A focused Grade 4 learning session for Fraction as Sum of Unit Fractions using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can write a fraction as a sum of unit fractions.
Fraction as Sum of Unit Fractions means using equal parts, number lines, and clear fraction language to describe parts of a whole.
Question: Which fraction bar shows \(\frac{4}{6}\) as a sum of unit fractions?
Why it works: In the fraction bar, we have 4 shaded parts out of 6 equal parts. Each piece is a unit fraction \(\frac{1}{6}\). So we have \(\mathbf{\frac{4}{6}=\underbrace{\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}}_{4 \text{ copies}}}\).
Answer: 4 parts shaded, 6 total
Question: A number line shows jumps of \(\frac{1}{3}\). Which number of jumps gets us to \(\frac{2}{3}\)?
Answer: 2 jumps
Question: Which picture shows \(\frac{3}{4}\) as a sum of unit fractions?
Answer: 3 of 4 parts
Question: A recipe needs \(\frac{2}{3}\) cup of flour. How can we write this as a sum of unit fractions?
Why it works: The recipe needs \(\frac{2}{3}\) cup of flour. This is 2 equal pieces, each \(\frac{1}{3}\) cup. So \(\mathbf{\frac{2}{3}=\frac{1}{3}+\frac{1}{3}}\).
Answer: \(\frac{1}{3}+\frac{1}{3}\)
Fraction as Sum 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.
Which expression shows \(\frac{3}{5}\) as a sum of unit fractions?
Answer B: \(\frac{1}{5}+\frac{1}{5}+\frac{1}{5}\)
A unit fraction always has a numerator of \(1\). So \(\frac{3}{5}\) breaks down into three copies of \(\frac{1}{5}\): \(\mathbf{\frac{3}{5}=\frac{1}{5}+\frac{1}{5}+\frac{1}{5}}\).
Which fraction bar shows \(\frac{4}{6}\) as a sum of unit fractions?
Answer A: 4 parts shaded, 6 total
In the fraction bar, we have 4 shaded parts out of 6 equal parts. Each piece is a unit fraction \(\frac{1}{6}\). So we have \(\mathbf{\frac{4}{6}=\underbrace{\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}}_{4 \text{ copies}}}\).
What is \(\frac{2}{3}\) as a sum of unit fractions?
Answer B: \(\frac{1}{3}+\frac{1}{3}\)
\(\frac{2}{3}\) means two pieces, each of size \(\frac{1}{3}\). So \(\mathbf{\frac{2}{3}=\frac{1}{3}+\frac{1}{3}}\)—two unit fractions added together.
Sam has a strip of paper divided into 8 equal parts. He colors 5 parts. Which expression shows the fraction colored as a sum of unit fractions?
Answer A: \(\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}\)
Sam colored 5 pieces out of 8 equal parts, so the fraction is \(\frac{5}{8}\). This is the sum of five unit fractions: \(\mathbf{\frac{5}{8}=\underbrace{\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}}_{5 \text{ copies}}}\).
Which number sentence is correct?
Answer B: \(\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=\frac{3}{4}\)
When we add unit fractions with the same denominator, we keep the denominator and add the numerators. \(\frac{1}{4}+\frac{1}{4}+\frac{1}{4}\) has three 1's in the numerator, so it equals \(\mathbf{\frac{3}{4}}\). The other choices incorrectly change the denominator.
Ming shares a pizza cut into 12 equal slices. He eats 3 slices. Show how many slices he ate as a sum of unit fractions.
Answer B: \(\frac{1}{12}+\frac{1}{12}+\frac{1}{12}\)
Ming ate 3 slices out of 12 equal slices, so the fraction is \(\frac{3}{12}\). Breaking this into unit fractions: \(\mathbf{\frac{3}{12}=\frac{1}{12}+\frac{1}{12}+\frac{1}{12}}\)—three slices, each representing \(\frac{1}{12}\) of the pizza.
A number line shows equal hops from 0 to \(\frac{6}{10}\). How many hops of \(\frac{1}{10}\) are needed?
Answer C: 6 hops
To reach \(\frac{6}{10}\) with hops of \(\frac{1}{10}\), we count: each hop is one unit fraction, and we need 6 copies to equal \(\frac{6}{10}\). So \(\mathbf{6 \text{ hops}}\) gets us there!
Ava splits a granola bar into 6 equal pieces. She gives away 4 pieces. Write the fraction given away as a sum of unit fractions.
Answer C: \(\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\)
Ava gave away 4 pieces out of 6 equal pieces, which is \(\frac{4}{6}\). As a sum of unit fractions: \(\mathbf{\frac{4}{6}=\underbrace{\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}}_{4 \text{ copies}}}\).
How many unit fractions of \(\frac{1}{7}\) make \(\frac{5}{7}\)?
Answer B: 5
\(\frac{5}{7}\) means we have 5 equal pieces, and each piece is \(\frac{1}{7}\). So \(\mathbf{5}\) unit fractions of \(\frac{1}{7}\) make up \(\frac{5}{7}\).
A number line shows jumps of \(\frac{1}{3}\). Which number of jumps gets us to \(\frac{2}{3}\)?
Answer B: 2 jumps
Each jump moves us forward by \(\frac{1}{3}\). To land on \(\frac{2}{3}\), we need \(\mathbf{2 \text{ jumps}}\): \(\frac{1}{3}+\frac{1}{3}=\frac{2}{3}\).
Which picture shows \(\frac{3}{4}\) as a sum of unit fractions?
Answer A: 3 of 4 parts
\(\frac{3}{4}\) shows 3 shaded parts out of 4 equal parts. Since each part is \(\frac{1}{4}\), we have \(\mathbf{\frac{3}{4}=\frac{1}{4}+\frac{1}{4}+\frac{1}{4}}\)—three unit fractions added.
