## Mr Barton Maths Podcast

Long-form conversations about teaching and learning with craig barton.

## Angles and ratio: TES Maths Resource of the Week

To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here

What is it? Ever since ratio was given an increased value in the current GCSE specification, it has been sneaking in to all sorts of topics and questions. Gone are the days when all students needed to know how to do was simplify a ratio or share a few sweets out. Now ratio pops up in algebra, probability, fractions and percentages to name but a few; you name the topic and sure enough ratio will be there.

How can it be used? I have been on the lookout for resources to help my students gain valuable practice in combining different topics with ratio. That is where this wonderful resource comes in handy. It is a set of questions that requires both knowledge of angle facts and ratio to solve them and there are some combinations that I would never have thought of myself, such as basic angle facts, triangle properties, and circle theorems.

Thanks for sharing! Craig Barton

Download: Angles and ratio View the author’s other resources

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## 15 Ratio Questions And Practice Problems (KS3 & KS4): Harder GCSE Exam Style Questions Included

Sophie Bessemer

Ratio questions appear throughout KS3 and KS4 building on what students have learnt in primary school. Here we provide a range of ratio questions and practice problems of varying complexity to use with your own students in class or as inspiration for creating your own.

## What is ratio?

Ratio is used to compare the size of different parts of a whole. For example, in a whole class of 30 students there are 10 girls and 20 boys. The ratio of girls:boys is 10:20 or 1:2. For every one girl there are two boys.

## Uses of ratio

You might see ratios written on maps to show the scale of the map or telling you the currency exchange rate if you are going on holiday.

Ratio will be seen as a topic in its own right as well as appearing within other topics. An example of this might be the area of two shapes being in a given ratio or the angles of a shape being in a given ratio.

## Ratio in KS3 and KS4

In KS3, ratio questions will involve writing and simplifying ratios, using equivalent ratios, dividing quantities into a given ratio and will begin to look at solving problems involving ratio. In KS4 these skills are recapped and the focus will be more on problem solving questions using your knowledge of ratio.

Download this 15 Ratio Questions And Practice Problems (KS3 & KS4) Worksheet

Help your students prepare for their Maths GSCE with this free Ratio worksheet of 15 multiple choice questions and answers.

GCSE MATHS 2024: STAY UP TO DATE Join our email list to stay up to date with the latest news, revision lists and resources for GCSE maths 2024. We’re analysing each paper during the course of the 2024 GCSEs in order to identify the key topic areas to focus on for your revision. Thursday 16th May 2024: GCSE Maths Paper 1 2024 Analysis & Revision Topic List Monday 3rd June 2024: GCSE Maths Paper 2 2024 Analysis & Revision Topic List Monday 10th June 2024: GCSE Maths Paper 3 2024 Analysis GCSE 2024 dates GCSE 2024 results GCSE results 2023

## Proportion and ratio

Ratio often appears alongside proportion and the two topics are related. Whereas ratio compares the size of different parts of a whole, proportion compares the size of one part with the whole. Given a ratio, we can find a proportion and vice versa.

Take the example of a box containing 7 counters; 3 red counters and 4 blue counters:

The ratio of red counters:blue counters is 3:4.

For every 3 red counters there are four blue counters.

The proportion of red counters is \frac{3}{7} and the proportion of blue counters is \frac{4}{7}

3 out of every 7 counters are red and 4 out of every 7 counters are blue.

## Direct proportion and inverse proportion

In KS4, we learn about direct proportion and inverse proportion. When two things are directly proportional to each other, one can be written as a multiple of the other and therefore they increase at a fixed ratio.

## How to solve a ratio problem

When looking at a ratio problem, the key pieces of information that you need are what the ratio is, whether you have been given the whole amount or a part of the whole and what you are trying to work out.

If you have been given the whole amount you can follow these steps to answer the question:

- Add together the parts of the ratio to find the total number of shares
- Divide the total amount by the total number of shares
- Multiply by the number of shares required

If you have been been given a part of the whole you can follow these steps:

- Identify which part you have been given and how many shares it is worth
- Use equivalent ratios to find the other parts
- Use the values you have to answer your problem

Ratio tables are another technique for solving ratio problems.

## How to solve a proportion problem

As we have seen, ratio and proportion are strongly linked. If we are asked to find what proportion something is of a total, we need to identify the amount in question and the total amount. We can then write this as a fraction:

Proportion problems can often be solved using scaling. To do this you can follow these steps:

- Identify the values that you have been given which are proportional to each other
- Use division to find an equivalent relationship
- Use multiplication to find the required relationship

## Real life ratio problems and proportion problems

Ratio is all around us. Let’s look at some examples of where we may see ratio and proportion:

## Cooking ratio question

When making yoghurt, the ratio of starter yogurt to milk should be 1:9. I want to make 1000ml of yoghurt. How much milk should I use?

Here we know the full amount – 1000ml.

The ratio is 1:9 and we want to find the amount of milk.

- Total number of shares = 1 + 9 = 10
- Value of each share: 1000 ÷ 10 = 100
- The milk is 9 shares so 9 × 100 = 900

I need to use 900ml of milk.

## Maps ratio question

The scale on a map is 1:10000. What distance would 3.5cm on the map represent in real life?

Here we know one part is 3.5. We can use equivalent ratios to find the other part.

The distance in real life would be 35000cm or 350m.

## Speed proportion question

I travelled 60 miles in 2 hours. Assuming my speed doesn’t change, how far will I travel in 3 hours?

This is a proportion question.

- I travelled 60 miles in 2 hours.
- Dividing by 2, I travelled 30 miles in one hour
- Multiplying by 3, I would travel 90 miles in 3 hours

## KS2 ratio questions

Ratio is introduced in KS2. Writing and simplifying ratios is explored and the idea of dividing quantities in a given ratio is introduced using word problems such as the question below, before being linked with the mathematical notation of ratio.

## Example KS2 worded question

Richard has a bag of 30 sweets. Richard shares the sweets with a friend. For every 3 sweets Richard eats, he gives his friend 2 sweets. How many sweets do they each eat?

## KS3 ratio questions

In KS3 ratio questions ask you to write and simplify a ratio, to divide quantities into a given ratio and to solve problems using equivalent ratios.

You may also like:

- Year 6 Maths Test
- Year 7 Maths Test
- Year 8 Maths Test
- Year 9 Maths Test

## Ratio questions year 7

1. In Lucy’s class there are 12 boys and 18 girls. Write the ratio of girls:boys in its simplest form.

The question asks for the ratio girls:boys so girls must be first and boys second. It also asks for the answer in its simplest form.

2. Gertie has two grandchildren, Jasmine, aged 2, and Holly, aged 4. Gertie divides £30 between them in the ratio of their ages. How much do they each get?

Jasmine £15, Holly £15

Jasmine £15, Holly £7.50

Jasmine £10, Holly £20

Jasmine £2, Holly £4

£30 is the whole amount.

Gertie divides £30 in the ratio 2:4.

The total number of shares is 2 + 4 = 6.

Each share is worth £30 ÷ 6 = £5.

Jasmine gets 2 shares, 2 x £5 = £10.

Holly gets 4 shares, 4 x £5 = £20.

## Ratio questions year 8

3. The ratio of men:women working in a company is 3:5. What proportion of the employees are women?

In this company, the ratio of men:women is 3:5 so for every 3 men there are 5 women.

This means that for every 8 employees, 5 of them are women.

Therefore \frac{5}{8} of the employees are women.

4. The ratio of cups of flour:cups of water in a pizza dough recipe is 9:4. A pizza restaurant makes a large quantity of dough, using 36 cups of flour. How much water should they use?

The ratio of cups of flour:cups of water is 9:4. We have been given one part so we can work this out using equivalent ratios.

## Ratio questions year 9

5. The angles in a triangle are in the ratio 3:4:5. Work out the size of each angle.

30^{\circ} , 40^{\circ} and 50^{\circ}

22.5^{\circ}, 30^{\circ} and 37.5^{\circ}

60^{\circ} , 60^{\circ} and 60^{\circ}

45^{\circ} , 60^{\circ} and 75^{\circ}

The angles in a triangle add up to 180 ^{\circ} . Therefore 180 ^{\circ} is the whole and we need to divide 180 ^{\circ} in the ratio 3:4:5.

The total number of shares is 3 + 4 + 5 = 12.

Each share is worth 180 ÷ 12 = 15 ^{\circ} .

3 shares is 3 x 15 = 45 ^{\circ} .

4 shares is 4 x 15 = 60 ^{\circ} .

5 shares is 5 x 15 = 75 ^{\circ} .

6. Paint Pro makes pink paint by mixing red paint and white paint in the ratio 3:4.

Colour Co makes pink paint by mixing red paint and white paint in the ratio 5:7.

Which company uses a higher proportion of red paint in their mixture?

They are the same

It is impossible to tell

The proportion of red paint for Paint Pro is \frac{3}{7}

The proportion of red paint for Colour Co is \frac{5}{12}

We can compare fractions by putting them over a common denominator using equivalent fractions

\frac{3}{7} = \frac{36}{84} \hspace{3cm} \frac{5}{12}=\frac{35}{84}

\frac{3}{7} is a bigger fraction so Paint Pro uses a higher proportion of red paint.

## KS4 ratio questions

In KS4 we apply the knowledge that we have of ratios to solve different problems. Ratio is an important topic in all exam boards, including Edexcel, AQA and OCR. Ratio questions can be linked with many different topics, for example similar shapes and probability, as well as appearing as problems in their own right.

Read more: Question Level Analysis Of Edexcel Maths Past Papers (Foundation)

## Ratio GCSE exam questions foundation

7. The students in Ellie’s class walk, cycle or drive to school in the ratio 2:1:4. If 8 students walk, how many students are there in Ellie’s class altogether?

We have been given one part so we can work this out using equivalent ratios.

The total number of students is 8 + 4 + 16 = 28

8. A bag contains counters. 40% of the counters are red and the rest are yellow.

Write down the ratio of red counters:yellow counters. Give your answer in the form 1:n.

If 40% of the counters are red, 60% must be yellow and therefore the ratio of red counters:yellow counters is 40:60. Dividing both sides by 40 to get one on the left gives us

Since the question has asked for the ratio in the form 1:n, it is fine to have decimals in the ratio.

9. Rosie and Jim share some sweets in the ratio 5:7. If Jim gets 12 sweets more than Rosie, work out the number of sweets that Rosie gets.

Jim receives 2 shares more than Rosie, so 2 shares is equal to 12.

Therefore 1 share is equal to 6. Rosie receives 5 shares: 5 × 6 = 30.

10. Rahim is saving for a new bike which will cost £480. Rahim earns £1500 per month. Rahim spends his money on bills, food and extras in the ratio 8:3:4. Of the money he spends on extras, he spends 80% and puts 20% into his savings account.

How long will it take Rahim to save for his new bike?

Rahim’s earnings of £1500 are divided in the ratio of 8:3:4.

The total number of shares is 8 + 3 + 4 = 15.

Each share is worth £1500 ÷ 15 = £100 .

Rahim spends 4 shares on extras so 4 × £100 = £400 .

20% of £400 is £80.

The number of months it will take Rahim is £480 ÷ £80 = 6

## Ratio GCSE exam questions higher

11. The ratio of milk chocolates:white chocolates in a box is 5:2. The ratio of milk chocolates:dark chocolates in the same box is 4:1.

If I choose one chocolate at random, what is the probability that that chocolate will be a milk chocolate?

To find the probability, we need to find the fraction of chocolates that are milk chocolates. We can look at this using equivalent ratios.

To make the ratios comparable, we need to make the number of shares of milk chocolate the same in both ratios. Since 20 is the LCM of 4 and 5 we will make them both into 20 parts.

We can now say that milk:white:dark is 20:8:5. The proportion of milk chocolates is \frac{20}{33} so the probability of choosing a milk chocolate is \frac{20}{33} .

12. In a school the ratio of girls:boys is 2:3.

25% of the girls have school dinners.

30% of the boys have school dinners.

What is the total percentage of students at the school who have school dinners?

In this question you are not given the number of students so it is best to think about it using percentages, starting with 100%.

100% in the ratio 2:3 is 40%:60% so 40% of the students are girls and 60% are boys.

25% of 40% is 10%.

30% of 60% is 18%.

The total percentage of students who have school dinners is 10 + 18 = 28%.

13. For the cuboid below, a:b = 3:1 and a:c = 1:2.

Find an expression for the volume of the cuboid in terms of a.

If a:b = 3:1 then b=\frac{1}{3}a

If a:c = 1:2 then c=2a.

## Difficult ratio GCSE questions

14. Bill and Ben win some money in their local lottery. They share the money in the ratio 3:4. Ben decides to give £40 to his sister. The amount that Bill and Ben have is now in the ratio 6:7.

Calculate the total amount of money won by Bill and Ben.

Initially the ratio was 3:4 so Bill got £3a and Ben got £4a. Ben then gave away £40 so he had £(4a-40).

The new ratio is 3a:4a-40 and this is equal to the ratio 6:7.

Since 3a:4a-40 is equivalent to 6:7, 7 lots of 3a must be equal to 6 lots of 4a-40.

The initial amounts were 3a:4a. a is 80 so Bill received £240 and Ben received £320.

The total amount won was £560.

15. On a farm the ratio of pigs:goats is 4:1. The ratio of pigs:piglets is 1:6 and the ratio of gots:kids is 1:2.

What fraction of the animals on the farm are babies?

The easiest way to solve this is to think about fractions.

\\ \frac{4}{5} of the animals are pigs, \frac{1}{5} of the animals are goats.

\frac{1}{7} of the pigs are adult pigs, so \frac{1}{7} of \frac{4}{5} is \frac{1}{7} \times \frac{4}{5} = \frac{4}{35}

\frac{6}{7} of the pigs are piglets, so \frac{6}{7} of \frac{4}{5} is \frac{6}{7} \times \frac{4}{5} = \frac{24}{35}

\frac{1}{3} of the goats are adult goats, so \frac{1}{3} of \frac{1}{5} is \frac{1}{3} \times \frac{1}{5} = \frac{1}{15}

\frac{2}{3} of the goats are kids, so \frac{2}{3} of \frac{1}{5} is \frac{2}{3} \times \frac{1}{5} = \frac{2}{15}

The total fraction of baby animals is \frac{24}{35} + \frac{2}{15} = \frac{72}{105} +\frac{14}{105} = \frac{86}{105}

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## Related articles

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Each set of exam papers contains the three papers that your students will expect to find in their GCSE mathematics exam.

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## 20 December 2017

New gcse: ratio.

- Mel from JustMaths collated ratio Higher GCSE questions from sample and specimen papers here , and has written up her solutions here .
- If you subscribe to MathsPad then you'll be pleased to hear that they have lovely resources for ratio including a set of questions for Higher GCSE with loads of examples like the problems I've featured in this post.
- Don Steward has plenty of ratio tasks including his set of ' Harder Ratio Questions ' and a really helpful collection of GCSE ratio and proportion questions .
- On MathsBot you can generate ratio questions, revision grids and practice papers. Select 'ratio, proportion and rates of change' at the top.
- There are exam style questions in this collection from Lucy Kilgariff on TES.
- OCR has a 'Calculations with Ratio' Topic Check In and AQA has a Ratio and Proportion Topic Test .
- David Morse of Maths4Everyone has shared a set of revision exercises and ratio exam style questions .

## 20 comments:

My ratio pages don't get much attention - not sure why since I think they're instructive and easy to use. They don't support the particular type of harder questions described in the post (but I'll look to add something along those lines), but they do help understanding the concept of a ratio and it's utility. Manipulation of ratio quantities: http://thewessens.net/ClassroomApps/Main/ratios.html?topic=number&path=Main&id=7 Introduction to the ratio concept: http://www.thewessens.net/blog/2015/03/19/ratios-the-super-fractions/ Bar model visualisation of ratios: http://thewessens.net/ClassroomApps/Models/BarModels/visualfractionratio.html?topic=models&path=Models&id=17 Multiplicative word problems: http://thewessens.net/ClassroomApps/Models/BarModels/multiplicationwordproblems.html?topic=models&path=Models&id=8 Ken

Fantastic! Thanks Ken.

Thanks so much for your blog on ratio question types. Although I've been a maths teacher/tutor for over 30 year, ratio has always been a bug bear for me. I could wing it with old style gcse because I learnt the types of solutions required, however I have been stressed on the new types. This blog has made me think through ratios and I am certainly a lot happier. Bryan

Excellent, I'm so pleased it helps.

On your fractions approach, a quick trick is to realise that a/c = a/b x b/c. Makes it quite quick to work out (That is, if the students are good with cancelling down when multiplying). However, what I find confuses students about writing ratios as fractions is that it confuses the part:part idea of a ratio with the part:whole idea of a fraction. Perhaps that's why it's somewhat counter-intuitive. Also, final point is that ratios (fractions) and vectors is another application of harder ratio questions that often pops up on the new GCSE. Thanks for the post, Farah

Thanks for the comment!

This is a fabulous resource on work that is missing from the new GCSE texts that I have seen. Lovely challeging questions to make students think.

Thanks! Glad it's helpful.

I've been using equivalent ratios for these type of questions. Find what doesn't change - the total number of sweets. Write ratios as equivalent ratios where the parts that doesn't change are the same. 3:7 has 10 parts, 3:5 has 8 parts LCM of 8 and 10 is 40 Ratios are 12:28 and 15:25 Number of sweets given is 3. Also works for following question Ratio of blue to red counters in a bag is 1:2, I add 12 blue counters and the ratio is 5:7. How many red counters are in the bag? What doesn't change? Red counters LCM of 2 and 7 is 14 Ratios are 7:14 and 10:14 3 parts are 12 counters, 1 part is 4 counters and 14 parts are 56 red counters. Also Jill is 4 times older than Jack. In 14 years time the ratio of Jack's age to Jill is 5:7. How old is Jill now? Ratios are 1:4 and 5:7. What doesn't change? The difference between their ages Find two equivalent ratios where difference between them is the same. 4 - 1 = 3 and 7 - 5 = 2 LCM of 2 and 3 is 6 Equivalent ratios are 2:8 and 15:21 13 parts = 26 years, 1 part is 2 years, Jill is 16.

This is the approach I use. I think it's logical.

Thank you! Yes, this is logical. Same approach as bar modelling (but without the visual).

Oops, my mistake, third example should be .....in 26 years time the ratio of their ages is 5:7 ..... I did try to represent these using bar modelling at first but struggled to find a model that was intuitive and actually helped with the question. I would be grateful if anyone has ideas on this.

Although some bar modelling experts would disagree, I don't think bar modelling is intuitive/helpful for harder ratio questions. Bar modelling is fantastic for easier ratio questions, but when the questions get more complicated it's often really hard to figure out how to draw the scenario - definitely not as easy as some people make out!

Thank you for the post. Brilliant as usual. I actually did the sweets question in my class once. I simply said that Alice fraction of sweets changed from 7/10 to 5/8 when she gave the 3 sweets away. If we just subtract those fractions, the fraction remaining, 7/10 - 5/8 = 3/40. This means that Alice originally had 40 sweets.

Hadnt considered tis method but I love it

Thanks Stephen. I guess it makes sense, as the fraction lost is equivalent to the 3 sweets divided by the total.

Love this! Thanks for sharing.

Hi Jo, thanks for the post which I came across via a tweet you put out a couple of days ago - which also tied in with a question and the same method I saw in my step-daughters book the very next day - freaky! It is a more compact method than I would normally use in my teaching and will be switching to it. I think the only tweak I might make is to write the algebra ratio above the numeric one so the starting fractions are (7x-3)/5 : (3x+3)/3 The reason being that some students might get a little scared seeing algebra as part of the denominator but less so when faced with a number.

Good idea - thank you!

Hi Jo, One method I use when teaching questions like the first one above (Alice gives 3 sweets to Olivia) is the following. To begin with Alice has 7/10 of the sweets and then after giving three to Olivia, her share has reduced to 5/8 of the sweets. So Alice's share has reduced by (7/10 - 5/8=) 3/40 which is equivalent to 3 sweets, therefore there must be 40 sweets in total. Students can then proceed in answering the relevant question. I must admit I only use this method with the top sets.

## Qwen2-VL: To See the World More Clearly

DEMO GITHUB HUGGING FACE MODELSCOPE API DISCORD

After a year’s relentless efforts, today we are thrilled to release Qwen2-VL ! Qwen2-VL is the latest version of the vision language models based on Qwen2 in the Qwen model familities. Compared with Qwen-VL, Qwen2-VL has the capabilities of:

SoTA understanding of images of various resolution & ratio : Qwen2-VL achieves state-of-the-art performance on visual understanding benchmarks, including MathVista, DocVQA, RealWorldQA, MTVQA, etc.

Understanding videos of 20min+ : Qwen2-VL can understand videos over 20 minutes for high-quality video-based question answering, dialog, content creation, etc.

Agent that can operate your mobiles, robots, etc. : with the abilities of complex reasoning and decision making, Qwen2-VL can be integrated with devices like mobile phones, robots, etc., for automatic operation based on visual environment and text instructions.

Multilingual Support : to serve global users, besides English and Chinese, Qwen2-VL now supports the understanding of texts in different languages inside images, including most European languages, Japanese, Korean, Arabic, Vietnamese, etc.

We opensource Qwen2-VL-2B and Qwen2-VL-7B with Apache 2.0 license, and we release the API of Qwen2-VL-72B! The opensource is integrated to Hugging Face Transformers, vLLM, and other third-party frameworks. Hope you enjoy!

## Performance #

We evaluate our model’s visual capabilities across six key dimensions: complex college-level problem-solving, mathematical abilities, document and table comprehension, multilingual text-image understanding, general scenario question-answering, video comprehension, and agent-based interactions. Overall, our 72B model showcases top-tier performance across most metrics, often surpassing even closed-source models like GPT-4o and Claude 3.5-Sonnet. Notably, it demonstrates a significant edge in document understanding.

At the 7B scale, we’ve managed to retain support for image, multi-image, and video inputs, delivering competitive performance in a more cost-effective model size. Specifically, our model excels in document understanding tasks such as DocVQA and in multilingual text understanding from images, as assessed by MTVQA, establishing state-of-the-art performance.

Additionally, we’re excited to introduce a smaller 2B model, optimized for potential mobile deployment. Despite its compact size, this model boasts strong performance in image, video, and multilingual comprehension. It particularly shines in video-related tasks, document understanding, and general scenario question-answering when compared to other models of similar scale.

## 2. Visual Reasoning: Solving Real-World Problems #

In this iteration, we have significantly enhanced Qwen2-VL’s mathematical and coding proficiencies. The model is not only capable of solving problems by analyzing pictures but can also interpret and solve complex mathematical problems through chart analysis. Extremely aspect-ratio-distorted images can also be correctly interpreted. Additionally, we have reinforced the model’s capability to extract information from real-world images and charts and improved its instruction-following skills. This fusion of visual perception and logical reasoning empowers the model to tackle practical issues, bridging the gap between abstract concepts and tangible solutions.

To solve the “Snake in Matrix” problem, we need to implement a function that takes the size of the matrix n and a list of commands, and returns the final position of the snake after executing all the commands. Here’s a step-by-step approach to solve this problem:

Initialize Variables :

- Initialize the current position of the snake as 0 .
- Initialize the direction of the snake as “RIGHT” (initially, the snake moves to the right).

Define Movement Functions :

- Create a function to move the snake based on the current direction and the size of the matrix n .
- Update the position of the snake accordingly.

Process Commands :

- Iterate through each command in the list of commands.
- For each command, update the direction and position of the snake.

Return Final Position :

- After processing all commands, return the final position of the snake.

Here’s the Python code to implement the solution:

This code defines a class Solution with a method finalPositionOfSnake that takes the size of the matrix n and a list of commands, and returns the final position of the snake after executing all the commands. The movement functions ( move_right , move_down , move_left , move_up ) are used to update the position of the snake based on the current direction.

Since triangle ABC is isosceles, we know that AC = BC. Therefore, we can set the expressions for AC and BC equal to each other and solve for x:

4x + 1 = 5x - 0.5

Subtracting 4x from both sides, we get:

1 = x - 0.5

Adding 0.5 to both sides, we get:

Now that we know the value of x, we can substitute it back into the expression for AC to find its length:

AC = 4x + 1

AC = 4(1.5) + 1

Therefore, the length of AC is 7.

The page titles in the screenshot of the search result are:

- QwenLM/Qwen2
- Qwen2 - a Qwen Collection
- Qwen2-Math，新一代数学模型
- Qwen/Qwen2-7B-Instruct
- [2407.10671] Qwen2 Technical Report

To determine the number of days between Ruka’s and Yuki’s birthdays, we need to calculate the difference between their respective birth dates.

- Ruka’s birthday is on June 24.
- Yuki’s birthday is on September 17.

Let’s break it down step by step:

From June 24 to June 30:

- June 24 to June 30 is 6 days.

From July 1 to August 31:

- July has 31 days.
- August has 31 days.
- Total days in July and August: 31 + 31 = 62 days.

From September 1 to September 17:

- September 1 to September 17 is 17 days.

Now, we add all these days together:

- June 24 to June 30: 6 days
- July 1 to August 31: 62 days
- September 1 to September 17: 17 days

Total days = 6 + 62 + 17 = 85 days

Therefore, there are 85 days between Ruka’s and Yuki’s birthdays.

以下是图中每日的最高气温和最低气温整理成的表格：

日期 | 最高气温 | 最低气温 |
---|---|---|

08/12 | 31°C | 23°C |

08/13 | 30°C | 22°C |

08/14 | 30°C | 23°C |

08/15 | 31°C | 24°C |

08/16 | 31°C | 24°C |

08/17 | 30°C | 24°C |

08/18 | 30°C | 23°C |

08/19 | 30°C | 22°C |

## 3. Video Understanding and Live Chat #

Beyond static images, Qwen2-VL extends its prowess to video content analysis. It can summarize video content, answer questions related to it, and maintain a continuous flow of conversation in real-time, offering live chat support. This functionality allows it to act as a personal assistant, helping users by providing insights and information drawn directly from video content.

## 4. Visual Agent Capabilities: Function Calling and Visual Interactions. #

Qwen2-VL demonstrates strong potential as a visual agent, facilitating interactions similar to human perceptions of the world.

- The model facilitates Function Calling, enabling it to harness external tools for real-time data retrieval – be it flight statuses, weather forecasts, or package tracking – by deciphering visual cues. This integration of visual interpretation with functional execution elevates its utility, making it a powerful tool for information management and decision-making.
- Visual Interactions represent a significant stride towards mimicking human perception. By allowing the model to engage with visual stimuli akin to human senses, we’re pushing the boundaries of AI’s ability to perceive and respond to its environment. This capability paves the way for more intuitive and immersive interactions, where Qwen2-VL acts not just as an observer, but an active participant in our visual experiences.

Certainly, the model is not perfect and has some limitations that I hope you can understand. For example, the model is unable to extract audio from videos, and its knowledge is only up to date as of June 2023. Additionally, the model cannot guarantee complete accuracy when processing complex instructions or scenarios, and it is relatively weak in tasks involving counting, character recognition, and 3D spatial awareness.

## Model Architecture #

Overall, we’ve continued with the Qwen-VL architecture, which leverages a Vision Transformer (ViT) model and Qwen2 language models. For all these variants, we utilized a ViT with approximately 600M parameters, designed to handle both image and video inputs seamlessly. To further enhance the model’s ability to effectively perceive and comprehend visual information in videos, we introduced several key upgrades:

- A key architectural improvement in Qwen2-VL is the implementation of Naive Dynamic Resolution support . Unlike its predecessor, Qwen2-VL can handle arbitrary image resolutions, mapping them into a dynamic number of visual tokens, thereby ensuring consistency between the model input and the inherent information in images. This approach more closely mimics human visual perception, allowing the model to process images of any clarity or size.
- Another key architectural enhancement is the innovation of Multimodal Rotary Position Embedding (M-ROPE) . By deconstructing the original rotary embedding into three parts representing temporal and spatial (height and width) information，M-ROPE enables LLM to concurrently capture and integrate 1D textual, 2D visual, and 3D video positional information.

## Developing with Qwen2-VL #

To use the largest Qwen2-VL model, Qwen2-VL-72B, you can access it through our official API (sign up the account and obtain the API key through DashScope ) temporarily as demonstrated below:

The 2B and 7B models of the Qwen2-VL series are open-sourced and accessible on Hugging Face and ModelScope. You can explore the model cards for detailed usage instructions, features, and performance metrics. Below we provide an example of the simplest usage with HF Transformers.

Make sure you install transformers from source by pip install git+https://github.com/huggingface/transformers as codes for Qwen2-VL were just merged into the main branch. If you didn’t install it from source, you may encounter the following error:

We offer a toolkit to help you handle various types of visual input more conveniently. It supports inputs including base64, URLs, and interleaved images and videos. You can install it using the following command:

Here is a code snippet for demonstration. Specifically, we recommend using flash attention 2 if possible for the sake of acceleration and memory saving.

To facilitate seamless integration and use of our latest models, we support a range of tools and frameworks in the open-source ecosystem, including quantization ( AutoGPTQ , AutoAWQ ), deployment ( vLLM ), finetuning ( Llama-Factory ), etc.

Both the opensource Qwen2-VL-2B and Qwen2-VL-7B are under Apache 2.0.

## What’s Next #

We look forward to your feedback and the innovative applications you will build with Qwen2-VL. In the near future, we are going to build stronger vision language models upon our next-version language models and endeavor to integrate more modalities towards an omni model!

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## Place value and Estimating - Full lesson including MCQs, Problem Solving, Exam Questions

Subject: Mathematics

Age range: 11-14

Resource type: Lesson (complete)

Last updated

27 August 2024

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A comprehensive lesson on the topic of Place Value and Estimating, ideal for students studying the GCSE Mathematics curriculum. The lesson is designed to build a solid understanding of place value, which is crucial for accurate estimation and other mathematical operations.

The resource include:

*** Exam Questions: Practice questions that align with the GCSE syllabus, helping students prepare effectively for their exams.

*** Multiple Choice Questions (MCQs): Quick, focused questions that test students’ grasp of key concepts and reinforce learning.

*** Literacy Task: A task designed to enhance students’ mathematical vocabulary and understanding of key terms related to place value and estimation.

*** Problem-Solving Activities: Engaging challenges that require students to apply their knowledge in real-world contexts, fostering critical thinking and practical application.

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Subject: Mathematics. Age range: 14-16. Resource type: Worksheet/Activity. File previews. docx, 18.26 KB. Ratio problems that involve a bit of thinking, such as combining ratios. Perfect for practice for the new GCSE. Creative Commons "Sharealike". to let us know if it violates our terms and conditions.

GCSE 9-1 Exam Question Practice (Ratio) Subject: Mathematics. Age range: 14-16. Resource type: Lesson (complete) I regularly upload resources that I have created during 30 years as a teacher. Most of these are maths, but there are some ICT/Computing and Tutor Time activities.

Subject: Mathematics. Age range: 14-16. Resource type: Worksheet/Activity. File previews. pdf, 207.39 KB. Worksheet with 9 Problem Solving, Exam Style Questions on RATIO. The idea behind the resource is to help students be able to solve problem solving questions. It could be used towards the end of a set of lessons on RATIO or used as revision.

Ratio problem solving GCSE questions. 1. One mole of water weighs 18 18 grams and contains 6.02 \times 10^ {23} 6.02 × 1023 water molecules. Write this in the form 1gram:n 1gram: n where n n represents the number of water molecules in standard form. (3 marks)

To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here. What is it? Ever since ratio was given an increased value in the current GCSE specification, it has been sneaking in to all sorts of topics and questions.

game was a win, a draw or a loss. The ratio of the games they won to the games they did not win was 9:7 The ratio of games they lo. games they did not lose was 1:7. Given the team played less than 50 games, work out the highes. amount of games they could have won.9 The points A, B, C. line.AB:BD =.

3: 53: 5. 3 + 5 = 83 + 5 = 8. 40 ÷ 8 = 540 ÷ 8 = 5. Then you multiply each part of the ratio by 5.5. 3 × 5: 5 × 5 = 15: 253 × 5: 5 × 5 = 15: 25. This means that Charlie will get 1515 sweets and David will get 2525 sweets. There can be ratio word problems involving different operations and types of numbers.

KS4 ratio questions. In KS4 we apply the knowledge that we have of ratios to solve different problems. Ratio is an important topic in all exam boards, including Edexcel, AQA and OCR. Ratio questions can be linked with many different topics, for example similar shapes and probability, as well as appearing as problems in their own right.

Ratio: Problem Solving Textbook Exercise. Click here for Questions. Textbook Exercise. Previous: Ratio: Difference Between Textbook Exercise. Next: Reflections Textbook Exercise. GCSE Revision Cards. 5-a-day Workbooks. Primary Study Cards. Search.

The Corbettmaths Practice Questions on Ratio. Previous: Percentages of an Amount (Non Calculator) Practice Questions

flipchart, 190.92 KB. Included is: An Active Inspire presentation with examples and Challenge Exam question (created by myself) Two worksheets on three way ratios that I found. The second one is really challenging. Answers included. A worksheet on equivalent ratios with algebra (created by myself). Answers included.

Reasoning and Problem Solving - Ratio and Proportion Problems - Year 6 Expected. 7a.Lucy is making photo frames using buttons. She needs 5 red buttons for every 3 blue and 4 yellow buttons. The costs are as follows: Red: 45p each Blue: 90p each Yellow: 25p each. She has spent £17.85 in total.

Hard. Very Hard. All answers. 1 2 marks. In a box of pens, there are: three times as many red pens as green pens. and two times as many green pens as blue pens. For the pens in the box, write down. the ratio of the number of red pens to the number of green pens to the number of blue pens.

Football-themed word problems to engage students Emphasis on ratio concepts to strengthen mathematical skills Suitable for Key Stage 2 and Key Stage 3 students Each question is designed to promote critical thinking and problem-solving abilities Easy-to-understand format for seamless integration into your lesson plans PDF Download:

Greater Depth Explain whether a statement about ratio of 3 sets of objects is correct. Objects arranged randomly and out of sequence. Questions 3, 6 and 9 (Problem Solving) Developing Determine how many objects there are when given a ratio of 2 different objects and find the new ratio when a number of one of the objects is taken away. Using 2,

We can write a:b:c as one ratio if we get the b parts to match. a: b can be written as 6:15. b:c can be written as 15:50. So a:b:c is 6:15:50. This shows that the ratio a:c is 6:50, which simplifies to 3:25. And here's another type of question: Punch is made my mixing orange juice and cranberry juice in the ratio 7:2.

This worksheet is aimed at Year 8 students and covers a range of ratio questions in a variety of contexts, such as fish in a lake, animals on a farm, angles within a shape and sharing money. The sheet covers all ways ratio is commonly asked in exams, and is designed to take approximately 40 minutes, so this worksheet is perfect for homework, or ...

Subject: Mathematics. Age range: 14-16. Resource type: Worksheet/Activity. My resources are all free! And all maths...at the moment! File previews. docx, 149.05 KB. docx, 207.07 KB. A couple of worksheets I put together to try to train students in the style of questions on ratio common in the new GCSE.

In this iteration, we have significantly enhanced Qwen2-VL's mathematical and coding proficiencies. The model is not only capable of solving problems by analyzing pictures but can also interpret and solve complex mathematical problems through chart analysis. Extremely aspect-ratio-distorted images can also be correctly interpreted.

Maths Ratio & Proportion Year 6. This sequence of lessons cover: - solving problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts. -solving problems involving unequal sharing and grouping using knowledge of fractions and multiples. -solving problems involving ...

We are excited to present our latest teaching resource designed to engage and inspire students in the world of mathematics. Our "Ratio Cars Themed Maths Word Problems" is a comprehensive set of 8 word questions that are both challenging and fun, aimed at improving students' understanding of ratios through real-life scenarios.

KS2 Maths (Ratio + Proportion) These topic-focused SATs questions at the end of a unit will help to test and extend students' understanding as well as helping them to prepare for SATs next year. These questions have fully-worked solutions which can be displayed on a whiteboard making feedback with students more efficient.

The lesson includes a step-by-step explanation of finding HCF and LCM, practical examples, and a variety of problem-solving questions, including GCSE-style questions for exam preparation… A worksheet accompanying the lesson provides additional practice with Stretch and Challenge questions, allowing students to apply what they've learned in ...

PowerPoint includes fully animated examples. Split screen with Teacher example and Pupil's turn followed by questions with animated answers. Questions use intelligent practice to allow pupils to see links and build a deeper understanding of the topic. With problem solving questions to use the knowledge taught to solve more complex problems.

These questions provide students with the opportunity to practice their skills in a format that mirrors what they will encounter in their exams, building their confidence and familiarity with exam conditions. *** Problem-Solving Tasks: Engaging and challenging problems that require students to apply their mathematical knowledge and reasoning ...

Place value and Estimating - Full lesson including MCQs, Problem Solving, Exam Questions. Subject: Mathematics. Age range: 11-14. Resource type: Lesson (complete) O Hay's Shop. Last updated. 27 August 2024. Share this. Share through email; ... Tes Global Ltd is registered in England (Company No 02017289) with its registered office at Building 3 ...