Problem Solving Study Guide

Problem solving is an essential skill in mathematics that involves the ability to understand a problem, develop a plan to solve it, carry out the plan, and evaluate the solution for accuracy. Here are some key steps and strategies to help you become a better problem solver:

  • Understand the Problem: Read the problem carefully and make sure you understand what is being asked. Identify the known and unknown quantities, and determine the relationships between them.
  • Devise a Plan: Consider different strategies for solving the problem, such as drawing a diagram, making a table, using logical reasoning, working backwards, or using a similar problem as a model.
  • Carry Out the Plan: Once you have a strategy in mind, start solving the problem step by step, making sure to show all your work and calculations.
  • Evaluate the Solution: After finding a solution, check to see if it makes sense and satisfies all the conditions given in the problem. Also, consider if there are alternative ways to solve the problem or if the answer could be expressed differently.

Here are some common strategies for problem solving:

  • Draw a Diagram: When dealing with geometric or spatial problems, drawing a diagram can help you visualize the situation and identify the key elements.
  • Make a Table or Chart: Organizing information in a table or chart can help you identify patterns , relationships, or trends that can lead to a solution.
  • Work Backwards: Start with the end goal and work backwards to determine the steps needed to reach that goal.
  • Use Logical Reasoning: Apply logic and reasoning to make educated guesses and eliminate unlikely possibilities.
  • Look for a Pattern: Sometimes problems can be solved by identifying a pattern or sequence in the given information.

By practicing these problem-solving strategies and approaches, you can become more confident and proficient in tackling mathematical problems of varying complexity.

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Mathematics - Fourth Grade - Study Guide: Problem Solving

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problem solving class 4

Grade 4 Word Problem Worksheets

Free printable fourth grade math worksheets to help your students improve their ability to solve word problems! Applying mathematical concepts to solve word problems can be challenging. These free worksheets are great repetition for your students! Click on the images below to download the word problem worksheets. They’re perfect for daily math warm ups! Don’t forget to check out the word problem task cards. Print them off, laminate them and use them for early finishers during maths!

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Word problems.

Grade 4 word problems with a focus on the four operations - addition, subtraction, multiplication & division.

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Free Mother's Day Poetry Resource

This Mother’s Day resource includes a PowerPoint, vocabulary, example poems and a writing template.

problem solving class 4

Maths Problems With Answers - Grade 4

A set of Maths problems with answers for grade 4 are presented. Also Solutions and explanations are included.

  • Jim drove 768 miles of a 1200 miles journey. How many more miles does he need to drive to finish his journey?
  • There are 123 boxes of sweets in a store. There are 25 sweets in each box. How many sweets are in the store?
  • There are 365 days in one year, and 100 years in one century. How many days are in one century?
  • Billy read 2 books. He read the first one in one week with 25 pages everyday. He read the second book in 12 days with 23 pages everyday. What is the total number of pages that Billy read?
  • 123 school girls are to be transported in small vans. Each van can carry 8 girls only. What is the smallest possible number of vans that are needed to transport all 123 school girls?
  • John had $100 to buy drinks and sandwiches for his birhtday party. He bought 5 small boxes of drinks at $4 each box and 8 boxes of sandwiches at $6 each box. How much money was left after the shopping?
  • A factory produces 5500 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
  • Tom, Julia, Mike and Fran have 175 cards to use in a certain game. They decided to share them equally. How many cards should each one take and how many cards are left?
  • Sam, Carla and Sarah spent on afternoon collecting sea shells. Sam collected 11. If we add the number of sea shells collected by Sam and Carla, the total would be 24. If we add the number of sea shells collected by Carla and Sarah, the total would be 25 shells. How many shells did each one collect?
  • Mr Joshua runs 6 kilometers everyday from Monday to Friday. He also runs 12 kilometers a day on Saturday and Sunday. How many kilometers does Joshua run in a week?
  • Tom and Bob are brothers and they each had the same amount of money which they put together to buy a toy. The cost of the toy was $22. If the cashier gave them a change of 6$, how much money did each have?
  • John has 5 boxes of sweets. One group of boxes has 5 sweets in each box. The second group of boxes has 4 sweets in each box. John has a total of 22 sweets. How many boxes of each type John has?(Hint: use table)
  • There is a total of 16 chickens and rabbits in a farm. The total number of legs (chickens and rabbits) is equal to 50. How many chickens and how many rabbits are there?(Hint:use a table)
  • There are 4 more chickens than rabbits in a farm. The total number of legs (chickens and rabbits) is equal to 44. How many chickens and how many rabbits are there?(Hint:use a table)

Answers to the Above Questions

  • a) UK b) Russia c) 7,500,148 d) 49,839,760 e) Russia, Canada, USA, China, India, Uk.
  • 3075 sweets
  • 36,500 days in one century
  • 16 vans (no decimal values)
  • 1375 toys per day
  • 43 each and 3 left
  • 80 cm squared
  • Sam: 11, Carla: 13 and Sarah: 12
  • 54 kilometers
  • 2 boxes with 5 sweets each and 3 boxes with 4 sweets each
  • 7 chickens and 9 rabbits
  • 10 chickens and 6 rabbits

References and Links

Free Printable Mixed Operation Word Problems Worksheets for 4th Class

Mixed Operation Word Problems: Discover a collection of free printable worksheets for Class 4 students, focusing on math mixed operation word problems. Enhance learning and problem-solving skills with Quizizz.

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Explore printable Mixed Operation Word Problems worksheets for 4th Class

Mixed Operation Word Problems worksheets for Class 4 are an essential tool for teachers looking to enhance their students' math skills and problem-solving abilities. These worksheets provide a variety of math word problems that require students to apply their knowledge of addition, subtraction, multiplication, and division in real-life situations. With engaging scenarios and relatable contexts, these worksheets help students develop a deeper understanding of mathematical concepts and their practical applications. Teachers can use these Class 4 Mixed Operation Word Problems worksheets to supplement their existing math curriculum, reinforce key concepts, and assess student progress. By incorporating these worksheets into their lesson plans, teachers can ensure that their students are well-equipped to tackle more complex math problems as they advance in their education.

In addition to Mixed Operation Word Problems worksheets for Class 4, teachers can also utilize Quizizz, an interactive learning platform that offers a wide range of resources to support math instruction. Quizizz provides teachers with access to a vast library of math quizzes and activities, including math word problems, that can be easily integrated into their lesson plans. This platform allows teachers to create customized quizzes, track student progress, and provide instant feedback, making it an invaluable tool for both in-person and remote learning environments. By combining the use of Class 4 Mixed Operation Word Problems worksheets with Quizizz's engaging and interactive features, teachers can create a comprehensive and effective math learning experience for their students.

Decision making 101

Life is full of choices. Some are easy, such as what to have for dinner (cheeseburger thank you), and others, more serious, like, for instance, choosing a career. Regardless of how important a decision is, good decision skills are useful in life, especially if you feel indecisive about something and it’s getting you down. Get tips on how to make good decisions, and find out what to do when you can’t figure out a plan.

This can help if:

you’re working through a problem

you’re facing uncertainty

you’re struggling to make a decision.

Girl looking anxious sitting outside

Why good decision making helps

People make decisions all throughout their day, most of which are straightforward and don’t require much thought. However, when situations are more complicated and have longer term impacts, it’s easy to feel unsure or hesitant.

When faced with a tough decision it’s common to feel:

overwhelmed

stressed or anxious

Because indecision can have a negative impact on how you’re feeling, it’s important to learn strategies for making positive decisions in tough situations. While you may not be able to guarantee the outcome of a decision before you make it, at least you can know you put a lot of careful thought into it.

Tips for making decisions

Step 1. Don’t let stress get the better of you. It’s easy to feel stressed out and anxious when you’re facing a tough choice. You might tend to rush your decisions without thinking them through, or you avoid making a decision at all because the stress has put you off your game. If you’re feeling anxious about a decision, try to manage your stress so that it doesn’t cloud your thinking. Go for a walk on the beach. Hit up a yoga class or hang out with friends.

Step 2. Give yourself some time (if possible). It’s hard to think clearly under pressure, and sometimes your first idea isn’t always your best one. Give yourself the chance to sit on a problem for a while so that you can process your options and feel confident about the course of action you choose.

Step 3. Weigh the pros and cons. When faced with a big decision, sometimes we lose sight of the big picture. Write a list of pros and cons for each course of action and then compare them. Sometimes the cons aren’t nearly as bad as we imagine them to be, or the pros might make your options more obvious.

Step 4. Think about your goals and values. It’s important to be true to ourselves and what we value in life. When you factor into a decision the things that are important to you, the best option might become obvious. At any rate, you’re more likely to end up with an outcome you’re happy with.

Step 5. Consider all the possibilities. Making a decision can result in several different outcomes and not all of them may be obvious. When considering each option, don’t just list the positives and negatives; write down any likely consequences.

Step 6. Talk it out. It can be helpful to get another person’s perspective on your issue, particularly if they’ve faced a similar decision in their own life.

Step 7. Keep a diary. If you feel like you’re on a bit of an emotional rollercoaster, it might help to keep track of your feelings by writing them down.

Step 8. Plan how you’ll tell others . If you think someone may have a bad response to your decision, think through what their reaction is likely to be. Put yourself in their shoes to help you think of a good way to manage the situation.

Step 9. Rethink your options. If you’re up against a lot of pressure over a decision, or there are some new factors to consider, look over your options again. You might decide that your original decision is still the best one, but give yourself the option of changing course. If a decision no longer feels right for you, go through these steps again to figure out a better solution.

If you’re having a tough time

If you’re finding your indecision over a situation is affecting how you get on day to day, it’s a good idea to talk to someone you trust, or visit a counsellor . They’ll be able to help you work through the process of decision making, and guide you through different strategies.

What can I do now?

Work on your problem solving skills.

Talk to someone you trust about your situation and see if they have any insights to offer.

Learn about building good coping skills .

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Division Worksheets Grade 4 Solving Division Problems

Welcome to our Division Worksheets Grade 4 page. Here you will find a wide range of free 4th Grade Division Worksheets, which will help your child learn to solve division problems across a range of different contexts.

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Division Worksheets Grade 4

Solving division problems.

The worksheets on this page have been designed to support your child on their division journey from the start of 4th grade to the end.

The first two sets of sheets involve working out division problems where there is no remainder.

The second two sets involve working out harder division problems with remainders.

In order to solve the second sets of word problems, the remainder needs to be rounded up or down, depending on the context.

Each set of division word problems has been subdivided into 3 worksheets:

  • Sheet A - an easier worksheet;
  • Sheet B - a medium worksheet;
  • Sheet C - a harder worksheet.

Division Worksheets Grade 4 - Worksheets

Set 1 - solving division problems with no remainder..

  • Division Problems 4.1 Sheet A
  • PDF version
  • Division Problems 4.1 Sheet B
  • Division Problems 4.1 Sheet C

Set 2 - solving division problems with no remainder.

  • Division Problems 4.2 Sheet A
  • Division Problems 4.2 Sheet B
  • Division Problems 4.2 Sheet C

Set 3 with remainders

This set involves solving division problems with a remainder. The answer needs to be rounded up or down, depending on the context.

  • Division Problems 4.3 Sheet A
  • Division Problems 4.3 Sheet B
  • Division Problems 4.3 Sheet C

Set 4 with remainders

  • Division Problems 4.4 Sheet A
  • Division Problems 4.4 Sheet B
  • Division Problems 4.4 Sheet C

Looking for some easier Division worksheets

Our 3rd grade division worksheets are similar to those on this page but at an easier level.

The link below will take you to our division worksheets for 3rd grade.

  • Division Worksheets Grade 3 Word Problems
  • Division Facts to 10x10 Worksheets
  • Long Division Worksheets 3rd Grade

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

More Division Worksheets

  • Divide a multi-digit number by a single digit;
  • Use remainders when dividing;
  • Calculate division facts related to multiplication facts.
  • Divding by Multiples of 10 and 100 Worksheets
  • 4th Grade Long Division Worksheets
  • Division Facts Worksheets (randomly generated)

More Fourth Grade Math Problems

Here is our set of 4th grade math problems to help your child with their problem solving skills.

Each problem sheet comes complete with answers, and is available in both standard and metric units where applicable.

Many of the problems are based around 'real-life' problems and data such as the world's heaviest animals.

Using these sheets will help your child to:

  • apply their addition, subtraction and problem solving skills;
  • apply their knowledge of rounding and place value;
  • solve a range of 'real life' problems;
  • attempt more challenging longer problems.

Using the problems in this section will help your child develop their problem solving and reasoning skills.

These sheets involve solving one or two more challenging longer problems.

  • 4th Grade Math Problems

These sheets involve solving many 'real-life' problems involving data.

  • 4th Grade Math Word Problems

These sheets involve solving a range of multiplciation problems.

  • Multiplication Word Problems 4th Grade

Fourth Grade Math Games

Here you will find a range of free printable 4th Grade Math games. All children like to play Math games, and you will find a good range of Grade 4 Math Games here for your child to play and enjoy.

The following games involve different 4th Grade Math activities which you and your child can enjoy together.

All the free 4th Grade Math Worksheets in this section support the Elementary Math Benchmarks for Fourth Grade.

  • Math Games 4th Grade
  • 4th Grade Math Puzzles

Here you will find a range of printable 4th grade math puzzles for your child to enjoy.

The puzzles will help your child practice and apply their addition, subtraction, multiplication and division facts as well as developing their thinking and reasoning skills in a fun and engaging way.

Using these puzzles will help your child to:

  • learn and practice their addition facts;
  • practice adding both positive and negative numbers;
  • practice their subtraction facts;
  • practice multiplication and division facts;
  • develop problem solving skills and reasoning.

All the puzzles support elementary math benchmarks for 4th grade.

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OpenAI’s new GPT-4o can be sarcastic, sing happy birthday and teach math

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Join us in returning to NYC on June 5th to collaborate with executive leaders in exploring comprehensive methods for auditing AI models regarding bias, performance, and ethical compliance across diverse organizations. Find out how you can attend here .

OpenAI ’s new GPT-4o is here — and it can laugh at bad jokes (and crack its own), sing in tune and help hail London cabs with realistic emotion and amidst regular human interruption. 

OpenAI today released 16 videos of GPT-4o (short for GPT-4 omni) in action, showing the multimodal foundation large language model (LLM) interacting with the world in male and female voices in real time based on audio, visual and text inputs. 

For instance, after correctly identifying that the human it was speaking with (OpenAI president Greg Brockman) was preparing to make a big announcement — based on his professional attire and the presence of studio lights and a microphone — the model was informed that it was the subject.  

A female voice replied, seemingly coyly: “The announcement is about me? Well color me intrigued. You’ve got me on the edge of my…well, I don’t really have a seat but you get the idea.”

The AI Impact Tour: The AI Audit

Join us as we return to NYC on June 5th to engage with top executive leaders, delving into strategies for auditing AI models to ensure fairness, optimal performance, and ethical compliance across diverse organizations. Secure your attendance for this exclusive invite-only event.

OpenAI revealed the new free model today at its highly-anticipated Spring Updates event, with a notable 113,000 people joining the livestream. The model’s text and image input roll out today in OpenAI’s API and ChatGPT, with voice and video available in the coming weeks.

Say hello to GPT-4o, our new flagship model which can reason across audio, vision, and text in real time: https://t.co/MYHZB79UqN Text and image input rolling out today in API and ChatGPT with voice and video in the coming weeks. pic.twitter.com/uuthKZyzYx — OpenAI (@OpenAI) May 13, 2024

Praising math abilities, giving fashion advice

GPT-4o can identify a users’ emotional state and surroundings, realistically simulate various emotions of its own and offer advice on a multitude of topics. Models on different devices can also interact with each other. 

For instance, in one of the videos posted today by OpenAI , the model was told that it would be conversing with another version of itself. To this, a female voice responded: “Well, well well, just when I thought things couldn’t get any more interesting — talking to another AI that can see the world. This sounds like a plot twist in the AI universe.”

After being asked to be punchy, direct and describe everything in their line of vision, the models took turns describing a man who was “sleek and stylish with their black leather jacket and light colored shirt” sitting in a room with “natural and artificial” lighting that was “dramatic and modern” and featuring a plant in the background that added “a touch of green to the space.” 

When a second person entered to give bunny ears to the first, GPT-4o was asked to sing a song based on what happened — and it did, crooning, “surprise guests with a playful streak.” 

In other videos, the model laughs at dad jokes (“that’s perfectly hilarious”) performs real-time translation of Spanish to English and vice versa, sings in a lullaby about “majestic potatoes” (first replying to the prompt, “now that’s what I call a mashup”), emulates a sarcastic voice much like the droll MTV cartoon character “Daria,” correctly identifies winners of rock-paper-scissors and recognizes that it’s someone’s birthday based on the presence of a piece of cake with a candle in it. 

It also interacts with puppies — replying in a sing-songy tone in the manner people talk to dogs, “well hello there cutie, what’s your name little fluff ball?” (it was Bowser by the way) — and guided a blind man through London, identifying through video input that the King was in residence based on the presence of the Royal Standard flag and described ducks “gently gliding across the water, moving in a fairly relaxed manner, not in a hurry.”

Additionally, GPT-4o can teach math; in one video it walks a young man through a problem based on an image of a triangle. The model asked the student to identify which sides of the triangle were the opposite adjacent and hypotenuse, relative to angle alpha. When he deduced that alpha equaled 7 over 25, the female voice praised: “You did a great job identifying the sides.”

GPT-4o can give fashion advice, too. In yet another video the LLM helped a mussy-haired job candidate wearing a slouchy T-shirt determine whether he looked presentable enough for an interview. 

A female voice chuckled and advised him to run a hand through his hair. The model also remarked drolly, “You definitely have the ‘I’ve been coding all night’ look down, which actually might work in your favor.” 

Winning the internet — or an underwhelming disappointment

Not surprisingly given the diversity of the AI community, the response, at least on social media, has been all over the place. 

Some are saying that it “wins the internet,” taking ChatGPT capabilities to whole new levels (and that it quickly rival Google Translate). One user called the video of AI teaching math “insane,” adding “The future is so, so bright.” 

This demo is insane. A student shares their iPad screen with the new ChatGPT + GPT-4o, and the AI speaks with them and helps them learn in *realtime*. Imagine giving this to every student in the world. The future is so, so bright. pic.twitter.com/t14M4fDjwV — Mckay Wrigley (@mckaywrigley) May 13, 2024

Nvidia senior research scientist Jim Fan — among others — noted how the assistant was “lively and even a bit flirty,” calling back to the 2013 sci-fi movie “Her.”

I know your timeline is flooded now with word salads of "insane, HER, 10 features you missed, we're so back". Sit down. Chill. <gasp> Take a deep breath like Mark does in the demo </gasp>. Let's think step by step: – Technique-wise, OpenAI has figured out a way to map audio to… pic.twitter.com/3fL9n8Mtch — Jim Fan (@DrJimFan) May 13, 2024

Still others called it “by far the most underrated OpenAI event ever.” 

this will prove to be in retrospect by far the most underrated openai event ever openai casually dropping text to 3d rendering in gpt4o and not even mentioning it (more ??) pic.twitter.com/dQ6bq3cV4J — Siqi Chen (@blader) May 13, 2024
My level of excitement for the new OpenAI chatbot launch. pic.twitter.com/mdFHLveC69 — Ted Gioia (@tedgioia) May 13, 2024

Ultimately, AI advisor and investor Allie K. Miller commented, “The super techies are disappointed that they don’t have some holographic laser beam that shoots out of their phone and reads their minds, and the wider business population didn’t seem to watch and weigh in.”

113,000 people joined live to watch the OpenAI new spring release livestream. Now, I’ll tell you right off the bat, the social media response (based on MY feed) is mixed. The super techies are disappointed that they don’t have some holographic laser beam that shoots out of their… — Allie K. Miller (@alliekmiller) May 13, 2024

But this is just day one reaction — it’ll be interesting to see and hear response once people have the chance to experiment with GPT-4o.

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Stormy Daniels Takes the Stand

The porn star testified for eight hours at donald trump’s hush-money trial. this is how it went..

This transcript was created using speech recognition software. While it has been reviewed by human transcribers, it may contain errors. Please review the episode audio before quoting from this transcript and email [email protected] with any questions.

It’s 6:41 AM. I’m feeling a little stressed because I’m running late. It’s the fourth week of Donald J. Trump’s criminal trial. It’s a white collar trial. Most of the witnesses we’ve heard from have been, I think, typical white collar witnesses in terms of their professions.

We’ve got a former publisher, a lawyer, accountants. The witness today, a little less typical, Stormy Daniels, porn star in a New York criminal courtroom in front of a jury more accustomed to the types of witnesses they’ve already seen. There’s a lot that could go wrong.

From “The New York Times,” I’m Michael Barbaro. This is “The Daily.”

Today, what happened when Stormy Daniels took the stand for eight hours in the first criminal trial of Donald J. Trump. As before, my colleague Jonah Bromwich was inside the courtroom.

[MUSIC PLAYING]

It’s Friday, May 10th.

So it’s now day 14 of this trial. And I think it’s worth having you briefly, and in broad strokes, catch listeners up on the biggest developments that have occurred since you were last on, which was the day that opening arguments were made by both the defense and the prosecution. So just give us that brief recap.

Sure. It’s all been the prosecution’s case so far. And prosecutors have a saying, which is that the evidence is coming in great. And I think for this prosecution, which is trying to show that Trump falsified business records to cover up a sex scandal, to ease his way into the White House in 2016, the evidence has been coming in pretty well. It’s come in well through David Pecker, former publisher of The National Enquirer, who testified that he entered into a secret plot with Trump and Michael Cohen, his fixer at the time, to suppress negative stories about Trump, the candidate.

It came in pretty well through Keith Davidson, who was a lawyer to Stormy Daniels in 2016 and negotiated the hush money payment. And we’ve seen all these little bits and pieces of evidence that tell the story that prosecutors want to tell. And the case makes sense so far. We can’t tell what the jury is thinking, as we always say.

But we can tell that there’s a narrative that’s coherent and that matches up with the prosecution’s opening statement. Then we come to Tuesday. And that day really marks the first time that the prosecution’s strategy seems a little bit risky because that’s the day that Stormy Daniels gets called to the witness stand.

OK, well, just explain why the prosecution putting Stormy Daniels on the stand would be so risky. And I guess it makes sense to answer that in the context of why the prosecution is calling her as a witness at all.

Well, you can see why it makes sense to have her. The hush money payment was to her. The cover-up of the hush money payment, in some ways, concerns her. And so she’s this character who’s very much at the center of this story. But according to prosecutors, she’s not at the center of the crime. The prosecution is telling a story, and they hope a compelling one. And arguably, that story starts with Stormy Daniels. It starts in 2006, when Stormy Daniels says that she and Trump had sex, which is something that Trump has always denied.

So if prosecutors were to not call Stormy Daniels to the stand, you would have this big hole in the case. It would be like, effect, effect, effect. But where is the cause? Where is the person who set off this chain reaction? But Stormy Daniels is a porn star. She’s there to testify about sex. Sex and pornography are things that the jurors were not asked about during jury selection. And those are subjects that bring up all kinds of different complex reactions in people.

And so, when the prosecutors bring Stormy Daniels to the courtroom, it’s very difficult to know how the jurors will take it, particularly given that she’s about to describe a sexual episode that she says she had with the former president. Will the jurors think that makes sense, as they sit here and try to decide a falsifying business records case, or will they ask themselves, why are we hearing this?

So the reason why this is the first time that the prosecution’s strategy is, for journalists like you, a little bit confusing, is because it’s the first time that the prosecution seems to be taking a genuine risk in what they’re putting before these jurors. Everything else has been kind of cut and dry and a little bit more mechanical. This is just a wild card.

This is like live ammunition, to some extent. Everything else is settled and controlled. And they know what’s going to happen. With Stormy Daniels, that’s not the case.

OK, so walk us through the testimony. When the prosecution brings her to the stand, what actually happens?

It starts, as every witness does, with what’s called direct examination, which is a fancy word for saying prosecutors question Stormy Daniels. And they have her tell her story. First, they have her tell the jury about her education and where she grew up and her professional experience. And because of Stormy Daniels’s biography, that quickly goes into stripping, and then goes into making adult films.

And I thought the prosecutor who questioned her, Susan Hoffinger, had this nice touch in talking about that, because not only did she ask Daniels about acting in adult films. But she asked her about writing and directing them, too, emphasizing the more professional aspects of that work and giving a little more credit to the witness, as if to say, well, you may think this or you may think that. But this is a person with dignity who took what she did seriously. Got it.

What’s your first impression of Daniels as a witness?

It’s very clear that she’s nervous. She’s speaking fast. She’s laughing to herself and making small jokes. But the tension in the room is so serious from the beginning, from the moment she enters, that those jokes aren’t landing. So it just feels, like, really heavy and still and almost oppressive in there. So Daniels talking quickly, seeming nervous, giving more answers than are being asked of her by the prosecution, even before we get to the sexual encounter that she’s about to describe, all of that presents a really discomfiting impression, I would say.

And how does this move towards the encounter that Daniels ultimately has?

It starts at a golf tournament in 2006, in Lake Tahoe, Nevada. Daniels meets Trump there. There are other celebrities there, too. They chatted very briefly. And then she received a dinner invitation from him. She thought it over, she says. And she goes to have dinner with Trump, not at a restaurant, by the way. But she’s invited to join him in the hotel suite.

So she gets to the hotel suite. And his bodyguard is there. And the hotel door is cracked open. And the bodyguard greets her and says she looks nice, this and that. And she goes in. And there’s Donald Trump, just as expected. But what’s not expected, she says, is that he’s not wearing what you would wear to a dinner with a stranger, but instead, she says, silk or satin pajamas. She asked him to change, she says. And he obliges.

He goes, and he puts on a dress shirt and dress pants. And they sit down at the hotel suite’s dining room table. And they have a kind of bizarre dinner. Trump is asking her very personal questions about pornography and safe sex. And she testifies that she teased him about vain and pompous he is. And then at some point, she goes to the bathroom. And she sees that he has got his toiletries in there, his Old Spice, his gold tweezers.

Very specific details.

Yeah, we’re getting a ton of detail in this scene. And the reason we’re getting those is because prosecutors are trying to elicit those details to establish that this is a credible person, that this thing did happen, despite what Donald Trump and his lawyers say. And the reason you can know it happened, prosecutors seem to be saying, is because, look at all these details she can still summon up.

She comes out of the bathroom. And she says that Donald Trump is on the hotel bed. And what stands out to me there is what she describes as a very intense physical reaction. She says that she blacked out. And she quickly clarifies, she doesn’t mean from drugs or alcohol. She means that, she says, that the intensity of this experience was such that, suddenly, she can’t remember every detail. The prosecution asks a question that cuts directly to the sex. Essentially, did you start having sex with him? And Daniels says that she did. And she continues to provide more details than even, I think, the prosecution wanted.

And I think we don’t want to go chapter and verse through this claimed sexual encounter. But I wonder what details stand out and which details feel important, given the prosecution’s strategy here.

All the details stand out because it’s a story about having had sex with a former president. And the more salacious and more private the details feel, the more you’re going to remember them. So we’ll remember that Stormy Daniels said what position they had sex in. We’ll remember that she said he didn’t use a condom. Whether that’s important to the prosecution’s case, now, that’s a much harder question to answer, as we’ve been saying.

But what I can tell you is, as she’s describing having had sex with Donald Trump, and Donald Trump is sitting right there, and Eric Trump, his son, is sitting behind him, seeming to turn a different color as he hears this embarrassment of his father being described to a courtroom full of reporters at this trial, it’s hard to even describe the energy in that room. It was like nothing I had ever experienced. And it was just Daniels’s testimony and, seemingly, the former President’s emotions. And you almost felt like you were trapped in there with both of them as this description was happening.

Well, I think it’s important to try to understand why the prosecution is getting these details, these salacious, carnal, pick your word, graphic details about sex with Donald Trump. What is the value, if other details are clearly making the point that she’s recollecting something?

Well, I think, at this point, we can only speculate. But one thing we can say is, this was uncomfortable. This felt bad. And remember, prosecutor’s story is not about the sex. It’s about trying to hide the sex. So if you’re trying to show a jury why it might be worthwhile to hide a story, it might be worth —

Providing lots of salacious details that a person would want to hide.

— exposing them to how bad that story feels and reminding them that if they had been voters and they had heard that story, and, in fact, they asked Daniels this very question, if you hadn’t accepted hush money, if you hadn’t signed that NDA, is this the story you would have told? And she said, yes. And so where I think they’re going with this, but we can’t really be sure yet, is that they’re going to tell the jurors, hey, that story, you can see why he wanted to cover that up, can’t you?

You mentioned the hush money payments. What testimony does Daniels offer about that? And how does it advance the prosecution’s case of business fraud related to the hush money payments?

So little evidence that it’s almost laughable. She says that she received the hush money. But we actually already heard another witness, her lawyer at the time, Keith Davidson, testify that he had received the hush money payment on her behalf. And she testified about feeling as if she had to sell this story because the election was fast approaching, almost as if her leverage was slipping away because she knew this would be bad for Trump.

That feels important. But just help me understand why it’s important.

Well, what the prosecution has been arguing is that Trump covered up this hush money payment in order to conceal a different crime. And that crime, they say, was to promote his election to the presidency by illegal means.

Right, we’ve talked about this in the past.

So when Daniels ties her side of the payment into the election, it just reminds the jurors maybe, oh, right, this is what they’re arguing.

So how does the prosecution end this very dramatic, and from everything you’re saying, very tense questioning of Stormy Daniels about this encounter?

Well, before they can even end, the defense lawyers go and they consult among themselves. And then, with the jury out of the room, one of them stands up. And he says that the defense is moving for a mistrial.

On what terms?

He says that the testimony offered by Daniels that morning is so prejudicial, so damning to Trump in the eyes of the jury, that the trial can no longer be fair. Like, how could these jurors have heard these details and still be fair when they render their verdict? And he says a memorable expression. He says, you can’t un-ring that bell, meaning they heard it. They can’t un-hear it. It’s over. Throw out this trial. It should be done.

Wow. And what is the response from the judge?

So the judge, Juan Merchan, he hears them out. And he really hears them out. But at the end of their arguments, he says, I do think she went a little too far. He says that. He said, there were things that were better left unsaid.

By Stormy Daniels?

By Stormy Daniels. And he acknowledges that she is a difficult witness. But, he says, the remedy for that is not a mistrial, is not stopping the whole thing right now. The remedy for that is cross-examination. If the defense feels that there are issues with her story, issues with her credibility, they can ask her whatever they want. They can try to win the jury back over. If they think this jury has been poisoned by this witness, well, this is their time to provide the antidote. The antidote is cross-examination. And soon enough, cross-examination starts. And it is exactly as intense and combative as we expected.

We’ll be right back.

So, Jonah, how would you characterize the defense’s overall strategy in this intense cross-examination of Stormy Daniels?

People know the word impeach from presidential impeachments. But it has a meaning in law, too. You impeach a witness, and, specifically, their credibility. And that’s what the defense is going for here. They are going to try to make Stormy Daniels look like a liar, a fraud, an extortionist, a money-grubbing opportunist who wanted to take advantage of Trump and sought to do so by any means necessary.

And what did that impeachment strategy look like in the courtroom?

The defense lawyer who questions Stormy Daniels is a woman named Susan Necheles. She’s defended Trump before. And she’s a bit of a cross-examination specialist. We even saw her during jury selection bring up these past details to confront jurors who had said nasty things about Trump on social media with. And she wants to do the same thing with Daniels. She wants to bring up old interviews and old tweets and things that Daniels has said in the past that don’t match what Daniels is saying from the stand.

What’s a specific example? And do they land?

Some of them land. And some of them don’t. One specific example is that Necheles confronts Daniels with this old tweet, where Daniels says that she’s going to dance down the street if Trump goes to jail. And what she’s trying to show there is that Daniels is out for revenge, that she hates Trump, and that she wants to see him go to jail. And that’s why she’s testifying against him.

And Daniels is very interesting during the cross-examination. It’s almost as if she’s a different person. She kind of squares her shoulders. And she sits up a little straighter. And she leans forward. Daniels is ready to fight. But it doesn’t quite land. The tweet actually says, I’ll dance down the street when he’s selected to go to jail.

And Daniels goes off on this digression about how she knows that people don’t get selected to go to jail. That’s not how it works. But she can’t really unseat this argument, that she’s a political enemy of Donald Trump. So that one kind of sticks, I would say. But there are other moves that Necheles tries to pull that don’t stick.

So unlike the prosecution, which typically used words like adult, adult film, Necheles seems to be taking every chance she can get to say porn, or pornography, or porn star, to make it sound base or dirty. And so when she starts to ask Daniels about actually being in pornography, writing, acting, and directing sex films, she tries to land a punch line, Necheles does. She says, so you have a lot of experience making phony stories about sex appear to be real, right?

As if to say, perhaps this story you have told about entering Trump’s suite in Lake Tahoe and having sex with him was made up.

Just another one of your fictional stories about sex. But Daniels comes back and says, the sex in the films, it’s very much real, just like what happened to me in that room. And so, when you have this kind of combat of a lawyer cross-examining very aggressively and the witness fighting back, you can feel the energy in the room shift as one lands a blow or the other does. But here, Daniels lands one back. And the other issue that I think Susan Necheles runs into is, she tries to draw out disparities from interviews that Daniels gave, particularly to N-TOUCH, very early on once the story was out.

It’s kind of like a tabloid magazine?

But some of the disparities don’t seem to be landing quite like Necheles would want. So she tries to do this complicated thing about where the bodyguard was in the room when Daniels walked into the room, as described in an interview in a magazine. But in that magazine interview, as it turns out, Daniels mentioned that Trump was wearing pajamas. And so, if I’m a juror, I don’t care where the bodyguard is. I’m thinking about, oh, yeah, I remember that Stormy Daniels said now in 2024 that Trump was wearing pajamas.

I’m curious if, as somebody in the room, you felt that the defense was effective in undermining Stormy Daniels’s credibility? Because what I took from the earlier part of our conversation was that Stormy Daniels is in this courtroom on behalf of the prosecution to tell a story that’s uncomfortable and has the kind of details that Donald Trump would be motivated to try to hide. And therefore, this defense strategy is to say, those details about what Trump might want to hide, you can’t trust them. So does this back and forth effectively hurt Stormy Daniels’s credibility, in your estimation?

I don’t think that Stormy Daniels came off as perfectly credible about everything she testified about. There are incidents that were unclear or confusing. There were things she talked about that I found hard to believe, when she, for instance, denied that she had attacked Trump in a tweet or talked about her motivations. But about what prosecutors need, that central story, the story of having had sex with him, we can’t know whether it happened.

But there weren’t that many disparities in these accounts over the years. In terms of things that would make me doubt the story that Daniels was telling, details that don’t add up, those weren’t present. And you don’t have to take my word for that, nor should you. But the judge is in the room. And he says something very, very similar.

What does he say? And why does he say it?

Well, he does it when the defense, again, at the end of the day on Thursday, calls for a mistrial.

With a similar argument as before?

Not only with a similar argument as before, but, like, almost the exact same argument. And I would say that I was astonished to see them do this. But I wasn’t because I’ve covered other trials where Trump is the client. And in those trials, the lawyers, again and again, called for a mistrial.

And what does Judge Marchan say in response to this second effort to seek a mistrial?

Let me say, to this one, he seems a little less patient. He says that after the first mistrial ruling, two days before, he went into his chambers. And he read every decision he had made about the case. He took this moment to reflect on the first decision. And he found that he had, in his own estimation, which is all he has, been fair and not allowed evidence that was prejudicial to Trump into this trial. It could continue. And so he said that again. And then he really almost turned on the defense. And he said that the things that the defense was objecting to were things that the defense had made happen.

He says that in their opening statement, the defense could have taken issue with many elements of the case, about whether there were falsified business records, about any of the other things that prosecutors are saying happened. But instead, he says, they focused their energy on denying that Trump ever had sex with Daniels.

And so that was essentially an invitation to the prosecution to call Stormy Daniels as a witness and have her say from the stand, yes, I had this sexual encounter. The upshot of it is that the judge not only takes the defense to task. But he also just says that he finds Stormy Daniels’s narrative credible. He doesn’t see it as having changed so much from year to year.

Interesting. So in thinking back to our original question here, Jonah, about the idea that putting Stormy Daniels on the stand was risky, I wonder if, by the end of this entire journey, you’re reevaluating that idea because it doesn’t sound like it ended up being super risky. It sounded like it ended up working reasonably well for the prosecution.

Well, let me just assert that it doesn’t really matter what I think. The jury is going to decide this. There’s 12 people. And we can’t know what they’re thinking. But my impression was that, while she was being questioned by the prosecution for the prosecution’s case, Stormy Daniels was a real liability. She was a difficult witness for them.

And the judge said as much. But when the defense cross-examined her, Stormy Daniels became a better witness, in part because their struggles to discredit her may have actually ended up making her story look more credible and stronger. And the reason that matters is because, remember, we said that prosecutors are trying to fill this hole in their case. Well, now, they have. The jury has met Stormy Daniels. They’ve heard her account. They’ve made of it what they will. And now, the sequence of events that prosecutors are trying to line up as they seek prison time for the former President really makes a lot of sense.

It starts with what Stormy Daniels says with sex in a hotel suite in 2006. It picks up years later, as Donald Trump is trying to win an election and, prosecutors say, suppressing negative stories, including Stormy Daniels’s very negative story. And the story that prosecutors are telling ends with Donald Trump orchestrating the falsification of business records to keep that story concealed.

Well, Jonah, thank you very much. We appreciate it.

Of course, thanks for having me.

The prosecution’s next major witness will be Michael Cohen, the former Trump fixer who arranged for the hush money payment to Stormy Daniels. Cohen is expected to take the stand on Monday.

Here’s what else you need to know today. On Thursday, Israeli Prime Minister Benjamin Netanyahu issued a defiant response to warnings from the United States that it would stop supplying weapons to Israel if Israel invades the Southern Gaza City of Rafah. So far, Israel has carried out a limited incursion into the city where a million civilians are sheltering, but has threatened a full invasion. In a statement, Netanyahu said, quote, “if we need to stand alone, we will stand alone.”

Meanwhile, high level ceasefire negotiations between Israel and Hamas have been put on hold in part because of anger over Israel’s incursion into Rafah.

A reminder, tomorrow, we’ll be sharing the latest episode of our colleague’s new show, “The Interview” This week on “The Interview,” Lulu Garcia-Navarro talks with radio host Charlamagne Tha God about his frustrations with how Americans talk about politics.

If me as a Black man, if I criticize Democrats, then I’m supporting MAGA. But if I criticize, you know, Donald Trump and Republicans, then I’m a Democratic shill. Why can’t I just be a person who deals in nuance?

Today’s episode was produced by Olivia Natt and Michael Simon Johnson. It was edited by Lexie Diao, with help from Paige Cowett, contains original music by Will Reid and Marion Lozano, and was engineered by Alyssa Moxley. Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly.

That’s it for “The Daily.” I’m Michael Barbaro. See you on Monday.

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  • May 17, 2024   •   51:10 The Campus Protesters Explain Themselves
  • May 16, 2024   •   30:47 The Make-or-Break Testimony of Michael Cohen
  • May 15, 2024   •   27:03 The Possible Collapse of the U.S. Home Insurance System
  • May 14, 2024   •   35:20 Voters Want Change. In Our Poll, They See It in Trump.
  • May 13, 2024   •   27:46 How Biden Adopted Trump’s Trade War With China
  • May 10, 2024   •   27:42 Stormy Daniels Takes the Stand
  • May 9, 2024   •   34:42 One Strongman, One Billion Voters, and the Future of India
  • May 8, 2024   •   28:28 A Plan to Remake the Middle East
  • May 7, 2024   •   27:43 How Changing Ocean Temperatures Could Upend Life on Earth
  • May 6, 2024   •   29:23 R.F.K. Jr.’s Battle to Get on the Ballot
  • May 3, 2024   •   25:33 The Protesters and the President
  • May 2, 2024   •   29:13 Biden Loosens Up on Weed

Hosted by Michael Barbaro

Featuring Jonah E. Bromwich

Produced by Olivia Natt and Michael Simon Johnson

Edited by Lexie Diao

With Paige Cowett

Original music by Will Reid and Marion Lozano

Engineered by Alyssa Moxley

Listen and follow The Daily Apple Podcasts | Spotify | Amazon Music | YouTube

This episode contains descriptions of an alleged sexual liaison.

What happened when Stormy Daniels took the stand for eight hours in the first criminal trial of former President Donald J. Trump?

Jonah Bromwich, one of the lead reporters covering the trial for The Times, was in the room.

On today’s episode

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Jonah E. Bromwich , who covers criminal justice in New York for The New York Times.

A woman is walking down some stairs. She is wearing a black suit. Behind her stands a man wearing a uniform.

Background reading

In a second day of cross-examination, Stormy Daniels resisted the implication she had tried to shake down Donald J. Trump by selling her story of a sexual liaison.

Here are six takeaways from Ms. Daniels’s earlier testimony.

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We aim to make transcripts available the next workday after an episode’s publication. You can find them at the top of the page.

The Daily is made by Rachel Quester, Lynsea Garrison, Clare Toeniskoetter, Paige Cowett, Michael Simon Johnson, Brad Fisher, Chris Wood, Jessica Cheung, Stella Tan, Alexandra Leigh Young, Lisa Chow, Eric Krupke, Marc Georges, Luke Vander Ploeg, M.J. Davis Lin, Dan Powell, Sydney Harper, Mike Benoist, Liz O. Baylen, Asthaa Chaturvedi, Rachelle Bonja, Diana Nguyen, Marion Lozano, Corey Schreppel, Rob Szypko, Elisheba Ittoop, Mooj Zadie, Patricia Willens, Rowan Niemisto, Jody Becker, Rikki Novetsky, John Ketchum, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Dan Farrell, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Summer Thomad, Olivia Natt, Daniel Ramirez and Brendan Klinkenberg.

Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Sam Dolnick, Paula Szuchman, Lisa Tobin, Larissa Anderson, Julia Simon, Sofia Milan, Mahima Chablani, Elizabeth Davis-Moorer, Jeffrey Miranda, Renan Borelli, Maddy Masiello, Isabella Anderson and Nina Lassam.

Jonah E. Bromwich covers criminal justice in New York, with a focus on the Manhattan district attorney’s office and state criminal courts in Manhattan. More about Jonah E. Bromwich

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    Please contact [email protected] and tell them exactly what you were doing to trigger this, and include this magic code: E_NOACTION.

  18. Decision making 101

    Tips for making decisions. Step 1. Don't let stress get the better of you. It's easy to feel stressed out and anxious when you're facing a tough choice. You might tend to rush your decisions without thinking them through, or you avoid making a decision at all because the stress has put you off your game.

  19. GCSE Business: Dame Sharon White

    Most suited to 14-16-year-old pupils across the UK in developing their understanding of ethics and careers. In England, Northern Ireland and Wales it is relevant to GCSE business. In Scotland it ...

  20. Friendships, problem-solving: How video games are helping U.S ...

    Most teens play games on consoles (73%) or smartphones (70%), though nearly a quarter are using virtual reality headsets. Zoom in: 56% of teens say video games have boosted their problem-solving skills, 47% say they've helped them build friendships, 41% say they've made it easier to work with others, and 32% say they're good for their mental ...

  21. Dallas Cowboys 'Pickle Juice' Problem: 4 Schedule Issues for Run

    Zimmer has faced Kyle Shanahan (49ers head coach), Kevin Stefanski (Browns head coach), and Todd Monken (Ravens coordinator) during his time as a head coach with an overall record of 2-3 lifetime.

  22. Division Worksheets Grade 4

    Here is a selection of Long Division worksheets for 4th Grade. Using these sheets will help your child to: Divide a multi-digit number by a single digit; Use remainders when dividing; Calculate division facts related to multiplication facts. Divding by Multiples of 10 and 100 Worksheets. 4th Grade Long Division Worksheets.

  23. OpenAI's new GPT-4o can be sarcastic, sing happy birthday and teach

    OpenAI today released 16 videos of GPT-4o (short for GPT-4 omni) in action, ... GPT-4o can teach math; in one video it walks a young man through a problem based on an image of a triangle.

  24. Stormy Daniels Takes the Stand

    On today's episode. Jonah E. Bromwich, who covers criminal justice in New York for The New York Times. Stormy Daniels leaving court on Thursday, after a second day of cross-examination in the ...

  25. A Unified Analysis of a Class of Proximal Bundle Methods for Solving

    This paper proposes a new algorithm for solving a class of composite convex-concave saddle-point problems. The new algorithm is a special instance of the hybrid proximal extragradient framework in which a Nesterov accelerated variant is used to approximately ...

  26. Grade 4 Fractions Worksheets

    3/4 = ___ /12: Equivalent fractions, (proper and improper fractions) 5/4 = ___ /20: Fractional part of a set: Fractional part of a set: 1 /3 of 9 = ___ Fraction word problems: Write and compare fractions word problems: Word problems: Add and subtract fractions word problems: Word problems: Multiply fractions by whole numbers: Word problems

  27. Electronics

    Moreover, more effective machine learning techniques will be introduced in future work to solve the potential class imbalance problem. A robust and reliable prediction model is vital to this study. The authors are also planning to analyze and quantify the potential relationship between courses and psychological factors by using a graph neural ...