Mathematical Process Standards>Using a Problem-Solving Model to Solve and Justify Solutions(TEKS.Math.6.1.B)
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Texas 6th Grade Math › Mathematical Process Standards>Using a Problem-Solving Model to Solve and Justify Solutions(TEKS.Math.6.1.B)
A class trip costs 180 dollars. The class has 24 dollars saved but must pay a one-time 12-dollar materials fee before selling bracelets. They will sell bracelets for 6 dollars each. How many bracelets are needed to reach the goal?
What is the first calculation you should do to plan the solution?
$180 \div 6$
$24 + 12$
$180 - 6$
$180 - 24 + 12$
Explanation
Analyze: Goal $=180$, current savings $=24$, one-time fee $=12$ reduces savings, each bracelet adds $6$. Plan: First find the remaining amount needed after accounting for savings and the fee: $180 - 24 + 12 = 168$. Then determine bracelets: $168 \div 6 = 28$. Determine solution: $28$ bracelets. Justify: The sequence mirrors the situation (apply fee and savings before dividing by price per bracelet). Evaluate: Check total: $24 - 12 + 6\times 28 = 12 + 168 = 180$, exactly the goal, so reasonable.
A recipe makes 12 muffins using 3 cups of flour. Carla wants to bake 20 muffins. One bag has 8 cups; she has half a bag at home.
Which expression will correctly find the cups of flour needed for 20 muffins?
$\left(\frac{3}{12}\right) \times 20$
$\left(\frac{12}{3}\right) \times 20$
$\left(\frac{3}{20}\right) \times 12$
$3 + 12 + 20$
Explanation
Analyze: Flour per muffin is $\frac{3}{12}$ cup. Plan: Multiply cups per muffin by the desired muffins: $\left(\frac{3}{12}\right)\times 20 = 5$ cups. Determine solution: Needs $5$ cups. Justify: Proportional reasoning keeps the recipe ratios. Evaluate: Carla has half a bag $=4$ cups, so she needs $5 - 4 = 1$ more cup. The calculations are consistent and reasonable.
A bike tune-up costs 25 dollars, and a new chain costs 12 dollars. Sales tax is 8%. Noah has a 10-dollar coupon that applies only to the tune-up. He wants to know the total cost to see if 40 dollars is enough.
Which calculation best checks the final total with the coupon applied before tax and then tax on the subtotal?
$25 + (12 \times 1.08) - 10$
$(25 + 12) \times 1.08 - 10$
$(25 - 10 + 12) \times 1.08$
$(25 - 10) \times 1.08 + 12$
Explanation
Analyze: Tune-up $=25$, coupon $=10$ off tune-up, chain $=12$, tax $=8%$. Plan: Apply coupon to tune-up, add chain, then tax the subtotal: $(25 - 10 + 12)\times 1.08$. Determine solution: $(25 - 10 + 12)=27$, then $27\times 1.08 = 29.16$ dollars. Justify: Tax applies to the after-coupon subtotal, not to just one item or after subtracting the coupon at the end. Evaluate: $29.16 \le 40$, so $40$ dollars is enough; the result is reasonable.