Discussion Questions Library
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Showing 68 of 68 discussion questions
A group of Year 10 students are tracking their house points at a school in Birmingham. House points can be awarded (positive numbers) or deducted (negative numbers) for various reasons. Over a week, t...
Created: 13 Feb 2026, 9:53 am
Two Year 11 students, Aisha and Ben, are revising for their GCSE Maths exam. They're discussing how to express one number as a fraction or percentage of another without a calculator. Aisha says: ...
Created: 13 Feb 2026, 9:41 am
A company's profits over 6 months are recorded as: January: -£2,500, February: £1,800, March: -£800, April: £3,200, May: -£1,200, June: £2,700. The finance director claims the company made ...
Created: 12 Feb 2026, 9:22 am
A group of Year 11 students are planning a sponsored hike along the Pennine Way to raise money for their school's sports equipment fund. They record their elevation changes throughout the day usi...
Created: 12 Feb 2026, 9:18 am
A popular UK clothing shop is having a sale. They advertise '50% off all prices' on Monday. On Tuesday, they change their sign to 'An additional 30% off the sale prices'. A Year 11...
Created: 12 Feb 2026, 9:06 am
A quadrilateral is drawn on a coordinate grid with vertices at A(0,0), B(4,0), C(5,3), and D(1,3). Two students are debating: Maya claims this is definitely a parallelogram because opposite sides appe...
Created: 11 Feb 2026, 10:32 am
A popular mobile phone company in the UK is launching a new model. They claim: 'Sales have increased by 150% compared to last year's model launch.' Last year, they sold 40,000 phones in...
Created: 11 Feb 2026, 9:52 am
Two friends, Aisha and Ben, are comparing their cycling routes on a map. Aisha's route goes from coordinates (2, 3) to (6, 11). Ben's route goes from (1, 1) to (5, 9). They both claim their ...
Created: 10 Feb 2026, 6:14 pm
In a quadrilateral ABCD, angle A is (3x + 10)°, angle B is (2x + 20)°, angle C is (4x - 30)°, and angle D is (x + 40)°. Two students, Priya and Liam, are discussing whether this quadrilateral coul...
Created: 10 Feb 2026, 9:01 am
During a GCSE revision session, a student claims: 'Percentages greater than 100% don't make sense in real life because you can't have more than a whole of something.' Another stude...
Created: 10 Feb 2026, 8:27 am
A group of Year 11 students are fundraising for their school prom. They have raised £480 so far, which is 60% of their target amount. They plan a bake sale where they expect to make 3/8 of their rema...
Created: 9 Feb 2026, 9:26 am
A group of Year 11 students are comparing mobile phone contracts. They find three different deals: 1) 'SuperSave Mobile' offers 15% off the standard £36 monthly fee for the first 12 months....
Created: 9 Feb 2026, 9:06 am
A group of Year 11 students are fundraising for their school prom. They have raised £480 so far. They need to reach a target of £1,200. During a discussion, three students propose different strategi...
Created: 5 Feb 2026, 10:43 am
A group of Year 11 students are fundraising for their GCSE prom. On Monday, they raised £120, which they later discovered was 3/8 of their total fundraising target. They debate how to calculate the f...
Created: 4 Feb 2026, 8:50 am
A quadrilateral is drawn on a coordinate grid with vertices at A(0,0), B(6,0), C(8,4), and D(2,4). Is this shape a parallelogram? Justify your answer using chains of reasoning about angles and side pr...
Created: 3 Feb 2026, 9:29 pm
Two parallel lines are crossed by a transversal. A student claims that when they labelled the angles, they found that corresponding angles were not equal. They argue: 'I measured carefully with m...
Created: 3 Feb 2026, 7:07 pm
A group of Year 11 students are comparing their mock GCSE results. They each achieved different scores on a mathematics test, but they've recorded them in different formats:
- Alex: "I got ...
Created: 3 Feb 2026, 10:19 am
A group of Year 11 students from Manchester are planning a school trip to Paris. They need to exchange £1,200 into euros. They find two different exchange offers: 1) A high street bank offers €1.15...
Created: 2 Feb 2026, 10:02 am
During a GCSE revision session, two students are debating how to simplify (2³)⁴. Priya says: 'You multiply the exponents, so it's 2¹² which is 4096.' Liam says: 'Actually, you...
Created: 2 Feb 2026, 9:51 am
A class of 30 GCSE students at a Manchester school took a mathematics test. The teacher calculated the mean score as 72%. However, she realised she had accidentally included her own 'test paper&#...
Created: 2 Feb 2026, 9:39 am
A UK company is deciding between two different pay structures for their part-time employees in Manchester. Structure A: £12.50 per hour with no holiday pay. Structure B: £11.75 per hour plus 12.07% ...
Created: 30 Jan 2026, 2:31 pm
A triangular garden at a school in Manchester is being redesigned. The school has £500 to spend on new turf. The triangular area has vertices at coordinates (0,0), (8,0), and (4,6) on a grid where ea...
Created: 30 Jan 2026, 9:43 am
Two friends, Sam and Alex, both work part-time jobs. Sam earns £12.50 per hour and works 15 hours per week. Alex earns £11.75 per hour and works 18 hours per week. They both pay 20% income tax on th...
Created: 30 Jan 2026, 9:25 am
Consider the expression: 2^x + 2^x + 2^x + 2^x. Alex simplifies this to 2^{4x} using the addition law for indices, arguing that since you're adding four terms of 2^x, you add the exponents. Sam d...
Created: 30 Jan 2026, 9:05 am
A shopkeeper says: 'I sell an item for £120 including VAT at 20%. If the government increases VAT to 25%, I'll need to increase my selling price to £125 to keep the same profit.' Is t...
Created: 29 Jan 2026, 10:13 am
A farmer needs to create a rectangular vegetable patch with an area of 120 m² using exactly 50 meters of fencing. However, they realize they can save fencing by using an existing straight stone wall ...
Created: 29 Jan 2026, 9:15 am
Jamal and Chloe are simplifying the expression 2³ × 2⁴. Jamal says the answer is 4⁷ because 'you add the indices and multiply the bases.' Chloe says the answer is 2⁷ because 'yo...
Created: 29 Jan 2026, 9:01 am
Two banks are offering different savings accounts to 15-year-old Maya who wants to save £500 from her part-time job. Bank A offers 3% annual compound interest with interest paid yearly. Bank B offers...
Created: 28 Jan 2026, 11:04 am
Consider the expression: (x⁵y³z²) / (x²y⁴z²). Two students, Alex and Bailey, are simplifying it. Alex says the simplified form is x³y⁻¹. Bailey says it's x³/y. They both claim their ...
Created: 28 Jan 2026, 9:14 am
Is it always true that (x²)(x³) = x⁵? Your group has been given three different student responses to this question: Student A says 'Yes, because you add the exponents: 2 + 3 = 5.' Studen...
Created: 26 Jan 2026, 11:45 am
Is it always better to convert decimals to whole numbers before dividing? Consider the problem: 4.8 ÷ 0.12. One student says 'Multiply both numbers by 100 to get 480 ÷ 12 = 40.' Another sa...
Created: 26 Jan 2026, 9:03 am
A mobile phone company offers two different monthly plans: Plan A has a fixed cost of £15 plus £0.10 per minute of calls. Plan B has a fixed cost of £5 plus £0.20 per minute of calls. Your friend ...
Created: 25 Jan 2026, 1:21 pm
A student claims: 'When dividing integers, if you get a negative answer, the divisor must be negative.' Is this statement always true, sometimes true, or never true? Work with your group to ...
Created: 23 Jan 2026, 10:18 am
Two friends, Maya and Liam, are comparing savings accounts. Maya's account offers 4% simple interest per year, while Liam's offers 3.5% simple interest per year. Maya says, 'I'll d...
Created: 23 Jan 2026, 9:50 am
Consider the expression: 2x³ + 3x² - 5x³ + 4x² - x³. Jamal says you can combine all terms with the same base and exponent to get -4x³ + 7x². Maya says you should first group the x³ terms toget...
Created: 23 Jan 2026, 9:12 am
A builder needs to check if a triangular roof section is a right-angled triangle. He measures the three sides as 4.5 m, 6.0 m, and 7.5 m. He claims it's a right-angled triangle because 4.5² + 6....
Created: 22 Jan 2026, 4:49 pm
Two students, Alex and Bailey, are working on finding the nth term of a linear sequence. Alex says the sequence 5, 8, 11, 14, 17... has the nth term 3n + 2. Bailey says the same sequence has the nth t...
Created: 22 Jan 2026, 11:49 am
Here are the first 5 terms of a linear sequence: 3, 7, 11, 15, 19. Two students are trying to find the rule for the nth term. Student A says: 'The rule is 4n - 1 because the difference is 4 and w...
Created: 22 Jan 2026, 9:25 am
Jamal and Priya are multiplying 2.4 × 0.15 using formal written methods. Jamal says: 'First I multiply 24 × 15 to get 360, then I count the decimal places. There are three decimal places total ...
Created: 22 Jan 2026, 8:48 am
A store is having a 'double discount' sale. They first reduce prices by 20%, then offer an additional 15% off the reduced price. Meanwhile, a competing store advertises '35% off everyth...
Created: 21 Jan 2026, 11:37 am
Here are the first 5 terms of a linear sequence: 3, 7, 11, 15, 19. Two students are discussing how to find the nth term rule. Student A says: 'The rule is 4n - 1 because the difference is 4 and w...
Created: 21 Jan 2026, 10:50 am
A store advertises '30% off all items' during a sale. The next day, they offer an additional '20% off the sale price'. A customer argues this is equivalent to 50% off the original ...
Created: 20 Jan 2026, 1:58 pm
A student claims that 6 ÷ 2(1 + 2) = 1, while another student insists it equals 9. Both are confident in their understanding of BIDMAS/BODMAS. Working in small groups, analyze this expression and pre...
Created: 20 Jan 2026, 1:19 pm
Consider the sequence defined by the rule: 'Start with 3, then each term is found by taking the previous term, multiplying by 2, and then subtracting 1.' Two students, Alex and Bailey, are d...
Created: 20 Jan 2026, 10:01 am
A clothing store advertises '30% off all items' for a sale. The next week, they add an additional '20% off the sale price' for clearance. A student claims this means you get '...
Created: 19 Jan 2026, 9:55 am
Is it always true that when you multiply two negative integers, the result is positive? Consider the statement: 'The product of two negative integers is always positive.' Working in small gr...
Created: 19 Jan 2026, 9:24 am
A shop advertises '30% off all items!' After the discount, a jacket costs £56. Two students are arguing about how to find the original price. Maya says: 'You need to find 70% of someth...
Created: 16 Jan 2026, 12:38 pm
A company claims their new energy drink 'increases concentration by 200%'. In their small trial, the average test score improved from 40% to 80%. Is their claim mathematically valid? Work wi...
Created: 16 Jan 2026, 12:37 pm
A rectangular swimming pool measures 25 meters long, 10 meters wide, and has an average depth of 1.8 meters. The pool needs to be filled with water, but the water delivery company charges per cubic me...
Created: 16 Jan 2026, 11:14 am
A shop advertises: 'Prices reduced by 20% in our sale!' After the sale, the shop increases prices back to their original amounts. Is this increase also 20%? Work with your group to investiga...
Created: 16 Jan 2026, 10:58 am
Two students are discussing sequences. Alex says: 'My sequence starts at 5, and each term is double the previous term.' Bailey says: 'My sequence starts at 5, and each term is 2 more th...
Created: 16 Jan 2026, 10:19 am
Consider the sequence defined by the rule: 'Start with 5, then multiply by 2 and subtract 3 each time.' Two students, Alex and Bailey, generate the sequence differently. Alex says: 'The...
Created: 16 Jan 2026, 10:16 am
A student claims that 'multiplying by 0.1 is the same as dividing by 10, and multiplying by 0.01 is the same as dividing by 100, so these operations are essentially just division problems in disg...
Created: 15 Jan 2026, 9:49 am
A clothing store increases the price of a jacket from £80 to £100, then later decreases it from £100 back to £80. The manager claims 'the price went up 25% and then down 20%, so overall there...
Created: 14 Jan 2026, 11:06 am
Consider the inequality: 3(2x - 1) ≤ 2(x + 4). Two students, Alex and Sam, are solving it. Alex expands the brackets first, getting 6x - 3 ≤ 2x + 8, then solves to find x ≤ 2.75. Sam divides bot...
Created: 14 Jan 2026, 9:08 am
A student claims: 'Multiplying any number by 10² always gives a larger result, and dividing any number by 10² always gives a smaller result.' Is this statement always true? Work with your ...
Created: 13 Jan 2026, 7:52 pm
A clothing store is having a 'Buy One, Get One 50% Off' sale on all items. The store manager claims this is equivalent to a 25% discount on both items. A customer argues it's actually b...
Created: 13 Jan 2026, 11:26 am
A school is planning a charity bake sale. They have a budget of £50 to buy ingredients. They plan to sell two types of cookies: chocolate chip (costs £2 per batch to make, sells for £5 per batch) a...
Created: 13 Jan 2026, 10:47 am
Two friends, Alex and Bailey, are solving the equation 3(x + 4) = 2(x - 1) + 20. Alex expands the brackets first, getting 3x + 12 = 2x - 2 + 20, then simplifies to 3x + 12 = 2x + 18. Bailey subtracts ...
Created: 13 Jan 2026, 8:56 am
Is 36 the 'best' number when it comes to having lots of factors? Your group must decide on what makes a number 'good' at having factors, then find at least one number you think mig...
Created: 12 Jan 2026, 9:46 am
A scientist is measuring microscopic organisms and finds one that is 0.000025 metres long. Her colleague says this is 2.5 × 10⁻⁵ metres in standard form. Another colleague says it's 25 × 10...
Created: 7 Jan 2026, 12:57 pm
A scientist is measuring bacteria under a microscope. She finds that one bacterium has a width of 0.0000025 meters, while another has a width of 3,800,000 nanometers. Which bacterium is wider? Work to...
Created: 7 Jan 2026, 12:43 pm
Two students, Alex and Bailey, are solving the equation 3(x + 4) = 27. Alex says: 'First, I'll divide both sides by 3 to get x + 4 = 9, then subtract 4 to get x = 5.' Bailey says: '...
Created: 7 Jan 2026, 12:36 pm
A mysterious number has exactly 6 factors. When you list all its factors in order, the product of the first and last factor is 175, and the product of the second and second-last factor is also 175. Wh...
Created: 26 Oct 2025, 10:45 am
A baker is preparing for a community festival and needs to create identical gift boxes containing cookies and cupcakes. The cookies come in packs of 18, and the cupcakes come in packs of 24. The baker...
Created: 26 Oct 2025, 10:44 am
A rectangular garden is measured as 8.5m long by 6.2m wide, both measurements given to 1 decimal place. Students are debating how to calculate the maximum possible error in the area. Team A says: ...
Created: 25 Oct 2025, 10:50 pm
A construction company needs to build a wheelchair ramp for a new building. The ramp must rise 1.2 meters vertically and have a maximum slope ratio of 1:12 (meaning for every 1 unit of vertical rise, ...
Created: 25 Oct 2025, 10:49 pm
You're on a game show with three doors. Behind one door is a car, and behind the other two are goats. You choose Door 1. The host, who knows what's behind all the doors, opens Door 3 to reve...
Created: 25 Oct 2025, 10:35 pm