Daily Practice Problems (DPP‑1)
Grade 5 – Mathematics
Topic: Four Fundamental Operations & Roman Numerals
1. Quick Concept Refresher
| Skill | Key Idea |
|---|---|
| Addition / Subtraction | Line up digits by place value; carry or borrow with care. |
| Multiplication / Division | Think “groups of” (×) and “how many groups fit” (÷); use the long methods for larger numbers. |
| Order of Operations | B → O → D M → A S (Brackets, Orders, Division & Multiplication, Addition & Subtraction). |
| Roman Numerals | I (1), V (5), X (10), L (50), C (100), D (500), M (1000). Place a smaller symbol before a larger one to subtract (IV = 4); otherwise add. |
2. Daily Questions
- Using each of the digits 1 through 8 exactly once, arrange them to form an eight‑digit number that can be divided without any remainder by 6, 7, and 11.
- Think of a two‑digit number whose value is five times the sum of its two digits. In addition, the digit in the ones place is three more than the digit in the tens place. What number are we thinking of?
- A teacher writes the expression
562 + 15 × [48 − (6 × 5 − 3)] ÷ 3
on the board and asks the class to evaluate it. What answer should the students obtain if they follow the order‑of‑operations rules correctly? - Maria chooses four consecutive counting numbers, multiplies them together, and then adds 1 to the product. She discovers that, no matter which consecutive numbers she starts with, the final answer is always divisible by the same two‑digit number. Which number is it, and how can you show that Maria is right?
- Ravi is studying ancient history and comes across the Roman‑numeral calculation
CML − { [ LXXXIV − ( XXV − IX ) ] + XLII }.
Work out the value of the expression and give your final answer in Roman numerals. - Leena has the Roman numeral
DLXXV. She wants to add the smallest possible Roman numeral to it so that the result is exactly divisible byCLIX. What numeral should she add? - A craft shop sells packets of stickers for ₹ 2.40 each and packets of badges for ₹ 1.50 each. A packet of glitter costs ₹ 0.90 more than twice the price of a badge. Maia buys 2 packets of stickers, 3 packets of badges, and 1 packet of glitter. How much does she pay altogether?
- Use each of the digits 1 to 9 once, and only once, to make three different three‑digit numbers so that the second number is three times the first and the third number is four times the first. List every possible ordered triple that works.
- How many three‑digit numbers are there in which each digit is smaller than the digit to its left? (That is, the hundreds digit is greater than the tens digit, and the tens digit is greater than the units digit.)
- Find all sets of three different whole numbers, each greater than 2, whose product is 84 and whose sum is a prime number. If no such set exists, explain clearly why.
3. Challenge Corner (Optional Extra)
Rewrite Question 4 in your own words and explain why the same two‑digit divisor always works — without using a calculator or a big multiplication table.
4. Performance Checklist
| Skill | 😊 Confident | 😐 Needs Review |
|---|---|---|
| Order of Operations | ☐ | ☐ |
| Multi‑step Word Problems | ☐ | ☐ |
| Roman‑Numeral Arithmetic | ☐ | ☐ |
| Logical Digit Puzzles | ☐ | ☐ |
Tick the boxes after marking your work, then review any sections you found tricky. Keep practising, and see you in DPP‑2!