enVision Mathematics Topics 12-13
3rd Grade; February – March (4 weeks); 3rd Trimester
Embedded Files
Topic Title(s):
Understand Fractions as Numbers (Topic 12)
Fraction Equivalence and Comparison (Topic 13)
Prepared Graduates:
MP2. Reason abstractly and quantitatively.
MP3. Construct viable arguments and critique the reasoning of others.
MP7. Look for and make use of structure.
Standard(s):
1. Number and Quantity
3. Data, Statistics, and Probability
4. Geometry
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):
3.NF.A. Number & Operations—Fractions: Develop understanding of fractions as numbers.
Describe a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. (CCSS: 3.NF.A.1)
Describe a fraction as a number on the number line; represent fractions on a number line diagram. (CCSS: 3.NF.A.2)
Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. (CCSS: 3.NF.A.2.a)
Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. (CCSS: 3.NF.A.2.b)
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. (CCSS: 3.NF.A.3)
Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. (CCSS: 3.NF.A.3.a)
Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model. (CCSS: 3.NF.A.3.b)
Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. (CCSS: 3.NF.A.3.c)
Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (CCSS: 3.NF.A.3.d)
3.MD.B. Measurement & Data: Represent and interpret data.
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters. (CCSS: 3.MD.B.4)
3.G.A. Geometry: Reason with shapes and their attributes.
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape. (CCSS: 3.G.A.2)
Flexibly describe fractions both as parts of other numbers but also as numbers themselves. (Personal Skills: Adaptability/Flexibility)
Analyze and use information presented visually (for example, number lines, fraction models, and diagrams representing parts and wholes) that support an understanding of fractions as numbers. (Entrepreneurial Skills: Literacy/Reading)
Reason about the number line in a new way by understanding and using fractional parts between whole numbers. (MP2)
Critique the reasoning of others when comparing fractions that may refer to different wholes. (MP3)
Use the structure of fractions to locate and compare fractions on a number line. (MP7)
Model real-world quantities with statistical representations such as bar graphs and line graphs. (MP4)
Decompose geometric shapes into polygons of equal area. (MP7)
Inquiry Questions
How does the denominator of a unit fraction connect to the number of unit fractions that must be added to make a whole?
When the numerators of two different fractions are the same, how can the denominators be used to compare them?
How does changing the scale of a bar graph or line plot change the appearance of the data?
(Given two identical squares) Divide each of these squares into four equal parts, but in different ways. If you compare a part of one with a part of the other, are their areas the same? How do you know?
Coherence Connections
This expectation (3.NF.A) represents major work of the grade.
This expectation (3.MD.B & 3.G.A) supports the major work of the grade.
In Grade 2, students (a) relate addition and subtraction to length, (b) measure and estimate lengths in standard units, and (c) reason with shapes and their attributes, including partitioning circles and rectangles into halves, thirds, and fourths.
In Grade 3, this expectation connects to the solving of problems involving measurement and estimation of intervals of time, liquid volumes, and mass of objects and is further supported by the expectation to represent and interpret data.
In Grade 3, this expectation supports developing an understanding of fractions as numbers.
In Grade 4, students build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers and extend their understanding of fraction equivalence and ordering. In Grade 6, students apply and extend previous understandings of numbers (including fractions) to the system of rational numbers.
In Grade 4, students represent and interpret data by making line plots representing fractional measurements and solving addition and subtraction problems using information presented in line plots.
Academic Vocabulary & Language Expectations:
Fraction, unit fraction, numerator, denominator, nearest half inch, line plot, nearest fourth inch, equivalent fractions
Assessments:
Instructional Resources & Notes:
enVision Mathematics Topics 12-13
Additional enVision Mathematics Resources
Let's Investigate! Measuring a Lemon (TE) (supports Lessons 12-6, 12-7)
Let's Investigate! Making Gumbo (TE) (supports Lessons 13-3, 13-4, 13-5)
3-Act Math Recording Sheets (Topic 13)
Additional Math Games: Fractions (additional materials and preparation may be required)
Tier 1 Intervention & Supports (i-Ready Tools for Instruction):
Tier 1 Intervention Topic 12: Parts of a Set, Modeling Fractions, Fractions on a Number Line, Place Fractions on Number Lines
Tier 1 Intervention Topic 13: Equivalent Fractions, Find Equivalent Fractions, Use Symbols to Compare Fractions
Coherence Map/Concept Progressions: 3.NF.A.1, 3.NF.A.2.b, 3.NF.A.3.b, 3.NF.A.3.c, 3.NF.A.3.d, 3.MD.B.4, 3.G.A.2
Page updated
Report abuse