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# FRACTION OF A WHOLE NUMBER

**1. Mathematics**

Fraction of a Whole Number (students will demonstrate knowledge using the
following methods)

▪ Create a model of a fraction of a number using connecting cubes, red/white
counters, and 1cms

square grid paper.

▪ Solve fractions of a number using the mathematical algorithm of whole
number
is

(whole number * numerator) รท denominator or

**2. Grade Level:** 6^{th} Grade

**3. Manipulatives or Tools Needed:** connecting cubes,
red/white counters, 1cm square grid paper

(blackline master #35), colored pencils, scissors

**4. Before Stage** (estimated time -- 10 minutes)

▪ Pre-requisite Skills: multiplying whole numbers, comparing and understanding
fractional parts,

adding/subtracting fractions, simplifying fractions, changing improper fractions
to mixed numbers and vise

versa, multiplication terminology (of means to multiply).

▪ Related Tasks: Students work in groups of 4 according to the table
arrangement. Tasks are shown by

teacher reading them out loud and writing number sentences on the board.

Task 1: Demonstrate 3*5 using each a) connecting cubes, b)
red/white counters, & c) 1cm square grid paper.

(Walk around to check each group’s models; go over what was done & possible
interesting methods students might use)

What does the model represent? (3 groups/rows of 5) The first factor tells how
much/how many groups/rows of

the second factor you have. Now demonstrate 5*3 using methods a, b, & c. What
does this represent? (5

groups/rows of 3)

Task 2: Demonstrate 1/3 using each a) connecting cubes, b)
red/white counters, & c) 1cm square grid paper.

(Walk around to check each group’s models) Now demonstrate
using any of the three methods.

(Have students share their models)

**5. During Stage** (estimated time -- 25 minutes)

Task 3: Ask students to work with their partner & another set of partners (four
students total per group), using

the manipulative and tools they have been given, to create a model of
. Remind students to think about the

problems the class did previously to help them figure out how to solve the
problem. Tell students that they will

be expected to share their results with the class, so they need to fully
understand the model they create. When

students have figured out their model, tell them to choose a spokesperson for
their group.

**Discussion:** One group at a time, the groups’ chosen
spokesperson stands and explains their group’s

model/method to the class. The class can gather around the group’s work area if
necessary. See how many

different methods students found for multiplying a whole number by a fraction.

**Prediction: **I anticipate students struggling with this task, because of
their lack of exposure to and use of

manipulative and models. If they struggle, I will direct them to first represent
the whole number. Then ask

them how many parts each whole needs to be divided into. (hint: look at the
denominator; 5 parts) Once students

receive that hint, they should be able to proceed to figure out the model. If
this does not work, help the students

to draw out a model of four rectangles, divided into 5 parts, with 3 parts of
each rectangle shaded.

**6. After Stage** (estimated time -- 15 minutes)

Summarize & Explain: Ask students if they have noticed a pattern of how to solve
this and other similar

problems mathematically. If a student seems to have a valid method, ask them to
explain it on the whiteboard

for the rest of the students. After all students have shared their ideas,
explain to them the algorithm using

The whole number 4 tells you how many wholes rectangles
you may have. Draw 4

rectangles.

The denominator of the fraction tells you how many parts
each rectangle has.

Divide each rectangle into 5 sections to represent fifths.

The numerator tells you how many sections of each
rectangle to shade. Shade 3

fifths of all 4 rectangles.

Multiply to find the number of shaded parts (3 parts x the
4 wholes). Represent the

shaded parts as a

fraction.

Simplify if possible.

Assign Practice: Ask students to work problems (p. 271) 1,
2, 11, & 23 on their own. After they have finished

them, they will get back into their groups and compare answers. The students
will do their best to correct others

misunderstandings. If they have questions, I will help them. If it sounds like
the students need more

instruction, do so. Otherwise assign the following problems to work on during
class: 3-8 (using a model to find

answer), 12-15, 16-27.

**7. What Comes Next?**

▪ Students will build on their knowledge of multiplying a whole number by a
fraction in following lessons

by learning to multiply fractions, and later on, divide fractions.

▪ Students will be given practice worksheets throughout the week and be
instructed to solve the problems

using both the algorithm and some sort of drawn model.