Download Multiplying Fractions w/Rectangles

Differentiated Activities for NF.4.a/b – Multiplying with Rectangles
Models:
- Model how to use an area model to show the product of ¼ x ½ by
folding and shading paper. Explain. Then have students model the same
problem. Repeat with others.
Centimeter Grid paper (click here for grid paper)
- Have students create area problems for rectangles, using fractions for the
base and height. Students roll a number cube twice to create each
fraction. The greater number rolled is the denominator.
- Then have students model the problems by drawing a rectangle with a
base the length of the denominator of one fraction and a height the
length of the denominator of the other fraction.
- Students can use the model to find the area, which is the product of the
base and the height.
Counting Tape
- Give each student a strip of counting tape about 6 inches long. Write ½ x
1/3 on the board. Help students model how to find the product using that
counting tape. How can we show 2/3 by folding and shading the tape?
Into how many parts will we fold each third? How many equal parts are
there in the whole tape now? What will you do next to find ½ of 2/3?
How many parts out of the total number of parts did you mark?
Folding Paper
- Write ¾ x ½ on board. Help students model how to find product by
folding paper.
- Show second factor first. How many equal parts will we fold the paper
vertically? How many parts will we shade yellow to show ½?
- Into how many equal parts will we fold the paper horizontally to show
fourths? How many equal parts are there in the whole paper now? Are
we finding ¾ of the yellow shaded part or ¾ of the whole? How many
yellow shaded parts will we shade blue to show ¾ of ½? What fraction
of the whole is shaded blue?
Draw
- Work with students to draw a square and then divide it into 5 equal parts.
Have students shade on part. Write the fraction 1/5 on the board to
represent the shaded part.
- Ask students to draw a line across all the fifths. Discuss how the line
divides the shape into 2 equal parts, or halves, and have students shade
one part. Point out that only one pare is shaded both times. Write 1/5 x ½
on the board. How many parts are there in all? How many were shaded
twice?
Number Cubes
- Give each group two number cubes. Have them roll the two cubes twice
and form fractions less than 1 or whole numbers using some or all of the
numbers rolled. Have each person write a multiplication sentence with
the fractions they created. Then ask each member of the group to write a
word problem based on that multiplication sentence. Have them
exchange and solve each other’s word problems.
Grid Paper
- Have students draw a 4 by 5 rectangle on grid paper (click here for grid
paper) to model ¾ x 2/5?
- What fraction do you model first? How do you show ¾ of 2/5?
- What can you do to the numerators of the factors to get the numerators
of the product? Same for denominators?
Paper
- Have students use paper folding to find ½ x 3/8.