• Step 1: \(12 \times 10 = 120\)
• Step 2: \(120 \times 1 =\) 120 cubic centimeters
3 Base Area Storage Box Solution Key: 80 ft³
• Formula: \(V = B \times h\) where \(B = 20\text{ sq ft}\) and \(h = 4\text{ ft}\)
• Calculation: \(20 \times 4 =\) 80 cubic feet
Teacher Note: Connecting \(B\) to \(l \times w\)
Students often ask: "Why are there two different formulas?" Explain that they are the exact same thing! Capital B is just shorthand for the bottom rectangle's area: \(B = \text{length} \times \text{width}\). Have students draw a circle around length and width, and write a big capital B over it.
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Teacher Answer Key & Guide
Strategy Parentheses First
Teacher Read-Aloud Script
"Parentheses are like a VIP pass in math! Whatever is inside the curved parentheses gets solved first, no matter what else is around it. Look for the parentheses, draw a line under them, and solve that part first. Then rewrite the rest of the problem."
1 Darius Dog Walking: \(7 \times (15 + 25)\) Key: 280 minutes
• Step 1: Inside parentheses first: \(15 + 25 =\) 40
• Step 2: Multiply by 7: \(7 \times 40 =\) 280 minutes
Meaning: Darius walks 40 minutes per day for 7 days.
2 Evaluate: \(9 + (21 - 6) \div 3\) Key: 14
• Step 1 (Parentheses): \(21 - 6 =\) 15
• Step 2 (Division before Addition): \(15 \div 3 =\) 5
• Step 3 (Addition): \(9 + 5 =\) 14
3 Why parentheses are important in \(6 \times (32 - 8)\) Key: Choice A
Correct: A. "They show we must subtract teachers first to find students." Without parentheses, standard order of operations would multiply \(6 \times 32\) first, which does not match the real-world situation!
Common Misconception Alert
Solving left-to-right regardless of symbols: In Problem 2, low-decoding students frequently try \(9 + 21 = 30\), then \(30 - 6 = 24\), then \(24 \div 3 = 8\). Intervention: Have them use a physical index card to cover everything except the parentheses. Once that number is solved, rewrite the problem directly below.
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Teacher Answer Key & Guide
Translation Words into Expressions
Teacher Read-Aloud Script
"Math is its own language. When you hear the word 'sum', that means add (+). When you hear 'difference', that means subtract (−). When you hear 'product', that means multiply (×). When you hear 'quotient', that means divide (÷). Watch out for 'subtracted from'—it means start with the other number!"
1 Clue Word Matching Answers All 4 Matched
Sum = + (Add)
Diff = − (Subtract)
Prod = × (Multiply)
Quot = ÷ (Divide)
2 "2 times the difference of 8 and 1" Key: \(2 \times (8 - 1)\)
Filled in: 2 × ( 8 − 1 ). If evaluated: \(2 \times 7 = 14\).
3 "6 plus the quotient of 15 and 3" Key: \(6 + (15 \div 3)\)
Filled in: 6 + ( 15 ÷ 3 ). If evaluated: \(6 + 5 = 11\).
4 Which phrase matches \(24 - \frac{1}{2} \times (3 + 5)\)? Key: Choice B
Correct: B. "Half the sum of 3 and 5 subtracted from 24." Notice that \((3 + 5)\) is "the sum of 3 and 5", multiplying by \(\frac{1}{2}\) is "half", and subtracting from 24 means 24 is in front!
Decoding Trap: "Subtracted From" Order Reversal
Students reading below grade level often translate word by word from left to right. When they read "subtracted from 24", they often place \(- 24\) at the end. Remind them: "If I take $5 away from your $20, you started with $20! So 20 comes first: \(20 - 5\)."
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