Bay State Math Mastery Slides MCAS Prep Series
Bay State Math Mastery
Expressions, Equations, and Geometric Reasoning
Algebra
Geometry
Reasoning
Today's Blueprint
Objectives
Solve multi-step linear equations.
Apply area and perimeter formulas.
Master the 4-point CR strategy.
Why This Matters
MCAS focuses on **application**. It's not just "find x"—it's using math to solve real problems.
"Constructed Response questions are 20-25% of your total points."
Core Review: Equations
The Balance Method
1. Distribute & Combine
Clear parentheses and merge like terms on both sides.
2. Isolate the Variable
Move terms using inverse operations (+/-).
3. Divide to Conquer
Divide by the coefficient to find your final answer.
\[ 3(2x - 5) + 4 = 19 \]
Distribute 6x - 15 + 4 = 19
Combine 6x - 11 = 19
Add 11 6x = 30
Result x = 5
Geometry: Divide and Conquer
Most MCAS problems use **composite figures**. Don't let them intimidate you!
The Strategy
Slice into basic rectangles and triangles.
Add the area of each smaller part.
Subtract any "holes" or cutouts.
Area = (Tri + Rect) - Circle
Triangle
\( \frac{1}{2}bh \)
Circle
\( \pi r^2 \)
The 4-Point Secret
How Constructed Response (CR) is graded:
1
Minimal
Only the correct answer is provided, or one tiny part is solved correctly with no work.
2
Partial
About half the parts are correct, or the logic is clear but the math has big mistakes.
3
Substantial
Everything is almost perfect. Maybe one small calculation error, but logic is 100%.
4
Advanced
Perfect math + clearly shown steps + written explanation using units and vocab.
The Power of "Because"
Score: 1-2 (The Minimum)
I did 10 times 5.
Then I added 50 + 20.
The answer is 70.
Missing: Units, Variable definitions, and "WHY".
Score: 4 (The Master)
I used the equation
C = 10(5) + 20 = 70.
The total cost for 5 hours is $70.
Included: Equation, Units, and logical flow.
Bay State Math Practice Worksheet Bay State Math Practice
Expressions, Equations, and Geometry Review
Student:
Date:
PART 1
Expressions and Equations
1. Which value of \( x \) makes the equation below true? [MA.8.EE.C.7]
\( 4(x - 3) + 2x = 18 \)
A \( x = 1 \)
B \( x = 3 \)
C \( x = 5 \)
D \( x = 7 \)
2. Solve the inequality for \( y \). Show your work in the box. [MA.7.EE.B.4]
\( -3y + 15 < 33 \)
Final Answer:
PART 2
Geometric Reasoning
3. A school banner is made of a rectangle and a right triangle as shown below. [MA.7.G.B.6]
10 in 10 in h = 6 in
Diagram not to scale
What is the total area, in square inches, of the banner?
100 sq in
130 sq in
160 sq in
200 sq in
4. Lines \( m \) and \( n \) are parallel. Find the value of \( x \). [MA.8.G.A.5]
m n \( (2x + 10)^\circ \) \( 130^\circ \)
Explain your steps and the geometry property you used to solve for \( x \).
Value of \( x \):
Garden Blueprint Task The Garden Blueprint
MCAS Constructed Response Performance Task
Score
/4
The Design Proposal
The City of Boston is planning a community garden. The design features a rectangular vegetable patch (30 ft by 20 ft) and two identical semi-circular herb gardens attached to the 20-ft ends. A stone walkway will be built along the entire outer perimeter.
30 ft 20 ft
Master Site Plan
A
Calculate the total area of the entire garden. Use 3.14 for \( \pi \).
Define your formulas, show all substitution, and include units.
B
The city has a budget of $1,200 for the stone walkway. The total cost is calculated as: \( \text{Cost} = 150 + 35p \), where \( p \) is the linear feet of the garden's outer perimeter.
What is the maximum perimeter (\( p \)) the city can afford with their $1,200 budget? Show your equation and solving steps.
C
Based on your findings in Part B, does the city have enough money to build the walkway for the garden designed in the scenario? Justify your answer using the actual perimeter of the garden.
Official MCAS 0-4 Point Rubric Applied
Bay State Math Mastery Guide TEACHER GUIDE
Bay State Math Mastery Answer Key & Rubric
MCAS 2026 PREP
Practice Worksheet: Answer Key
Question 1: Equation Solving
Correct Answer: C (\( x = 5 \))
Steps: \( 4x - 12 + 2x = 18 \)
Question 2: Inequalities
Correct Answer: \( y > -6 \)
Steps: \( -3y < 18 \).Note: Students must flip the inequality symbol when dividing by \(-3\).
Question 3: Composite Area
Correct Answer: 130 sq in
Rect: \( 10 \times 10 = 100 \).
Question 4: Parallel Lines
Correct Answer: \( x = 60 \)
Reason: Alternate interior angles are equal.
Garden Blueprint: Solutions & Scoring
Full Credit Response (4 Points)
Part A:
Area = Rectangle + 1 Circle (2 halves).
Part B:
\( 1200 = 150 + 35p \).
Part C:
No, they do not have enough. The garden's perimeter is two 30-ft sides plus the circumference of a circle (diameter 20).
Score Performance Descriptors 4 Completes all parts accurately. Provides clear mathematical reasoning and units. Demonstrates advanced understanding of both geometry and algebra. 3 Completes almost all parts. One minor calculation error is present, but logic and setup are correct. 2 Shows partial understanding. Successfully completes 2 parts or uses correct procedures with multiple errors. 1 Minimal understanding. Solves only one part correctly or provides answer without work. 0 No correct response or response irrelevant to the prompt.
