Last Review Before the Friday Mock Test
The amount of space inside a 3D figure, measured in cubic units.
Two numbers in parentheses (x, y) that name an exact location on the coordinate plane.
A math phrase with numbers and operations — but no equal sign. It names a value without solving it.
A shape made by combining two or more simple shapes. To find its volume, split it into parts.
Any 2D shape with exactly 4 straight sides. Rectangles, squares, rhombuses, and trapezoids are all types.
Which formula gives the volume of a rectangular prism?
❌ Adding dimensions just gives a sum — not a measurement of space inside.
❌ This gives area (2D), not volume (3D). Missing the height!
✅ Correct! Multiply all three dimensions to find volume in cubic units.
❌ This is the perimeter formula for a rectangle — totally different concept.
Point A is at (3, 7). Point B is at (7, 3).
Are they the same point?
Which shape is always a parallelogram?
❌ A trapezoid has only ONE pair of parallel sides. A parallelogram needs TWO pairs.
✅ A rectangle always has 2 pairs of parallel sides and 4 right angles — it's always a parallelogram.
❌ A kite has 2 pairs of adjacent equal sides, but its sides are NOT parallel.
❌ A pentagon has 5 sides — it's not even a quadrilateral!
💡 DON'T LEAVE BLANKS. YOU'VE GOT THIS.
Even if you're stuck, make your best guess. Blank = 0 points guaranteed. A guess = at least a 25% chance on multiple choice.
For constructed response, WRITE SOMETHING — even a partially-right answer or a model earns partial credit.
You've prepared for this. Trust your work. Breathe.
How to use it: On the real SBA Friday, if you hit a hard question — write your best thinking, draw a model, or eliminate wrong answers and guess.
Volume = the space INSIDE a 3D figure
This is the same as V = B × h where B = area of the base (l × w)
Always label your answer in cubic units (cm³, in³, ft³)
A box is 12 cm × 5 cm × 8 cm. What is the volume?
Step 1: Write the formula
Step 2: Plug in values
Step 3: Multiply first pair
Step 4: Multiply by height
V = 324 cm³, B = 36 cm². What is the height?
Step 1: Write the formula
Step 2: Plug in what you know
Step 3: Divide to isolate h
A block is 4 × 3 × 2 cm. You stack 4 blocks. What is the total volume?
Step 1: Find ONE block's volume
Step 2: Calculate
Step 3: Multiply by 4 blocks
Step 1: Split into two prisms along the dotted line
Part A: 6 cm × 9 cm × 3 cm | Part B: 4 cm × 4 cm × 3 cm
Step 2: Volume of Part A
Step 3: Volume of Part B
Step 4: Add both parts
A box is 3 × 4 × 5. Two students found the volume:
❌ Adding dimensions doesn't measure space — it's meaningless for volume.
✅ Multiplying all three dimensions gives the actual space inside!
Tina is correct. Volume ALWAYS comes from multiplying l × w × h. Adding just gives a random number with no meaning.
💡 Use J/K keys to compare, or click to expand
Marcus says V = l + w + h gives the volume. Using a box that is 3 × 4 × 5, show why he is wrong.
Step 1: Show what Marcus did
Step 2: Show the correct calculation
Step 3: Explain WHY
Volume measures the space inside a 3D shape. You need to multiply all three dimensions because you're counting how many unit cubes fit inside — layers of rows of cubes. Adding just sums the lengths, which doesn't describe space.
A box is 2 ft long, 1 ft wide, 3 ft tall. Convert to inches first (1 ft = 12 in), then find volume in cubic inches.
Step 1: Convert each dimension
2 ft = 24 in | 1 ft = 12 in | 3 ft = 36 in
Step 2: Write the formula with converted values
Step 3: Multiply in stages
You know the base area is 42 cm² and the height is 7 cm. Which formula is fastest?
This works, but you'd need to find l and w separately first — more steps.
✅ You already know B (42) and h (7). Just multiply: 42 × 7 = 294 cm³!
❌ This is the area formula (2D), not volume (3D).
❌ Perimeter measures the distance around a 2D shape — nothing to do with volume.
Volume = space inside a 3D figure. Always use cubic units (cm³, in³, ft³).
Two formulas: V = l × w × h OR V = B × h (where B = base area). Pick whichever matches the info you're given.
Composite figures: Split into parts → find each volume → add them together.
MULTIPLY, never add! Adding dimensions does NOT give volume.
We just reviewed volume formulas, composite figures, and measurement conversions. Next up: coordinate plane and shape properties!
Tell your partner: What's the ONE thing from the volume section you want to remember for Friday's test?
Sentence starter: "The most important thing about volume is ___."
Write the ordered pair for each point.
Point A: Count right 4, up 5
A = (4, 5)
Point B: Count right 6, up 2
B = (6, 2)
Plot (1, 2), (1, 8), (7, 8), (7, 2). Connect them. What shape? What are ALL the names?
ALL the names for this shape:
Rectangle (4 right angles, opposite sides equal) → also a Parallelogram (2 pairs parallel) → also a Quadrilateral (4 sides) → also a Polygon (closed shape, straight sides)
"All squares are rhombuses."
TRUE ✅ — A square has 4 equal sides (that's what makes a rhombus) PLUS 4 right angles. So every square qualifies as a rhombus.
"All rhombuses are squares."
FALSE ❌ — A rhombus needs 4 equal sides but does NOT need right angles. A tilted diamond is a rhombus but not a square.
"A trapezoid is a parallelogram."
FALSE ❌ — A trapezoid has only ONE pair of parallel sides. A parallelogram needs TWO pairs.
Pencils cost $0.50 each. Erasers cost $0.25 each. Fill in the table for 1–6 of each.
| Count | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Pencils | $0.50 | $1.00 | $1.50 | $2.00 | $2.50 | $3.00 |
| Erasers | $0.25 | $0.50 | $0.75 | $1.00 | $1.25 | $1.50 |
Which line is steeper? Why?
Pencils — the pencil line is steeper because pencils cost more per item ($0.50 vs $0.25), so the total grows faster.
Both patterns form straight lines on the graph. Why? And why is the pencil line steeper than the eraser line?
Why straight lines?
Both patterns add the same amount each time (pencils: +$0.50, erasers: +$0.25). A constant rate of change always makes a straight line.
Why is the pencil line steeper?
Pencils add $0.50 per item — twice as much as erasers ($0.25). The bigger the jump per step, the steeper the line. The pencil cost is always double the eraser cost for the same count.
Ordered pairs: (x, y) — go right x, up y. Order matters! (3, 7) ≠ (7, 3).
Shape hierarchy: Square → Rectangle → Parallelogram → Quadrilateral → Polygon. "All squares are rectangles" = TRUE. "All rectangles are squares" = FALSE.
Patterns on graphs: Constant rate → straight line. Bigger rate → steeper line.
"Add 3 and 7, then multiply by 4."
Write this as a numerical expression.
Step 1: "Add 3 and 7" — write this first
Step 2: "THEN multiply by 4" — the word "then" means do it in that order
We need parentheses to force the addition first!
Evaluate: 3 + 7 × 4 = ?
Common mistake: doing 3 + 7 first = 10, then 10 × 4 = 40 ❌
Correct: Multiply FIRST (order of operations)
Then add
Place parentheses to make this true:
Without parentheses: 8 + (2 × 5) = 8 + 10 = 18 ≠ 50
Try grouping the addition first:
Write a real-world problem that matches this expression:
Think: What adds up to (15 + 8), then gets doubled?
Example: You have 15 red marbles and 8 blue marbles in a bag. You have 2 bags just like this. How many marbles total?
A rectangular fish tank is 50 cm long, 30 cm wide, and 40 cm tall. It is filled 34 of the way. What is the volume of water?
Step 1: Find the TOTAL volume of the tank
Step 2: Find 34 of the total
Plot: (2, 1), (2, 5), (6, 5), (6, 1). Name the shape, then find its perimeter AND area.
Shape: Rectangle
Width = 6 − 2 = 4 units | Height = 5 − 1 = 4 units
Wait — all sides are equal! It's also a square!
Perimeter: Add all sides
Area: length × width
A toy store sells card games for $3 each and board games for $4.50 each. You buy 5 card games and 3 board games. Write an expression for the total cost, then evaluate it.
Step 1: Write the expression
Step 2: Evaluate card games cost
Step 3: Evaluate board games cost
Step 4: Add both costs
Explain why ALL squares are rectangles, but NOT all rectangles are squares. Use at least 2 properties in your explanation.
Property 1: Angles
Both squares AND rectangles have 4 right angles (90°). So a square meets this rectangle requirement. ✅
Property 2: Sides
A rectangle needs opposite sides equal. A square has ALL 4 sides equal — which also makes opposite sides equal. ✅
But the reverse isn't true:
A rectangle can have sides of different lengths (like 3 cm and 7 cm). A square requires ALL sides to be equal. So a 3 × 7 rectangle is NOT a square. ❌
Use V = l × w × h
Count right 3, up 6 from origin
Use property check — does a square have 4 equal sides? Yes → TRUE
Use order of operations — parentheses first!
Knowing which tool to grab is half the battle on SBA.
Complete all 4 on your whiteboard. Raise it when done.
A rectangular prism has l = 7, w = 4, h = 10.
What is the volume? Show your work and label units.
V = 7 × 4 × 10 = 280 cubic units
Plot (3, 5) and (8, 1). What ordered pair for a third point would make a right triangle?
Accept any point forming a 90° angle — e.g., (3, 1) or (8, 5)
Select ALL true statements:
☐ a) A cube with edge 3 has volume 9
☐ b) (6 + 2) × 3 = 24
☐ c) A right triangle has exactly one 90° angle
☐ d) 1 ft = 10 in
☐ e) Point (0, 5) is on the y-axis
✅ b, c, e
a) 3³ = 27 not 9 | d) 1 ft = 12 in
Write an expression:
"Subtract 4 from 12, then divide by 2."
Then evaluate it.
V = l × w × h — always cubic units. Composite shapes: split, solve, add.
Ordered pairs = (x, y). Over then up. Shapes on grids have real side lengths.
Translate words → math. Use parentheses. Follow order of operations (PEMDAS).
Label everything. Eliminate wrong answers. Re-read the question before you click submit.
🏆 Friday = Mock Test Day — You're ready!
Get a good night's sleep. Eat breakfast. Trust your brain.