A focused Grade 4 learning session for Multiplying Fractions by Whole Numbers using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can multiply a fraction by a whole number.
Multiplying Fractions by Whole Numbers means using equal parts, number lines, and clear fraction language to describe parts of a whole.
Question: Which picture shows \(2\times\frac{1}{3}\)?
Why it works: When we multiply \(2\times\frac{1}{3}\), we're taking 2 copies of \(\frac{1}{3}\), which gives us \(\frac{2}{3}\). Picture A shows one whole divided into thirds with exactly 2 parts shaded. This is \(\mathbf{\text{Picture A}}\).
Answer: Picture A shows two thirds shaded.
Question: Which equation does this bar model show?
Answer: \(2\times\frac{1}{2}\)
Question: Which picture shows \(3\times\frac{1}{4}\)?
Answer: Picture A
Question: Ming has 5 bags of marbles. Each bag has \(\frac{3}{10}\) pound of marbles. What is the total weight?
Why it works: Ming has 5 bags, each with \(\frac{3}{10}\) pound. Multiply: \(5\times\frac{3}{10}=\frac{5\times3}{10}=\frac{15}{10}=1\frac{1}{2}\) pounds. The answer is \(\mathbf{1\frac{1}{2} \text{ pounds}}\).
Answer: \(\frac{15}{10}\) or \(1\frac{1}{2}\) pounds
Multiplying Fractions by Whole Numbers 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.
What is \(4\times\frac{2}{5}\)?
Answer D: \(\frac{8}{5}\)
We have 4 copies of \(\frac{2}{5}\). Multiply the whole number by the numerator: \(4\times\frac{2}{5}=\frac{4\times2}{5}=\frac{8}{5}\). The answer is \(\mathbf{\frac{8}{5}}\).
What is \(3\times\frac{1}{4}\)?
Answer C: \(\frac{3}{4}\)
We take 3 copies of \(\frac{1}{4}\). Multiply the whole number by the numerator: \(3\times\frac{1}{4}=\frac{3\times1}{4}=\frac{3}{4}\). The answer is \(\mathbf{\frac{3}{4}}\).
Which picture shows \(2\times\frac{1}{3}\)?
Answer A: Picture A
When we multiply \(2\times\frac{1}{3}\), we're taking 2 copies of \(\frac{1}{3}\), which gives us \(\frac{2}{3}\). Picture A shows one whole divided into thirds with exactly 2 parts shaded. This is \(\mathbf{\text{Picture A}}\).
What is \(5\times\frac{1}{6}\)?
Answer C: \(\frac{5}{6}\)
We take 5 copies of \(\frac{1}{6}\) and add them together. Multiply the whole number by the numerator: \(5\times\frac{1}{6}=\frac{5\times1}{6}=\frac{5}{6}\). The answer is \(\mathbf{\frac{5}{6}}\).
Sam has 3 cookies. Each cookie is \(\frac{2}{3}\) of a cup of flour. How much flour is in all of Sam's cookies?
Answer A: \(\frac{6}{3}\) cup or \(2\) cups
Sam has 3 cookies, each using \(\frac{2}{3}\) cup of flour. Multiply: \(3\times\frac{2}{3}=\frac{3\times2}{3}=\frac{6}{3}=2\) cups. The answer is \(\mathbf{2 \text{ cups}}\).
What is \(2\times\frac{3}{4}\)?
Answer A: \(\frac{6}{4}\) or \(1\frac{1}{2}\)
We take 2 copies of \(\frac{3}{4}\). Multiply: \(2\times\frac{3}{4}=\frac{2\times3}{4}=\frac{6}{4}=1\frac{2}{4}=1\frac{1}{2}\). The answer is \(\mathbf{1\frac{1}{2}}\).
Use the number line to find \(3\times\frac{1}{5}\).
Answer A: \(\frac{3}{5}\)
On the number line, we make 3 jumps of \(\frac{1}{5}\) each. Starting at 0: hop to \(\frac{1}{5}\), then \(\frac{2}{5}\), then \(\frac{3}{5}\). This shows \(3\times\frac{1}{5}=\frac{3}{5}\). The answer is \(\mathbf{\frac{3}{5}}\).
Which equation does this bar model show?
Answer D: \(2\times\frac{1}{2}\)
The bar model shows two bars, each divided in half with one half shaded in each. This matches \(2\times\frac{1}{2}\), which means 2 copies of \(\frac{1}{2}\). The answer is \(\mathbf{2\times\frac{1}{2}}\) (Choice D).
What is \(6\times\frac{1}{8}\)?
Answer C: \(\frac{6}{8}\) or \(\frac{3}{4}\)
We take 6 copies of \(\frac{1}{8}\). Multiply: \(6\times\frac{1}{8}=\frac{6\times1}{8}=\frac{6}{8}=\frac{3}{4}\). The answer is \(\mathbf{\frac{3}{4}}\).
Ava drinks \(\frac{1}{4}\) cup of juice 4 times a day. How much juice does she drink altogether?
Answer A: \(\frac{4}{4}\) cup or \(1\) cup
Ava drinks \(\frac{1}{4}\) cup 4 times, so we calculate \(4\times\frac{1}{4}=\frac{4\times1}{4}=\frac{4}{4}=1\) cup. The answer is \(\mathbf{1 \text{ cup}}\).
What is \(2\times\frac{2}{5}\)?
Answer C: \(\frac{4}{5}\)
We take 2 copies of \(\frac{2}{5}\). Multiply: \(2\times\frac{2}{5}=\frac{2\times2}{5}=\frac{4}{5}\). The answer is \(\mathbf{\frac{4}{5}}\).
