A focused Grade 3 learning session for Generating Simple 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 is equivalent.
Generating Simple Equivalent Fractions means using equal parts, number lines, and clear fraction language to describe parts of a whole.
Question: Look at the fraction bars below. Which fractions are equivalent?
Why it works: Both bars show the same shaded length. When you split each half into 2 equal parts, 1 half becomes 2 fourths. So \(\frac{1}{2}=\frac{2}{4}\).
Answer: \(\frac{1}{2}\) and \(\frac{2}{4}\)
Question: Look at the rectangle divided into \(8\) equal parts. Which fraction in eighths describes the shaded part?
Answer: \(\frac{4}{8}\)
Question: Which two fraction bars show equivalent fractions?
Answer: \(\frac{2}{3}\) and \(\frac{4}{6}\)
Question: Which fraction is equivalent to \(\frac{3}{4}\)?
Why it works: If you divide a figure into 4 parts and shade 3, then divide each part in half, you get 8 parts with 6 shaded. So \(\frac{3}{4}=\frac{6}{8}\) because \(\frac{3\times2}{4\times2}=\frac{6}{8}\).
Answer: \(\frac{6}{8}\)
Generating Simple 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 \(\frac{3}{4}\)?
Answer C: \(\frac{6}{8}\)
If you divide a figure into 4 parts and shade 3, then divide each part in half, you get 8 parts with 6 shaded. So \(\frac{3}{4}=\frac{6}{8}\) because \(\frac{3\times2}{4\times2}=\frac{6}{8}\).
Look at the fraction bars below. Which fractions are equivalent?
Answer C: \(\frac{1}{2}\) and \(\frac{2}{4}\)
Both bars show the same shaded length. When you split each half into 2 equal parts, 1 half becomes 2 fourths. So \(\frac{1}{2}=\frac{2}{4}\).
Which fraction is equivalent to \(\frac{1}{3}\)?
Answer B: \(\frac{2}{6}\)
Multiply numerator and denominator by 2: \(\frac{1\times2}{3\times2}=\frac{2}{6}\).
Which fraction equals \(\frac{1}{2}\)?
Answer C: \(\frac{4}{8}\)
Multiply numerator and denominator by 4: \(\frac{1\times4}{2\times4}=\frac{4}{8}\).
Which fraction is NOT equivalent to \(\frac{2}{4}\)?
Answer D: \(\frac{2}{3}\)
\(\frac{2}{4}\) equals \(\frac{1}{2}\) (divide by 2). Choices A, B, and C are all equivalent to \(\frac{1}{2}\). Only \(\frac{2}{3}\) is different.
Which fraction is equivalent to \(\frac{1}{2}\) by multiplying numerator and denominator by 3?
Answer B: \(\frac{3}{6}\)
Multiply numerator and denominator by 3: \(\frac{1\times3}{2\times3}=\frac{3}{6}\).
Which two circles show equivalent fractions?
Answer C: Circles 1 and 3
Circle 1 shows \(\frac{1}{2}\) (half shaded) and Circle 3 shows \(\frac{2}{4}\) (half shaded). These are equivalent because \(\frac{1\times2}{2\times2}=\frac{2}{4}\).
\(\frac{2}{3}=\frac{?}{6}\). What number goes in the box?
Answer B: 4
The denominator was multiplied by 2 (from 3 to 6). Multiply the numerator by 2: \(2\times2=4\). So \(\frac{2}{3}=\frac{4}{6}\).
\(\frac{1}{4}=\frac{2}{?}\). What number goes in the box?
Answer C: 8
The numerator was multiplied by 2 (from 1 to 2). Multiply the denominator by 2: \(4\times2=8\). So \(\frac{1}{4}=\frac{2}{8}\).
Look at the rectangle divided into \(8\) equal parts. Which fraction in eighths describes the shaded part?
Answer C: \(\frac{4}{8}\)
The rectangle has \(8\) equal parts and \(4\) are shaded, so the shaded fraction written in eighths is \(\frac{4}{8}\).
Which fraction equals \(\frac{1}{4}\)?
Answer B: \(\frac{2}{8}\)
Multiply numerator and denominator by 2: \(\frac{1\times2}{4\times2}=\frac{2}{8}\).
