In-Class Reference Sheet
Big Idea 4: Fractions and mixed numbers with like denominators (same size parts) can be added or subtracted.
Topic 3: Addition and Subtraction of Mixed Numbers
Key Concept: Whole numbers and proper fractions can be added to mixed numbers or subtracted from mixed
numbers.
Prior Knowledge:
1. Writes and models improper fractions and mixed numbers.
2. Illustrates addition and subtraction of like fractions using a variety of models.
3. Understands that addition and subtraction are inverse operations.
4. Understands that fractions that are combined can make up a whole.
Activity 1: Add & Subtract Mixed Numbers: No Converting
Description
Students use models to add and
subtract mixed numbers.
Vocabulary
Content: mixed number, sum, fractional part, common denominator
Process: shade, model
Preparation for
Learning
Open the Adding Fractions with Common Denominators tool.
• Use the models only. Turn off numerical fractions option.
• Show a model of a mixed numbers. Have students write the mixed number
that is represented in the model.
• Ask students to provide the improper fraction for the shown mixed number.
• Review/Introduce that when adding mixed numbers we add all of the
fractional parts.
• Ask: “How many wholes does this model show? How many parts?”
• Use this information to correctly determine the sum of the equation.
Open the Subtraction Fractions with Common Denominators tool.
• Again, use only the models.
• Ask: “How many wholes are in the subtrahend? How many parts?” Explain
that the number of wholes and number of parts in the subtrahend need to be
subtracted/taken away from the minuend.
• Drag the model to show this, and determine the difference of the equation.
While students are working in the software, be sure to circulate and ask:
• How many wholes are in the fraction? How many parts?
• What would a model of that sum/difference/equation look like?
Teacher/Student
Dialogue
Indicators of
Understanding *
Represents an addition and subtraction problems involving mixed numbers
using concrete manipulatives or computer models.
• Finds the sum or difference of two mixed numbers.
* Indicators of Understanding are in addition to the formative assessment at the end of each activity.
•
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1
In-Class Reference Sheet
Big Idea 4: Fractions and mixed numbers with like denominators (same size parts) can be added or subtracted.
Topic 3: Addition and Subtraction of Mixed Numbers
Key Concept: Whole numbers and proper fractions can be added to mixed numbers or subtracted from mixed
numbers.
Prior Knowledge:
1. Writes and models improper fractions and mixed numbers.
2. Illustrates addition and subtraction of like fractions using a variety of models.
3. Understands that addition and subtraction are inverse operations.
4. Understands that fractions that are combined can make up a whole.
Activity 2: Convert Improper Fractions
Description
Students convert improper fractions
to mixed numbers.
Vocabulary
Content: convert, amount, improper fraction, rewrite, whole, mixed number
Process: No new vocabulary
Preparation for
Learning
Teach students the definition of convert, and model usage during lesson.
Provide students with fraction circle manipulatives:
• Ask students to build an improper fraction such as 5/4 with their circles.
• Ask, “How many wholes are there?” and “How many parts of the whole
remain?” Lastly, ask, “How many parts is the whole in this example divided
into?”
• Have students rewrite the improper fraction as a mixed number.
• Provide students with multiple examples for practice.
• Have students generate other ways 1 whole can be written as a fraction.
Repeat more examples with manipulatives having students state the number of
wholes and x parts more.
Open the Indenting Fractions tool and create models of improper fractions. On chart
paper record both the improper fraction and the mixed number for the models
created.
• Model and define terms rewriting and converting.
While students are working in the software, be sure to circulate and ask:
• How many wholes are in that model? How many parts?
• How many groups of __(numerator) can you get from __(denominator)? How
many times does __(numerator) go into __(denominator)?
Teacher/Student
Dialogue
Indicators of
Understanding *
Converts improper fractions to mixed numbers.
Can describe a model in terms of improper fractions or mixed numbers.
Can state and write a whole number as a fraction.
* 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 4: Fractions and mixed numbers with like denominators (same size parts) can be added or subtracted.
Topic 3: Addition and Subtraction of Mixed Numbers
Key Concept: Whole numbers and proper fractions can be added to mixed numbers or subtracted from mixed
numbers.
Prior Knowledge:
1. Writes and models improper fractions and mixed numbers.
2. Illustrates addition and subtraction of like fractions using a variety of models.
3. Understands that addition and subtraction are inverse operations.
4. Understands that fractions that are combined can make up a whole.
Activity 3: Addition with Mixed Numbers: Converting
Description
Students model addition problems
will like fractions and convert the
sums to mixed numbers.
Vocabulary
Preparation for
Learning
Teacher/Student
Dialogue
Indicators of
Understanding *
Content: rewrite/rewritten, convert, mixed number, improper fraction, equation
Process: No new vocabulary
Review key vocabulary and model usage during lesson.
As with the last activity, provide students with fraction circle manipulatives:
• Review Activity 2 for converting improper fractions to mixed numbers.
• Have students work with a partner. Have each partner build one of the
addends of an equation with two like fraction, of which the sum is greater
than 1.
• Have students add the wholes and then add the fractional parts of the models.
Ask, “What is the sum of your equation? How many wholes are there? How
many parts of the whole remain?”
• Have the students record the answer without converting and then converted.
Reinforce that both show the same value, however, when the fractional part is
improper we rewrite it. Provide students with multiple examples for practice
reinforcing that adding mixed numbers is similar to adding whole numbers and
proper fractions.
While students are working in the software, be sure to circulate and ask:
• How many wholes are in the sum? How many parts remain?
• What strategies did you use to check your work?
•
•
Adds two equations with like fractions whose sum is greater than 1.
Uses models, manipulatives, and cognitive strategies to convert a fraction
from an improper fraction to a mixed number.
* 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 4: Fractions and mixed numbers with like denominators (same size parts) can be added or subtracted.
Topic 3: Addition and Subtraction of Mixed Numbers
Key Concept: Whole numbers and proper fractions can be added to mixed numbers or subtracted from mixed
numbers.
Prior Knowledge:
1. Writes and models improper fractions and mixed numbers.
2. Illustrates addition and subtraction of like fractions using a variety of models.
3. Understands that addition and subtraction are inverse operations.
4. Understands that fractions that are combined can make up a whole.
Activity 4: Convert Mixed Numbers
Description
Students use models to convert
mixed numbers to improper
fractions.
Vocabulary
Content: convert, mixed number, improper fraction, divided
Process: No new vocabulary
Preparation for
Learning
Teacher/Student
Dialogue
Indicators of
Understanding *
Review key vocabulary and model usage during lesson.
Open the Identifying Fractions tool.
• Review Activity 2 for converting improper fractions to mixed numbers. Tell
students that today you will be converting mixed numbers to improper
fractions using inverse thinking. Instead of looking at the number of wholes
with the number of remaining parts, you are now looking at the number of
parts in total.
• Show students an example of a mixed number using the model only in the
tool. Ask students to tell you what the model represents numerically.
• Students need to understand that the same model can be represented by an
improper fraction or mixed number.
• Provide students with multiple examples for practice.
While students are working in the software, be sure to circulate and ask:
• How many parts are in each whole? How many parts do you have total?
• What would a model for that fraction look like?
• Approximately where on the number line would that sum be located?
•
•
Correctly labels models with mixed number and improper fraction.
Converts mixed numbers to improper 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
4
In-Class Reference Sheet
Big Idea 4: Fractions and mixed numbers with like denominators (same size parts) can be added or subtracted.
Topic 3: Addition and Subtraction of Mixed Numbers
Key Concept: Whole numbers and proper fractions can be added to mixed numbers or subtracted from mixed
numbers.
Prior Knowledge:
1. Writes and models improper fractions and mixed numbers.
2. Illustrates addition and subtraction of like fractions using a variety of models.
3. Understands that addition and subtraction are inverse operations.
4. Understands that fractions that are combined can make up a whole.
Activity 5: Subtraction with Mixed Numbers: Converting
Description
Students use models to subtract two
fraction numbers in which the
minuend is greater than 1. Students
convert mixed numbers differences
to improper fractions.
Vocabulary
Preparation for
Learning
Teacher/Student
Dialogue
Indicators of
Understanding *
Content: difference, mixed number, improper fraction, equation
Process: drag, complete, arrow
Review greater than, less than, and equal to signs and concepts.
Open the Subtracting Fractions with Common Denominators tool.
• Show students a model (without numerical labels) in which the minuend is
greater than 1.
• Drag the subtrahend to cover the minuend and show students that sometimes
you cannot take the subtrahend away from the remaining parts, but you have
to take it from the whole.
• Therefore, in order to do this mathematically, it is easiest to convert the mixed
number into an improper fraction. Show them how if they convert the mixed
number to an improper fraction, they can subtract the like improper fractions,
just like any other two fractions. Review multiple examples.
Open the subtracting Fractions with Uncommon Denominator tool and create the
problem 1 1/5 – 3/10.
• Model step 1 and find a common denominator.
• Drag the model of 3/10 on next to the fractional part 2/10 to illustrate the need
to convert.
While students are working in the software, be sure to circulate and ask:
• How many parts do you have in total? How many parts do you need to
subtract from the whole?
• What would a model for that fraction look like?
Subtracts like fractions whose minuend is greater than 1.
Uses models, manipulatives, and cognitive strategies to convert a fraction
from a mixed number to an improper fraction.
* 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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