In-Class Reference Sheet
Big idea 5: Equivalent fractions name the same amount by using different-sized fractional parts.
Topic 1: Introduction to Equivalent Fractions
Key Concept: Equivalent fractions represent the same part of a whole.
Prior Knowledge:
1. Understands the relationship between numerator and denominator of a fraction.
2. Models and writes fractions.
3. Understands the concept of multiplication.
4. Understands equality.
Activity 1: Make Equivalent Fractions
Description
.
Students are given the model of one
fraction and are directed to shade
parts of a second to show an
equivalent.
Vocabulary
Content: equivalent, equal, ordinal numbers (thirds, fourths, etc.)
Process: more, fewer, shade, parts, model
Preparation for
Learning
Teacher/Student
Dialogue
Provide students with fraction circles and have students cover one half of the circle.
• Ask students to find different ways to cover the remaining half of the circle and
record answers on a chart by color, for example two blues.
• Explain that these fractions are equivalent if they cover the same amount of
the circle. They have the same value.
• Explain that this is true for any model that represents fractions.
Open the Equivalent Fractions tool. Hide the numbers, select the area model, and
shade one half of each of the three models.
• Note: you can also provide students with squares that they can fold while
following along.
• Use the slider for the model in the center to partition it into fourths.
• Partition the model on the right into sixths.
• You can keep working with the models to partition into eighths, tenths, and
twelfths.
Guide students in discovering that the area of each model is the same, but the number
of equal parts is more and therefore the number of shaded parts is more.
While students are working in the software, be sure to circulate and ask:
• How do you know these fractions are equal?
• If your model of an equivalent has two times as many equal parts how many
times as many shaded parts will there be?
• How do we know when fractions are equivalent?
Indicators of
Understanding*
•
•
•
Can model at least one equivalent for a given fraction.
Explains what is meant by an equivalent fraction.
Indicators of Understanding are in addition to the formative assessment at the end of each activity.
www.conceptuamath.com
© 2010 Conceptua Math LLC
1
In-Class Reference Sheet
Big idea 5: Equivalent fractions name the same amount by using different-sized fractional parts.
Topic 1: Introduction to Equivalent Fractions
Key Concept: Equivalent fractions represent the same part of a whole.
Prior Knowledge:
1. Understands the relationship between numerator and denominator of a fraction.
2. Models and writes fractions.
3. Understands the concept of multiplication.
4. Understands equality.
Activity 2: Make More Equivalent Fractions
Description
.
Students are given the model of one
fraction and are directed to shade
parts of a second to show an
equivalent. Models are linked to
numbers showing the relationship
between the models and fraction
numbers.
Vocabulary
Content: equivalent, equal, ordinal numbers (thirds, fourths, etc.)
Process: more, fewer, shade, parts, model
Preparation for
Learning
Teacher/Student
Dialogue
Open the Equivalent Fractions tool. Select the vertical bar model and shade one half
of each of the three models. Build on the previous lesson by reinforcing vocabulary.
• Have students brainstorm and create models that are equivalent to 1/2.
• Draw students’ attention to the fraction number each time they create an
equivalent.
• Have students record the fraction 1/2 and each of the equivalent fractions.
• Guide students in discovering the proportional relationship between the
fractions (e.g., four times as many equal parts, and four times as many shaded
parts).
• Guide students in discovering that the area of each model is the same but the
number of equal parts is more, and therefore the number of shaded parts is
more.
While students are working in the software, be sure to circulate and ask:
• How do you know these fractions are equal?
• If your model of an equivalent has two times as many equal parts, how many
times as many shaded parts will there be?
• How do we know when fractions are equivalent?
Indicators of
Understanding*
•
•
•
Can model at least one equivalent for a given fraction.
Explains what is meant by an equivalent fraction.
Explains that equivalent fractions have the same value (shaded area).
*Indicators of Understanding are in addition to the formative assessment at the end of each activity.
www.conceptuamath.com
© 2010 Conceptua Math LLC
2
In-Class Reference Sheet
Big idea 5: Equivalent fractions name the same amount by using different-sized fractional parts.
Topic 1: Introduction to Equivalent Fractions
Key Concept: Equivalent fractions represent the same part of a whole.
Prior Knowledge:
1. Understands the relationship between numerator and denominator of a fraction.
2. Models and writes fractions.
3. Understands the concept of multiplication.
4. Understands equality.
Activity 3: Model and Write Equivalent Fractions
Description
.
Students are given the model of one
fraction and are directed to shade
parts of a second to show an
equivalent and write the equivalent
fraction number.
Vocabulary
Content: equivalent, equal, ordinal numbers (thirds, fourths, etc.)
Process: more, fewer, shade, parts, model
Preparation for
Learning
Provide students with a set of manipulative and a chart. Have students use the models
to create equivalent models for 1/2 and record the fraction numbers on a chart.
• Repeat with equivalent models for 1/4, for example.
Open the Equivalent Fractions tool. Create a model and unlink the fraction models.
• Ask students to think of an equivalent that has twice as many equal parts as the
given. Have students provide the denominator. Prompt students if needed to
discover that the numerator is also twice as many shaded parts as the given.
• Have a student create the model that matches their answer. Drag the fraction
parts of the model to the given to see if it is equivalent, adjust if necessary.
Teacher/Student
Dialogue
While students are working in the software, be sure to circulate and ask:
• How do you know these fractions are equivalent?
• If your model of an equivalent has 2 times as many equal parts how many times
as many shaded parts will there be?
• Are these fractions the same value? Why or why not?
• Explains what is meant by an equivalent fraction.
• Explains that equivalent fractions have the same value (shaded area).
• Can model and write at least one equivalent fraction for a given fraction.
Indicators of
Understanding*
*Indicators of Understanding are in addition to the formative assessment at the end of each activity.
www.conceptuamath.com
© 2010 Conceptua Math LLC
3
In-Class Reference Sheet
Big idea 5: Equivalent fractions name the same amount by using different-sized fractional parts.
Topic 1: Introduction to Equivalent Fractions
Key Concept: Equivalent fractions represent the same part of a whole.
Prior Knowledge:
1. Understands the relationship between numerator and denominator of a fraction.
2. Models and writes fractions.
3. Understands the concept of multiplication.
4. Understands equality.
Activity 4: Equivalence on a Grid
Description
.
Students are given an area in red that
represents the value of a whole. They
must either write the value for other
areas or create areas for fractions that
are given. At least two shaded areas
are equivalent.
Vocabulary
Preparation for
Learning
Teacher/Student
Dialogue
Indicators of
Understanding*
•
Content: area, fractional area, equivalent
Process: last, over
Give students an index card or rectangular piece of paper.
• Ask students to fold the paper into sixths.
• Have them label each square with the fractional value (1/6).
• Have them turn the paper over and shade in yellow and name every two
blocks of the rectangle. Model if necessary (1/3).
• Guide students in discovering that 2/6 equals the same shaded area as 1/3.
• Review equivalence and vocabulary.
• Have students shade three squares in orange and write the fractional value
(1/2).
• Guide students to discover that the fraction 1/2 is equivalent to 3/6.
Open the Unitizing Fractions on a Grid tool.
• Create a shape with eight squares.
• Ask students, if 2 squares = 1 what is another way to represent the value of the
whole? (4/4) Fill in squares with colors to represent equivalents (e.g., blue for
1/2 and yellow for 2/4).
While students are working in the software, be sure to circulate and ask:
• What is the value of the whole in this grid? What is the value of each square?
• What strategy can you use to find the fraction for the __ colored area?
• Which areas show the same value? What fractions represent the areas? Are
they equivalent?
• Explains what is meant by an equivalent fraction.
• Explains that equivalent fractions have the same value (shaded area).
• Can express a shaded area using 2 equivalent fractions.
Indicators of Understanding are in addition to the formative assessment at the end of each activity.
www.conceptuamath.com
© 2010 Conceptua Math LLC
4