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Using Concrete and Pictorial Tools to Help Students Understand Fractions
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srpowell@austin.utexas.edu @sarahpowellphd
119
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Instructional Platform
INSTRUCTIONAL DELIVERY Explicit instruction Precise language Multiple representations INSTRUCTIONAL STRATEGIES Fluency building Problem solving instruction Motivation component
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Explicit Instruction Modeling Practice Clear Explanation Guided
Independent Practice Planned Examples Supporting Practices Asking the right questions Eliciting frequent responses Providing immediate specific feedback Maintaining a brisk pace
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Use formal math language
Precise Language Use formal math language concise Use terms precisely
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Multiple Representations
Abstract Pictorial Concrete
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Length/Measurement Fractions are appropriated by length
Fraction tiles/bars
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Length/Measurement Fractions are appropriated by length
Cuisenaire rods
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Length/Measurement Fractions are appropriated by length Number line
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Select a fraction and teach using the length model.
Explicit instruction Precise language Multiple representations
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Area/Region Shapes divided into equal sections Fraction circles
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Area/Region Shapes divided into equal sections Geoboards
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Area/Region Shapes divided into equal sections Pattern blocks
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Area/Region Shapes divided into equal sections Legos
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Area/Region Shapes divided into equal sections Anglegs
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Select a fraction and teach using the area model.
Explicit instruction Precise language Multiple representations
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Set/Discrete Individual shapes match the fraction Two-color counters
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Set/Discrete Individual shapes match the fraction
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Select a fraction and teach using the set model.
Explicit instruction Precise language Multiple representations
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Improper Fractions Mixed Numbers
Fractions equal to or greater than 1 Numerator is equal to or greater than denominator Select a fraction and teach using two models of fractions. Explicit instruction Multiple representations Precise language Mixed Numbers A mix of a whole number and a fraction
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Equivalent Fractions Determine equivalent fractions.
Explicit instruction Precise language Multiple representations
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Multiple representations
Comparing Fractions Compare two fractions. Explicit instruction Precise language Multiple representations
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Multiple representations
Ordering Fractions Compare to benchmark fractions Order three fractions. Explicit instruction Precise language Multiple representations
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Addition
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Addition
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Multiple representations
Explicit instruction Precise language Multiple representations
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Addition
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Addition 2: 2, 4, 6, 8, 10 4: 4, 8, 12, 16, 20
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Addition
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Multiple representations
Explicit instruction Precise language Multiple representations
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Subtraction
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Multiple representations
Explicit instruction Precise language Multiple representations
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Subtraction Take away from this set This is for reference
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Multiple representations
Explicit instruction Precise language Multiple representations
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Multiplication Multiplication Interpret multiplication sign as “of”
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One-half of four-fourths
Multiplication Show One-half of four-fourths
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One-half of two-fourths
Multiplication Show One-half of two-fourths
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One-half of one-fourth One-half of one-fourth
Multiplication Show One-half of one-fourth One-half of one-fourth
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One-half of three-fourths
Multiplication Show One-half of three-fourths
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One-half of one-fourth One-half of one-fourth One-half of one-fourth
Multiplication Show One-half of one-fourth One-half of one-fourth One-half of one-fourth
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Multiplication Show
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Multiplication
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Division Division “How many sets of the second fraction fit into the first fraction?”
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Division Show 1 set of one-third 2 sets of one-third
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Division Show 1 set of one-third 2 sets of one-third
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Two-thirds set of one-half
Division Show 1 set of one-half Two-thirds set of one-half
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Division Show
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Division
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Instructional Platform
INSTRUCTIONAL DELIVERY Explicit instruction Concise language Multiple representations INSTRUCTIONAL STRATEGIES Fluency building Problem solving instruction Motivation component
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srpowell@austin.utexas.edu @sarahpowellphd
119
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