A focused Grade 6 learning session for Translating Words into Expressions using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving translating words into expressions.
Translating Words into Expressions means choosing a model, naming what each number means, and explaining the strategy.
Question: This expression tree represents which phrase?
Why it works: The tree shows \(4\) and \(x\) combining via multiplication into \(4x\). This represents the product of \(4\) and \(x\).
Answer: The product of \(4\) and \(x\)
Question: This tree represents which phrase?
Answer: The sum of \(3x\) and \(5\)
Question: The tape diagram shows a total length. Which phrase does this represent?
Answer: A number \(x\) plus \(6\)
Question: One box has \(20\) marbles. A second box has \(15\) more. How many marbles are in the second box?
Why it works: Add \(15\) to \(20\): \(20+15=35\).
Answer: \(35\)
Translating Words into Expressions 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.
Which expression represents "the sum of a number \(n\) and \(7\), divided by \(2\)"?
Answer B: \(\frac{n+7}{2}\)
"The sum of \(n\) and \(7\)" means \(n+7\). "Divided by \(2\)" places the entire sum over \(2\): \(\frac{n+7}{2}\).
Which expression means "a number \(x\) minus \(9\)"?
Answer B: \(x - 9\)
"A number \(x\) minus \(9\)" means we subtract \(9\) from \(x\), giving \(x - 9\). Order matters: \(9 - x\) would be wrong.
Which expression represents "the quotient of \(20\) and a number \(p\)"?
Answer D: \(\frac{20}{p}\)
"Quotient" means division. The quotient of \(20\) and \(p\) is \(\frac{20}{p}\) or \(20 \div p\).
Which expression matches "the difference of a number \(t\) and \(3\)"?
Answer B: \(t - 3\)
"The difference of \(t\) and \(3\)" starts with \(t\), so we compute \(t - 3\). Order matters: \(3 - t\) gives a different result.
Write an expression for "a number \(b\) more than \(12\)".
Answer D: \(12 + b\)
"\(b\) more than \(12\)" means we add \(b\) to \(12\), giving \(12 + b\).
Write an expression for "the sum of three times a number \(d\) and \(5\)".
Answer A: \(3d + 5\)
"Three times a number \(d\)" is \(3d\). "The sum of \(3d\) and \(5\)" means \(3d + 5\).
Which expression matches "the product of \(2\) and the sum of \(x\) and \(4\)"?
Answer D: \(2(x + 4)\)
"The sum of \(x\) and \(4\)" is \((x + 4)\). "The product of \(2\) and" that sum requires parentheses: \(2(x + 4)\).
Write an expression for "\(9\) divided by the difference of \(c\) and \(2\)".
Answer A: \(\frac{9}{c - 2}\)
"The difference of \(c\) and \(2\)" is \((c - 2)\). "\(9\) divided by" that difference requires parentheses in the denominator: \(\frac{9}{c - 2}\).
Which expression represents "the quotient of a number \(g\) and \(3\), increased by \(1\)"?
Answer A: \(\frac{g}{3} + 1\)
"The quotient of \(g\) and \(3\)" is \(\frac{g}{3}\). "Increased by \(1\)" means add \(1\): \(\frac{g}{3} + 1\).
Write an expression for "the product of \(6\) and the difference of \(h\) and \(2\)".
Answer D: \(6(h - 2)\)
"The difference of \(h\) and \(2\)" is \((h - 2)\). "The product of \(6\) and" that difference is \(6(h - 2)\).
Which expression matches "twice the quotient of \(15\) and \(j\)"?
Answer D: \(2 \cdot \frac{15}{j}\)
"The quotient of \(15\) and \(j\)" is \(\frac{15}{j}\). "Twice" that quotient means multiply by \(2\): \(2 \cdot \frac{15}{j}\).
