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LFS DIGITAL > Instructional Unit Topics > Math Unit Topics > Fractions  

Fractions

LFS-DIGITAL K-U-D for Unit: Fractions

 

                                                                                                 Key Learning

(What is the big understanding for this unit?  What will you ultimately want students to understand as a result of the instruction?  This is a “big picture” understanding, based both on the most critical standards and the thematic focus of the unit.)

 

 

Knowledge of fractions and equivalence can be used to develop algorithms for adding, subtracting, multiplying, and dividing fractions

 

Unit Essential Question

(What broad question will students be able to answer as a result of the instruction? This question should reflect the most critical standards on which the instruction is based.  This question is the inverse of the Key Learning; the Key Learning would provide an “ideal” response to this question.)

 

 

How can knowledge of fractions and equivalence be used to develop algorithms for adding, subtracting, multiplying, and dividing fractions?

 

Unit Description

(Briefly summarize the focus and content of the unit.)

This is a unit on developing the algorithms for adding, subtracting, multiplying, and dividing with fractions and mixed numbers.

Grade-Level Standards Addressed in the Unit

(List the critical grade-level standards on which the instruction will be based.  Since many of the standards are recursive, reinforced throughout the year’s instruction, list only those that will be the focus of the instruction and assessments for this unit.)

 

 

DE:  1 – Numeric Reasoning 

 

CC:  4.NF Number and Operations with Fractions and 6.NS.1 Dividing Fractions

 

 

 

Know

(Factual: nouns or noun phrases related to key concepts; terminology, academic vocabulary, formulas, etc., often found or implied in the language of the grade-level standards.)

Understand

(Conceptual:  key understandings that students will gain as a result of the instruction within the unit, found in the language of the grade-level standards, and generally written in complete sentences. These understandings will contribute to the overall key learning of the unit.)

Do

(Procedural, Extending Thinking:  written as verb phrases, often found or implied in the language of the grade-level standards. These statements provide discreet targets for demonstrating learning.  Often the assessments for the learning will be selected

 from this column.)

How to find a common denominator

 

The procedure to convert an improper fraction into a mixed number

 

The steps to simplify a fraction

 

Use estimation for fraction computations

 

How to find the reciprocal of a number

 

Steps to develop an algorithm for adding, subtraction, multiplying, and dividing fractions

 

Knowledge of fractions and equivalence can be used to develop algorithms for adding, subtraction, multiplying, and dividing fractions

Multiply fractions by whole numbers and explain the result

 

Multiply fractions by other fractions using physical models, ratio/rate tables, and arrays

 

Connect multiplication by a unit fraction (such as 1/3,1/4, 1/5, 1/10, 1/100) to division by its multiplicative inverse (3, 4, 5, 10, 100) using models

 

Add and subtract fractions with unlike denominators and use physical models to justify your answer

 

* Gather data, examine patterns, and apply information for decision making using digital tools and resources to develop an algorithm to add, subtract, and multiply fractions. (1,4)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 Below is a description of LoTi level 3 instructional focus in the classroom. For more information about LoTi and descriptions of higher LoTi levels please follow the link below.
 www.loticonnections.com

 

At a Level 3 (Infusion), the instructional focus emphasizes student higher order thinking (i.e., application, analysis, synthesis, evaluation) and engaged learning. Though specific learning activities may or may not be perceived as authentic by the student, instructional emphasis is, nonetheless, placed on higher levels of cognitive processing and in-depth treatment of the content using a variety of thinking skill strategies (e.g., problem-solving, decision-making, reflective thinking, experimentation, scientific inquiry). Teacher-centered strategies including the concept attainment, inductive thinking, and scientific inquiry models of teaching are the norm and guide the types of products generated by students using the available digital assets.

Digital tools and resources are used by students to carry out teacher-directed tasks that emphasize higher levels of student cognitive processing relating to the content under investigation.

 

 

 

 

 

 

 

 

 

 

Print Resources

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 
 
Discovery Education Resources


Videos:

 Addition and Subtraction of Integers: Algorithms

Algorithms for Arithmetic Operations and Computations

Example 1: Addition and Subtraction--Travel Tickets

Example 2: Multiplication--Earnings

Example 3: Division--Daily Vegetables

A Basic Method

Mixed Numbers & Improper Fractions

Changing Mixed Numbers to Improper Fractions

Changing to Improper Fractions: A Shortcut

Changing Improper Fractions to Mixed Numbers

Changing to Mixed Numbers: A Shortcut

Adding Mixed Numbers: Two Methods

Reviewing Fractions & Mixed Numbers

Example 1: Overestimation

Example 2: Underestimation

Example 3: Estimating a Range

Indirect Measurements

Finding Common Denominators

Multiplying-Through to Find a Common Denominator

The Least Common Multiple

Reviewing Three Common Denominator Strategies

Math Overview:

Grades 06-07: Multiplying Fractions and Mixed Numbers

Grades 06-07: Dividing Fractions and Mixed Numbers

Grades 06-07: Adding and Subtracting Fractions

Grades 06-07: Mixed Numbers and Improper Fractions


Open Resources


Resource 1: Equivalent fractions, Adding and subtracting fractions, Multiplying fractions, Dividing fractions, Simplifying fractions, Improper fractions and mixed numbers
Media type: video, print, interactivity
Description: These lessons include explanatory videos, problem sets, and games for these topics.
Level: Intermediate

Credit: HelpingWithMath.com
License: NC SA

Notes/activity suggestions: This is a very comprehensive resource with many activities that can be used with students at various levels.
Tags: grade6, math, fractions, equivalent fractions, adding fractions, subtracting fractions, multiplying fractions, dividing, fractions, simplifying fractions, improper fractions, mixed numbers

 


Resource 2: Adding Fractions, Subtracting Fractions, Subtracting Fractions with Borrowing, Subtracting Fractions from Whole Numbers, Multiplying Fractions, Dividing Fractions  
Media type: video
Description: Very short videos on basic operations with fractions; the problems worked all begin with mixed numbers
Level: Intermediate

Credit: Duane Habecker
License:

Notes/activity suggestions: These are quick and probably better for students who are more advanced and already have mastery of the basics of fractions. After these students have mastered the concepts, have them make their own videos showing how to do different kinds of fraction problems.
Tags: grade6, math, fractions, adding fractions, subtracting fractions, multiplying fractions, dividing, fractions

 


Resource 3: Starting with Fractions (click “Click here to launch” to begin)
Media type: interactivity
Description: A Qedoc quiz with three sections. The first has students identify how the numerator and denominator are used in basic operations. The second has students solve simple problems like how many minutes are in 1/3 of an hour. The third has more difficult problems including ones with decimals and multiple steps.
Level: Intermediate

Credit: Qedoc Educational Team
License: CC BY NC SA

Notes/activity suggestions: good for independent practice, especially for students who already grasp the basics
Tags: grade6, math, fractions, Qedoc

 


Resource 4: Basic operations with fractions
Media type: text
Description: Online textbook chapter with sections on adding, subtracting, multiplying, and dividing fractions and mixed numbers; includes problems with answers
Level: Intermediate/advanced

Credit: Open University
License: CC NC SA

Notes/activity suggestions: Best for students who can work independently and may be able to work independently especially in an accelerated mode.
Tags: grade6, math, fractions, adding fractions, subtracting fractions, multiplying fractions, dividing, fractions, simplifying fractions, mixed numbers


Resource 5: Fractions
Media type: video
Description: This is a very basic video that introduces the concept of a what a fraction is, as well as the terms numerator and denominator.
Level: Beginning

Credit: K12 Handhelds
License: CC By

Notes/activity suggestions: This is a good video for students who don’t understand the basics of fractions or need a review.
Tags: grade6, math, fractions, numerator, denominator



Resource 6: Multiplication tables games
Media type: interactivity
Description: simple games to practice multiplication tables
Level: Beginning

Credit: HelpingWithMath.com
License: NC SA

Notes/activity suggestions: remediation and practice for students who have not mastered multiplication tables

Tags: grade6, fractions, multiplication

 


Resource 8: Khan Academy videos: Greatest common divisor, Least common multiple, Adding and subtracting fractionsMultiplying fractions, Dividing fractions, Equivalent fractions, Mixed numbers and improper fractions
Media type: video
Description: Short talking chalkboard explanations of math concepts
Level: Intermediate

Credit: Sal Khan
License: CC BY SA

Notes/activity suggestions:
Tags: grade6, fractions, multiplication

 

* new Resource 9:  FlexMath -> Prime -> Operations with Fractions

Media type: interactive
Description: Interactive drill practice of math skills. Wrong answers are penalized, and a 90% score is needed to pass. Topics include equivalent fractions, reducing fractions, adding and subtracting fractions (with common and unlike denominators), muliplying and dividing fractions, and more advanced topics.
Level: Intermediate, Advanced

Credit: CK12
License: CC BY NC ND

Notes/activity suggestions:

Tags: grade5, math, fractions, adding fractions, subtracting fractions, multiplying fractions, dividing fractions

 

 

Thinkfinity Resources

 

Fraction Game

Media Type:  interactive

Description: Interactive practice for recognizing the relationships of  fractions on a number line and the relationships between combining fractions and equivalence. 

 

Equivalent Fraction Game

Media Type:  interactive

Description:  Interactive practice making equivalent fractions with rectangle models and placing them on a number line.

Last modified at 7/20/2011 11:13 AM  by SEAFORD\jwwhite