Week 1 Concept Mastery Check

Estimated Time: 35–45 minutes

Goal: Demonstrate what you've mastered from Week 1 and identify what we should continue practicing before moving into Week 2.

📋 Directions

Show your work whenever possible.
Rewrite expressions one step at a time.
If you get stuck, leave your work. You'll earn more credit for showing your thinking than leaving it blank.

⭐ Tier 1 — Mechanical Fluency

These questions assess the core skills we practiced this week.

1. Mixed Number Subtraction

Solve using the vertical layout method.

7\frac{2}{9}-4\frac{5}{9}

2. Mixed Number Multiplication

Convert both mixed numbers to improper fractions. Cross-simplify if possible, then multiply.

2\frac{1}{4}\times1\frac{7}{9}

3. Fraction • Decimal • Percent

Complete the missing forms.

Fraction	Decimal	Percent
$\frac{7}{20}$	__________	__________

4. Order of Operations

Rewrite the expression after every major step.

(-2\times4\frac{1}{2})+16\div(-4)-(3-5)

Rewrite #1

Rewrite #2

Rewrite #3

Final Answer

⭐⭐ Tier 2 — Apply What You Know

These problems look different, but they use the exact same math skills.

5. Hallway Tile Problem

A hallway wall is $12\frac{4}{5}$ feet long. Each custom tile is $1\frac{3}{5}$ feet wide. How many tiles can fit across the wall?

Step A

Which operation should you use?

☐ Addition

☐ Subtraction

☐ Multiplication

☐ Division

Step B

Convert each mixed number to an improper fraction.

Wall:

Tile:

Step C

Solve and Answer:

6. Banking Balance

Liam's account starts at $15.50. He deposits $60. A monthly subscription charges $12.25.

Step A

Write one numerical expression:

Step B

Find the final balance:

7. Contextual SOL Synthesis (Multi-Step Math 7 Scenarios)

Problem 7A — The Compounding Trail Run

Maya is setting up a training loop around a regional park in Fairfax.

On Day 1, she maps out a path that is exactly 4.5 miles long.
On Day 2, she increases her Day 1 distance by exactly 20%.
On Day 3, she decides to run exactly $1\frac{1}{2}$ times her Day 2 distance.

Calculate the exact number of miles Maya ran on Day 3.

Write your final answer as a simplified decimal.

Problem 7B — The Laboratory Temperature Shift

A science experiment at a local Northern Virginia middle school requires a liquid chemical compound to start at exactly $8.4^\circ\text{C}$ .

First, a heating element increases the temperature by

15.6^\circ\text{C}

Next, a cooling vacuum decreases the new temperature by

4.5^\circ\text{C}

each hour for 3 consecutive hours.

Write one numerical expression that models the entire situation.

⭐⭐⭐ Tier 3 — Pre-Algebra Advanced Applications

These problems show how the Week 1 skills you've been practicing (fractions, signed numbers, order of operations, and mixed numbers) begin to appear in Grade 8 Pre-Algebra.

Take your time. Organize your work neatly and rewrite each step as you solve.

8. Complex Fraction Evaluation

Evaluate the expression completely.

Leave your final answer as a simplified improper fraction.

\frac{-3\left(\frac{2}{3}\right)^2+1.5}{2\frac12-3\frac14}

9. Pre-Algebra Application — Evaluating Multi-Variable Expressions

In Pre-Algebra, variables represent unknown numbers.

When the values of the variables are given, substitute them into the expression and solve using PEMDAS.

Evaluate

3x^2-4y+2z

when

x=-2

y=1.5

z=-\frac34

Step 1 — Substitute the values

Rewrite the expression with each variable replaced by its value.

Step 2 — Evaluate the exponent

Step 3 — Complete all multiplication

Step 4 — Combine the remaining terms

Final Value

10. Pre-Algebra Application — Verifying Fractional Linear Solutions

In Pre-Algebra, solving an equation means finding a value that keeps both sides equal.

Test whether

x=-1\frac13

is the correct solution to

6x-5=3

Line 1

Convert the mixed number to an improper fraction.

x=

Line 2

Substitute into the left side.

$6(\hspace{1cm})-5=3$

Line 3

Multiply carefully, paying attention to the signs.

(\hspace{2cm})-5=3

Line 4

Simplify.

Is this the correct solution?

☐ YES — Both sides equal 3.

☐ NO — The two sides are not equal.

🔭 Looking Ahead — Week 2 Readiness Radar

These questions help us decide which topics we should emphasize next week.

Do your best.

1. Unit Rates

A package of 6 sports drinks costs $9.00.

What is the cost of 1 drink?

2. Percent

A restaurant bill is $80.00.

Find 15% of the bill.

3. Proportions

Solve.

\frac45=\frac{x}{35}

4. Scale Factors

A blueprint uses the scale

1 inch = 12 feet

A bedroom wall measures 3.5 inches on the blueprint.

How long is the real wall?

🧠 Reflection

Take one minute to think about your work.

⭐ Which question felt the easiest?

⭐ Which question challenged you the most?

⭐ What is one topic you would like us to review together next session?

⭐ How confident do you feel about this week's material?

☐ 😊 Very Confident

☐ 🙂 Mostly Confident

☐ 😐 Somewhat Confused

☐ 😕 I Need More Practice