enVision Mathematics Topic 8
4th Grade; January (3 weeks); 2nd Trimester
Embedded Files
Topic Title(s):
Extend Understanding of Fraction Equivalence and Ordering
Prepared Graduates:
MP3. Construct viable arguments and critique the reasoning of others.
MP5. Use appropriate tools strategically.
MP6. Attend to precision.
MP7. Look for and make use of structure.
Standard(s):
1. Number and Quantity
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
4.NF.A. Number & Operations—Fractions: Extend understanding of fraction equivalence and ordering.
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) 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. (CCSS: 4.NF.A.1)
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 1/2. 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. (CCSS: 4.NF.A.2)
Explain the equivalence of fractions. (MP3)
Use visual models and benchmark fractions as tools to aid in fraction comparison. (MP5)
Precisely refer to numerators, denominators, parts, and wholes when explaining fraction equivalence and comparing fractions. (MP6)
Use 1, the multiplicative identity, to create equivalent fractions by structuring 1 in the fraction form n/n. (MP7)
Inquiry Questions
Why does it work to compare fractions either by finding common numerators or by finding common denominators?
How can you be sure that multiplying a fraction by n/n does not change the fraction’s value?
Coherence Connections
This expectation represents major work of the grade.
In Grade 3, students develop an understanding of fractions as numbers and the meaning of the denominator of a unit fraction.
In Grade 4, this expectation connects to building fractions from unit fractions, using decimal notation and comparing decimal fractions, and using the four operations with whole numbers to solve problems.
In Grade 5, students use equivalent fractions as a strategy to add and subtract fractions with unlike denominators and apply and extend previous understandings of multiplication and division to fractions.
Academic Vocabulary & Language Expectations:
Fraction, numerator, denominator, equivalent fractions, common factor, benchmark fraction
Assessments:
Instructional Resources & Notes:
enVision Mathematics Topic 8
Additional enVision Mathematics Resources
Let's Investigate! Spin for Fractions (TE) (supports Lessons 8-5, 8-6)
Additional Math Games: Fractions (additional materials and preparation may be required)
Tier 1 Intervention & Supports (i-Ready Tools for Instruction):
Tier 1 Intervention: Understand Comparing Fractions, Equivalent Fractions, Compare Fractions
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