Day 3: Area of a Rectangle with Fractional Side Lengths
Title: Let’s Go on a Picnic!
Grade: Fifth
NYS Common Core Standards and NCTM Standards:
NYS Common Core Standards:
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Number & Operations- Fractions (5.NF):
Apply and extend previous understandings of multiplication and division to
multiply and divide fraction.
4. Apply and extend previous understandings of multiplication to multiply a fraction or
whole number by a fraction.
b. find the area of a rectangle with fractional side lengths by tiling it with unit
squares of the appropriate unit fraction side lengths, and show that the area is the
same as would be found by multiplying the side lengths. Multiply fractional side
lengths to find areas of rectangles, and represent fraction products as rectangular
areas.
NCTM Standards:
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Number and Operations Standard for Grade 3-5
o develop understanding of fractions as parts of unit wholes, as parts of a collection,
as locations on number lines, and as divisions of whole numbers
o use models, benchmarks, and equivalent forms to judge the size of fractions
o understand various meanings of multiplication and division
o develop and use strategies to estimate computations involving fractions and
decimals in situations relevant to students' experience
Learning Objectives:
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Students will understand how to find the area of a rectangle with fractional side lengths.
Students will multiply two fractions to find the area of a rectangle.
Students will represent the multiplication of two fractions visually.
Students will explain how to multiply two fractions to find the area of a rectangle by
through a presentation.
Materials:
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Paper
Transparencies
Markers for the transparencies
Rulers
“Multiplication Madness” worksheets
Markers
Color pencils
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Tablecloth
Rectangular shaped cornbread
Rectangular shaped cake
Rectangular shaped whole brownie
Plastic knives
Plates
“Let’s Go on a Picnic” worksheets
Teacher checklist
Instructional Plan:
Introduction:
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The teacher will activate prior knowledge by asking students to recall the formula for
finding the area of a rectangle.
As a class students will use the formula A = lw to find the area of a rectangle drawn on
the board with a length of 8in and width of 9in.
The teacher will ask students, “Do you think we could use this formula to find the area of
a rectangle if the side lengths are fractions? Why?”
Modeling:
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The teacher will model finding the area of a rectangle with sides of length ½ and 1/3.
He or she will solve the problem ½ x 1/3 by dividing a rectangle on a piece of paper into
thirds and labeling the thirds on one of the corresponding sides of the rectangle.
He or she will shade 1 of these thirds using one color.
He or she will then divide a rectangle on a transparency of the same size as the paper one,
into halves, and label the halves on one of the corresponding sides of the rectangle.
He or she will shade 1 of these halves using a different color.
The teacher will then overlap the transparency onto the paper and point out where the
shadings overlap and the new total number of equal parts the rectangle is divided into.
The teacher will model counting the boxes and realizing the answer is 1/6 of the whole
rectangle.
Guided Practice:
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As a class, students will repeat the steps the teacher took while modeling for the problems
on the worksheet “Multiplication Madness.”
The teacher will then present a table cloth representing a picnic blanket and tell students
the class is going on a picnic but only needs 2/3 of 3/4 of the tablecloth.
The teacher will ask students, “Estimate how much tablecloth the product will be? Do
you think the product be larger than 1 or smaller than 1? Why?”
As a class, students will draw lines using a yard stick and marker on the tablecloth to
divide it into quarters first, shading 3 of the quarters with lines using one color marker.
Students will then divide the tablecloth into thirds and shade 2 of the thirds using a
different color marker. Students will see that 6/12 of the tablecloth is shaded by both
colors.
Independent Practice:
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The teacher will ask students, “Now that we have our picnic blanket ready, what is
missing?”
The teacher will divide students into groups of 3-4 students.
Each group will receive one of the following rectangular foods:
o Cornbread
o Cake
o Whole brownie
Each group will also receive a multiplication of two fractions problem on their “Let’s Go
on a Picnic” activity sheets.
The teacher will ask groups, “Before solving your problem, estimate the size of the food
you will bring on the picnic by looking at the fractions in your multiplication problem.”
Students will share their thoughts and reasoning.
Groups will solve their problem by creating and shading visual models on their “Let’s Go
on a Picnic” activity sheets and using a transparency if necessary.
Once a group’s work is approved they will cut their food item by dividing it into
fractional side lengths to represent the portion of their rectangular shaped food they will
be bringing on the picnic.
Assessment:
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Each group will present their portion of the food item resulting from their multiplication
of two fractions problem explaining how they arrived at their answer using visual
supports.
The teacher will complete a checklist as a method of formative assessment.
Name: __________________________________
Date: _____________
Multiplication Madness
Directions: Use the rectangular papers and transparencies
to find the areas of the following problems. Show your work below.
2/3 x ¾ = _____________
(divide into quarters and
shade 3/4)
2/3 x 1/2 = _____________
1/2 x 5/6 = ______________
(divide into thirds and
shade 2/3)
(combine the first 2
boxes and shadings)
Name: __________________________________
Date: _____________
Let’s Go on a Picnic! Group 1
Directions: Show your work for how we determined as a class the area of the
picnic blanket we need below.
½ x 1/3 = _____________
Directions: In your group, determine the area of the cornbread you need
and show all work below. Once your work is approved by the teacher, cut the
correct amount of cornbread.
1/4 x 2/3 = _____________
Name: __________________________________
Date: _____________
Let’s Go on a Picnic! Group 2
Directions: Show your work for how we determined as a class the area of the
picnic blanket we need below.
½ x 1/3 = _____________
Directions: In your group, determine how much brownie you need and show
all work below. Once your work is approved by the teacher, cut the correct
amount of brownie.
4/5 x 1/2 = _____________
Name: __________________________________
Date: _____________
Let’s Go on a Picnic! Group 3
Directions: Show your work for how we determined as a class the area of the
picnic blanket we need below.
½ x 1/3 = _____________
Directions: In your group, determine how much cornbread you need and
show all work below. Once your work is approved by the teacher, cut the
correct amount of cornbread.
3/5 x 2/3 = _____________
“Let’s Go on a Picnic” Teacher Checklist
Each student will receive a check plus if he or she has mastered the topic, a check if he or she
understands the topic, and a check minus if he or she is still learning the topic.
Student
Demonstrates understanding of
finding the area of a rectangle
with fractional side lengths.
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