A focused Grade 4 learning session for Adding and Subtracting Mixed Numbers using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can add and subtract mixed numbers with like denominators.
Adding and Subtracting Mixed Numbers means using place value, operations, and equations to reason accurately with numbers.
Question: What is the sum shown by the bar diagrams above?
Why it works: Add the wholes: \(2+1=3\). Add the fractions: \(\frac{3}{8}+\frac{4}{8}=\frac{7}{8}\). The sum is \(\mathbf{3\frac{7}{8}}\).
Answer: \(3\frac{7}{8}\)
Question: Using the number line, what is \(1\frac{3}{4}+1\frac{1}{4}\)?
Answer: \(3\)
Question: What is the sum of the three amounts shown?
Answer: \(3\)
Question: Sam has \(1\frac{2}{4}\) yards of red ribbon and \(2\frac{1}{4}\) yards of blue ribbon. How many yards of ribbon does Sam have in total?
Why it works: Add the wholes: \(1+2=3\). Add the fractions: \(\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\). The total is \(\mathbf{3\frac{3}{4}}\) yards.
Answer: \(3\frac{3}{4}\) yards
Adding and Subtracting Mixed Numbers becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Understand the model before choosing the operation.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
What is \(2\frac{3}{5}+1\frac{1}{5}\)?
Answer C: \(3\frac{4}{5}\)
Add the wholes: \(2+1=3\). Add the fractions: \(\frac{3}{5}+\frac{1}{5}=\frac{4}{5}\). Put them together: \(\mathbf{3\frac{4}{5}}\).
Sam has \(1\frac{2}{4}\) yards of red ribbon and \(2\frac{1}{4}\) yards of blue ribbon. How many yards of ribbon does Sam have in total?
Answer C: \(3\frac{3}{4}\) yards
Add the wholes: \(1+2=3\). Add the fractions: \(\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\). The total is \(\mathbf{3\frac{3}{4}}\) yards.
What is \(3\frac{4}{6}+1\frac{2}{6}\)?
Answer C: \(5\)
Add the wholes: \(3+1=4\). Add the fractions: \(\frac{4}{6}+\frac{2}{6}=\frac{6}{6}=1\). Since \(\frac{6}{6}\) is a whole, combine: \(4+1=\mathbf{5}\).
Mia mixed \(2\frac{1}{3}\) cups of flour with \(1\frac{1}{3}\) cups of sugar. What is the total amount?
Answer B: \(3\frac{2}{3}\) cups
Add the wholes: \(2+1=3\). Add the fractions: \(\frac{1}{3}+\frac{1}{3}=\frac{2}{3}\). The total is \(\mathbf{3\frac{2}{3}}\) cups.
What is the sum shown by the bar diagrams above?
Answer A: \(3\frac{7}{8}\)
Add the wholes: \(2+1=3\). Add the fractions: \(\frac{3}{8}+\frac{4}{8}=\frac{7}{8}\). The sum is \(\mathbf{3\frac{7}{8}}\).
What is \(1\frac{3}{10}+2\frac{5}{10}\)?
Answer C: \(3\frac{8}{10}\)
Add the wholes: \(1+2=3\). Add the fractions: \(\frac{3}{10}+\frac{5}{10}=\frac{8}{10}\). The sum is \(\mathbf{3\frac{8}{10}}\).
Noah had \(3\frac{2}{6}\) meters of string. He added \(1\frac{4}{6}\) meters more. How long is the string now?
Answer C: \(5\) meters
Add the wholes: \(3+1=4\). Add the fractions: \(\frac{2}{6}+\frac{4}{6}=\frac{6}{6}=1\). Combine: \(4+1=\mathbf{5}\) meters.
What is \(2\frac{5}{8}+1\frac{3}{8}\)?
Answer B: \(4\)
Add the wholes: \(2+1=3\). Add the fractions: \(\frac{5}{8}+\frac{3}{8}=\frac{8}{8}=1\). Combine into a whole: \(3+1=\mathbf{4}\).
Ava made a necklace. First she used \(1\frac{4}{5}\) meters of string. Then she used \(2\frac{1}{5}\) more meters. What is the total length?
Answer C: \(4\) meters
Add the wholes: \(1+2=3\). Add the fractions: \(\frac{4}{5}+\frac{1}{5}=\frac{5}{5}=1\). Combine: \(3+1=\mathbf{4}\) meters.
What is \(4\frac{1}{4}+1\frac{2}{4}\)?
Answer C: \(5\frac{3}{4}\)
Add the wholes: \(4+1=5\). Add the fractions: \(\frac{1}{4}+\frac{2}{4}=\frac{3}{4}\). The sum is \(\mathbf{5\frac{3}{4}}\).
Diego walked \(2\frac{3}{10}\) miles on Monday and \(1\frac{4}{10}\) miles on Tuesday. How many miles did he walk in total?
Answer C: \(3\frac{7}{10}\) miles
Add the wholes: \(2+1=3\). Add the fractions: \(\frac{3}{10}+\frac{4}{10}=\frac{7}{10}\). The total is \(\mathbf{3\frac{7}{10}}\) miles.
