Download 5.NF.7.11.3.11

5.NF.7
2011
Domain: Number and Operations in Base Ten
Cluster: Apply and extend previous understandings of multiplication and division to multiply and divide fractions
Standards 7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers
by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create
a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and
division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷
(1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that
4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit
fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each
person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
Essential Questions

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How can you use
models to show
division of
fractions?
How can drawing a
picture and writing
an equation help to
solve a problem?
How can you model
dividing a fraction
by a whole number?
Content Statements
Enduring Understandings



Information in a problem
can be represented by a
model or diagram and
used to solve the
problem.
Dividing a whole number
by a fraction results in a
quotient greater than the
original whole number.
The inverse relationships
between division and
multiplication can be
Activities, Investigation, and Student Experiences
1. Fold a square sheet of paper vertically in half. Fold the
paper vertically in half again. Ask students the fraction
represented by each section of the sheet of paper.
Fold the paper in half horizontally. Ask students the
fraction represented by each section of the sheet of
paper.
Shade ¾ of the vertical sections red and ½ of the
horizontal sections blue.
The part that is shaded both red and blue shows ½ x ¾.
Ask students to solve ½ x ¾.
5.NF.7


Students will use
models or mental
math to divide
fractions.
used to divide the
fractions.
Students can use
diagrams and
equations to solve
problems.
Assessments
5.NF.7

Four students sitting at a table were given 1/3 of a
pan of brownies to share. How much of a pan will
each student get if they share the pan of brownies
equally?
o The diagram shows the 1/3 pan divided into
4 equal shares with each share equaling
1/12 of the pan.

You have 1/8 of a bag of pens and you need to
share them among 3 people. How much of the bag
does each person get?

How many 1/3 –cup servings are in 2 cups of
2011
2. Fractions on a ruler:
Use the ruler to model for students how to find how
many ½ inch segments are in 2 inches.
How many ½ inch segments are in 3 inches? How many
¼ inch segments are in 2 inches? 3 inches?
Have pairs take turns posing similar questions to one
another. Encourage them to use different fractional
segments and whole inch measurements.
5.NF.7
raisins?
o Student Answer – I know that there are
three 1/3 cup servings in 1 cup of raisins.
Therefore, there are 6 servings in 2 cups of
raisins. I can also show this since 2 divided
by 1/3 = 2x3 = 6 servings of raisins.
Knowing how many in each group/share and finding
how many groups/shares

Angelo has 4 lbs of peanuts. He wants to give each
of his friends 1/5 lb. How many friends can
receive 1/5 lb of peanuts?
A diagram for 4 ÷ 1/5 is shown below. Students
explain that since there are five fifths in one whole,
there must be 20 fifths in 4 lbs.
1 lb. of peanuts

How much rice will each person get if 3 people
share 1/2 lb of rice equally?
2011
5.NF.7
2011
o A student may think or draw ½ and cut it
into 3 equal groups then determine that
each of those part is 1/6.
o A student may think of ½ as equivalent to
3/6. 3/6 divided by 3 is 1/6.
Equipment Needed:
Teacher Resources:
Student whiteboards

http://www.math-drills.com/fractions.shtml
Calculators

http://illuminations.nctm.org/ActivityDetail.aspx?ID=
64

http://www.ixl.com/math/grade-5/divide-fractions-bywhole-numbers

http://mathstory.com/algebrah/Algebrahindex.html

http://illuminations.nctm.org/ActivityDetail.aspx?ID=
80
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http://illuminations.nctm.org/ActivityDetail.aspx?ID=
64

http://www.superteacherworksheets.com/fractions/fr
action-word-problems-easy.pdf

http://www.thirteen.org/edonline/adulted/lessons/stuf
f/lp46_fracword.pdf\
Internet
Smartboard
Manipulatives
Overhead
5.NF.7
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2011
http://coedpages.uncc.edu/abpolly/math/core/unpacki
ng/unpacked-5th.pdf