Exercises: Understand that rewriting an expression in different forms can shed light on the problem - Common Core Math - Grade 7

A

Recall / Warm-Up

1.

Which expression correctly simplifies $n + 0.08n$ ?

A.

$1.08n$

B.

$1.8n$

C.

$n + 8$

D.

$0.08n$

2.

Which expression is equivalent to $3(2x + 5)$ ?

A.

$6x + 5$

B.

$6x + 15$

C.

$5x + 15$

D.

$6x + 8$

3.

Write 7% as a decimal: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲

decimal form:

B

Fluency Practice

C

Varied Practice

D

Word Problems

1.

A store charges 9% sales tax on all purchases.

If an item costs $c$ dollars, the total cost including tax is ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ $\cdot c$ dollars.

multiplier:

$Two-panel diagram with blanks: left panel shows expanded form s + ___s to be completed; right panel shows factored form ___ · s to be completed. Panels connected by equals sign. Caption: Same value — two ways to see it.$

2.

Amara's annual salary is $s$ dollars. She receives a 4% raise.

1.

Write Amara's new salary in expanded form: $s +$ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ $\cdot s$ dollars.

raise rate:

2.

Rewrite Amara's new salary as a single multiplier: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ $\cdot s$ dollars.

multiplier:

3.

A store marks all items at a price of $0.85p$ , where $p$ is the original price.

Which statement best explains what $0.85p$ reveals about the price?

A.

The price after a 15% markdown — the item costs 85% of the original price $p$

B.

The price after a 15% markup — the original price increased by 15%

C.

The price reduced by 85 dollars from the original price

D.

The item is 85% off — it costs only 15% of the original price

4.

A jacket originally priced at 80 dollars is marked down by 35%.

What is the sale price of the jacket, in dollars?

E

Error Analysis

$Error contrast card: Student Work panel shows a + 15 with red X and label '15 is not 15% of a, rate used as a dollar amount'; Correct Work panel shows a + 0.15a = 1.15a with checkmark and label '0.15a = 15% of a, rate converted to decimal first'.$

1.

A student wrote the following expression for 'the total bill for a restaurant meal that costs $a$ dollars, including a 15% tip':

Student's expression: $a + 15$

Which response correctly identifies the student's error and gives the right expression?

A.

The student multiplied by 15 instead of dividing. The correct expression is $a \div 15$ .

B.

The student added 15 as a dollar amount instead of computing 15% of $a$ . The correct expression is $a + 0.15a = 1.15a$ .

C.

The student's expression is correct — 15% tip means adding 15 to the bill.

D.

The student added the tip but should have subtracted it. The correct expression is $a - 0.15a$ .

$Error contrast card: Student Work shows 1.25p with red X and label '1.25 > 1: price went UP, used 1 + 0.25 (wrong direction)'; Correct Work shows 0.75p with checkmark and label '0.75 < 1: price went DOWN, used 1 - 0.25 = 0.75'.$

2.

A student wrote the following expression for 'the sale price of an item originally priced at $p$ dollars, after a 25% markdown':

Student's expression: $1.25p$

Which response correctly identifies the student's error and gives the right expression?

A.

The student multiplied instead of dividing. The correct expression is $p \div 1.25$ .

B.

The student used an increase multiplier instead of a decrease multiplier. For a 25% markdown, the correct expression is $0.75p$ .

C.

The student's expression is correct — a 25% markdown means multiplying by 1.25.

D.

The student should have subtracted 25 from $p$ . The correct expression is $p - 25$ .

F

Challenge / Extension

1.

A sporting goods store increases all prices by 10% for the new season. During a later sale, the store then decreases all prices by 10%.

If a jacket originally cost $p$ dollars, what is the jacket's final price after both changes?

A.

$p$ (back to the original price)

B.

$0.99p$ (1% less than the original price)

C.

$1.01p$ (1% more than the original price)

D.

$1.21p$ (21% more than the original price)

2.