A focused Grade 4 learning session for Fractions as Multiples of Unit Fractions using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can write a fraction as a multiple of a unit fraction.
Fractions as Multiples of Unit Fractions means using equal parts, number lines, and clear fraction language to describe parts of a whole.
Question: Which picture shows \(\frac{2}{5}\) as two unit fractions of \(\frac{1}{5}\)?
Why it works: Count the shaded parts: there are \(2\) shaded parts. Count the equal parts: there are \(5\) total parts. So the fraction bar shows \(2\) copies of \(\frac{1}{5}\), which is \(\frac{2}{5}\).
Answer: Picture A
Question: Which multiplication sentence matches the fraction bar below?
Answer: \(3 \times \frac{1}{4}\)
Question: The fraction bar below is divided into equal parts. How many parts are shaded, and what fraction do they represent?
Answer: \(4\) parts; \(\frac{4}{5}\)
Question: A ribbon is \(\frac{9}{10}\) meter long. How many tenths is that?
Why it works: The numerator \(9\) tells us exactly how many tenths we have. So \(\frac{9}{10} = 9 \times \frac{1}{10}\), which means we have \(\mathbf{9}\) tenths.
Answer: \(9\) tenths
Fractions as Multiples of Unit Fractions becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Equal parts first, fraction name second.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
How many copies of \(\frac{1}{6}\) are in \(\frac{5}{6}\)?
Answer B: \(5\)
The fraction \(\frac{5}{6}\) means \(5\) copies of the unit fraction \(\frac{1}{6}\), so \(\frac{5}{6}=5\times\frac{1}{6}\). The answer is \(\mathbf{5}\) copies.
Write \(\frac{3}{4}\) as a multiplication of a whole number and a unit fraction.
Answer B: \(3 \times \frac{1}{4}\)
The numerator \(3\) tells us how many unit fractions we have, and the denominator \(4\) tells us the unit fraction is \(\frac{1}{4}\). So \(\frac{3}{4}\) equals \(3 \times \frac{1}{4}\).
Which picture shows \(\frac{2}{5}\) as two unit fractions of \(\frac{1}{5}\)?
Answer A: Picture A
Count the shaded parts: there are \(2\) shaded parts. Count the equal parts: there are \(5\) total parts. So the fraction bar shows \(2\) copies of \(\frac{1}{5}\), which is \(\frac{2}{5}\).
How many \(\frac{1}{8}\)'s are in \(\frac{7}{8}\)?
Answer B: \(7\)
The fraction \(\frac{7}{8}\) is equal to \(7\) copies of the unit fraction \(\frac{1}{8}\), so we have \(7 \times \frac{1}{8} = \frac{7}{8}\). There are \(\mathbf{7}\) unit fractions.
Which multiplication sentence matches \(\frac{4}{10}\)?
Answer B: \(4 \times \frac{1}{10}\)
The fraction \(\frac{4}{10}\) is the same as \(4\) copies of \(\frac{1}{10}\). We write this multiplication as \(4 \times \frac{1}{10}\).
A number line shows jumps of \(\frac{1}{3}\) starting at \(0\). If you make \(6\) jumps, where do you land?
Answer C: \(2\)
Each jump is \(\frac{1}{3}\). Making \(6\) jumps is the same as \(6 \times \frac{1}{3} = \frac{6}{3}\). Since \(3\) thirds make one whole, \(\frac{6}{3}\) equals \(\mathbf{2}\) wholes.
Which of the following is the same as \(5 \times \frac{1}{12}\)?
Answer A: \(\frac{5}{12}\)
When we multiply a whole number by a unit fraction, we get that many copies of the unit fraction. So \(5 \times \frac{1}{12}\) means \(5\) copies of \(\frac{1}{12}\), which is \(\frac{5}{12}\).
How many unit fractions \(\frac{1}{4}\) are needed to make \(\frac{3}{4}\)?
Answer C: \(3\)
To make \(\frac{3}{4}\), we need \(3\) copies of \(\frac{1}{4}\). So we need \(\mathbf{3}\) unit fractions.
A fraction bar is divided into \(6\) equal parts with \(4\) parts shaded. Express this as a multiplication of a unit fraction.
Answer A: \(4 \times \frac{1}{6}\)
Count the shaded parts: \(4\) parts. Count the equal parts: \(6\) total. So this shows \(4\) copies of \(\frac{1}{6}\), which we write as \(4 \times \frac{1}{6}\).
Ava ate \(\frac{6}{8}\) of a pizza. How many eighths is that?
Answer B: \(6\)
The numerator tells us how many eighths there are. Since the numerator is \(6\), there are \(\mathbf{6}\) eighths in \(\frac{6}{8}\).
Which number sentence is true?
Answer B: \(3 \times \frac{1}{5} = \frac{3}{5}\)
Let's check each one: A: \(2 \times \frac{1}{5} = \frac{2}{5}\), not \(\frac{1}{10}\). B: \(3 \times \frac{1}{5} = \frac{3}{5}\) \checkmark. C: \(4 \times \frac{1}{5} = \frac{4}{5}\), not \(\frac{4}{20}\). D: \(5 \times \frac{1}{5} = 1\), not \(\frac{1}{5}\).
