A focused Grade 4 learning session for Equivalent Fractions using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can generate an equivalent fraction and explain why it has the same value.
Equivalent Fractions means using equal parts, number lines, and clear fraction language to describe parts of a whole.
Question: Look at the two fraction bars. Both bars are the same length. Which fraction should replace the question mark?
Why it works: The shaded parts in both bars cover the same length, even though the second bar has more pieces. When you divide each half into 2 more pieces, \(\frac{1}{2}\) becomes \(\frac{2}{4}\)—same amount, more pieces.
Answer: \(\frac{2}{4}\)
Question: Look at the two fraction bars. Both bars are the same length. What number replaces the question mark?
Answer: 4
Question: Sam shaded \(\frac{1}{2}\) of a circle. Which other circle shows an equivalent fraction?
Answer: Circle B: \(\frac{2}{4}\)
Question: A ribbon is cut into 2 equal pieces, and 1 piece is painted. Another identical ribbon is cut into 4 equal pieces, and 2 pieces are painted. Are the painted amounts equivalent?
Why it works: Ribbon 1: \(\frac{1}{2}\) painted. Ribbon 2: \(\frac{2}{4}\) painted—simplify to \(\frac{2}{4} = \frac{1}{2}\). Same amount painted on both!
Answer: Yes, both are \(\frac{1}{2}\)
Equivalent 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 fraction is equivalent to \(\frac{2}{3}\)?
Answer D: \(\frac{4}{6}\)
To find an equivalent fraction, multiply both the numerator and denominator by the same number. Here, multiply by 2: \(\frac{2}{3}=\frac{2\times2}{3\times2}=\frac{4}{6}\). Both pieces are twice as many, but they"re the same size!
Look at the two fraction bars. Both bars are the same length. Which fraction should replace the question mark?
Answer D: \(\frac{2}{4}\)
The shaded parts in both bars cover the same length, even though the second bar has more pieces. When you divide each half into 2 more pieces, \(\frac{1}{2}\) becomes \(\frac{2}{4}\)—same amount, more pieces.
What fraction is equivalent to \(\frac{1}{2}\)?
Answer C: \(\frac{3}{6}\)
Multiply both top and bottom by 3: \(\frac{1}{2} = \frac{1\times3}{2\times3} = \frac{3}{6}\). This gives you more pieces, but they still cover the same amount!
Which fraction is in simplest form and equivalent to \(\frac{6}{8}\)?
Answer A: \(\frac{3}{4}\)
To simplify, divide both top and bottom by the same number. Here, divide by 2: \(\frac{6}{8} = \frac{6\div2}{8\div2} = \frac{3}{4}\). This gives you fewer, bigger pieces.
Look at the two circle models. They are the same size. Which fraction should replace the question mark?
Answer A: \(\frac{2}{8}\)
The shaded wedges in both circles are the same size. The first circle is split into 4 pieces (1 shaded), the second into 8 pieces (2 shaded). They cover the same amount: \(\frac{1}{4} = \frac{2}{8}\).
Multiply the numerator and denominator of \(\frac{3}{5}\) by 2. What fraction do you get?
Answer A: \(\frac{6}{10}\)
Multiply the numerator and denominator by 2: \(\frac{3}{5} = \frac{3\times2}{5\times2} = \frac{6}{10}\).
Which of these is NOT equivalent to \(\frac{1}{3}\)?
Answer C: \(\frac{2}{5}\)
Check each option: \(\frac{1}{3} = \frac{2}{6} = \frac{3}{9} = \frac{4}{12}\). All equivalent! But \(\frac{2}{5}\) is different because when you cross-multiply, \(2 \times 3 = 6\) but \(5 \times 1 = 5\).
Look at the two fraction bars. Both bars are the same length. What number replaces the question mark?
Answer D: 4
Both bars show the same shaded length. Since we"re going from thirds to sixths (multiply denominator by 2), multiply the numerator by 2 also: \(\frac{2}{3} = \frac{2\times2}{3\times2} = \frac{4}{6}\).
Which fraction equals \(\frac{3}{4}\)?
Answer A: \(\frac{6}{8}\)
Multiply both the numerator and denominator by 2: \(\frac{3}{4} = \frac{3\times2}{4\times2} = \frac{6}{8}\).
Sam shaded \(\frac{1}{2}\) of a circle. Which other circle shows an equivalent fraction?
Answer D: Circle B
The shaded parts show the same area. \(\frac{1}{2}\) and \(\frac{2}{4}\) are equivalent because we split each half in half, creating twice as many pieces. Circle C shows only \(\frac{1}{4}\), which is much less.
If you multiply the numerator and denominator of \(\frac{2}{5}\) by 3, what fraction do you get?
Answer D: \(\frac{6}{15}\)
Multiply both top and bottom by 3: \(\frac{2}{5} = \frac{2\times3}{5\times3} = \frac{6}{15}\).
