You can use the area model to represent multiplying two fractions. The model can be made into a grid throughout the assignment by having the student draw the appropriate number of lines. The number of squares needs to be the least common multiple of both denominators.
When multiplying fractions, students will shade the numerators of the fractions. One numerator will be shaded from the left; the other from the bottom. See the example below. (PDF coming soon.) The shaded region that overlaps is the numerator of the product. The denominator remains the number of squares in the grid.
Preparation:
- Laminate a model for each of your students.
- Offer each student enough transparency sheets to cover the entire model and an erasable marker.
Student Instructions: Use the model to help you multiply the following fractions. The number of squares in the model is the least common multiple of your denominators. You want both denominators to be a factor of your grid. In using the model, shade from the left side the number of boxes in your first numerator and shade from the bottom the number of boxes in your second numerator. (PDF coming soon.)
½ × ¾ =
½ was shaded from the left.
¾ was shaded from the bottom.
6 of the 16 squares are overlapping shaded regions. This reduces to 3 out of 8, so the answer is ⅜.
½ × ¾ = ⅜
Use the example to help you complete the following:
- ½×⅔=
- ⅗×⅙=
- ⅚×¼=
- ⅔×⅘=
Use the PDF for the following activity: (PDF coming soon)
1. Make a list of colors in the work of art and record 5 of the most prominent colors in the first column.
2. Count the number of squares on the work of art that contain the corresponding color in the first column.
3. Create a fraction; reduce to lowest terms
4. Convert fraction to a decimal
5. Calculate percentage
Evaluate Data
1. Analyze parts of the painting according to the different percentages of color present
2. Discuss which colors were used more frequently and less frequently. Why?
Notes:
1. Count the number of squares on the work of art that contain the corresponding color in the first column.
2. Create a fraction; reduce to lowest terms
3. Convert fraction to a decimal
4. Calculate percentage