Multiplication with Fractions
Age
9-10 years
Aim
Direct: understand that multiplication in fractions is taking a fractional part of a fraction
Indirect: reinforce that multiplication is repeated addition; multiplication of fractions by a fraction results in a smaller fraction
Materials
box of fractional pieces, fractional grid overlays
Presentation 1 - Multiplication by a Whole Number
1. Invite the child to the lesson.
2. “Today, we are going to look at multiplication of a fraction by a whole number. Let’s take onesixth two times.”
3. Place the fractional pieces on the rug.
4. “How will we know how many we have?” Put the
fractional pieces together to record two-sixths.
5. Remember to simplify the fraction to one-third.
6. “There is another way to write a whole number as a
fraction. When you were first introduced to fractions
you learned that the denominator was the number of
pieces that a whole was cut into.”
7. If I have four wholes, this is what it would look like with our fraction pieces.”
8. “How many parts is each whole cut into? Yes, just one. How many parts of one are there?
Yes, there are four. So this fraction of four wholes can be written as
4 .”
1
Upper Elementary Math Manual
36
© 2014 ETC Montessori Inc.
Presentation 2 - Multiplication by a Fraction
1. Invite the child to the lesson.
2. “Today, we are using a new piece of material. These are the fraction overlays.”
3. Explain to the child how the colored parts of the rectangle represent the fractional parts.
4.“Let’s say I wish to take one-half of one-fourth. Listen to the
problem. What will I begin with?”
5.Lay out one-fourth.
6.“Now, we need to take one-half of this one-fourth.”
7.Select the clear one-half fraction overlay and
place it on top of the one-fourth perpendicularly.
8.“When we add the clear ½ overlay, we can see
that our denominator has now changed to eighths.”
9.“However, this represents two-halves of ¼ and
we only want one-half of one-fourth.”
10.With your hand or a piece of paper cover up onehalf of the overlay that has the eights denominator. “How many eights
are colored? Yes, one-eight is the product.”
11. “Did you notice anything about the relationship of the fractions and
their product?”
12.The child should discover that the product in the multiplication
of a fraction becomes smaller instead of larger as in whole number
multiplication.
13.Have the child record the problem in their math notebook.
14.As the child continues through the work it is noted that the word OF in the problem is
replaced by a X sign. Have the child make note that in mathematical statements, the word
“of” is translated into multiplication.
Follow Up
1. Division of a fraction by a whole number
2. Division of a fraction by a fraction
Upper Elementary Math Manual
37
© 2014 ETC Montessori Inc.