A focused Grade 4 learning session for Multiples of a Fraction using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can find and represent multiples of a fraction.
Multiples of a Fraction means using equal parts, number lines, and clear fraction language to describe parts of a whole.
Question: Sam has a number line with hops of \(\frac{1}{4}\). Which point represents \(3\times\frac{1}{4}\)?
Why it works: Starting at 0, each hop moves us forward by \(\frac{1}{4}\). After three hops, we land at \(3 \times \frac{1}{4} = \frac{3}{4}\), which is Point C.
Answer: Point C
Question: A number line shows hops of \(\frac{2}{5}\). How many hops to reach \(\frac{10}{5}\)?
Answer: 5 hops
Question: Noah skipped by \(\frac{1}{8}\) along a number line. He stopped at \(\frac{3}{8}\). How many skips did he make?
Answer: 3 skips
Question: Which shows the error in this student work? The student said \(\frac{1}{4} + \frac{1}{4} = \frac{2}{8}\).
Why it works: When adding fourths, the denominator stays the same! \(\frac{1}{4} + \frac{1}{4} = \frac{2}{4}\), not \(\frac{2}{8}\). The student mistakenly added the denominators.
Answer: Adding the numerators and denominators separately (mistake)
Multiples of a Fraction 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.
Which shows a multiple of \(\frac{2}{3}\)?
Answer C: \(\frac{4}{3}\)
The multiples of \(\frac{2}{3}\) are: \(\frac{2}{3}, \frac{4}{3}, \frac{6}{3}, \ldots\) Each one is obtained by multiplying \(\frac{2}{3}\) by whole numbers. Since \(\frac{4}{3} = 2 \times \frac{2}{3}\), the answer is \(\mathbf{\frac{4}{3}}\).
Sam has a number line with hops of \(\frac{1}{4}\). Which point represents \(3\times\frac{1}{4}\)?
Answer C: Point C
Starting at 0, each hop moves us forward by \(\frac{1}{4}\). After three hops, we land at \(3 \times \frac{1}{4} = \frac{3}{4}\), which is Point C.
Which fraction is a multiple of \(\frac{1}{5}\)?
Answer A: \(\frac{2}{5}\)
A multiple of \(\frac{1}{5}\) means we count by fifths. We can write \(\frac{2}{5} = 2 \times \frac{1}{5}\), so it"s a multiple. The others don"t fit that pattern.
Maya lined up 4 unit-fraction tiles. If each tile is \(\frac{1}{6}\), what is the total?
Answer C: \(\frac{4}{6}\)
Four tiles, each \(\frac{1}{6}\), combine to make \(4 \times \frac{1}{6} = \frac{4}{6}\).
Which shows the first four consecutive multiples of \(\frac{1}{3}\) in order?
Answer B: \(\frac{1}{3}, \frac{2}{3}, \frac{3}{3}, \frac{4}{3}\)
Multiples of \(\frac{1}{3}\) count by thirds: first \(\frac{1}{3}\), then \(\frac{2}{3}\), then \(\frac{3}{3}\), then \(\frac{4}{3}\). The fraction \(\frac{3}{3}\) equals \(1\), but it is written in thirds here to show the counting pattern. That"s exactly what choice B shows!
What is \(5 \times \frac{1}{4}\)?
Answer C: \(\frac{5}{4}\)
When we multiply by the numerator, we keep the denominator the same. So \(5 \times \frac{1}{4} = \frac{5}{4}\).
A number line shows hops of \(\frac{2}{5}\). How many hops to reach \(\frac{10}{5}\)?
Answer D: 5 hops
Each hop is \(\frac{2}{5}\). To reach \(\frac{10}{5}\), we need \(5 \times \frac{2}{5} = \frac{10}{5}\), so it takes 5 hops.
Which is NOT a multiple of \(\frac{1}{6}\)?
Answer C: \(\frac{2}{5}\)
Multiples of \(\frac{1}{6}\) count by sixths. That gives us \(\frac{1}{6}, \frac{2}{6}, \frac{3}{6}, \frac{4}{6}, \frac{5}{6}, \frac{6}{6}, \ldots\) But \(\frac{2}{5}\) doesn"t fit this pattern, so it"s not a multiple.
Noah skipped by \(\frac{1}{8}\) along a number line. He stopped at \(\frac{3}{8}\). How many skips did he make?
Answer C: 3 skips
Noah skips in eighths: \(\frac{1}{8}, \frac{2}{8}, \frac{3}{8}\). After 3 skips, he"s at \(\frac{3}{8}\).
A fraction bar is divided into 5 equal parts. If 2 parts are shaded and each part is \(\frac{1}{10}\), what fraction is shaded?
Answer A: \(\frac{2}{10}\)
When 2 parts are shaded and each part is \(\frac{1}{10}\), we get \(2 \times \frac{1}{10} = \frac{2}{10}\).
What is \(6 \times \frac{1}{3}\)?
Answer B: \(\frac{6}{3}\)
Six thirds means \(6 \times \frac{1}{3} = \frac{6}{3}\). Since \(\frac{6}{3}\) is our answer, that"s \(\mathbf{\frac{6}{3}}\).
