NF-Develop+Understanding+of+Fractions+as+Numbers

3.NF.1. Understand 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//. 3.NF.2.Understand a fraction as a number on the number line; represent fractions on a number line diagram. a. 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. b. 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. 3.NF.3.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., 1/2 = 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 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.// d. 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. || ===‍‍‍‍‍‍**Anchor Standard/Mathematical Practice(s)**=== 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning ||
 * ===**Common Core Standards**===
 * Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.**
 * Develop understanding of fractions as numbers.**
 * 3.NF.1 3.NF.2 3.NF.2a 3.NF.2b 3.NF.3 3.NF.3a 3.NF.3b 3.NF.3c 3.NF.3d**
 * ===‍‍‍‍‍‍**Information Technology Standard**===

**3.TT.1 Use technology tools and skills to reinforce classroom concepts and activities.**
|| ===‍‍‍‍‍‍**Revised Bloom's Level of thinking**=== Can the student break information into arts to explore understandings and relationships? (Comparing, Organizing, Deconstructing, Interrogating, Finding, Differentiating, Attributing) Can the student generate new ideas, products, or ways of viewing things, putting elements together to form a coherent or functional whole, reorganize elements into a new pattern of structure? (designing, generating, constructing, planning, producing, inventing) Can the student explain ideas or concepts, construct meaning from instructional messages, including oral, written, and graphic communication? (Interpreting, summarizing, paraphrasing, classifying, explaining, exemplifying, inferring, comparing) Can the student justify a decision or course of action or make judgments based on a criteria or a standard? (checking, hypothesizing, critiquing, experimenting, and judging.) Can the student use information in another familiar situation; carry out or use a procedure in a given situation? (Implementing, carrying out, using, executing) ||
 * 3.NF.1 3.NF.2b 3.NF.3d Analyzing**
 * 3.NF.2 3.NF.2a Creating**
 * 3.NF.3a Understanding**
 * 3.NF.3b** ** Evaluating **
 * 3.NF.3c Applying**

‍‍‍‍‍‍**I can...**

 * 3.NF.1 I can understand 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. **
 * Explain that a fraction is a number that represents a part to whole relationship.
 * Recognize that a numerator (top number) is a part of a whole when the whole is divided into EQUAL parts.
 * Recognize that a denominator (bottom number) is the number of EQUAL parts that make up the whole.
 * Partition and label areas models (e.g., shapes, length of a ruler, distance on a number line, a complete turn of the hands on a clock) into equal parts.
 * Compose fractions from unit fractions of area models (e.g., 3/8 of circle model is composed of 3 pieces that have the size of 1/8).
 * Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts.

3.NF.2 3.NF.2a I can i <span style="font-family: Arial,sans-serif; font-size: 10pt;">**dentify locations of fractions on open number lines and predetermined number lines**.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Divide the distance between 0 and 1 into equal parts on a predetermined number line.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Generate number lines where the interval between 0-1 represents the whole, and the whole is partitioned into b equal parts.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Represent unit fractions (1/b) on a student-generated number line (where the interval between 0-1 represents the whole and is partitioned into b equal parts).
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">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.

//<span style="font-family: Arial,sans-serif; font-size: 10pt;">*Note: Focus on fractions with denominators 2, 3, 4, 6, 8* //


 * 3.NF.3 3.NF.3a I can d<span style="font-family: Arial,sans-serif; font-size: 10pt;">etermine whether two fractions are equivalent by their size or their location on a number line. **


 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Name equivalent fractions for a specified fraction using a variety of models (e.g., shapes and number lines).
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.


 * <span style="font-family: Arial,sans-serif;">3.NF.3b I can u **<span style="font-family: Arial,sans-serif; font-size: 10pt;">**se models to recognize, generate, and explain why fractions are equivalent**.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Explain equivalent fractions using a variety of models (e.g. fraction bars, number lines, rulers, shapes)
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Generate equivalent fractions and justify their equivalence.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">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 <span style="color: #141413; font-family: Arial,sans-serif; font-size: 10pt;">.


 * <span style="color: #141413; font-family: Arial,sans-serif;">3.NF.3c I can e **<span style="font-family: Arial,sans-serif; font-size: 10pt;">**xpress whole numbers as fractions and recognize fractions that are equivalent to whole numbers.**
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Recognize fractions equivalent to a whole number.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Represent a whole number as a written fraction.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Relate the meaning of a fraction to simple division contexts.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

> same whole <span style="font-family: Georgia,serif; font-size: 10pt;">. // *Note: Focus in on use of models to determine equivalent fractions; algorithms & memorized procedures are not introduced at this time. //
 * <span style="font-family: Arial,sans-serif;">3.NF.3d I can e **<span style="font-family: Arial,sans-serif; font-size: 10pt;">**xplain why one fraction is greater than or less than another using words and/or models**.
 * Compare two fractions with the same numerator or denominator using a variety of models (e.g., shapes, number lines, rulers, fraction bars).
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Recognize that comparisons are valid only when the two fractions refer to the
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Record comparisons of fractions symbolically using >, =, and <.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Explain why one fraction is greater than or less than another using words and/or models (e.g., //1/4 of a soda is greater than 1/8 of a soda. If I were to share a soda among four people, I would get a bigger share than if I shared with eight people//).
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Compare two identical fractions that belong to different sized wholes (e.g., 1/2 of a small pizza is less than 1/2 of a larger pizza); explain reasoning.

‍‍‍‍‍‍**Essential Vocabulary** Teacher Glossary


 * **3.NF.1** || **3.NF.2 3.NF.2a** || **3.NF.3 3.NF.3a** || **3.NF.3b** || **3.NF.3c** || **3.NF.3d** ||
 * <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Partition(ed) <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Equal parts  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Equal share  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Fraction  <span style="display: block; font-family: arial,sans-serif; font-size: 10pt; text-align: center;">Equal distance(intervals) <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Equivalent  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Equivalence  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Reasonable  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Denominator  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Numerator  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Comparison  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Compare  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">>  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;"><  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">=  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Unit fraction  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Justify  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Half  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Quarter  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Whole number  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Increases  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Decreases  || <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Number line  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Interval  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Numerator  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Denominator  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Partition  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Justify  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Endpoint  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Unit fraction  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Whole  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Equal portion  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Equal share  || <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Equivalent  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Number lines  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Unit fraction  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Partition  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Equal part  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Compare  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Fraction  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Numerator  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Denominator  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Equal distance  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Segment  || <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Equivalent  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Number lines  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Unit fraction  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Partition  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Equal part  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Compare  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Fraction  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Numerator  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Denominator  <span style="display: block; font-family: arial,sans-serif; font-size: 10pt; text-align: center;">Equal distance <span style="font-family: Arial,sans-serif; font-size: 10pt;">Segment || <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Equivalent  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Number lines  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Unit fraction  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Partition  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Equal part  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">compare  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Fraction  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Numerator  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Denominator  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Division  || <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Equivalent  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Number lines  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Unit fraction  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Partition  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Equal part  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Compare  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Fraction  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Numerator  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Denominator  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Division  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Valid  <span style="font-family: Arial,sans-serif; font-size: 10pt;">Symbols ||

‍‍‍‍‍‍**Sample Assessments**

 * 1) **Formal and informal teacher made assessments using RBT question stems.**
 * 2) **District predictive assessments.**
 * 3) **Standardized tests.**
 * 4) **Observations, data collection (student data books), and conferences.**
 * 5) **Scholastic Math Inventory**
 * 6) **Pre Assessments power point ideas**

‍‍‍‍‍‍**Differentiation**

 * 1) ** Learning style surveys (student interest and teacher created). **
 * 2) ** Small group settings based on skill levels. **
 * 3) ** Peer tutors. **
 * 4) ** Tiered assignments. **
 * 5) ** Flexible grouping **
 * 6) ** Centers (finding, identifying, creating patterns with numbers, week by week essentials games) **
 * 7) **Learning Contracts**
 * 8) **Choice boards (create math games, make flashcards)**
 * 9) **Investigations website**
 * 10) Illuminations site

‍‍‍‍‍‍**Intervention:**

 * **Scholastic Math Inventory**
 * **Math Tutors**
 * **One on one direct instruction**
 * **Math based web sites ([|www.multiplication.com], [|www.abcya.com], [|www.ixl.com], [|www.sheppardssoftware.com]www.mrsgoldsclass.comwww.mathplayground.com**
 * **Intervention sites**: (JennyLendElementary) www.mathwire.com
 * **Investigations Math site**
 * **Illuminations site**

‍‍‍‍‍‍**Enrichment:**

 * 1) **Math based web sites ([|www.multiplication.com],[| www.abcya.com], [|www.ixl.com], [|www.sheppardssoftware.com])**
 * 2) **Scholastic Math Inventory**
 * 3) **Group projects (creating games, make flashcards, pose questions)**
 * 4) **Illuminations site**

‍‍‍‍‍‍**Instructional Resources**
=== Envisions Math Student Pages NF.1 NF.3d NF.3d NF3.d 3.NF3.a 3.NF3.c === Investigations Math Websites Manipulatives (hands-on instruction) equivalent fractions activity, fraction bars, half inch, quarter inch, number lines, graph paper of various designs, virtual fraction tools, virtual fraction models