In Class Reference Sheet
Big Idea 4: Fractions and mixed numbers with like denominators (same size parts) can be added or subtracted.
Topic 4: Apply Your Knowledge
Key Concept: Addition and subtraction of fractions can be used to solve a variety of problems.
Prior Knowledge:
1. Understands part/whole relationships.
2. Writes mixed numbers and improper fractions
Activity 1: Improper Fractions with Pattern Blocks
Description
Students use pattern blocks to
model improper fractions.
Vocabulary
Preparation for
Learning
Teacher/Student
Dialogue
Indicators of
Understanding *
Content: area, shape, fractional part
Process: drag, click, fill
Provide students with pattern blocks. Have student take out a hexagon and cover it
with trapezoids. Ask students to provide the fractions represented by the trapezoids
(1/2).
• Rephrase the problem stating that the trapezoid represents 1 whole. How
many wholes are there in the hexagon? (2)
• Ask students to cover the hexagon with triangles. If the hexagon represents
2 wholes, what does each triangle represent? (thirds) How many thirds in all?
• Tell students that they need to identify the whole first and then the fractional
parts.
Open the Unitizing with Pattern Blocks tool.
• Select a grey area and place it on the grid, making sure to lock the grid.
• Set the value of the grey area as a fractional representation greater than
1 whole.
• Review the process terms of drag and click as you demonstrate.
• Ask: “How many triangles does it take to cover the design? How many wholes
are in this design? How many parts does ___ cover?”
• Again, have students first identify the whole then the fractional parts.
While students are working in the software, be sure to circulate and ask:
• How is this area divided?
• What is the sum of the fractional parts?
• Is there a different way you could show the same fraction?
Can determine the whole (unit).
Writes the value of a fractional part of a whole when the whole is defined.
Uses addition strategies to check that the sum of all parts is equal to the
whole.
* 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 4: Fractions and mixed numbers with like denominators (same size parts) can be added or subtracted.
Topic 4: Apply Your Knowledge
Key Concept: Addition and subtraction of fractions can be used to solve a variety of problems.
Prior Knowledge:
1. Understands part/whole relationships.
2. Writes mixed numbers and improper fractions.
Activity 2: Mixed Numbers with Pattern Blocks
Description
Students use pattern blocks to model
mixed numbers.
Vocabulary
Content: area, shape, fractional part, value, unknown
Process: drag, blocks, create, overlap
Preparation for
Learning
Teacher/Student
Dialogue
Indicators of
Understanding *
Review Activity 1, reminding students that an improper fraction can be written as a
mixed number.
Open the Unitizing with Pattern Blocks tool.
• Select a grey area and place it on the grid, making sure to lock the grid.
• Create a grey area of a hexagon and set the value to 2.
• Review the process terms of drag and click as you demonstrate.
• Ask: How many wholes are in this design? How many triangles do we need to
cover the whole? Cover 5 parts of the wholes with blue. Have students
determine what improper and mixed number is represented.
• Discuss how finding the whole can help you determine the value or number
for each colored part of the shape.
• Show multiple examples assisting students in first determining the whole and
then the value of each colored part.
While students are working in the software, be sure to circulate and ask:
• What part is equal to one whole? How many triangles create a whole?
• 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)?
Can determine the whole (unit).
Determines the value of a fractional part when more than one whole is
provided.
• Uses addition to check that the sum of all parts is equal to the given unit
number.
* 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 4: Fractions and mixed numbers with like denominators (same size parts) can be added or subtracted.
Topic 4: Apply Your Knowledge
Key Concept: Addition and subtraction of fractions can be used to solve a variety of problems.
Prior Knowledge:
1. Understands part/whole relationships.
2. Writes mixed numbers and improper fractions.
Activity 3: Challenge: Improper Fractions & Mixed Numbers
Description
Students synthesize their
knowledge of adding and
subtracting mixed numbers and
improper fractions with like
denominators to determine the
missing elements of a given
equation.
Vocabulary
Content: proper fractions, improper fractions, mixed numbers, convert, equation
Preparation for
Learning
Teacher/Student
Dialogue
Indicators of
Understanding *
Process: complete, missing, fill
Review key vocabulary and model usage during lesson.
Play Mystery Equation:
• Show students an equation using mixed numbers with like fractions that has
two parts missing.
• Have students work in groups to figure out the missing parts.
• Encourage students to use a variety of models, manipulatives, and
mathematical strategies to figure out and check their solution.
• Have students share. Discuss and compare the strategies of different groups.
• Repeat with a variety of equations.
Help students to learn and apply the inverse operations of addition and subtraction to
find the missing parts.
• Encourage students to begin with what they know. For example first fill in the
denominators (these are all like fractions).
While students are working in the software, be sure to circulate and ask:
• What mathematical strategies are you using to complete these equations?
• What would a model for this equation show? How can you use the model to
assist you?
Solves addition and subtraction problems with mixed numbers and improper
fraction with like denominators.
• Uses mathematical strategies and models to complete equations with missing
elements.
• Uses mathematical terms to explain his/ her mathematical thinking as he/she
determines missing elements of an equation.
* Indicators of Understanding are in addition to the formative assessment at the end of each activity.
•
www.conceptuamath.com
© 2010 Conceptua Math LLC
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