A focused Grade 4 learning session for Decomposing Fractions using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can decompose a fraction in different ways.
Decomposing Fractions means using equal parts, number lines, and clear fraction language to describe parts of a whole.
Question: The fraction bar shows \(\frac{5}{6}\) divided into parts. Which equation shows this decomposition?
Why it works: Look at the bar—the light blue section is \(\frac{2}{6}\) and the dark blue is \(\frac{3}{6}\). Add them: \(2+3=5\), so \(\frac{2}{6}+\frac{3}{6}=\frac{5}{6}\) \checkmark.
Answer: \(\frac{2}{6}+\frac{3}{6}\)
Question: Look at the two fraction bars: This represents which mixed number?
Answer: \(1\frac{2}{3}\)
Question: Which fraction is shown on the number line?
Answer: \(\frac{3}{4}\)
Question: A recipe uses \(\frac{9}{4}\) cups of flour. This equals how many whole cups and extra fourths?
Why it works: Break apart \(\frac{9}{4}\): two wholes are \(\frac{4}{4}+\frac{4}{4}\), then add \(\frac{1}{4}\) more. That's \(2\frac{1}{4}\) cups \checkmark.
Answer: \(2\) wholes and \(\frac{1}{4}\) extra
Decomposing 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 shows \(\frac{7}{8}\) decomposed correctly?
Answer A: \(\frac{4}{8}+\frac{3}{8}\)
\(\frac{7}{8}\) can split apart. Let's check A: \(\frac{4}{8}+\frac{3}{8}\)—add the numerators: \(4+3=7\), so we get \(\frac{7}{8}\) \checkmark. Perfect!
The fraction bar shows \(\frac{5}{6}\) divided into parts. Which equation shows this decomposition?
Answer A: \(\frac{2}{6}+\frac{3}{6}\)
Look at the bar—the light blue section is \(\frac{2}{6}\) and the dark blue is \(\frac{3}{6}\). Add them: \(2+3=5\), so \(\frac{2}{6}+\frac{3}{6}=\frac{5}{6}\) \checkmark.
Which decomposition of \(\frac{9}{10}\) is correct?
Answer A: \(\frac{4}{10}+\frac{5}{10}\)
When the denominators match, add the numerators! \(4+5=9\), so we get \(\frac{4}{10}+\frac{5}{10}=\frac{9}{10}\) \checkmark.
\(\frac{5}{8}\) can be written as \(\frac{2}{8}+\frac{2}{8}+\frac{1}{8}\). Which other decomposition is correct?
Answer A: \(\frac{1}{8}+\frac{1}{8}+\frac{3}{8}\)
Let's verify A: \(1+1+3=5\), so \(\frac{1}{8}+\frac{1}{8}+\frac{3}{8}=\frac{5}{8}\) \checkmark. This breaks \(\frac{5}{8}\) into three parts!
Here is a number line showing \(\frac{6}{8}\): Which shows one correct way to decompose this into two equal jumps?
Answer A: Jump \(\frac{3}{8}\), then jump \(\frac{3}{8}\)
Two equal jumps of \(\frac{3}{8}\) each: \(3+3=6\), so \(\frac{3}{8}+\frac{3}{8}=\frac{6}{8}\) \checkmark. Both parts are the same!
\(\frac{4}{5}\) can be written as the sum of four unit fractions:
Answer A: \(\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}\)
A unit fraction always has a numerator of 1. Four copies of \(\frac{1}{5}\): \(1+1+1+1=4\), giving us \(\frac{4}{5}\) \checkmark.
\(\frac{5}{4}\) is the same as \(1\frac{1}{4}\). Which shows this decomposition?
Answer A: \(\frac{4}{4}+\frac{1}{4}\)
\(\frac{4}{4}\) is one whole, and \(\frac{1}{4}\) more makes \(1\frac{1}{4}\). Add: \(4+1=5\), so \(\frac{4}{4}+\frac{1}{4}=\frac{5}{4}\) \checkmark.
Look at the two fraction bars: This represents which mixed number?
Answer A: \(1\frac{2}{3}\)
The top bar is a complete whole. The bottom bar shows \(\frac{2}{3}\). Together: one whole plus \(\frac{2}{3}\) equals \(\mathbf{1\frac{2}{3}}\) \checkmark.
Mia has a string of length \(\frac{11}{12}\) yard. She cuts it into two pieces where one piece is \(\frac{6}{12}\) yard. Which shows this decomposition?
Answer A: \(\frac{6}{12}+\frac{5}{12}\)
Mia's string is \(\frac{11}{12}\) long. One piece is \(\frac{6}{12}\), so the other must be \(\frac{11}{12}-\frac{6}{12}=\frac{5}{12}\). Check: \(6+5=11\) \checkmark.
Which does NOT correctly decompose \(\frac{8}{10}\)?
Answer C: \(\frac{2}{10}+\frac{5}{10}\)
Option C: \(2+5=7\), so \(\frac{2}{10}+\frac{5}{10}=\frac{7}{10}\), not \(\frac{8}{10}\). The answer is C \checkmark.
\(\frac{7}{6}\) equals \(1\frac{1}{6}\). Which decomposition shows this?
Answer A: \(\frac{6}{6}+\frac{1}{6}\)
One whole is \(\frac{6}{6}\), plus \(\frac{1}{6}\) more: \(6+1=7\), so \(\frac{6}{6}+\frac{1}{6}=\frac{7}{6}=1\frac{1}{6}\) \checkmark.
