Source:  Wiggins, G., & McTighe, J. Understanding by Design. Merrill Prentice Hall: 1998.
For further information about Backward Design refer to http://www.ubdexchange.org/

 Title:  Wormy Fractions          Subject/Course: IntermathAlgebra   Topic: Introduction to simple fractions  Grade(s): MID 6th-8th grade or 2nd grade Designer(s):  Meg Ramsey _______________________ Stage 1 – Desired Results Established Goal(s) Standard: Relates a fraction to a part of a whole, a part of a set, and a point on a number line; uses models to determine equivalent fractions. Uses fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, 16, or 100. Understanding(s) Students will understand that... 1.      a fraction is made up of numerator  and denominator 2.   a fraction is written as the part /whole 3.   the larger the denominator, the smaller the pieces will be U Essential Question(s) 1.     What is a fraction? 2.   How do you make a fraction? 3.   Which number goes on top, the part or the whole? 4.   What is a numerator? 5.   What is a denominator? 6.   What happens when the numerator and the denominator are the same number?   Q Students will know... numerator denominator fraction part whole 1/2, 1/3, 2/3, 1/4, 2/4, 3/4,   K Students will be able to... write a fraction based on a concrete model or a pictorial model. tell how many pieces a gummy worm would have to be cut into in order to share between 2, 3 or 4 people tell what the relationship is between the top and the bottom numbers of a fraction in fractions with 1 as a denominator, identify which fraction is smallest or largest, by comparing the denominators S Stage 2 – Assessment Evidence Performance Task(s) Summary in G.R.A.S.P.S. form 1.       Students will be able to identify which fraction is represented, based on a concrete (gummy worm) or pictorial (worksheet) model. 2.       I’ll present how to divide a gummy worm into one, two, three, or four equal parts, and relate how these worms now represent fractions (1/2, 2/2, 1/3, 2/3, 3/3, ¼, 2/4, ¾, 4/4, 1/1). 3.       My audience is the group of MID/MOID Special Ed students who I work with currently.  My performance will be self-monitored by how well the students can grasp the concept of fractions. 4.       Our students have been studying habitats and worms in Science.  Each student is already familiar with worms.  Each student has their own individual worm habitat which he or she is responsible to care for, on a weekly basis. I thought it would be an attention-grabbing, fun way to introduce fractions to our students. 5.       Students will be assessed using classroom participation, as well as fraction worksheet. (gummy worm worksheet)   T Key Criteria: Classroom participation, fraction worksheet. Other Evidence Teacher observation, follow-up fraction homework.

Stage 3 – Learning Plan

Learning Activities Consider the W.H.E.R.E.T.O. elements.

 1.       We’ve been cooking in our class, and have had to use fractions like ½ (cup) and ¼.  I will ask if any students can tell me what “1/2” means. If someone can, I will ask if they can draw a picture of “1/2” for me on the whiteboard. 2.       “Today, we are going to use gummy worms to show how we “make” fractions.”  Our students have been working with real earthworms in our class, and really enjoy the worms. 3.       I will demonstrate first, and then ask students to demonstrate  how we can make a gummy worm into: one equal part, two equal parts, three equal parts, and four equal parts (1/1, ½, 1/3, ¼).  Talk about “How could I share this gummy worm equally with Ashley?  With Ashley and Brent?  With Ashley, Brent and Corey? 4.       I will have the students help me to demonstrate 1/1, ½, 2/2, 1/3,  2/3, 3/3, ¼, 2/4, ¾, 4/4, using the gummy worms.  “How many pieces of the worm do we need to make ¾?”  We will use the whiteboard to demonst4rate a pictorial example of the cut up worms in their corresponding fractions.