Exit Ticket Library
Browse and reuse previously generated exit tickets.
🔒 Download Restricted
You must be logged in to download resources.
Create a free account to unlock downloads and track your usage!
Addition and Subtraction of Fractions
1 ticket
A recipe for scones requires ¾ of a cup of plain flour and ⅔ of a cup of wholemeal flour. Sam only has a 1-cup measuring jug. He wants to measure the total amount of flour needed in one go, using the 1-cup jug. Can he do this? Explain your reasoning using equivalent fractions.
Context: White Rose Maths small step: Year 7, Spring, Block 4 (Addition and Subtraction of Fractions), Step 6: Understand And Use Equivalent Fractions. Target this step directly in the question.
Angles in Parallel Lines and Polygons
1 ticket
Aisha is constructing a parallelogram ABCD for her GCSE maths project. She knows that AB = 8 cm, AD = 5 cm, and angle DAB = 60°. She draws side AB first, then uses a protractor to measure angle DAB and draws AD. She then uses a ruler to mark point C so that BC is parallel to AD and DC is parallel to AB. However, when she measures the length of diagonal AC, she gets 12.5 cm. Explain whether her construction is correct or if she has made an error, and justify your answer using geometric reasoning.
Context: White Rose Maths small step: Year 8, Summer, Block 1 (Angles in Parallel Lines and Polygons), Step 6: Construct Triangles And Special Quadrilaterals. Target this step directly in the question.
Area of Trapezia and Circles
3 tickets
A circular pizza has a diameter of 30 cm. It is cut into 8 equal slices.
(a) Calculate the total area of the pizza.
(b) A trapezium-shaped serving tray has parallel sides of length 25 cm and 35 cm, and a perpendicular height of 20 cm.
Which has the larger area: one slice of pizza or the serving tray? Show your working and explain your reasoning.
Context: White Rose Maths small step: Year 8, Summer, Block 2 (Area of Trapezia and Circles), Step 4: Investigate The Area Of A Circle. Target this step directly in the question.
A composite shape is made by joining a rectangle and a right-angled triangle along one side. The rectangle measures 8 cm by 5 cm. The triangle has a perpendicular height of 4 cm and its base is the same length as the rectangle's width. A student calculates the total area as follows:
Area of rectangle = 8 × 5 = 40 cm²
Area of triangle = ½ × 5 × 4 = 10 cm²
Total area = 40 + 10 = 50 cm²
Explain whether the student's calculation is correct. If it is incorrect, identify the error and calculate the correct total area.
Context: White Rose Maths small step: Year 8, Summer, Block 2 (Area of Trapezia and Circles), Step 1: Calculate The Area Of Triangles, Rectangles And Parallelograms. Target this step directly in the question.
A trapezium-shaped garden bed at Kew Gardens has parallel sides of length 4.2 metres and 6.8 metres. The perpendicular distance between the parallel sides is 3.5 metres. A circular pond with diameter 2 metres is dug in the centre of the garden bed. What area of the garden bed remains for planting flowers? Give your answer to 2 decimal places.
Context: White Rose Maths small step: Year 8, Summer, Block 2 (Area of Trapezia and Circles), Step 2: Calculate The Area Of A Trapezium. Target this step directly in the question.
Calculate Percentage Increase And Decrease
1 ticket
A shop increases the price of a jacket by 20% in January. In February, they decrease the new price by 20%. A customer says: 'The price is back to the original amount since 20% up and 20% down cancel out.' Is the customer correct? Show your calculations and explain your reasoning.
Context: Auto-generated from Flow tool
Constructing and Measuring
3 tickets
Aisha is drawing a right-angled triangle for her maths homework. She needs to draw triangle ABC where angle ABC is 90°, side AB is 6.5 cm, and side BC is 4.8 cm. She has a ruler and a protractor.
Explain the steps Aisha should take to accurately construct this triangle. What is the length of side AC to the nearest millimetre?
Context: White Rose Maths small step: Year 7, Summer, Block 1 (Constructing and Measuring), Step 2: Draw And Measure Line Segments Including Geometric Figures. Target this step directly in the question.
A diagram shows triangle ABC with point D on side AC. The diagram is labelled with the following notation: AB = 5 cm, BC = 7 cm, ∠ABC = 42°, and AD:DC = 2:3.
Explain what each part of this notation means and why it is important when constructing or describing this triangle. Then, identify which pieces of information would be sufficient to construct a unique triangle ABC, and which would not be sufficient on their own.
Context: White Rose Maths small step: Year 7, Summer, Block 1 (Constructing and Measuring), Step 1: Understand And Use Letter And Labelling Conventions Including Those For Geometric Figures. Target this step directly in the question.
Two students, Aisha and Ben, are each constructing a triangle with sides of length 5 cm and 7 cm, and an included angle of 40°. Aisha draws the 5 cm side first, then measures and draws the 40° angle, then draws the 7 cm side. Ben draws the 7 cm side first, then measures and draws the 40° angle, then draws the 5 cm side. Will their triangles be congruent? Explain your reasoning, referring to the triangle construction condition they are using.
Context: White Rose Maths small step: Year 7, Summer, Block 1 (Constructing and Measuring), Step 13: Construct Triangles Using Sss, Sas And Asa. Target this step directly in the question.
Converting between Fractions, Decimals and Percentages
1 ticket
A student claims that 0.125, 12.5%, and 1/8 are all equivalent. Is the student correct? Justify your answer by converting between all three forms and explaining your reasoning.
Context: Auto-generated from Flow tool
Delving into Data
3 tickets
A Year 10 student is conducting a survey about screen time habits among teenagers in their school. They plan to ask: 'How many hours per day do you spend on your phone?' They collect responses from 30 students in their own maths class.
(a) Is this data primary or secondary? Explain your reasoning.
(b) The student wants to use their findings to make a claim about 'all UK teenagers'. Identify two limitations of using this data for this purpose and suggest one improvement to their data collection method.
Context: White Rose Maths small step: Year 10, Summer, Block 1 (Delving into Data), Step 3: Primary And Secondary Data. Target this step directly in the question.
A sixth form college in Manchester is conducting a survey about student satisfaction with their canteen. The college has 1200 students across three year groups: Year 12 has 480 students, Year 13 has 420 students, and Year 14 (a small cohort for resits) has 300 students. The college wants to survey a stratified sample of 120 students.
1. Calculate how many students should be selected from each year group for the stratified sample.
2. A student argues: 'Since Year 12 has the most students, we should just take our sample of 120 entirely from Year 12 to make it easier.' Explain why this would not be a valid stratified sample and what problem it would cause for the survey results.
Context: White Rose Maths small step: Year 10, Summer, Block 1 (Delving into Data), Step 2: Construct A Stratified Sample. Target this step directly in the question.
A survey was conducted on the number of books read by Year 10 students in a UK school over the summer holiday. The raw data is: 0, 2, 5, 1, 3, 4, 2, 6, 1, 2, 0, 3, 7, 2, 4, 1, 3, 2, 5, 0, 8, 2, 1, 4, 3.
Construct a grouped frequency table for this data using class intervals 0-1, 2-3, 4-5, 6-7, 8-9. Then, on a separate set of axes, sketch the frequency polygon that would be drawn from this table. A student claims, 'The frequency polygon shows that most students read exactly 2 books.' Explain why this statement is incorrect, referring to the properties of grouped data and frequency polygons.
Context: White Rose Maths small step: Year 10, Summer, Block 1 (Delving into Data), Step 4: Construct And Interpret Frequency Tables And Frequency Polygons. Target this step directly in the question.
Describe And Continue A Sequence Given Diagrammatically
1 ticket
The diagrams below show a sequence of growing patterns made from squares.
Pattern 1: □
Pattern 2: □□
□
Pattern 3: □□□
□□
□
(a) Draw Pattern 4 in the sequence.
(b) How many squares would be in Pattern 10?
(c) A student says Pattern 100 would have 200 squares. Explain why this is incorrect.
Context: Auto-generated from Flow tool
Difference of Two Squares
1 ticket
A student claims that 4x² - 9y⁴ can be factored as (2x - 3y²)(2x + 3y²), but also claims that 16 - 25x⁶ can be factored as (4 - 5x³)(4 - 5x³). Are both factorizations correct? Explain why or why not, and identify any errors in the student's reasoning.
Context: Auto-generated from Flow tool
Direct and Inverse Proportion
1 ticket
A factory produces widgets using two machines. Machine A takes 4 hours to produce 100 widgets working alone. When Machine A and Machine B work together, they take 3 hours to produce 180 widgets. If the number of widgets produced is directly proportional to the number of hours worked, and the machines work at constant rates:
(a) How long would Machine B take to produce 100 widgets working alone?
(b) If Machine A breaks down and only Machine B is available, how many widgets would Machine B produce in 6 hours?
Context: Auto-generated from Flow tool
Directed Number
1 ticket
The temperature in London at 6am was -4°C. By 9am it had risen by 7°C. At midday it was 2°C warmer than at 9am. By 3pm it had fallen by 5°C from the midday temperature. Place these four temperatures in order from coldest to warmest, using the appropriate inequality symbols (< or >) between them. Explain how you used a number line to help you order them.
Context: White Rose Maths small step: Year 7, Spring, Block 3 (Directed Number), Step 2: Order Directed Numbers Using Lines And Appropriate Symbols. Target this step directly in the question.
Enlargement and Similarity
3 tickets
Two similar triangles are shown on a GCSE maths worksheet. Triangle A has side lengths of 6 cm, 8 cm, and 10 cm. Triangle B is an enlargement of Triangle A with a scale factor of 2.5.
A student claims: 'Since Triangle B is an enlargement of Triangle A, all corresponding angles are equal, and the perimeter of Triangle B will be exactly 2.5 times the perimeter of Triangle A.'
Is the student correct? Explain your reasoning fully, showing calculations to support your answer.
Context: White Rose Maths small step: Year 9, Summer, Block 1 (Enlargement and Similarity), Step 1: Recognise Enlargement And Similarity. Target this step directly in the question.
Triangle ABC has vertices at A(2, 1), B(4, 1), and C(3, 4). It is enlarged with centre of enlargement (1, 1) and scale factor -2.
(a) Plot the image of triangle ABC after this enlargement.
(b) Explain how the position and orientation of the image triangle differs from the original triangle.
(c) A student says: 'A negative scale factor enlargement is just a rotation of 180° about the centre of enlargement.' Is this statement completely correct? Justify your answer.
Context: White Rose Maths small step: Year 9, Summer, Block 1 (Enlargement and Similarity), Step 5: Enlarge A Shape By A Negative Scale Factor. Target this step directly in the question.
Two similar triangles are shown. Triangle ABC has sides AB = 8 cm, BC = 12 cm, and AC = 10 cm. Triangle DEF is an enlargement of triangle ABC. Side DE corresponds to AB and measures 12 cm. Side EF corresponds to BC and measures 18 cm. Angle ABC is 55°.
(a) Calculate the length of side DF.
(b) Find the size of angle DEF.
(c) Explain why you cannot find the length of side DF using only the given side lengths of triangle DEF.
Context: White Rose Maths small step: Year 9, Summer, Block 1 (Enlargement and Similarity), Step 6: Work Out Missing Sides And Angles In A Pair Of Given Similar Shapes. Target this step directly in the question.
Exchange Rates and Currency Conversions
1 ticket
Sarah is traveling from the UK to Japan. She exchanges £150 to Japanese Yen when the exchange rate is £1 = ¥160. In Japan, she spends ¥18,400. When she returns to the UK, she exchanges her remaining Yen back to Pounds, but the exchange rate has changed to £1 = ¥155. How many Pounds does Sarah have left after converting her remaining Yen back to Pounds?
Context: Auto-generated from Flow tool
Expanding and Factorising
1 ticket
A rectangle has an area given by the expression (x + 3)(2x - 5). The area is known to be 0 square centimetres.
(a) Write down an equation that could be solved to find the possible values of x.
(b) Solve your equation to find all possible values of x.
(c) Explain why one of your solutions from part (b) would not be a valid length for the side of a real rectangle.
Context: White Rose Maths small step: Year 11, Autumn, Block 4 (Expanding and Factorising), Step 5: Solve Equations Equal To 0. Target this step directly in the question.
Expanding two brackets
1 ticket
Expand and simplify (2x - 3)(x² + 4x - 1). Explain why the final answer contains an x³ term but no x² term.
Context: Auto-generated from Flow tool
FDP Equivalence
1 ticket
A Year 7 class is conducting a survey on favourite school subjects. The results show that 1.25 times as many students prefer Maths compared to those who prefer English. 40% of the class prefer Science. The remaining 3 students prefer History. The class size is 30.
(a) What fraction of the class prefers Maths? Give your answer in its simplest form.
(b) What percentage of the class prefers English?
(c) Show that the decimal representation of the fraction of students who prefer Science is a terminating decimal.
Context: White Rose Maths small step: Year 7, Autumn, Block 5 (FDP Equivalence), Step 15: Explore Fractions Above One, Decimals And Percentages. Target this step directly in the question.
Fractions and Percentages
2 tickets
A Year 8 class is comparing their test scores. Fatima says 'I got 16 out of 25 on the test, which is 64%'. Jamal says 'I got 13 out of 20, which is 65%'. Fatima argues that since 16/25 is equivalent to 64/100, her percentage must be exactly 64%, while Jamal's 13/20 is equivalent to 65/100, so his is exactly 65%. Therefore, Jamal did better. Is Fatima's reasoning correct? Explain your answer fully, showing your working and using conversions between fractions, decimals and percentages.
Context: White Rose Maths small step: Year 8, Spring, Block 4 (Fractions and Percentages), Step 1: Convert Fluently Between Key Fractions, Decimals And Percentages. Target this step directly in the question.
A student claims that 0.125, 12.5%, and 1/8 are all equivalent.
(a) Is the student correct? Explain your reasoning.
(b) A different student says that 0.125 is also equal to 125%. Explain why this is incorrect, and state the correct percentage equivalent of 0.125.
Context: White Rose Maths small step: Year 8, Spring, Block 4 (Fractions and Percentages), Step 1: Convert Fluently Between Key Fractions, Decimals And Percentages. Target this step directly in the question.
Geometric Reasoning
2 tickets
A regular polygon has interior angles that each measure 162°. Ishaan says, 'This must be a 20-sided polygon because 180 - 162 = 18, and 360 ÷ 18 = 20.' Is Ishaan correct? Explain your reasoning fully, showing your working.
Context: White Rose Maths small step: Year 7, Summer, Block 2 (Geometric Reasoning), Step 8: Find And Use The Angle Sum Of Any Polygon. Target this step directly in the question.
Two parallel lines are crossed by a transversal. One angle formed is labelled as 3x + 20°. The corresponding angle on the other parallel line is labelled as 5x - 40°.
(a) Find the value of x.
(b) Find the size of both angles.
(c) Explain why these two angles must be equal, referring to the geometric property involved.
(Note: All measurements are in degrees.)
Context: White Rose Maths small step: Year 7, Summer, Block 2 (Geometric Reasoning), Step 9: Investigate Angles In Parallel Lines. Target this step directly in the question.
Indices and Roots
1 ticket
A scientist is studying bacteria growth. She calculates that the number of bacteria in a petri dish is 2.5 × 10⁸. After applying an antibiotic, the number reduces to 4 × 10⁵.
Calculate how many times larger the initial bacteria population was compared to the final population. Give your answer in standard form.
(Note: This question assesses your ability to perform calculations with numbers in standard form, including division and expressing the result appropriately.)
Context: White Rose Maths small step: Year 10, Summer, Block 4 (Indices and Roots), Step 8: Calculate With Numbers In Standard Form. Target this step directly in the question.
Know How To Add, Subtract And Multiply Fractions
1 ticket
Work out (a) 3/4 − 1/2 and (b) 2/5 × 3/4. Give each answer as a fraction in its simplest form.
Context: Curated for Vault Viewer promo presentation (Year 10 fractions)
Line Symmetry and Reflection
1 ticket
A shape has vertices at coordinates (2, 1), (4, 1), (4, 3), and (2, 3). It is reflected in the vertical line x = 3. Two students discuss the result:
**Aisha:** "The reflected shape will be a rectangle with vertices at (4, 1), (6, 1), (6, 3), and (4, 3)."
**Ben:** "The reflected shape will be a rectangle with vertices at (1, 1), (3, 1), (3, 3), and (1, 3)."
Who is correct? Explain your reasoning fully, including how you found the coordinates of the reflected shape and why the other student's answer is incorrect.
Context: White Rose Maths small step: Year 8, Summer, Block 3 (Line Symmetry and Reflection), Step 2: Reflect A Shape In A Horizontal Or Vertical Line 1 Shapes( Touching The Line). Target this step directly in the question.
Multiplicative Reasoning
1 ticket
A construction company is laying pipes for a new housing estate in Manchester. They find that 8 workers can complete the pipe-laying in 15 days. The site manager needs to complete the work in 10 days instead. She realises this is an inverse proportion situation.
(a) Write an equation connecting the number of workers (w) and the number of days (d) to complete the work.
(b) Use your equation to calculate how many workers are needed to finish in 10 days.
(c) The site manager checks her calculations and finds she can only get 12 workers. How many days would it take 12 workers to complete the work?
Context: White Rose Maths small step: Year 11, Spring, Block 1 (Multiplicative Reasoning), Step 6: Construct Inverse Proportion Equations. Target this step directly in the question.
Multiply And Divide Integers And Decimals By Powers Of 10
1 ticket
A student calculates 4.5 × 10³ and gets 45,000. Another student calculates 4.5 ÷ 10² and gets 0.045. For each calculation, explain whether the answer is correct or incorrect, and describe what happens to the decimal point when multiplying or dividing by powers of 10.
Context: Auto-generated from Flow tool
Multiplying decimals
1 ticket
A rectangular garden measures 2.5 meters by 3.8 meters. Calculate the area of the garden. Then, explain why your answer makes sense by comparing it to what the area would be if the garden measured 3 meters by 4 meters instead.
Context: Auto-generated from Flow tool
Non-calculator Methods
2 tickets
A rectangular garden at a school in Manchester has length (√12 + √3) metres and width (√12 - √3) metres.
(a) Show that the area of the garden can be written in the form a + b√c, where a, b and c are integers to be found.
(b) The school wants to put fencing around the garden. Calculate the exact perimeter, giving your answer in the simplest surd form.
Context: White Rose Maths small step: Year 10, Summer, Block 2 (Non-calculator Methods), Step 7: Calculate With Surds. Target this step directly in the question.
A Year 10 student is revising for their GCSE maths exam. They need to calculate 4.7 - 1.85 without a calculator. They write down: 4.70 - 1.85 = 3.15.
Explain whether their answer is correct or incorrect. If incorrect, identify the error in their working and calculate the correct answer using a written column subtraction method suitable for non-calculator assessment.
Context: White Rose Maths small step: Year 10, Summer, Block 2 (Non-calculator Methods), Step 1: Mentalwritten/ Methods Of Integerdecimal/ Addition And Subtraction. Target this step directly in the question.
Place Value and Rounding
1 ticket
A Year 7 class at a school in Manchester is collecting data about their town. They find that the population of Manchester is approximately 553,230 people. They need to round this number to the nearest 10, 100, 1,000, 10,000, and 100,000 for different parts of their project.
(a) Complete the table below by rounding 553,230 to each of the required degrees of accuracy.
| Round to the nearest... | Rounded Population |
|-------------------------|--------------------|
| 10 | |
| 100 | |
| 1,000 | |
| 10,000 | |
| 100,000 | |
(b) A student says, 'When I round 553,230 to the nearest 100,000, I get 600,000. But when I round it to the nearest 10,000 first, and then round that result to the nearest 100,000, I get 500,000. This doesn't make sense.' Explain why these two processes give different results and which method is correct for rounding to the nearest 100,000.
Context: White Rose Maths small step: Year 7, Autumn, Block 4 (Place Value and Rounding), Step 5: Round Integers To The Nearest Power Of Ten. Target this step directly in the question.
Prime Numbers and Proof
2 tickets
A student in your class makes the following conjecture: 'All prime numbers are odd numbers.'
1) Is this conjecture true or false?
2) If it is false, provide a counterexample to disprove it.
3) Explain why your counterexample disproves the conjecture.
Context: White Rose Maths small step: Year 7, Summer, Block 5 (Prime Numbers and Proof), Step 10: Use Counterexamples To Disprove A Conjecture. Target this step directly in the question.
Isabella is investigating prime numbers. She notices that 2, 3, 5, 7, 11, and 13 are all prime. She makes the following conjecture: 'All prime numbers are odd numbers.'
(a) Explain why Isabella's conjecture is incorrect.
(b) Isabella then tests a new conjecture: 'If you add 1 to any prime number (except 2), the result is always an even number.' Is this conjecture always true, sometimes true, or never true? Justify your answer with clear mathematical reasoning.
Context: White Rose Maths small step: Year 7, Summer, Block 5 (Prime Numbers and Proof), Step 9: Make And Test Conjectures. Target this step directly in the question.
Probability
3 tickets
A bag contains 4 red counters and 6 blue counters. Two counters are taken from the bag at random, one after the other. The first counter is NOT replaced before the second is taken.
Sam says: 'The probability that both counters are red is (4/10) × (4/10) = 16/100 or 0.16'
Is Sam correct? Explain your reasoning fully, showing your working.
Context: White Rose Maths small step: Year 10, Spring, Block 6 (Probability), Step 7: Calculate Probability With Independent Events. Target this step directly in the question.
A bag contains 5 red counters and 3 blue counters. Two counters are taken from the bag at random, one after the other. The first counter is NOT replaced before the second is taken.
Explain whether the events 'first counter is red' and 'second counter is blue' are independent. Justify your answer with calculations.
Context: White Rose Maths small step: Year 9, Summer, Block 4 (Probability), Step 4: Independent Events. Target this step directly in the question.
A bag contains 3 red counters, 5 blue counters and some green counters. Two counters are taken from the bag at random, without replacement. The probability that both counters are the same colour is 11/36.
Use a tree diagram or other suitable diagram to work out how many green counters are in the bag.
Context: White Rose Maths small step: Year 9, Summer, Block 4 (Probability), Step 7: Use Diagrams To Work Out Probabilities. Target this step directly in the question.
Probability tree diagrams
1 ticket
A bag contains 3 red marbles and 2 blue marbles. Two marbles are drawn from the bag without replacement. Using a probability tree diagram, find the probability that the two marbles are different colors. Show your work and explain why you multiply or add probabilities at each stage.
Context: Auto-generated from Flow tool
Product of prime factors
1 ticket
A number is expressed as 2² × 3 × 5³. Without calculating the actual number, explain whether it is divisible by 8, 9, 15, and 25. Justify your reasoning for each case using the prime factorisation.
Pythagoras' Theorem
1 ticket
A right-angled triangle has sides of length 6 cm and 8 cm. Is the hypotenuse necessarily 10 cm? Explain your reasoning with a diagram or calculation.
Context: Auto-generated from Flow tool
Rates
2 tickets
A water tank is being filled at a constant rate. The graph shows the volume of water in the tank over time.
[Imagine a graph with axes labelled: Time (minutes) on the horizontal axis, Volume (litres) on the vertical axis. The line is straight, starting at (0, 0) and passing through the point (5, 150).]
1. What is the rate of flow into the tank in litres per minute?
2. The tank has a total capacity of 750 litres. How long will it take to fill the tank completely from empty?
3. After 8 minutes of filling, the flow rate is suddenly doubled. How would this change be shown on the graph? Describe the new line segment from this point onwards.
Context: White Rose Maths small step: Year 9, Summer, Block 3 (Rates), Step 5: Solve Flow Problems And Their Graphs. Target this step directly in the question.
A delivery van travels 120 kilometres in 2 hours and 30 minutes. The van's fuel consumption is 8 litres per 100 kilometres. Fuel costs £1.45 per litre. Calculate the van's average speed in kilometres per hour, the total fuel cost for the journey, and the fuel cost per hour of travel.
Context: White Rose Maths small step: Year 9, Summer, Block 3 (Rates), Step 6: Convert Compound Units. Target this step directly in the question.
Ratio and Proportion
1 ticket
Two different shops in Manchester are selling the same brand of pens.
Shop A: Pack of 5 pens for £3.75
Shop B: Pack of 8 pens for £6.00
Which shop offers the better value for money? Justify your answer with clear calculations and reasoning.
Context: White Rose Maths small step: Year 9, Summer, Block 2 (Ratio and Proportion), Step 6: Solve Best‘ Buy’ Problems. Target this step directly in the question.
Sets and Probability
1 ticket
A bag contains some coloured counters. The probability of picking a red counter is 0.4. The probability of picking a blue counter is 0.35. The probability of picking a green counter is 0.2. The bag also contains yellow counters.
1. Place the probabilities of picking red, blue, and green counters on a probability scale from 0 to 1.
2. Is it possible for the bag to contain only red, blue, green, and yellow counters? Explain your reasoning.
3. What is the probability of picking a yellow counter? Show your working.
Context: White Rose Maths small step: Year 7, Summer, Block 4 (Sets and Probability), Step 9: Understand And Use The Probability Scale. Target this step directly in the question.
Simultaneous equations
1 ticket
Solve the simultaneous equations using the substitution method: y = 2x - 3 and 3x + 2y = 16. Explain why you chose to substitute one particular equation into the other, and what would happen if you made the opposite substitution choice.
Context: Focus on substitution method
The Data Handling Cycle
3 tickets
A Year 8 class at a school in Manchester collected data on the time spent on homework each evening. They grouped the data into intervals: 0-30 minutes, 31-60 minutes, 61-90 minutes, and 91-120 minutes. The frequency table shows: 0-30 mins: 4 students, 31-60 mins: 12 students, 61-90 mins: 8 students, 91-120 mins: 6 students.
1. Explain why you cannot calculate the exact mean from this grouped data.
2. Estimate the mean time spent on homework. Show your working and state any assumptions you make.
3. A student says, 'The modal class is 31-60 minutes, so most students spent exactly 45 minutes on homework.' Is this statement correct? Explain your reasoning.
Context: White Rose Maths small step: Year 8, Summer, Block 4 (The Data Handling Cycle), Step 8: Represent And Interpret Grouped Quantitative Data. Target this step directly in the question.
A Year 8 class at a school in Manchester is planning a statistical enquiry about how students travel to school. They want to find out if there is a difference between how Year 7 students and Year 8 students travel.
Explain the first two stages of the data handling cycle they must complete to set up this enquiry. For each stage, give a specific example of what they would need to decide or do. Identify one common mistake students make when setting up an enquiry like this and explain why it is a problem.
Context: White Rose Maths small step: Year 8, Summer, Block 4 (The Data Handling Cycle), Step 1: Set Up A Statistical Enquiry. Target this step directly in the question.
A student is designing a questionnaire to find out how many hours per week Year 9 students at their school spend on homework. They propose the following question: 'How much time do you spend on homework?' with the response options: 'A little', 'Some', 'A lot'. Criticise this question design. Suggest two specific improvements to make it more effective for collecting useful data, and explain why each improvement is needed.
Context: White Rose Maths small step: Year 8, Summer, Block 4 (The Data Handling Cycle), Step 2: Design And Criticise Questionnaires. Target this step directly in the question.
Types of Number and Sequences
1 ticket
A Year 10 class is discussing factors and multiples. Priya says: 'For any two whole numbers, the largest factor of the first number is always less than or equal to the smallest multiple of the second number.' Is Priya correct? Justify your answer with a clear mathematical explanation and at least two specific examples that support your reasoning.
Context: White Rose Maths small step: Year 10, Summer, Block 3 (Types of Number and Sequences), Step 1: Understand The Difference Between Factors And Multiples. Target this step directly in the question.
completing the square
1 ticket
A student is asked to complete the square for the quadratic expression x² + 6x + 10. They write: x² + 6x + 10 = (x + 3)² + 1. Is their answer correct? Explain your reasoning by showing the correct method and identifying any errors in their working.
Context: Auto-generated from Flow tool
laws of indices
1 ticket
Simplify the expression (2x³y²)⁴ ÷ (4x²y⁵)² and explain why your answer cannot contain negative exponents.
Context: Auto-generated from Flow tool
multiplying fractio9ns
1 ticket
A recipe requires 2/3 cup of flour to make 12 cookies. If you want to make 3/4 of the recipe, how much flour will you need? Explain your reasoning.
nonexistent_topic_xyz_123
1 ticket
A student claims that when you multiply any two numbers together, the result is always larger than either of the original numbers. Is this statement always true, sometimes true, or never true? Provide at least two specific examples to justify your answer, including one that shows why the student might think this way and one that reveals why their reasoning is incomplete.
Context: Auto-generated from Flow tool
quadratic equations
1 ticket
A student is solving the quadratic equation x² - 5x + 6 = 0. They correctly factor it as (x - 2)(x - 3) = 0, but then write the solutions as x = -2 and x = -3. Explain what misconception the student has, and show the correct method to find the solutions.
Context: Auto-generated from Flow tool
test
1 ticket
A student claims that when you multiply two negative numbers, the result is always negative. Is this correct? Explain your reasoning using a real-world example or mathematical principle.
Context: Auto-generated from Flow tool
the quadratic formula
1 ticket
A student solves the quadratic equation 2x² - 8x + 8 = 0 using the quadratic formula and gets x = 2. Another student says this is incorrect because quadratic equations should have two solutions. Who is right? Explain your reasoning using the quadratic formula and what it reveals about this specific equation.
Context: Auto-generated from Flow tool