Mathematics • Year 7 • Unit 1 • Lesson 15
Unit 1 Skills Refresh
Build a quick refresh across the whole unit: integers, BODMAS, fractions, decimals, percentages and ratios. One worked example, one fade, and eight graduated practice problems that touch every topic.
1. I do, fully worked example
Watch a worked BODMAS calculation that touches integers, brackets and order of operations, all of Unit 1's "number" skills in one expression.
Problem. Calculate (−3) × (−4) + (−2) × 5.
Step 1, Identify the operations using BODMAS.
No brackets to expand, no orders. We have two multiplications and one addition.
Reason: BODMAS says do × and ÷ before + and −.
Step 2, Do the first multiplication: (−3) × (−4).
Negative × negative = positive: 3 × 4 = 12, so (−3) × (−4) = +12.
Reason: two negatives in multiplication cancel to a positive.
Step 3, Do the second multiplication: (−2) × 5.
Negative × positive = negative: (−2) × 5 = −10.
Reason: only one negative → the product is negative.
Step 4, Now add the two results.
12 + (−10) = 12 − 10 = 2.
Answer: (−3) × (−4) + (−2) × 5 = 2.
2. We do, fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank line. 4 marks
Problem. Calculate 3/4 + 1/6.
Step 1, Find the LCD (lowest common denominator) of 4 and 6:
Multiples of 4: 4, 8, 12, 16, … Multiples of 6: 6, 12, 18, … LCD = _______.
Step 2, Convert each fraction so both have the LCD as the denominator:
3/4 = (3 × 3)/(4 × 3) = _______/12.
1/6 = (1 × 2)/(6 × 2) = _______/12.
Step 3, Add the numerators (keep the denominator):
_______/12 + _______/12 = _______/12.
Step 4, Simplify if possible:
_______/12 (already in simplest form? _______).
3. You do, independent practice
Show working under each problem. The first four are foundation, the middle two are standard, and the last two are extension. Each problem labels which Unit 1 topic it covers.
Foundation, single step
3.1 (Integers) Calculate 5 − (−3). 1 mark
3.2 (Fractions) Simplify 18/24 to lowest terms. 1 mark
3.3 (Decimals) Calculate 12 ÷ 0.4. Shift both dots before dividing. 1 mark
3.4 (Percentages) Find 25% of 84. Use the "÷ 4" shortcut. 1 mark
Standard, combine two ideas
3.5 (BODMAS) Calculate 6 + 3 × (4 − 1). Show every step in BODMAS order. 2 marks
3.6 (Ratios) Share $180 in the ratio 4:5. List both shares. 2 marks
Extension, push your thinking
3.7 (Fractions + decimals) Convert 3/8 to a decimal, then express it as a percentage. Show both conversions. 3 marks
3.8 (Rates) A train travels 360 km in 4 hours 30 minutes. Find its speed in km/h. Be careful with the time conversion. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2, We do (3/4 + 1/6)
Step 1: LCD = 12.
Step 2: 3/4 = 9/12; 1/6 = 2/12.
Step 3: 9/12 + 2/12 = 11/12.
Step 4: 11/12, HCF(11, 12) = 1, so already simplified: yes.
3.1-5 − (−3)
Subtracting a negative = adding the positive: 5 + 3 = 8.
3.2, Simplify 18/24
HCF(18, 24) = 6. 18 ÷ 6 = 3, 24 ÷ 6 = 4. Answer: 3/4.
3.3-12 ÷ 0.4
Shift both 1 place right: 120 ÷ 4 = 30.
3.4-25% of 84
25% = 1/4. 84 ÷ 4 = 21.
3.5-6 + 3 × (4 − 1)
Brackets first: 4 − 1 = 3. Then multiplication: 3 × 3 = 9. Then addition: 6 + 9 = 15.
3.6, $180 in ratio 4:5
Total parts = 9. One part = $180 ÷ 9 = $20. Shares: 4 × $20 = $80 and 5 × $20 = $100. Check: $80 + $100 = $180 ✓.
3.7-3/8 as decimal and %
Decimal: 3 ÷ 8 = 0.375. Percentage: 0.375 × 100 = 37.5%.
3.8, Train speed
4 h 30 min = 4.5 h (not 4.3 h, 30 min is half an hour). Speed = 360 ÷ 4.5 = 3600 ÷ 45 = 80 km/h. Check: 80 × 4.5 = 360 ✓.