when you solve for a missing minuend or subtrahend?
• How is the process similar when you solve for a missing addend versus when
you solve for a missing minuend or subtrahend?
• How is the model helping you to solve for the unknown?
• When students get to the examples without models ask: What would a model
look like for this equation?
• How are addition and subtraction similar? How are they different?
Indicators of
• Determines the correct value of the missing addend in an addition equation
Understanding*
with two like fractions.
• Determines the correct value of the missing minuend or subtrahend in a
subtraction equation with two like fractions.
* Indicators of Understanding are in addition to the formative assessment at the end of each activity.
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© 2010 Conceptua Math LLC
3
In-Class Reference Sheet
Big Idea 2: Fractions with like denominators (same size parts) are numbers that can be easily added or
subtracted because the size of the parts in each of the wholes is the same.
Topic 3: Missing Parts
Key Concept: Inverse relationships that occur in whole numbers also occur with fractions.
Prior Knowledge:
1. Writes and models fractions less than 1 whole.
2. Illustrates addition and subtraction of like fractions using a variety of models.
3. Addition and subtraction of whole numbers including solving for unknowns.
4. Understands that addition and subtraction are inverse operations.
5. Addition and subtraction of like fractions.
Activity 4: Compare Sums and Differences of Proper Fractions
Description
Students compare sums and
differences of proper fractions.
Vocabulary
Preparation for
Learning
Teacher/Student
Dialogue
Indicators of
Understanding*
Math: symbol, less than, greater than
Process: compare
Open the Addition with Common Denominators tool, and review terms while modeling.
Comparing Sums Mystery Bags:
• Place a large variety of index cards in a bag containing addition with like fraction
equations (one equation per card.)
• Partner students. Take turns calling each set of students to the front of the class.
Each student selects a card from the bag, reads, models, and solves the
equation.
• Partners share their thinking aloud to decide which sum was greater.
• If the partnership cannot determine which sum is greatest, they can seek help
from their classmates. Do not allow classmates to give them the answer, but
rather, only suggest strategies for approaching a solution.
Repeat “Comparing Mystery Bags,” but instead of for sums, do a Comparing Differences
Mystery bag containing subtraction with like fraction equations.
While students are working in the software, be sure to circulate and ask:
• What is the sum/difference of that equation?
• Is the difference of that equation closer to 0, 1/2, or 1?
Determines the sum of two equations.
Determines the differences of two equations.
Estimates the location of a sum or difference on a number line.
Given a pair of like fractions, determines the greater fraction.
Correctly reads an equation showing the greater than or less than symbols.
* Indicators of Understanding are in addition to the formative assessment at the end of each activity.
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© 2010 Conceptua Math LLC
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