Learner Name:
Grade & Section:
Date:
Status:
STUDY GUIDE
Review these core mathematical rules, estimation techniques, and MDAS strategies before starting the mock exam!
➕ 1. Addition & Subtraction
Arithmetic
- Vertical Alignment: Always align digits cleanly by place value (ones under ones, tens under tens).
- Addition Regrouping: Carry over to the next column when a column sum reaches 10 or greater.
- Subtraction Borrowing Across Zeros: Regroup from the nearest non-zero digit to the left (e.g., in 50,000 − 18,462, borrow from 5 to make 9, 9, 9, 10).
🎯 2. Estimating Sums & Differences
Estimation
- The Rounding Rule: Look at the digit to the right of the target place value. If 0 to 4, round down; if 5 to 9, round up (+1).
- Estimation Method: Round *first*, then add or subtract!
- Example: 4,821 + 3,190 rounded to nearest thousand: 5,000 + 3,000 = 8,000.
✖️ 3. 1-Digit & 2-Digit Multiplication
Products
- 1-Digit Multiplier: Multiply ones, then tens, then hundreds; add carried numbers after multiplying.
- 2-Digit Multiplier: Calculate 1st partial product (ones). Write a placeholder 0 in the ones column before finding the 2nd partial product (tens). Add the partial products together!
➗ 4. Long Division (Single-Digit)
Quotients
- The 4 Steps (DMSB): Divide → Multiply → Subtract → Bring down.
- Remainder Rule: The remainder must ALWAYS be smaller than the divisor (Remainder < Divisor).
- Verification Formula: (Quotient × Divisor) + Remainder = Dividend.
⚡ 5. Estimating Products & Quotients
Mental Math
- Products: Round factors to their highest non-zero place value (e.g., 682 × 38 ≈ 700 × 40 = 28,000).
- Compatible Numbers for Division: Change the dividend to a close multiple of the divisor that divides evenly (e.g., 3,540 ÷ 6 ≈ 3,600 ÷ 6 = 600).
🚦 6. MDAS Order of Operations
Order
- Step 1 (First Priority): Perform Multiplication and Division as equal twins from Left to Right.
- Step 2 (Second Priority): Perform Addition and Subtraction as equal twins from Left to Right.
- Watch out: In 24 ÷ 6 × 2, divide first (4 × 2 = 8).
💡
EXAM TRAP WARNINGS:
1) Placeholder Zero: Forgetting the 0 in the second partial product when multiplying by 2-digit numbers is the #1 student error!
2) MDAS Left-to-Right: Multiplication does NOT automatically beat Division—they are equal partners; compute whichever appears first on the left!
3) Word Problems: Always read the final question sentence twice to identify the requested unit (e.g., "how many left over", "how much in total").
Learner Name:
Date:
Score: / 8
SECTION A
Multi-Digit Operations & Regrouping: Align numbers vertically and show your complete solutions in each workspace.
1
Add with regrouping: 48,659 + 27,485 =
Show vertical alignment & carries:
48,659
+ 27,485
───────
Sum:
2
Add 3 numbers: 15,240 + 8,675 + 12,398 =
Stack all 3 addends vertically:
15,240
8,675
+ 12,398
───────
Total:
3
Subtract across zeros: 70,000 − 34,582 =
Show regrouping across zeros:
70,000
− 34,582
───────
Difference:
4
Subtract with regrouping: 52,416 − 28,749 =
Show vertical borrowing:
52,416
− 28,749
───────
Difference:
5
Multiply 4-digit by 1-digit: 4,638 × 7 =
Multiply ones, tens, hundreds, thousands:
4,638
× 7
───────
Product:
6
Multiply 3-digit by 1-digit: 829 × 6 =
Show regrouping carries:
829
× 6
───────
Product:
7
Multiply 2-digit by 2-digit: 64 × 38 =
Write partial products & placeholder 0:
Partial 1 (64 × 8): ________________
Partial 2 (64 × 30): _______________ (use 0!)
Add Partial Products:
Product:
8
Multiply 3-digit by 2-digit: 325 × 24 =
Write partial products & placeholder 0:
Partial 1 (325 × 4): _______________
Partial 2 (325 × 20): ______________ (use 0!)
Add Partial Products:
Product:
Learner Name:
Date:
Score: / 8
SECTION B
Long Division & Estimation: Show all DMSB long division steps and rounded values in the spaces provided.
9
Divide exactly (no remainder): 728 ÷ 4 =
Show DMSB steps (Divide, Multiply, Subtract, Bring down):
________
4 ) 7 2 8
Quotient:
10
Divide with remainder: 849 ÷ 6 =
Find quotient and remainder (R < 6):
________
6 ) 8 4 9
Answer: R
11
Division with zero in quotient: 6,180 ÷ 6 =
Watch place-value alignment (0 in tens place!):
__________
6 ) 6 1 8 0
Quotient:
12
Division check: If 523 ÷ 5 = 104 R 3, verify:
Use formula: (Quotient × Divisor) + Remainder
Step 1: 104 × 5 = ____________
Step 2: ____________ + 3 = ____________
Does result equal dividend 523?
Verification:
13
Estimate sum (nearest thousand): 6,845 + 4,210 ≈
Round each number to nearest thousand first:
6,845 rounds to: ____________
4,210 rounds to: ____________
Estimated Sum = ____________ + ____________
Estimated Sum:
14
Estimate difference (nearest hundred): 9,482 − 3,219 ≈
Round each number to nearest hundred first:
9,482 rounds to: ____________
3,219 rounds to: ____________
Estimated Diff = ____________ − ____________
Estimated Diff:
15
Estimate product (highest place value): 582 × 49 ≈
Round 582 to hundreds, and 49 to tens:
582 rounds to: ____________
49 rounds to: ____________
Estimated Product = ____________ × ____________
Estimated Product:
16
Estimate quotient (compatible numbers): 4,185 ÷ 7 ≈
Find nearest multiple of 7 close to 4,185:
Compatible dividend: ____________ (Hint: 4,200)
Divide: ____________ ÷ 7 = ____________
Estimated Quotient:
Learner Name:
Date:
Score: / 8
SECTION C: MDAS
Order of Operations (17–20): Follow strict MDAS left-to-right rules. Show each step.
17
MDAS 2-Step: 24 + 8 × 5 =
Step 1 (Multiply first): 8 × 5 = ______
Step 2 (Add): 24 + ______ = ______
Final Answer:
18
MDAS Twin Rule: 32 ÷ 8 × 4 =
Step 1 (Divide first, on left): 32 ÷ 8 = ______
Step 2 (Multiply): ______ × 4 = ______
Final Answer:
19
MDAS 3-Step: 50 + 6 × 7 − 25 =
Step 1 (Multiply): 6 × 7 = ______
Step 2 (Add/Sub Left-to-Right): 50 + ______ − 25 = ______
Final Answer:
20
MDAS 4-Step: 90 − 48 ÷ 6 + 14 =
Step 1 (Divide): 48 ÷ 6 = ______
Step 2 (Add/Sub Left-to-Right): 90 − ______ + 14 = ______
Final Answer:
SECTION D: WORD PROBLEMS
Mixed Word Problems (21–24): Write number sentence, show scratch work, and label answer.
Teacher Ana bought 8 packs of notebooks at ₱45 per pack and a box of pens for ₱120. She paid with a ₱1,000 bill. How much change did she receive?
Number Sentence:
1,000 − [(8 × 45) + 120] = ______
Change: ₱
Scratch / Solution Box:
Step 1 (Notebooks): 8 × 45 = ₱______
Step 2 (Total Spent): ______ + 120 = ₱______
Step 3 (Change): 1,000 − ______ = ₱______
Mang Pedro baked 435 hot pan de sal. He packs them into brown paper bags containing 8 pan de sal each. How many full bags can he pack, and how many pan de sal will be left over?
Number Sentence:
435 ÷ 8 = ______
Full: Left:
Scratch / Division Box:
Show DMSB Long Division:
435 ÷ 8 = ______ Quotient with Remainder ______
A farmer harvested 6 crates of ripe mangoes weighing 45 kg each. He donated 70 kg to a community pantry and distributed the rest equally among 4 market stalls. How many kg did each stall receive?
Number Sentence:
[(6 × 45) − 70] ÷ 4 = ______
Each stall: kg
Scratch / Solution Box:
Step 1 (Total harvest): 6 × 45 = ______ kg
Step 2 (After donation): ______ − 70 = ______ kg
Step 3 (Equal share): ______ ÷ 4 = ______ kg
Christian saves ₱65 every day from his allowance for 14 school days. He then bought 2 math workbooks for ₱275 each. How much of his savings does he have left?
Number Sentence:
(14 × 65) − (2 × 275) = ______
Remaining: ₱
Scratch / Solution Box:
Step 1 (Total saved): 14 × 65 = ₱______
Step 2 (Total spent): 2 × 275 = ₱______
Step 3 (Remaining): ______ − ______ = ₱______
SCORING GUIDE
Use this master solution guide to verify answers, diagnose arithmetic learning gaps, and discuss multi-step problem solving.
PARTS I & II: COMPUTATION & DIVISION
ITEMS 1–12
1. 76,144 — 48,659 + 27,485 = 76,144 (regrouping in hundreds and thousands).
2. 36,313 — 15,240 + 8,675 + 12,398 = 36,313 (vertical alignment with three addends).
3. 35,418 — 70,000 − 34,582 = 35,418 (borrowing across three consecutive zeros).
4. 23,667 — 52,416 − 28,749 = 23,667 (standard vertical borrowing).
5. 32,466 — 4,638 × 7 = 32,466 (multi-digit regrouping carries).
6. 4,974 — 829 × 6 = 4,974.
7. 2,432 — Partial products: 64 × 8 = 512; 64 × 30 = 1,920; Sum = 2,432.
8. 7,800 — Partial products: 325 × 4 = 1,300; 325 × 20 = 6,500; Sum = 7,800.
9. 182 — 728 ÷ 4 = 182 (exact quotient, no remainder).
10. 141 R 3 — 849 ÷ 6 = 141 remainder 3 (141 × 6 = 846; 849 − 846 = 3).
11. 1,030 — 6,180 ÷ 6 = 1,030 (crucial placeholder zero in tens place!).
12. Verified! — (104 × 5) + 3 = 520 + 3 = 523 (matches dividend).
ESTIMATION, MDAS & WORD PROBLEMS
ITEMS 13–24
13. 11,000 — 6,845 ≈ 7,000; 4,210 ≈ 4,000; Sum = 11,000.
14. 6,300 — 9,482 ≈ 9,500; 3,219 ≈ 3,200; Diff = 6,300.
15. 30,000 — 582 ≈ 600; 49 ≈ 50; Product = 600 × 50 = 30,000.
16. 600 — Compatible dividend 4,200 ÷ 7 = 600.
17. 64 — Multiply first: 8 × 5 = 40; then 24 + 40 = 64.
18. 16 — Left-to-right rule: 32 ÷ 8 = 4; then 4 × 4 = 16.
19. 67 — Multiply first: 6 × 7 = 42; then 50 + 42 − 25 = 67.
20. 96 — Divide first: 48 ÷ 6 = 8; then 90 − 8 + 14 = 82 + 14 = 96.
21. ₱520 change — Notebooks: 8 × 45 = ₱360; Total: 360 + 120 = ₱480; Change: 1,000 − 480 = ₱520.
22. 54 bags • 3 left over — 435 ÷ 8 = 54 R 3.
23. 50 kg — Harvest: 6 × 45 = 270 kg; Remaining: 270 − 70 = 200 kg; Stalls: 200 ÷ 4 = 50 kg.
24. ₱360 left — Saved: 14 × 65 = ₱910; Spent: 2 × 275 = ₱550; Left: ₱910 − ₱550 = ₱360.
DIAGNOSTIC RUBRIC
Total Score Evaluation & Grade 4 Math Proficiency Band (Total: 24 Points)
🌟 Advanced Master
22 – 24 pts
Flawless mastery in arithmetic, multi-step MDAS, and word problem modeling. Big-school exam ready!
👍 Proficient
18 – 21 pts
Solid arithmetic foundations; minor calculation slips on borrowing across zeros or remainder notation.
⚠️ Approaching
13 – 17 pts
Needs targeted reinforcement on 2-digit partial products and MDAS left-to-right rules.
🚨 Developing
0 – 12 pts
Significant conceptual gaps in multi-step problem solving. Recommended for PERSONALIZED Tutoring.
📐 Clinical Teacher Insight for Grade 4 Math:
Students who struggle with multi-step word problems (Items 21–24) rarely lack computation skills—they struggle with sentence decoding and identifying intermediate answers. Encourage students to bracket each step: Step 1 (find total harvested), Step 2 (subtract donation), Step 3 (divide remaining). Visualizing the scenario prevents rushing into the wrong operation!
