Representing Mixed Numbers with Area Models
Representing Mixed Numbers with Area Models is a Grade 4 math skill that uses shaded rectangles to give mixed numbers a concrete visual meaning. A mixed number like 2 3/4 is shown as 2 fully shaded rectangles (representing 2 wholes) and one rectangle with 3 out of 4 sections shaded (the 3/4 part). This visual grounding helps students understand what mixed numbers actually represent — amounts greater than 1 whole — and connects to conversions between mixed numbers and improper fractions. Taught in the fraction chapters of Eureka Math Grade 4.
Key Concepts
Property A mixed number in the form $W \frac{N}{100}$ is represented visually using area models. This consists of $W$ fully shaded grids (representing the whole number) and one partially shaded grid with $N$ out of 100 squares shaded (representing the fraction part).
Examples To represent $1 \frac{25}{100}$, you would shade one entire grid and then shade 25 squares in a second grid. To represent $2 \frac{7}{100}$, you would shade two entire grids and then shade 7 squares in a third grid. To represent $3 \frac{40}{100}$, you would shade three entire grids and then shade 40 squares (or 4 columns) in a fourth grid.
Explanation Area models provide a visual way to understand mixed numbers with hundredths. Each whole number is represented by a completely shaded 10x10 grid, which equals one whole. The fractional part is shown by shading the corresponding number of squares in another 10x10 grid. This method helps connect the abstract concept of a mixed number to a concrete visual quantity.
Common Questions
How do I represent a mixed number with an area model?
Draw as many fully shaded rectangles as the whole number part. Then draw one more rectangle divided into as many sections as the denominator, and shade the number of sections equal to the numerator. Together, these models show the complete mixed number.
How do I show 2 3/4 with an area model?
Draw 2 fully shaded rectangles for the 2 wholes. Draw a third rectangle divided into 4 equal sections and shade 3 of them for the 3/4 part. The 3 shaded models together represent 2 3/4.
How does an area model show the relationship between a mixed number and an improper fraction?
Count all the equal-sized sections in all the shaded models (including the wholes). For 2 3/4: each whole rectangle has 4 sections, so 2 wholes = 8 sections, plus 3 more = 11 sections total, each being 1/4. So 2 3/4 = 11/4. The count of all pieces is the numerator of the improper fraction.
Why use area models to introduce mixed numbers?
Area models make the abstract notion of a mixed number concrete — students can literally see the whole parts and the fractional part. This visual foundation prevents confusion about what mixed numbers mean and supports the conversion to improper fractions.
How does representing mixed numbers with area models connect to fraction decomposition?
An area model for a mixed number visually decomposes it into its whole parts and its fractional part. This mirrors the algebraic decomposition: 2 3/4 = 2 + 3/4. Students who internalize the model understand the decomposition naturally.
What grade uses area models for mixed numbers in Eureka Math?
Representing mixed numbers with area models is a Grade 4 skill developed in the fraction chapters of Eureka Math Grade 4, where students build conceptual understanding of mixed numbers before converting between mixed number and improper fraction forms.