4.5: Better Buy
Better Buy – Proportional Reasoning
Teacher Notes
Given the costs of items at two stores, Mac’s and Zac’s, students determine the unit price, or price for one, and compare the prices. In the first set of problems, one of the stores gives the unit price. The other store gives prices for 2 or 3 of the items.
In the Extras for Experts, two of the four problems, require students to figure out the unit price at both stores.
For all problems, students identify the store with the better buy and describe their solution process. They also compute the cost of multiple items at one of the two stores in the first set of problems, and in the Extras for Experts, they compute the costs of multiple items at both stores.
Solutions
Better Buy 1
- Mac’s
- Mac’s: 1 gallon is $4. Zac’s: 1 gallon is half of $10, or $5. \begin{align*}\$4 < \$5\end{align*}
$4<$5 -
\begin{align*}\$4 + \$4\end{align*}
$4+$4 , or $8
Better Buy 2
- Zac’s
- Mac’s: 1 bottle is $2. Zac’s: Since 3 bottles cost $3, 1 bottle is $1. \begin{align*}\$1 < \$2\end{align*}
$1<$2 -
\begin{align*}\$2 + \$2 + \$2\end{align*}
$2+$2+$2 , or $6
Better Buy 3
- Mac’s
- Mac’s: 1 pound is half of 40 ¢., or 20¢... Zac’s: 1 pound is 30¢. 20¢ < 30¢.
- 60¢
Better Buy 4
- Zac’s
- Mac’s: 1 plant is $12. Zac’s: Since 3 plants cost $30, 1 plant is $10. \begin{align*}\$10 < \$12\end{align*}
$10<$12 -
\begin{align*}\$12 + \$12 + \$12\end{align*}
$12+$12+$12 , or $36
Better Buy
Which store sells 1 box of noodles for less?
How did you figure it out?
\begin{align*}& \mathbf{Describe:} && \text{Mac's and Zac's sell noodles.}\\ &&& \text{Mac's: 1 box is \$5}\\ &&& \text{Zac's: 2 boxes are \$8}\\ & \mathbf{My \ Job:} && \text{Figure out the cost of one box of noodles at Mac's and at Zac's.}\\ &&& \text{Then tell which costs less.}\\ & \mathbf{Plan:} && \text{At Mac's, one box is \$5.}\\ &&& \text{At Zac's, 2 boxes are \$8.}\\ &&& \text{To figure out the cost of one box, take half of \$8.}\\ &&& \text{Then compare the prices.}\\ & \mathbf{Solve:} && \text{Half of \$8 is \$4. So, one box of noodles at Zac's is \$4.}\\ &&& \text{One box of noodles costs less at Zac's than at Mac's.}\\ & \mathbf{Check:} && \text{\$4 is less than \$5}\end{align*}
Better Buy 1
- Which store sells a gallon of milk for less?
- How did you decide?
- How much would it cost to buy 2 gallons of milk at Mac’s?
Better Buy 2
- Which store sells a bottle of water for less?
- How did you decide?
- How much would it cost to buy 3 bottles of water at Mac’s?
Better Buy 3
- Which store sells 1 pound of onions for less?
- How did you decide?
- How much would it cost to buy 2 pounds of onions at Zac’s?
Better Buy 4
- Which store sells 1 cactus plant or less?
- How did you decide?
- How much would it cost to buy 3 cactus plants at Mac’s?
Extras for Experts: Better Buy – Proportional Reasoning
Solutions:
Extra for Experts Better Buy 1
1. Zac’s
2. Mac’s: 1 box is half of $6, or $3
Zac’s: 1 sack is half of $8, or $4.
\begin{align*}\$3 < \$4\end{align*}
3. Mac’s: $12
Zac’s: $16
Extra for Experts Better Buy 2
1. Zac’s
2. Mac’s: 1 sack is half of $12, or $6
Zac’s: 1 sack is one-third of $15, or $5.
\begin{align*}\$5 < \$6\end{align*}
3. Mac’s: $24
Zac’s: $20
Extra for Experts Better Buy 1
1. Which store sells 1 box of strawberries for less?
2. How did you decide?
3. How much would it cost to buy 4 boxes of strawberries at:
Mac’s? ________________________________
Zac’s? _________________________________
Extra for Experts Better Buy 2
1. Which store sells 1 sack of oranges for less?
2. How did you decide?
3. How much would it cost to buy 4 sacks of oranges at:
Mac’s? _______________________________
Zac's? _______________________________