TEACHER GUIDE TO CLARIFICATION
Develop understanding of fractions as numbers
3.NF.3 a,b,c,d Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
b. Recognize and generate simple equivalent fractions, (e.g., ½=2/4, 4/6=2/3). Explain why the fractions are equivalent,
e.g., by using a visual fraction model.
c. Express whole numbers as fraction, and recognize fractions are equivalent to whole numbers. Examples: express 3 in the form 3=3/1; recognize 6/1=6; locate 4/4 and 1 at the same point of a number line diagram.
d. Compare two fractions with the same numerator of 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 conclusion, e.g., by using a visual fraction model.
Explain Equivalence of Fractions
This standard is asking students to explain their thinking of fractions and reason about their size. During class time teachers will need to provide opportunity for this reasoning to take place. Multiple representations of visual models will need to be utilized. Facilitation of student discussion will also help students to reason through and explain their thinking of fractions and equivalence.
3.NF.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line (not limited to the samples below).
Which fraction models represents ¼? Explain why.
3.NF.3b Recognize and generate simple equivalent fractions, (e.g., ½=2/4, 4/6=2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.
1. Provide a picture that show 1/3 and 2/6 as equal amounts.
Both are equal amounts, one model is split up into more pieces
2. Using the number lines below, mark the fraction equivalent to ¼.
3. On the same number line mark 1/2 & 4/8. What can you say about these points?
4. Brad split up a mile into 6 sections and ran 4/6 of those sections. Carl split up a mile into 3 sections. How many
sections would Carl have to run in order to go the same distance as Brad?
Draw a picture to prove your answer.
3. NF.3d Compare two fractions with the same numerator of the same denominator by reasoning about their size.
How can both of these shapes represent ½?
Coherence and Connections: Need to Know
Explanations and Examples: 3.NF.3a and 3.NF.3b These standards call for students to use visual fraction models (area models) and number lines to explore the idea of equivalent fractions. Students should only explore equivalent fractions using models, rather than using algorithms or procedures.
Important: Now is not the time to teach equivalent fractions with multiplying the numerators and denominators
This scoop is for your 3’s
This standard includes writing whole numbers as fractions. The concept relates to fractions as division problems, where the fraction 3/1 is 3 wholes divided into one group. This standard is the building block for later work where students divide a set of objects into a specific number of groups. Students must understand the meaning of a/1
Kansas Association of Teachers of Mathematics (KATM) Flipbooks.
Equivalent fractions Grade 3 students do some preliminary reasoning about equivalent fractions, in preparation for work in Grade 4. As students experiment on number line diagrams they discover that many fractions label the same point on the number line, and are therefore equal; that is, they are equivalent fractions. For example, the fraction 1/2 is equal to 2/4 and also to 3/6. Students can also use fraction strips to see fraction equivalence.3.NF.3ab.
Common Core Standards Writing Team. (2013, September 19).
Progressions for the Common Core State Standards in Mathematics(draft). 3-5 Number and Operations - Fractions. Tucson, AZ: Institute for Mathematics and Educations, University of Arizona.
Fraction equivalence is an important theme within the standards that begins in grade 3. In grade 4, students extend their understanding of fraction equivalence to the general case, a/b=(n x a)/(n x b) (3.NF.3 moving to 4.NF.1).11 They apply this understanding to compare fractions in the general case (3.NF.3d moving to 4.NF.2).
PARCC Model Content Frameworks: Mathematics Grades 3-11 (version 3). (2012, November 1).
Retrieved June 3, 2014, from http://www.parcconline.org/resources/educator-resources/model-content-frameworks/mathematics-model-content-framework
1. Shade ¾ of the rectangle in two different ways
Answers will vary
2. Cheryl says that ¾ and 6/8 are equivalent. Shade the 2 rectangles to prove she is right
3. I caught a spider that measured 5/8 on my ruler. Mark the length of the spider on the ruler.
PARCC EOY # 3 and 28
K-5 Teaching resource
1 - Enrichment Activity
2 - Additional Practice with equivalence activity- concrete/visual
3.NF.3c. Homework Activity
Compare and Order – additional practice
Problem of the Month
Performance Based Assessment