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: Pizza fractions
Subject/Course: Intermath Algebra
Topic: 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
Essential Question(s)
that...
1. A fraction represents how many pieces,
divided by the total number of pieces in the
whole.
2. A pizza cut into equal sized pieces represent
fractions.
3. A whole pizza is only 1 piece and would be
represented by the fraction 1/1.
1. What is a fraction?
2. How do you make a fraction?
3. How do you divide something into equal
parts?
4. What equivalent fractions can we find in a
pizzas cut into halves, fourths and eighths?
Q
U
Students will know...
Simple fraction
Equivalent fraction
What is represented by the numerator and the
denominator.
In comparing fractions with the numerator of 1,
the smaller the denominator, the larger the
piece, and vice versa.
K
Students will be able to...
Create a simple fraction to represent a piece of
a pizza cut into halves, fourths, or eighths.
Identify which simple fraction on the
worksheet represents the pizza fraction.
Compare small common fractions, and identify
which is biggest, which is smallest.
S
Source: Wiggins, G., & McTighe, J. Understanding by Design. Merrill Prentice Hall: 1998.
For further information about Backward Design refer to http://www.ubdexchange.org/
Stage 2 – Assessment Evidence
Performance Task(s) Summary in G.R.A.S.P.S. form
G – the goal is to use a familiar item (pizza) to further reinforce how we make and use fractions in
our daily lives.
R – My role is as the instructor.
A – (Audience) MID 6th-8th grade students. Evaluation by increased student understanding of
fractions.
S – (Situation) Special Ed self-contained Math class.
P – (Product) Students will be assessed thru class participation and fraction worksheets.
S – (Standards/Criteria) Students will be able to understand, make and compare common
fractions
T
Key Criteria:
Class participation. Pizza fractions worksheet. Other fraction worksheets on simple fractions.
Other Evidence
Teacher observation.
Assessment of student work (comparing fractions worksheet).OE
Source: Wiggins, G., & McTighe, J. Understanding by Design. Merrill Prentice Hall: 1998.
For further information about Backward Design refer to http://www.ubdexchange.org/
Stage 3 – Learning Plan
Learning Activities Consider the W.H.E.R.E.T.O. elements.
W – “Who can tell me what a fraction is?” Review elements of a fraction (part vs. whole,
numerator, denominator). “Today we are going to use something most of us like to eat, to further
explore fractions.”
H – “Who likes to eat pizza?” (Ask for show of hands) “What kind of pizza do you like to eat?”
(On whiteboard, record the kinds of pizza) “Today we will be use pizza to help us understand
more about fractions. When we are finished, we will have a special treat.” (pizza)
E – “Today we’ll be talking about fractions that are divided into eighths. Let’s say I have one
whole pizza, and I want to share it with 7 friends. How many equal parts will I need to divide it
into?” (eight) “Let’s pretend that my circle of brown paper here is our pizza dough. What
toppings shall we put on our pizza?” (Have pre-cut pepperoni, cheese, green peppers, black
olives) “Now that our pizza is finished, how many equal pieces do I need to cut it into?” (eight)
(Cut paper pizza into 8 equal slices. Pass out pieces to students.) “What fraction of my pizza did
I give to (student’s name)?” (1/8) (Give two students 3 slices each, and one student two slices of
pizza. ) “What fraction of my pizza did I give to (ask each of the 3 students’ names)?” “If we add
together the slices of pizza that each of the 3 students have, how many pieces of pizza do we
have? (8) “What would that fraction be?” (8/8)
R – Re-assemble the pizza slices to make 1 whole pizza. Show students a pre-made paper pizza
which has been divided (not cut) into fourths. Review what fraction each piece of that pizza is.
Show how 2 slices of an 8 piece pizza (2/8) is the same as 1 slice of a 4 piece pizza (1/4). “2/8
and ¼ are equivalent fractions…they are the same. Can anyone see another equivalent fraction?”
Help students see that 4/8 and 2/4 are equivalent, and that 8/8 and 4/4 are also equivalent
fractions. Repeat with a pre-made pizza cut into half, and a whole pizza (1/1). Have students
explore the different equivalent fractions in these pizzas. Have students demonstrate
understanding of equivalent fractions, using pizza pieces.
E – Student will create their own paper pizzas, using paper plates and markers. They will cut
their pizzas into fourths, halves, and one single pizza. They will then use their own pizza pieces to
help them complete the pizza fraction worksheet.
T – Some of my students will need more assistance to be able to complete the paper pizzas, and
the corresponding worksheet. Therefore, I may choose to pair a more advanced student with a
slower student. I also have some student who would not be able to cut a pizza into 4 equal parts,
or even 2 equal parts. To facilitate this, I’ll have the paper plates already divided into ¼’s ½’s and
1/1, with a marker. The students will then be able to cut along the lines. Also, for some of my
students, mastery of ¼ or ½ will be enough.
O – The concept of equal fractional pieces will be demonstrated by me, using a large paper model
of a pizza. Equivalent fractions will be similarly shown, using pre-cut paper pizza models.
Students will be paired and given a work sheet and paper pizzas to be cut out (on the lines – ¼’s,
½’s, and 1/1). The students will then use their paper pizzas to complete the fraction worksheet.
When the worksheets and paper pizzas are picked up, hot pizza (sliced into 8 equal pieces) will be
handed out to each student.
Source: Wiggins, G., & McTighe, J. Understanding by Design. Merrill Prentice Hall: 1998.
For further information about Backward Design refer to http://www.ubdexchange.org/