Mathematics • Year 7 • Unit 1 • Lesson 11
Decimal Operations, Mixed Challenge
Pull everything from Lesson 11 together: add and subtract by lining up dots, multiply by counting decimal places, divide by shifting dots, and spot a classic d.p. mistake. Finish with an open-ended digit puzzle.
1. Mixed problems, choose the right operation
Each question uses a different idea from Lesson 11. Decide which rule applies before you start. Show working. 2 marks each
1.1 Calculate 12.5 − 4.75. Show borrowing.
1.2 Calculate 0.4 × 0.15. Show the ignore-dots multiplication and total decimal places.
1.3 Calculate 3.24 ÷ 0.4. Shift both dots, then divide.
1.4 Calculate 3.45 + 2.8. Then check by estimating with rounding to whole numbers.
1.5 Calculate 2.5 × 0.4. State whether your answer is bigger or smaller than 2.5, and explain why in one sentence.
1.6 A 3.6 m plank is cut into pieces 0.8 m long. How many full pieces can you cut, and how much (in metres) is left over?
2. Find the mistake
Another Year 7 student tried to calculate 0.3 × 0.2. Their working is shown below. Exactly one line contains the mistake. Spot it, explain why it's wrong, then re-do the working correctly. 3 marks
Student's working, calculate 0.3 × 0.2:
Line 1: Ignore the dots. Multiply 3 × 2 = 6.
Line 2: Count decimal places: 0.3 has 1 d.p., 0.2 has 1 d.p.
Line 3: Total decimal places in the answer = 1.
Line 4: Place the dot in the answer: 0.6.
Line 5: Final answer: 0.3 × 0.2 = 0.6.
(a) Which line contains the mistake?
(b) Explain in one or two sentences why that line is wrong.
(c) Write out the corrected working in full, including the corrected final answer.
3. Open-ended challenge, make the dots count
This question has more than one correct answer. Show one that works and explain. 4 marks
3.1 Using each of the digits 2, 4, 5 and 8 exactly once, place a decimal point in each of the two numbers below so that their product is as close to 10 as possible.
_ . _ × _ . _
(i) Write down your two numbers and their product.
(ii) Explain in one or two sentences how counting decimal places helped you place the dots.
Bonus: What pair of numbers gives the largest possible product? What pair gives the smallest possible product greater than 1?
How did this worksheet feel?
What I'll revisit before next class:
1.1-12.5 − 4.75
Add trailing zero: 12.50 − 4.75. Hundredths: 0−5 borrow, 10−5 = 5. Tenths: 4−7 borrow, 14−7 = 7. Ones: 11−4 = 7. Answer: 7.75.
1.2-0.4 × 0.15
Ignore dots: 4 × 15 = 60. Total d.p. = 1 + 2 = 3. So 0.060 = 0.06.
1.3-3.24 ÷ 0.4
Shift both 1 place: 32.4 ÷ 4. 4 into 32 = 8. 4 into 4 = 1. Answer: 8.1.
1.4-3.45 + 2.8
Add trailing zero: 3.45 + 2.80. Hundredths: 5+0 = 5. Tenths: 4+8 = 12, write 2 carry 1. Ones: 3+2+1 = 6. Answer: 6.25. Estimate: 3 + 3 = 6 ✓.
1.5-2.5 × 0.4
Ignore dots: 25 × 4 = 100. Total d.p. = 1 + 1 = 2. So 1.00 = 1. Answer is smaller than 2.5 because multiplying by 0.4 (a number less than 1) shrinks the original.
1.6-3.6 m plank in 0.8 m pieces
3.6 ÷ 0.8: shift both 1 place → 36 ÷ 8 = 4.5. So 4 full pieces. Leftover = 0.5 × 0.8 m = 0.4 m. Check: 4 × 0.8 = 3.2, and 3.6 − 3.2 = 0.4 m ✓.
2, Find the mistake
(a) The mistake is on Line 3.
(b) The student forgot to add the decimal places. 0.3 has 1 d.p. and 0.2 has 1 d.p., so the total in the answer must be 2, not 1.
(c) Corrected working:
Line 1 (kept): 3 × 2 = 6.
Line 2 (kept): 0.3 has 1 d.p., 0.2 has 1 d.p.
Line 3 (fixed): total decimal places = 1 + 1 = 2.
Line 4 (fixed): place the dot → 6 becomes 0.06.
Line 5: 0.3 × 0.2 = 0.06.
Sanity check: 0.3 × 0.2 must be smaller than 0.3 (because we're multiplying by 0.2 < 1). 0.06 < 0.3 ✓; 0.6 was not.
3, Decimal placement puzzle (sample solution)
There are 24 ways to arrange the four digits in the four places. Checking them shows the closest product to 10 is 2.5 × 4.8 = 12.00, which is 2 away from 10. (The reverse order, 4.8 × 2.5, gives the same product.)
The product has two decimal places because each factor has one: 25 × 48 = 1200, then place the decimal point two places from the right to get 12.00.
Bonus: The largest product is 8.2 × 5.4 = 44.28 (82 × 54 = 4428, then place two decimal places). The smallest product greater than 1 is 2.5 × 4.8 = 12.00 (or its reverse). These extrema use all four digits exactly once.
Marking: 2 marks for the closest valid pair and product; 1 for explaining decimal-place counting; 1 for correctly identifying the largest or smallest valid product.