Fraction Grid Area Diagram
Grade 5 • Number & Operations — Fractions Area Model Concept Chart
Fraction Multiplication Grid Model
Modeling a 1 unit × 1 unit square partitioned into 4 rows and 5 columns.
Model Target \(\frac{2}{4} \times \frac{3}{5} = \frac{6}{20}\)
Total Width = 1 Unit (5 Columns)
3 columns shaded = \(\frac{3}{5}\) unit
2 unshaded
2 Rows \(\frac{2}{4}\) unit
2 Rows \(\frac{2}{4}\) unit
1 \(\frac{1}{20}\)
2 \(\frac{1}{20}\)
3 \(\frac{1}{20}\)
\(\frac{1}{20}\)
\(\frac{1}{20}\)
4 \(\frac{1}{20}\)
5 \(\frac{1}{20}\)
6 \(\frac{1}{20}\)
\(\frac{1}{20}\)
\(\frac{1}{20}\)
\(\frac{1}{20}\)
\(\frac{1}{20}\)
\(\frac{1}{20}\)
\(\frac{1}{20}\)
\(\frac{1}{20}\)
\(\frac{1}{20}\)
\(\frac{1}{20}\)
\(\frac{1}{20}\)
\(\frac{1}{20}\)
\(\frac{1}{20}\)
Shaded Overlap (6 cells)
Unshaded (14 cells)
Model Quantities
Total Grid Parts: 4 × 5 = 20 equal cells
Value of 1 Cell: \(\frac{1}{20}\) of the whole unit
Shaded Dimensions: 2 rows × 3 columns
Total Shaded Cells: 2 × 3 = 6 cells
Area Formula
\[ \text{Area} = \frac{2}{4} \times \frac{3}{5} = \frac{2 \times 3}{4 \times 5} = \frac{6}{20} = \frac{3}{10} \]
Simplified fraction: \(\frac{3}{10}\) • Decimal: \(0.30\)
How to Read & Construct the Grid Model
1
Define Whole
The entire outer square represents 1 unit of area (\(1 \times 1 = 1\)).
Total Area = 1.0
2
Partition Grid
Divide height into 4 equal rows (\(\frac{1}{4}\) each) and width into 5 equal columns (\(\frac{1}{5}\) each).
Denominator: 4×5 = 20
3
Shade Factors
Cover 2 of the 4 rows and 3 of the 5 columns. The overlap forms the shaded region.
Numerator: 2×3 = 6
4
Read Product
Count the shaded cells over total cells: 6 out of 20, which simplifies to \(\frac{3}{10}\).
\(\frac{6}{20} = \frac{3}{10} = 0.3\)
Multiple Representations
Connecting Fractions & Decimals
Both factors can be written as decimals or fractions. The resulting product is identical.
Fraction Form \(\frac{2}{4} \times \frac{3}{5} = \frac{6}{20} = \frac{3}{10}\)
Decimal Form \(0.5 \times 0.6 = 0.30\)
Why is the product smaller than the factors?
Since both factors are less than 1 (\(\frac{2}{4} < 1\) and \(\frac{3}{5} < 1\)), we are finding a part of a part. Therefore, the shaded product \(\frac{3}{10}\) is smaller than either factor.
Quick Check Questions Self-Review
Q1: What fraction of the total unit grid is unshaded? (\(\frac{14}{20}\) or \(\frac{7}{10}\))
Q2: How does simplifying \(\frac{2}{4}\) to \(\frac{1}{2}\) affect the equation? (\(\frac{1}{2} \times \frac{3}{5} = \frac{3}{10}\))
Unit Square Area Model • Visualizing Multiplication of Rational Numbers 1 Unit × 1 Unit Partition Model
