Georgia Department of Education Common Core Georgia Performance Standards Framework Fourth Grade Mathematics x Unit 2 Constructing Task: Write About Fractions
Adapted from Fosnot, C. The Field Trip, Context for Learning Mathematics.
STANDARDS FOR MATHEMATICAL CONTENT
MCC4.NF1 Explain why a fraction a/b is equivalent to a fraction (nxa)/(nxb) by using visual
fraction models, with attention to how the number and size of the parts differ even though the
two fractions themselves are the same size. Use this principle to recognize and generate
equivalent fractions.
MCC4.NF.2 Compare two fractions with different numerators and different denominators, e.g.,
by creating common denominators or numerators, or by comparing to a benchmark fraction such
as ½. Recognize that comparisons are valid only when the two fractions refer to the same whole.
Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by
using a visual fraction model.
STANDARDS FOR MATHEMATICAL PRACTICE
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
BACKGROUND KNOWLEDGE
Many students develop misconceptions about adding fractions, thinking the numerators can be
added and denominators can be added. For example, they might think that
1
3
1
2
+
equivalent to
2
5
ESSENTIAL QUESTIONS
x
x
x
How can you compare fraction quantities without adding fractions?
How do you know fractions are equivalent?
What can you do to decide whether your answer is reasonable?
MATERIALS
x
x
Connecting cubes
Strips of equal length paper
MATHEMATICS y GRADE 4y UNIT 2: Fraction Equivalents Georgia Department of Education Dr. John D. Barge, State School Superintendent May 2012 y Page 15 of 63 All Rights Reserved Georgia Department of Education Common Core Georgia Performance Standards Framework Fourth Grade Mathematics x Unit 2 x
x
Write About Fractions task sheet
Fraction Kits
GROUPING
Individual
TASK DESCRIPTION, DEVELOPMENT AND DISCUSSION
Comments: Students have had some opportunities to work with comparing unit fractions with
different denominators in context. By exploring this procedure in context and examining the
results, students are supported to develop deep understandings about fractions, thereby avoiding
common misconceptions.
Task directions:
Students will follow the directions below from the “Write About Fractions” task sheet.
Write a convincing argument for the following statement:
1
1
+
2
3
does not equal
2
5
FORMATIVE ASSESSMENT QUESTIONS
x
x
x
x
x
What do you notice about the unit fractions you have created?
How can drawing a model help you answer this question?
What strategies can you use to help write about this topic?
Can you give me an estimated size of the fraction you created with that cut?
Does your answer make sense? How do you know?
DIFFERENTIATION
Extension
x In addition to this task, student can identify a fraction that is equal to ½ + 1/3.
Intervention
x Provide fraction strips the students can manipulate to determine their response.
x Encourage students to use words, numbers and/or pictures in their explanation.
Name _________________________________________ Date___________________________
MATHEMATICS y GRADE 4y UNIT 2: Fraction Equivalents Georgia Department of Education Dr. John D. Barge, State School Superintendent May 2012 y Page 16 of 63 All Rights Reserved Georgia Department of Education Common Core Georgia Performance Standards Framework Fourth Grade Mathematics x Unit 2 Write About Fractions
Write a convincing argument for the following statement:
1
1
+
2
3
does not equal
2
5
Constructing Task: Benchmark Fractions
MATHEMATICS y GRADE 4y UNIT 2: Fraction Equivalents Georgia Department of Education Dr. John D. Barge, State School Superintendent May 2012 y Page 17 of 63 All Rights Reserved