A focused Grade 6 learning session for Variables in Real-World Problems using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving variables in real-world problems.
Variables in Real-World Problems means choosing a model, naming what each number means, and explaining the strategy.
Question: In the bar model shown, \(n\) is a number and \(8\) is a known value. Which expression represents the total?
Why it works: The bar model shows two parts: \(n\) and \(8\). The total is their sum: \(n+8\).
Answer: \(n+8\)
Question: The bar model shows two parts: \(p\) and \(12\). If the total is \(25\), what is the value of \(p\)?
Answer: \(13\)
Question: The table shows the relationship between pizzas and cost. What is the value of \(x\)?
| Number of Pizzas | Total Cost ($) |
|---|---|
| \(1\) | \(15\) |
| \(2\) | \(30\) |
| \(3\) | \(45\) |
| \(5\) | \(x\) |
Answer: \(75\)
Question: A book costs \(b\) dollars. A pencil costs \($2\) less than the book. Which expression shows the cost of the pencil in dollars?
Why it works: "\(2\) less than" means subtract \(2\) from the book's cost.
Answer: \(b-2\)
Variables in Real-World Problems 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.
Joel is \(y\) years old. His sister is \(4\) years older than Joel. Which expression represents the sister's age?
Answer B: \(y+4\)
"\(4\) years older" means add \(4\) to Joel's age: \(y+4\).
A book costs \(b\) dollars. A pencil costs \($2\) less than the book. Which expression shows the cost of the pencil in dollars?
Answer D: \(b-2\)
"\(2\) less than" means subtract \(2\) from the book's cost.
Maria has \(m\) marbles. Her friend has \(3\) times as many marbles as Maria. Which expression represents how many marbles her friend has?
Answer C: \(3m\)
"\(3\) times as many" means multiply \(m\) by \(3\).
A restaurant sells \(t\) tacos per day. Which expression represents the total number of tacos sold in \(7\) days?
Answer D: \(7t\)
Multiply the number of tacos per day by \(7\) days: \(7t\).
Sarah has \(s\) stickers. After giving \(8\) to her friend, she has \(s-8\) stickers left. What does the variable \(s\) represent?
Answer C: The total number of stickers Sarah had at first
In the expression \(s-8\), \(s\) represents the starting amount before giving away any stickers.
An orange costs \(o\) cents. A banana costs \(5\) cents more than an orange. If \(o=30\), what is the cost of a banana in cents?
Answer C: \(35\)
Banana costs \(o+5=30+5=35\) cents.
A store has \(p\) pairs of shoes. It receives a shipment of \(20\) more pairs. Which expression shows the total number of pairs after the shipment?
Answer C: \(p+20\)
Adding a shipment means add \(20\) to the starting number \(p\).
A recipe calls for \(c\) cups of flour. An increase in the recipe requires \(2\) times the flour. Which expression shows the new amount of flour needed?
Answer C: \(2c\)
"\(2\) times the flour" means multiply \(c\) by \(2\).
Luis has \($12\). His friend gives him \(d\) dollars. How much money does Luis have now?
Answer B: \(12+d\)
Receiving money means adding to what he already has: \(12+d\).
A student earns \($8\) per hour. If the student works \(h\) hours, which expression shows the total earnings?
Answer C: \(8h\)
Earnings = hourly rate \(\times\) hours worked = \(8 \times h = 8h\).
The length of a rectangle is \(\ell\) meters and the width is \(4\) meters less than the length. Which expression shows the width?
Answer B: \(\ell-4\)
"\(4\) meters less" means subtract \(4\) from the length.
